Finite Group Databasebeta

← #33250367

Subgroups — #33250367

Order 18688.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613123C211yesmaximal, characteristic, complemented
2#22613097C211yesmaximal, characteristic, complemented
3#22613079C211yesmaximal, characteristic, complemented
4#22613072C211yesmaximal, characteristic, complemented
5#22613055C211yesmaximal, characteristic, complemented
6#22613055C211yesmaximal, characteristic, complemented
7#22613055C211yesmaximal, characteristic, complemented
8#22613043C211yesmaximal, characteristic, complemented
9#22613006C211yesmaximal, characteristic, complemented
10#22612962C211yesmaximal, characteristic, complemented
11#22612927C211yesmaximal, characteristic, complemented
12#22612915C211yesmaximal, characteristic, complemented
13#22612880C211yesmaximal, characteristic, complemented
14#22612871C211yesmaximal, characteristic, complemented
15#22612780C211yesmaximal, characteristic, complemented
16#22612780C211yesmaximal, characteristic, complemented
17#22612746C211yesmaximal, characteristic, complemented
18#22612725C211yesmaximal, characteristic, complemented
19#22612698C211yesmaximal, characteristic, complemented
20#22612698C211yesmaximal, characteristic, complemented
21#22612644C211yesmaximal, characteristic, complemented
22#22612636C211yesmaximal, characteristic, complemented
23#22612626C211yesmaximal, characteristic, complemented
24#22612626C211yesmaximal, characteristic, complemented
25#22612592C211yesmaximal, characteristic, complemented
26#22612592C211yesmaximal, characteristic, complemented
27#22612574C211yesmaximal, characteristic, complemented
28#123×Dic73C211yesmaximal, characteristic, complemented
29#121×Dic73C211yesmaximal, characteristic, complemented
30#22612376C211yesmaximal, characteristic, complemented
31C2×#538×C73C211yesmaximal, characteristic
32C2×Q8×Dic73C2211yescharacteristic, complemented
33C2×D4×Dic73C2211yescharacteristic
34C2×D4×Dic73C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic, complemented
38C2×#14556550C2211yescharacteristic
39C2×#14556550C2211yescharacteristic
40C2×#14556550C2211yescharacteristic, complemented
41C22×C22⋊Dic73C2211yescharacteristic
42C22×C22⋊Dic73C2211yescharacteristic
43C22×C4×Dic73C2211yescharacteristic, complemented
44#17988494C2211yescharacteristic, complemented
45#17988494C2211yescharacteristic, complemented
46#17988494C2211yescharacteristic, complemented
47#17988490C2211yescharacteristic
48#17988490C2211yescharacteristic
49#17988490C2211yescharacteristic
50#17988490C2211yescharacteristic
51#17988490C2211yescharacteristic
52#17988490C2211yescharacteristic
53#17988490C2211yescharacteristic
54#17988490C2211yescharacteristic
55#17988490C2211yescharacteristic, complemented
56#17988486C2211yescharacteristic, complemented
57#17988486C2211yescharacteristic, complemented
58#17988486C2211yescharacteristic, complemented
59#17988486C2211yescharacteristic, complemented
60#17988486C2211yescharacteristic, complemented
61#17988486C2211yescharacteristic, complemented
62#17988480C2211yescharacteristic
63#17988480C2211yescharacteristic
64#17988480C2211yescharacteristic
65#17988480C2211yescharacteristic
66#17988480C2211yescharacteristic
67#17988480C2211yescharacteristic
68#17988480C2211yescharacteristic
69#17988480C2211yescharacteristic
70#17988480C2211yescharacteristic
71#17988480C2211yescharacteristic
72#17988480C2211yescharacteristic
73#17988480C2211yescharacteristic
74#17988480C2211yescharacteristic
75#17988480C2211yescharacteristic
76#17988480C2211yescharacteristic
77#17988480C2211yescharacteristic
78#17988480C2211yescharacteristic
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic
81#17988480C2211yescharacteristic
82#17988480C2211yescharacteristic
83#17988480C2211yescharacteristic
84#17988480C2211yescharacteristic
85#17988480C2211yescharacteristic
86#17988480C2211yescharacteristic, complemented
87#17988480C2211yescharacteristic, complemented
88#17988480C2211yescharacteristic, complemented
89#17988480C2211yescharacteristic, complemented
90#17988480C2211yescharacteristic, complemented
91#17988480C2211yescharacteristic, complemented
92#17988480C2211yescharacteristic, complemented
93#17988480C2211yescharacteristic, complemented
94#17988473C2211yescharacteristic, complemented
95#17988473C2211yescharacteristic, complemented
96#17988473C2211yescharacteristic, complemented
97#17988473C2211yescharacteristic, complemented
98#17988473C2211yescharacteristic, complemented
99#17988473C2211yescharacteristic, complemented
100#17988473C2211yescharacteristic, complemented
101#17988473C2211yescharacteristic, complemented
102#17988473C2211yescharacteristic, complemented
103#17988473C2211yescharacteristic, complemented
104#17988473C2211yescharacteristic, complemented
105#17988473C2211yescharacteristic, complemented
106#17988467C2211yescharacteristic
107#17988467C2211yescharacteristic
108#17988467C2211yescharacteristic
109#17988467C2211yescharacteristic
110#17988467C2211yescharacteristic
111#17988467C2211yescharacteristic
112#17988467C2211yescharacteristic
113#17988467C2211yescharacteristic
114#17988467C2211yescharacteristic
115#17988467C2211yescharacteristic
116#17988467C2211yescharacteristic
117#17988467C2211yescharacteristic
118#17988467C2211yescharacteristic, complemented
119#17988467C2211yescharacteristic, complemented
120#17988462C2211yescharacteristic
121#17988462C2211yescharacteristic
122#17988462C2211yescharacteristic
123#17988462C2211yescharacteristic
124#17988462C2211yescharacteristic
125#17988462C2211yescharacteristic
126#17988462C2211yescharacteristic
127#17988462C2211yescharacteristic
128#17988462C2211yescharacteristic, complemented
129#17988462C2211yescharacteristic, complemented
130#17988462C2211yescharacteristic, complemented
131#17988462C2211yescharacteristic, complemented
132#17988457C2211yescharacteristic, complemented
133#17988455C2211yescharacteristic, complemented
134#17988450C2211yescharacteristic
135#17988450C2211yescharacteristic
136#17988450C2211yescharacteristic, complemented
137#17988447C2211yescharacteristic
138#17988447C2211yescharacteristic
139#17988447C2211yescharacteristic, complemented
140#17988447C2211yescharacteristic, complemented
141#17988447C2211yescharacteristic, complemented
142#17988443C2211yescharacteristic
143#17988443C2211yescharacteristic
144C4⋊C4×Dic73C2211yescharacteristic, complemented
145C4⋊C4×Dic73C2211yescharacteristic, complemented
146C4⋊C4×Dic73C2211yescharacteristic, complemented
147C4⋊C4×Dic73C2211yescharacteristic, complemented
148C4⋊C4×Dic73C2211yescharacteristic, complemented
149C4⋊C4×Dic73C2211yescharacteristic, complemented
150C4×C4⋊Dic73C2211yescharacteristic, complemented
151C4×C4⋊Dic73C2211yescharacteristic, complemented
152C4×C4⋊Dic73C2211yescharacteristic, complemented
153C22⋊C4×Dic73C2211yescharacteristic
154C22⋊C4×Dic73C2211yescharacteristic
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic, complemented
162C22⋊C4×Dic73C2211yescharacteristic, complemented
163C22⋊C4×Dic73C2211yescharacteristic, complemented
164C22⋊C4×Dic73C2211yescharacteristic, complemented
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic, complemented
168#17988433C2211yescharacteristic, complemented
169#17988433C2211yescharacteristic, complemented
170#17988433C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic, complemented
172#538×C73C4116yescomplemented
173C2×#126×C73C2211yescharacteristic
174C2×#126×C73C2211yescharacteristic
175C2×#124×C73C2211yescharacteristic
176C2×#124×C73C2211yescharacteristic
177C2×#123×C73C2211yescharacteristic
178C2×#123×C73C2211yescharacteristic
179C2×C22⋊Q8×C73C2211yescharacteristic
180C2×#121×C73C2211yescharacteristic
181C2×#121×C73C2211yescharacteristic
182C2×#121×C73C2211yescharacteristic
183C2×#120×C73C2211yescharacteristic
184C2×#120×C73C2211yescharacteristic
185C2×C4×D4×C73C2211yescharacteristic
186C2×C4×D4×C73C2211yescharacteristic
187C22×C22⋊C4×C73C2211yescharacteristic
188C23×Dic73C2311yescharacteristic
189C23×Dic73C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192C23×Dic73C2311yescharacteristic
193C23×Dic73C2311yescharacteristic
194C23×Dic73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196Q8×Dic73—42no—
197D4×Dic73—42no—
198D4×Dic73—42no—
199D4×Dic73—42no—
200D4×Dic73—42no—
201D4×Dic73—42no—
202#14556550—42no—
203#14556550—42no—
204#14556550—42no—
205C2×C4⋊Dic73C2311yescharacteristic
206C2×C4⋊Dic73C2311yescharacteristic
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×C4⋊Dic73C2311yescharacteristic
210C2×C4⋊Dic73C2311yescharacteristic
211C2×C4⋊Dic73C2311yescharacteristic
212C2×C4⋊Dic73C2311yescharacteristic
213C2×C4⋊Dic73C2311yescharacteristic
214C2×C4⋊Dic73C2311yescharacteristic
215C2×C4⋊Dic73C2311yescharacteristic
216C2×C4⋊Dic73C2311yescharacteristic
217C2×C4⋊Dic73C2311yescharacteristic
218C2×C4⋊Dic73C2311yescharacteristic
219C2×C4⋊Dic73C2311yescharacteristic
220C2×C4⋊Dic73C2311yescharacteristic
221C2×C4⋊Dic73C2311yescharacteristic
222C2×C4⋊Dic73C2311yescharacteristic
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×C22⋊Dic73—42no—
226C2×C22⋊Dic73—42no—
227C2×C22⋊Dic73C2311yescharacteristic
228C2×C22⋊Dic73C2311yescharacteristic
229C2×C22⋊Dic73C2311yescharacteristic
230C2×C22⋊Dic73C2311yescharacteristic
231C2×C22⋊Dic73C2311yescharacteristic
232C2×C22⋊Dic73C2311yescharacteristic
233C2×C22⋊Dic73C2311yescharacteristic
234C2×C22⋊Dic73C2311yescharacteristic
235C2×C22⋊Dic73C2311yescharacteristic
236C2×C22⋊Dic73C2311yescharacteristic
237C2×C22⋊Dic73C2311yescharacteristic
238C2×C22⋊Dic73C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×C22⋊Dic73C2311yescharacteristic
244C2×C22⋊Dic73C2311yescharacteristic
245C2×C22⋊Dic73C2311yescharacteristic
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C22⋊Dic73C2311yescharacteristic
251C2×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C4×Dic73—42no—
260C2×C4×Dic73C2311yescharacteristic
261C2×C4×Dic73C2311yescharacteristic
262C2×C4×Dic73C2311yescharacteristic
263C2×C4×Dic73C2311yescharacteristic
264C2×C4×Dic73C2311yescharacteristic
265C2×C4×Dic73C2311yescharacteristic
266C2×C4×Dic73C2311yescharacteristic
267C2×C4×Dic73C2311yescharacteristic
268C2×C4×Dic73C2311yescharacteristic
269C2×C4×Dic73C2311yescharacteristic
270C2×C4×Dic73C2311yescharacteristic
271C2×C4×Dic73C2311yescharacteristic
272C2×C4×Dic73C2311yescharacteristic
273C2×C4×Dic73C2311yescharacteristic
274C2×C4×Dic73C2311yescharacteristic
275C2×C4×Dic73C2311yescharacteristic
276C2×C4×Dic73C2311yescharacteristic
277C2×C4×Dic73C2311yescharacteristic
278C2×C4×Dic73C2311yescharacteristic
279C2×C4×Dic73C2311yescharacteristic
280#14556498C2311yescharacteristic
281#14556498C2311yescharacteristic
282#14556498C2311yescharacteristic
283#14556498C2311yescharacteristic
284#14556498C2311yescharacteristic
285#14556498C2311yescharacteristic
286#14556498C2311yescharacteristic
287#14556498C2311yescharacteristic
288#14556498C2311yescharacteristic
289#14556498C2311yescharacteristic
290#14556498C2311yescharacteristic
291#14556498C2311yescharacteristic
292#14556498C2311yescharacteristic
293#14556498C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
298#14556498C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320C25×C73C2311yescharacteristic
321C22×Q8×C73C2311yescharacteristic
322C22×D4×C73C2311yescharacteristic
323C22×D4×C73C2311yescharacteristic
324C22×D4×C73C2311yescharacteristic
325C22×D4×C73C2311yescharacteristic
326C22×D4×C73C2311yescharacteristic
327C22×D4×C73C2311yescharacteristic
328C22×D4×C73C2311yescharacteristic
329C23×C4×C73C2311yescharacteristic
330C23×C4×C73C2311yescharacteristic
331C23×C4×C73C2311yescharacteristic
332C23×C4×C73C2311yescharacteristic
333#126×C73C2×C418yescomplemented
334#126×C73C2×C418yescomplemented
335#124×C73C2×C418yescomplemented
336#124×C73C2×C418yescomplemented
337#123×C73C2×C418yescomplemented
338#123×C73C2×C418yescomplemented
339C22⋊Q8×C73C2×C418yescomplemented
340#121×C73C2×C418yescomplemented
341#121×C73C2×C418yescomplemented
342#121×C73C2×C418yescomplemented
343#120×C73C2×C418yescomplemented
344#120×C73C2×C418yescomplemented
345C4×D4×C73C2×C418yescomplemented
346C4×D4×C73C2×C418yescomplemented
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2×C418yescomplemented
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368C2×C42×C73C2311yescharacteristic
369C2×C42×C73C2311yescharacteristic
370C22×Dic73—22no—
371C22×Dic73—22no—
372C22×Dic73—22no—
373C22×Dic73—22no—
374C22×Dic73—22no—
375C22×Dic73—41no—
376C22×Dic73—41no—
377C22×Dic73—41no—
378C22×Dic73—41no—
379C22×Dic73—41no—
380C22×Dic73—41no—
381C22×Dic73—41no—
382C22×Dic73—41no—
383C22×Dic73—41no—
384C22×Dic73—41no—
385C22×Dic73—41no—
386C22×Dic73—41no—
387C22×Dic73—41no—
388C22×Dic73—41no—
389C22×Dic73—41no—
390C22×Dic73—41no—
391C22×Dic73—41no—
392C22×Dic73—41no—
393C22×Dic73—41no—
394C22×Dic73C2411yescharacteristic
395C22×Dic73C2411yescharacteristic
396C22×Dic73C2411yescharacteristic
397C22×Dic73C2411yescharacteristic
398C22×Dic73C2411yescharacteristic
399C22×Dic73C2411yescharacteristic
400C22×Dic73C2411yescharacteristic
401C22×Dic73C2411yescharacteristic
402C22×Dic73C2411yescharacteristic
403C22×Dic73C2411yescharacteristic
404C22×Dic73C2411yescharacteristic
405C22×Dic73C2411yescharacteristic
406C22×Dic73C2411yescharacteristic
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C4⋊Dic73—22no—
411C4⋊Dic73—22no—
412C4⋊Dic73—22no—
413C4⋊Dic73—41no—
414C4⋊Dic73—41no—
415C4⋊Dic73—41no—
416C4⋊Dic73—41no—
417C4⋊Dic73—41no—
418C4⋊Dic73—41no—
419C4⋊Dic73—41no—
420C4⋊Dic73—41no—
421C4⋊Dic73—41no—
422C4⋊Dic73—41no—
423C4⋊Dic73—41no—
424C4⋊Dic73—41no—
425C4⋊Dic73—41no—
426C4⋊Dic73—41no—
427C4⋊Dic73—41no—
428C4⋊Dic73—41no—
429C4⋊Dic73—41no—
430C22⋊Dic73—22no—
431C22⋊Dic73—22no—
432C22⋊Dic73—22no—
433C22⋊Dic73—22no—
434C22⋊Dic73—22no—
435C22⋊Dic73—41no—
436C22⋊Dic73—41no—
437C22⋊Dic73—41no—
438C22⋊Dic73—41no—
439C22⋊Dic73—41no—
440C22⋊Dic73—41no—
441C22⋊Dic73—41no—
442C22⋊Dic73—41no—
443C22⋊Dic73—41no—
444C22⋊Dic73—41no—
445C22⋊Dic73—41no—
446C22⋊Dic73—41no—
447C22⋊Dic73—41no—
448C22⋊Dic73—41no—
449C22⋊Dic73—41no—
450C22⋊Dic73—41no—
451C22⋊Dic73—41no—
452C22⋊Dic73—41no—
453C22⋊Dic73—41no—
454C22⋊Dic73—41no—
455C22⋊Dic73—41no—
456C22⋊Dic73—41no—
457C22⋊Dic73—41no—
458C22⋊Dic73—41no—
459C22⋊Dic73—41no—
460C22⋊Dic73—41no—
461C22⋊Dic73—41no—
462C4×Dic73—22no—
463C4×Dic73—22no—
464C4×Dic73—22no—
465C4×Dic73—22no—
466C4×Dic73—22no—
467C4×Dic73—41no—
468C4×Dic73—41no—
469C4×Dic73—41no—
470C4×Dic73—41no—
471C4×Dic73—41no—
472C4×Dic73—41no—
473C4×Dic73—41no—
474C4×Dic73—41no—
475C4×Dic73—41no—
476C4×Dic73—41no—
477C4×Dic73—41no—
478C4×Dic73—41no—
479C4×Dic73—41no—
480C4×Dic73—41no—
481C4×Dic73—41no—
482C24×C73—41no—
483C24×C73—41no—
484C24×C73—41no—
485C24×C73—41no—
486C24×C73—41no—
487C24×C73—41no—
488C24×C73C22×C414yes—
489C24×C73C2411yescharacteristic
490C24×C73C2411yescharacteristic
491C24×C73C2411yescharacteristic
492C24×C73C2411yescharacteristic
493C24×C73C2411yescharacteristic
494C2×Q8×C73—41no—
495C2×Q8×C73—41no—
496C2×Q8×C73C22×C414yes—
497C2×D4×C73—41no—
498C2×D4×C73—41no—
499C2×D4×C73—41no—
500C2×D4×C73—41no—
501C2×D4×C73—41no—
502C2×D4×C73—41no—
503C2×D4×C73—41no—
504C2×D4×C73—41no—
505C2×D4×C73—41no—
506C2×D4×C73—41no—
507C2×D4×C73—41no—
508C2×D4×C73—41no—
509C2×D4×C73—41no—
510C2×D4×C73—41no—
511C2×D4×C73C22×C414yes—
512C2×D4×C73C22×C414yes—
513C2×D4×C73C22×C414yes—
514C2×D4×C73C22×C414yes—
515C2×D4×C73C22×C414yes—
516C2×D4×C73C22×C414yes—
517C2×D4×C73C22×C414yes—
518C22×C4×C73—41no—
519C22×C4×C73—41no—
520C22×C4×C73—41no—
521C22×C4×C73—41no—
522C22×C4×C73—41no—
523C22×C4×C73—41no—
524C22×C4×C73—41no—
525C22×C4×C73—41no—
526C22×C4×C73C22×C414yes—
527C22×C4×C73C22×C414yes—
528C22×C4×C73C22×C414yes—
529C22×C4×C73C22×C414yes—
530C22×C4×C73C2411yescharacteristic
531C22×C4×C73C2411yescharacteristic
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C22×C4×C73C2411yescharacteristic
537C22×C4×C73C2411yescharacteristic
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2411yescharacteristic
540C4⋊C4×C73C22×C414yes—
541C4⋊C4×C73C22×C414yes—
542C4⋊C4×C73C22×C414yes—
543C4⋊C4×C73C22×C414yes—
544C4⋊C4×C73C22×C414yes—
545C4⋊C4×C73C22×C414yes—
546C22⋊C4×C73C22×C414yes—
547C22⋊C4×C73C22×C414yes—
548C22⋊C4×C73C22×C414yes—
549C22⋊C4×C73C22×C414yes—
550C22⋊C4×C73C22×C414yes—
551C22⋊C4×C73C22×C414yes—
552C22⋊C4×C73C22×C414yes—
553C22⋊C4×C73C22×C414yes—
554C22⋊C4×C73C22×C414yes—
555C22⋊C4×C73C22×C414yes—
556C22⋊C4×C73C22×C414yes—
557C22⋊C4×C73C22×C414yes—
558C22⋊C4×C73C22×C414yes—
559C22⋊C4×C73C22×C414yes—
560C42×C73C22×C414yes—
561C42×C73C22×C414yes—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—44no—
593C23×C73—44no—
594C23×C73—44no—
595C23×C73—82no—
596C23×C73—82no—
597C23×C73—82no—
598C23×C73—82no—
599C23×C73C23×C412yes—
600C23×C73C23×C412yes—
601C23×C73C23×C412yes—
602C23×C73C23×C412yes—
603C23×C73C23×C412yes—
604C23×C73C2511yescharacteristic
605Q8×C73—44no—
606D4×C73—44no—
607D4×C73—44no—
608D4×C73—44no—
609D4×C73—44no—
610D4×C73—44no—
611D4×C73—44no—
612D4×C73—44no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—44no—
634C2×C4×C73—44no—
635C2×C4×C73—44no—
636C2×C4×C73—44no—
637C2×C4×C73C23×C412yes—
638C2×C4×C73C23×C412yes—
639C2×C4×C73C23×C412yes—
640C2×C4×C73C23×C412yes—
641C2×C4×C73C23×C412yes—
642C2×C4×C73C23×C412yes—
643C2×C4×C73C23×C412yes—
644C2×C4×C73C23×C412yes—
645C2×C4×C73C23×C412yes—
646C2×C4×C73C23×C412yes—
647C2×Dic73—21no—
648C2×Dic73—21no—
649C2×Dic73—21no—
650C2×Dic73—21no—
651C2×Dic73—21no—
652C2×Dic73—21no—
653C2×Dic73—21no—
654C2×Dic73—21no—
655C2×Dic73—21no—
656C2×Dic73—21no—
657C2×Dic73—21no—
658C2×Dic73—21no—
659C2×Dic73—21no—
660C2×Dic73—21no—
661C2×Dic73—21no—
662C2×Dic73—21no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—44no—
694C2×Dic73—44no—
695C2×Dic73—82no—
696C2×Dic73—82no—
697C2×Dic73—82no—
698C2×Dic73—82no—
699C2×Dic73—82no—
700C2×Dic73—82no—
701C2×Dic73H(5,𝔽2)12yes—
702C2×Dic73H(5,𝔽2)12yes—
703C22×C73—22no—
704C22×C73—22no—
705C22×C73—22no—
706C22×C73—22no—
707C22×C73—22no—
708C22×C73—22no—
709C22×C73—22no—
710C22×C73—22no—
711C22×C73—22no—
712C22×C73—22no—
713C22×C73—22no—
714C22×C73—22no—
715C22×C73—22no—
716C22×C73—22no—
717C22×C73—22no—
718C22×C73—41no—
719C22×C73—41no—
720C22×C73—41no—
721C22×C73—41no—
722C22×C73—41no—
723C22×C73—41no—
724C22×C73—41no—
725C22×C73—41no—
726C22×C73—41no—
727C22×C73—41no—
728C22×C73—41no—
729C22×C73—41no—
730C22×C73—41no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—88no—
739C22×C73C24×C411yescharacteristic
740C22×C73C2×H(5,𝔽2)11yescharacteristic
741C22×C73C2×H(5,𝔽2)11yescharacteristic
742C22×C73#58511yescharacteristic
743C22×C73#58511yescharacteristic
744C22×C73#58511yescharacteristic
745C22×C73#58511yescharacteristic
746C4×C73—22no—
747C4×C73—22no—
748C4×C73—22no—
749C4×C73—22no—
750C4×C73—22no—
751C4×C73—22no—
752C4×C73—22no—
753C4×C73—22no—
754C4×C73—22no—
755C4×C73—22no—
756Dic73—22no—
757Dic73—22no—
758Dic73—41no—
759Dic73—41no—
760Dic73—41no—
761Dic73—41no—
762Dic73—41no—
763Dic73—41no—
764Dic73—41no—
765Dic73—41no—
766Dic73—41no—
767Dic73—41no—
768Dic73—41no—
769Dic73—41no—
770Dic73—41no—
771Dic73—41no—
772#34451—731nomaximal, Sylow
773C2×C73—42no—
774C2×C73—42no—
775C2×C73—42no—
776C2×C73—42no—
777C2×C73—42no—
778C2×C73#342811yescharacteristic
779C2×C73C4×H(5,𝔽2)11yescharacteristic
780C2×C73C4×H(5,𝔽2)11yescharacteristic
781C2×C73#353311yescharacteristic
782C2×C73#354211yescharacteristic
783C2×C73#355111yescharacteristic
784C2×C73#356811yescharacteristic
785C2×#538D7311yescharacteristic
786#2383—731no—
787#2378—731no—
788#2376—731no—
789#2375—731no—
790#2373—731no—
791#2373—731no—
792#2373—731no—
793#2372—731no—
794#2367—731no—
795#2362—731no—
796#2359—731no—
797#2358—731no—
798#2354—731no—
799#2353—731no—
800#2342—731no—
801#2342—731no—
802#2337—731no—
803#2335—731no—
804#2333—731no—
805#2333—731no—
806#2326—731no—
807#2325—731no—
808#2324—731no—
809#2324—731no—
810#2321—731no—
811#2321—731no—
812#2319—731no—
813C4×#123—731no—
814C4×#121—731no—
815#2290—731no—
816C73#3445111yescharacteristic, complemented, Sylow
817#538Dic73116yescomplemented
818C2×#126C2×D7311yescharacteristic
819C2×#126C2×D7311yescharacteristic
820C2×#124C2×D7311yescharacteristic
821C2×#124C2×D7311yescharacteristic
822C2×#123C2×D7311yescharacteristic
823C2×#123C2×D7311yescharacteristic
824C2×C22⋊Q8C2×D7311yescharacteristic
825C2×#121C2×D7311yescharacteristic
826C2×#121C2×D7311yescharacteristic
827C2×#121C2×D7311yescharacteristic
828C2×#120C2×D7311yescharacteristic
829C2×#120C2×D7311yescharacteristic
830C2×C4×Q8—731no—
831C2×C4×D4—731no—
832C2×C4×D4—731no—
833C2×C4×D4—731no—
834C2×C4×D4—731no—
835C2×C4×D4—731no—
836C2×C4×D4C2×D7311yescharacteristic
837C2×C4×D4C2×D7311yescharacteristic
838C2×#117—731no—
839C2×#117—731no—
840C2×#117—731no—
841C22×C22⋊C4—731no—
842C22×C22⋊C4—731no—
843C22×C22⋊C4C2×D7311yescharacteristic
844C22×C42—731no—
845#391—731no—
846#391—731no—
847#391—731no—
848#390—731no—
849#390—731no—
850#390—731no—
851#390—731no—
852#390—731no—
853#390—731no—
854#390—731no—
855#390—731no—
856#390—731no—
857#389—731no—
858#389—731no—
859#389—731no—
860#389—731no—
861#389—731no—
862#389—731no—
863#388—731no—
864#388—731no—
865#388—731no—
866#388—731no—
867#388—731no—
868#388—731no—
869#388—731no—
870#388—731no—
871#388—731no—
872#388—731no—
873#388—731no—
874#388—731no—
875#388—731no—
876#388—731no—
877#388—731no—
878#388—731no—
879#388—731no—
880#388—731no—
881#388—731no—
882#388—731no—
883#388—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#387—731no—
896#387—731no—
897#387—731no—
898#387—731no—
899#387—731no—
900#387—731no—
901#387—731no—
902#387—731no—
903#387—731no—
904#387—731no—
905#387—731no—
906#387—731no—
907#386—731no—
908#386—731no—
909#386—731no—
910#386—731no—
911#386—731no—
912#386—731no—
913#386—731no—
914#386—731no—
915#386—731no—
916#386—731no—
917#386—731no—
918#386—731no—
919#386—731no—
920#386—731no—
921#385—731no—
922#385—731no—
923#385—731no—
924#385—731no—
925#385—731no—
926#385—731no—
927#385—731no—
928#385—731no—
929#385—731no—
930#385—731no—
931#385—731no—
932#385—731no—
933#384—731no—
934#383—731no—
935#381—731no—
936#381—731no—
937#381—731no—
938#380—731no—
939#380—731no—
940#380—731no—
941#380—731no—
942#380—731no—
943#379—731no—
944#379—731no—
945C4×C4⋊C4—731no—
946C4×C4⋊C4—731no—
947C4×C4⋊C4—731no—
948C4×C4⋊C4—731no—
949C4×C4⋊C4—731no—
950C4×C4⋊C4—731no—
951C4×C4⋊C4—731no—
952C4×C4⋊C4—731no—
953C4×C4⋊C4—731no—
954C4×C22⋊C4—731no—
955C4×C22⋊C4—731no—
956C4×C22⋊C4—731no—
957C4×C22⋊C4—731no—
958C4×C22⋊C4—731no—
959C4×C22⋊C4—731no—
960C4×C22⋊C4—731no—
961C4×C22⋊C4—731no—
962C4×C22⋊C4—731no—
963C4×C22⋊C4—731no—
964C4×C22⋊C4—731no—
965C4×C22⋊C4—731no—
966C4×C22⋊C4—731no—
967C4×C22⋊C4—731no—
968C4×C22⋊C4—731no—
969#376—731no—
970#376—731no—
971#376—731no—
972C2×#95—731no—
973C25C22×D7311yescharacteristic
974C22×Q8C22×D7311yescharacteristic
975C22×D4C22×D7311yescharacteristic
976C22×D4C22×D7311yescharacteristic
977C22×D4C22×D7311yescharacteristic
978C22×D4C22×D7311yescharacteristic
979C22×D4C22×D7311yescharacteristic
980C22×D4C22×D7311yescharacteristic
981C22×D4C22×D7311yescharacteristic
982C23×C4—731no—
983C23×C4—731no—
984C23×C4—731no—
985C23×C4—731no—
986C23×C4—731no—
987C23×C4—731no—
988C23×C4—731no—
989C23×C4—731no—
990C23×C4C22×D7311yescharacteristic
991C23×C4C22×D7311yescharacteristic
992C23×C4C22×D7311yescharacteristic
993C23×C4C22×D7311yescharacteristic
994#126C2×Dic7318yescomplemented
995#126C2×Dic7318yescomplemented
996#124C2×Dic7318yescomplemented
997#124C2×Dic7318yescomplemented
998#123C2×Dic7318yescomplemented
999#123C2×Dic7318yescomplemented
1000C22⋊Q8C2×Dic7318yescomplemented
1001#121C2×Dic7318yescomplemented
1002#121C2×Dic7318yescomplemented
1003#121C2×Dic7318yescomplemented
1004#120C2×Dic7318yescomplemented
1005#120C2×Dic7318yescomplemented
1006C4×Q8—2922no—
1007C4×D4—2922no—
1008C4×D4—2922no—
1009C4×D4—2922no—
1010C4×D4—2922no—
1011C4×D4—2922no—
1012C4×D4C2×Dic7318yescomplemented
1013C4×D4C2×Dic7318yescomplemented
1014#117—2922no—
1015#117—2922no—
1016#117—2922no—
1017C2×C4⋊C4—731no—
1018C2×C4⋊C4—731no—
1019C2×C4⋊C4—731no—
1020C2×C4⋊C4—731no—
1021C2×C4⋊C4—731no—
1022C2×C4⋊C4—731no—
1023C2×C4⋊C4—731no—
1024C2×C4⋊C4—731no—
1025C2×C4⋊C4—731no—
1026C2×C4⋊C4—731no—
1027C2×C4⋊C4—731no—
1028C2×C4⋊C4—731no—
1029C2×C4⋊C4—731no—
1030C2×C4⋊C4—731no—
1031C2×C4⋊C4—731no—
1032C2×C4⋊C4—731no—
1033C2×C4⋊C4—731no—
1034C2×C4⋊C4—731no—
1035C2×C4⋊C4—731no—
1036C2×C4⋊C4—731no—
1037C2×C4⋊C4C22×D7311yescharacteristic
1038C2×C4⋊C4C22×D7311yescharacteristic
1039C2×C4⋊C4C22×D7311yescharacteristic
1040C2×C4⋊C4C22×D7311yescharacteristic
1041C2×C4⋊C4C22×D7311yescharacteristic
1042C2×C4⋊C4C22×D7311yescharacteristic
1043C2×C22⋊C4—2922no—
1044C2×C22⋊C4—2922no—
1045C2×C22⋊C4—731no—
1046C2×C22⋊C4—731no—
1047C2×C22⋊C4—731no—
1048C2×C22⋊C4—731no—
1049C2×C22⋊C4—731no—
1050C2×C22⋊C4—731no—
1051C2×C22⋊C4—731no—
1052C2×C22⋊C4—731no—
1053C2×C22⋊C4—731no—
1054C2×C22⋊C4—731no—
1055C2×C22⋊C4—731no—
1056C2×C22⋊C4—731no—
1057C2×C22⋊C4—731no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—731no—
1060C2×C22⋊C4—731no—
1061C2×C22⋊C4—731no—
1062C2×C22⋊C4—731no—
1063C2×C22⋊C4—731no—
1064C2×C22⋊C4—731no—
1065C2×C22⋊C4—731no—
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4C2×Dic7318yescomplemented
1078C2×C22⋊C4C22×D7311yescharacteristic
1079C2×C22⋊C4C22×D7311yescharacteristic
1080C2×C22⋊C4C22×D7311yescharacteristic
1081C2×C22⋊C4C22×D7311yescharacteristic
1082C2×C22⋊C4C22×D7311yescharacteristic
1083C2×C22⋊C4C22×D7311yescharacteristic
1084C2×C22⋊C4C22×D7311yescharacteristic
1085C2×C22⋊C4C22×D7311yescharacteristic
1086C2×C22⋊C4C22×D7311yescharacteristic
1087C2×C22⋊C4C22×D7311yescharacteristic
1088C2×C22⋊C4C22×D7311yescharacteristic
1089C2×C22⋊C4C22×D7311yescharacteristic
1090C2×C22⋊C4C22×D7311yescharacteristic
1091C2×C22⋊C4C22×D7311yescharacteristic
1092C2×C42—2922no—
1093C2×C42—731no—
1094C2×C42—731no—
1095C2×C42—731no—
1096C2×C42—731no—
1097C2×C42—731no—
1098C2×C42—731no—
1099C2×C42—731no—
1100C2×C42—731no—
1101C2×C42—731no—
1102C2×C42—731no—
1103C2×C42—731no—
1104C2×C42—731no—
1105C2×C42—731no—
1106C2×C42—731no—
1107C2×C42—731no—
1108C2×C42—731no—
1109C2×C42—731no—
1110C2×C42—731no—
1111C2×C42—731no—
1112C2×C42—731no—
1113C2×C42C22×D7311yescharacteristic
1114C2×C42C22×D7311yescharacteristic
1115#95—731no—
1116#95—731no—
1117#95—731no—
1118#95—731no—
1119#95—731no—
1120#95—731no—
1121#95—731no—
1122#95—731no—
1123#95—731no—
1124#95—731no—
1125#95—731no—
1126#95—731no—
1127#95—731no—
1128#95—731no—
1129#95—731no—
1130#95—731no—
1131#95—731no—
1132#95—731no—
1133#95—731no—
1134#95—731no—
1135#95—731no—
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155C24—41no—
1156C24—41no—
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24C22×Dic7314yes—
1162C24C23×D7311yescharacteristic
1163C24C23×D7311yescharacteristic
1164C24C23×D7311yescharacteristic
1165C24C23×D7311yescharacteristic
1166C24C23×D7311yescharacteristic
1167C2×Q8—41no—
1168C2×Q8—41no—
1169C2×Q8C22×Dic7314yes—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4—41no—
1178C2×D4—41no—
1179C2×D4—41no—
1180C2×D4—41no—
1181C2×D4—41no—
1182C2×D4—41no—
1183C2×D4—41no—
1184C2×D4C22×Dic7314yes—
1185C2×D4C22×Dic7314yes—
1186C2×D4C22×Dic7314yes—
1187C2×D4C22×Dic7314yes—
1188C2×D4C22×Dic7314yes—
1189C2×D4C22×Dic7314yes—
1190C2×D4C22×Dic7314yes—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—2921no—
1200C22×C4—2921no—
1201C22×C4—2921no—
1202C22×C4—2921no—
1203C22×C4—2921no—
1204C22×C4—2921no—
1205C22×C4—2921no—
1206C22×C4—2921no—
1207C22×C4—2921no—
1208C22×C4—2921no—
1209C22×C4—2921no—
1210C22×C4—2921no—
1211C22×C4—2921no—
1212C22×C4—2921no—
1213C22×C4—2921no—
1214C22×C4—2921no—
1215C22×C4—2921no—
1216C22×C4—2921no—
1217C22×C4—2921no—
1218C22×C4—731no—
1219C22×C4—731no—
1220C22×C4—731no—
1221C22×C4—731no—
1222C22×C4—731no—
1223C22×C4—731no—
1224C22×C4—731no—
1225C22×C4—731no—
1226C22×C4—731no—
1227C22×C4—731no—
1228C22×C4—731no—
1229C22×C4—731no—
1230C22×C4—731no—
1231C22×C4—731no—
1232C22×C4—731no—
1233C22×C4—731no—
1234C22×C4—1462no—
1235C22×C4—1462no—
1236C22×C4—1462no—
1237C22×C4—1462no—
1238C22×C4—1462no—
1239C22×C4C22×Dic7314yes—
1240C22×C4C22×Dic7314yes—
1241C22×C4C22×Dic7314yes—
1242C22×C4C22×Dic7314yes—
1243C22×C4C23×D7311yescharacteristic
1244C22×C4C23×D7311yescharacteristic
1245C22×C4C23×D7311yescharacteristic
1246C22×C4C23×D7311yescharacteristic
1247C22×C4C23×D7311yescharacteristic
1248C22×C4C23×D7311yescharacteristic
1249C22×C4C23×D7311yescharacteristic
1250C22×C4C23×D7311yescharacteristic
1251C22×C4C23×D7311yescharacteristic
1252C22×C4C23×D7311yescharacteristic
1253C4⋊C4—2921no—
1254C4⋊C4—2921no—
1255C4⋊C4—2921no—
1256C4⋊C4—2921no—
1257C4⋊C4—2921no—
1258C4⋊C4—2921no—
1259C4⋊C4—2921no—
1260C4⋊C4—2921no—
1261C4⋊C4—2921no—
1262C4⋊C4—2921no—
1263C4⋊C4—2921no—
1264C4⋊C4—2921no—
1265C4⋊C4—2921no—
1266C4⋊C4—2921no—
1267C4⋊C4—2921no—
1268C4⋊C4—2921no—
1269C4⋊C4—2921no—
1270C4⋊C4—1462no—
1271C4⋊C4—1462no—
1272C4⋊C4—1462no—
1273C4⋊C4C22×Dic7314yes—
1274C4⋊C4C22×Dic7314yes—
1275C4⋊C4C22×Dic7314yes—
1276C4⋊C4C22×Dic7314yes—
1277C4⋊C4C22×Dic7314yes—
1278C4⋊C4C22×Dic7314yes—
1279C22⋊C4—2921no—
1280C22⋊C4—2921no—
1281C22⋊C4—2921no—
1282C22⋊C4—2921no—
1283C22⋊C4—2921no—
1284C22⋊C4—2921no—
1285C22⋊C4—2921no—
1286C22⋊C4—2921no—
1287C22⋊C4—2921no—
1288C22⋊C4—2921no—
1289C22⋊C4—2921no—
1290C22⋊C4—2921no—
1291C22⋊C4—2921no—
1292C22⋊C4—2921no—
1293C22⋊C4—2921no—
1294C22⋊C4—2921no—
1295C22⋊C4—2921no—
1296C22⋊C4—2921no—
1297C22⋊C4—2921no—
1298C22⋊C4—2921no—
1299C22⋊C4—2921no—
1300C22⋊C4—2921no—
1301C22⋊C4—2921no—
1302C22⋊C4—2921no—
1303C22⋊C4—2921no—
1304C22⋊C4—2921no—
1305C22⋊C4—2921no—
1306C22⋊C4—1462no—
1307C22⋊C4—1462no—
1308C22⋊C4—1462no—
1309C22⋊C4—1462no—
1310C22⋊C4—1462no—
1311C22⋊C4C22×Dic7314yes—
1312C22⋊C4C22×Dic7314yes—
1313C22⋊C4C22×Dic7314yes—
1314C22⋊C4C22×Dic7314yes—
1315C22⋊C4C22×Dic7314yes—
1316C22⋊C4C22×Dic7314yes—
1317C22⋊C4C22×Dic7314yes—
1318C22⋊C4C22×Dic7314yes—
1319C22⋊C4C22×Dic7314yes—
1320C22⋊C4C22×Dic7314yes—
1321C22⋊C4C22×Dic7314yes—
1322C22⋊C4C22×Dic7314yes—
1323C22⋊C4C22×Dic7314yes—
1324C22⋊C4C22×Dic7314yes—
1325C42—2921no—
1326C42—2921no—
1327C42—2921no—
1328C42—2921no—
1329C42—2921no—
1330C42—2921no—
1331C42—2921no—
1332C42—2921no—
1333C42—2921no—
1334C42—2921no—
1335C42—2921no—
1336C42—2921no—
1337C42—2921no—
1338C42—2921no—
1339C42—2921no—
1340C42—1462no—
1341C42—1462no—
1342C42—1462no—
1343C42—1462no—
1344C42—1462no—
1345C42C22×Dic7314yes—
1346C42C22×Dic7314yes—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—44no—
1378C23—44no—
1379C23—44no—
1380C23—82no—
1381C23—82no—
1382C23—82no—
1383C23—82no—
1384C23C23×Dic7312yes—
1385C23C23×Dic7312yes—
1386C23C23×Dic7312yes—
1387C23C23×Dic7312yes—
1388C23C23×Dic7312yes—
1389C23C24×D7311yescharacteristic
1390Q8—44no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—44no—
1395D4—44no—
1396D4—44no—
1397D4—44no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—44no—
1422C2×C4—2924no—
1423C2×C4—2924no—
1424C2×C4—5842no—
1425C2×C4—5842no—
1426C2×C4—5842no—
1427C2×C4—5842no—
1428C2×C4—5842no—
1429C2×C4—5842no—
1430C2×C4—732no—
1431C2×C4—732no—
1432C2×C4—1461no—
1433C2×C4—1461no—
1434C2×C4—1461no—
1435C2×C4—1461no—
1436C2×C4—1461no—
1437C2×C4—1461no—
1438C2×C4—1461no—
1439C2×C4—1461no—
1440C2×C4—1461no—
1441C2×C4—1461no—
1442C2×C4—1461no—
1443C2×C4—1461no—
1444C2×C4—1461no—
1445C2×C4—1461no—
1446C2×C4—1461no—
1447C2×C4—1461no—
1448C2×C4—1461no—
1449C2×C4—1461no—
1450C2×C4—1461no—
1451C2×C4—1461no—
1452C2×C4—1461no—
1453C2×C4—1461no—
1454C2×C4—1461no—
1455C2×C4—1461no—
1456C2×C4—1461no—
1457C2×C4—1461no—
1458C2×C4—1461no—
1459C2×C4—1461no—
1460C2×C4—1461no—
1461C2×C4—1461no—
1462C2×C4—1461no—
1463C2×C4—1461no—
1464C2×C4—1461no—
1465C2×C4—1461no—
1466C2×C4—1461no—
1467C2×C4—1461no—
1468C2×C4—1461no—
1469C2×C4—1461no—
1470C2×C4—1461no—
1471C2×C4—1461no—
1472C2×C4—1461no—
1473C2×C4—1461no—
1474C2×C4—1461no—
1475C2×C4—1461no—
1476C2×C4—1461no—
1477C2×C4—1461no—
1478C2×C4C23×Dic7312yes—
1479C2×C4C23×Dic7312yes—
1480C2×C4C23×Dic7312yes—
1481C2×C4C23×Dic7312yes—
1482C2×C4C23×Dic7312yes—
1483C2×C4C23×Dic7312yes—
1484C2×C4C23×Dic7312yes—
1485C2×C4C23×Dic7312yes—
1486C2×C4C23×Dic7312yes—
1487C2×C4C23×Dic7312yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—88no—
1524C22C24×Dic7311yescharacteristic
1525C22H(5,𝔽2)×D7311yescharacteristic
1526C22H(5,𝔽2)×D7311yescharacteristic
1527C22#1798942211yescharacteristic
1528C22#1798942211yescharacteristic
1529C22#1798942311yescharacteristic
1530C22#1798942311yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—22no—
1539C4—22no—
1540C4—22no—
1541C4—2921no—
1542C4—2921no—
1543C4—2921no—
1544C4—2921no—
1545C4—2921no—
1546C4—2921no—
1547C4—2921no—
1548C4—2921no—
1549C4—2921no—
1550C4—2921no—
1551C4—2921no—
1552C4—2921no—
1553C4—2921no—
1554C4—2921no—
1555C4—1462no—
1556C4—1462no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—42no—
1561C2—42no—
1562C2#2262313411yescharacteristic
1563C2H(5,𝔽2)×Dic7311yescharacteristic
1564C2H(5,𝔽2)×Dic7311yescharacteristic
1565C2#2262409811yescharacteristic
1566C2#2262424611yescharacteristic
1567C2#2262434811yescharacteristic
1568C2#2262462411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
Fitting, prime radicalC2×#538×C73C2
socle, cosocleC23×C73C25
hypercenterC2×#538D73
hypocenterC73#34451
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22613123C2semidirect
2. #22613097C2semidirect
3. #22613079C2semidirect
4. #22613072C2semidirect
5. #22613055C2semidirect
6. #22613055C2semidirect
7. #22613055C2semidirect
8. #22613043C2semidirect
9. #22613006C2semidirect
10. #22612962C2semidirect
11. #22612927C2semidirect
12. #22612915C2semidirect
13. #22612880C2semidirect
14. #22612871C2semidirect
15. #22612780C2semidirect
16. #22612780C2semidirect
17. #22612746C2semidirect
18. #22612725C2semidirect
19. #22612698C2semidirect
20. #22612698C2semidirect
21. #22612644C2semidirect
22. #22612636C2semidirect
23. #22612626C2semidirect
24. #22612626C2semidirect
25. #22612592C2semidirect
26. #22612592C2semidirect
27. #22612574C2semidirect
28. #123×Dic73C2semidirect
29. #121×Dic73C2semidirect
30. #22612376C2semidirect
32. C2×Q8×Dic73C22semidirect
37. C2×D4×Dic73C22semidirect
40. C2×#14556550C22semidirect
43. C22×C4×Dic73C22semidirect
44. #17988494C22semidirect
45. #17988494C22semidirect
46. #17988494C22semidirect
55. #17988490C22semidirect
56. #17988486C22semidirect
57. #17988486C22semidirect
58. #17988486C22semidirect
59. #17988486C22semidirect
60. #17988486C22semidirect
61. #17988486C22semidirect
86. #17988480C22semidirect
87. #17988480C22semidirect
88. #17988480C22semidirect
89. #17988480C22semidirect
90. #17988480C22semidirect
91. #17988480C22semidirect
92. #17988480C22semidirect
93. #17988480C22semidirect
94. #17988473C22semidirect
95. #17988473C22semidirect
96. #17988473C22semidirect
97. #17988473C22semidirect
98. #17988473C22semidirect
99. #17988473C22semidirect
100. #17988473C22semidirect
101. #17988473C22semidirect
102. #17988473C22semidirect
103. #17988473C22semidirect
104. #17988473C22semidirect
105. #17988473C22semidirect
118. #17988467C22semidirect
119. #17988467C22semidirect
128. #17988462C22semidirect
129. #17988462C22semidirect
130. #17988462C22semidirect
131. #17988462C22semidirect
132. #17988457C22semidirect
133. #17988455C22semidirect
136. #17988450C22semidirect
139. #17988447C22semidirect
140. #17988447C22semidirect
141. #17988447C22semidirect
144. C4⋊C4×Dic73C22semidirect
145. C4⋊C4×Dic73C22semidirect
146. C4⋊C4×Dic73C22semidirect
147. C4⋊C4×Dic73C22semidirect
148. C4⋊C4×Dic73C22semidirect
149. C4⋊C4×Dic73C22semidirect
150. C4×C4⋊Dic73C22semidirect
151. C4×C4⋊Dic73C22semidirect
152. C4×C4⋊Dic73C22semidirect
161. C22⋊C4×Dic73C22semidirect
162. C22⋊C4×Dic73C22semidirect
163. C22⋊C4×Dic73C22semidirect
164. C22⋊C4×Dic73C22semidirect
167. C4×C22⋊Dic73C22semidirect
168. #17988433C22semidirect
169. #17988433C22semidirect
170. #17988433C22semidirect
171. C2×#14556498C22semidirect
172. #538×C73C4semidirect
333. #126×C73C2×C4semidirect
334. #126×C73C2×C4semidirect
335. #124×C73C2×C4semidirect
336. #124×C73C2×C4semidirect
337. #123×C73C2×C4semidirect
338. #123×C73C2×C4semidirect
339. C22⋊Q8×C73C2×C4semidirect
340. #121×C73C2×C4semidirect
341. #121×C73C2×C4semidirect
342. #121×C73C2×C4semidirect
343. #120×C73C2×C4semidirect
344. #120×C73C2×C4semidirect
345. C4×D4×C73C2×C4semidirect
346. C4×D4×C73C2×C4semidirect
353. C2×C22⋊C4×C73C2×C4semidirect
816. C73#34451semidirect
817. #538Dic73semidirect
994. #126C2×Dic73semidirect
995. #126C2×Dic73semidirect
996. #124C2×Dic73semidirect
997. #124C2×Dic73semidirect
998. #123C2×Dic73semidirect
999. #123C2×Dic73semidirect
1000. C22⋊Q8C2×Dic73semidirect
1001. #121C2×Dic73semidirect
1002. #121C2×Dic73semidirect
1003. #121C2×Dic73semidirect
1004. #120C2×Dic73semidirect
1005. #120C2×Dic73semidirect
1012. C4×D4C2×Dic73semidirect
1013. C4×D4C2×Dic73semidirect
1077. C2×C22⋊C4C2×Dic73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226131232
#226130972
#226130792
#226130722
#226130552
#226130432
#226130062
#226129622
#226129272
#226129152
#226128802
#226128712
#226127802
#226127462
#226127252
#226126982
#226126442
#226126362
#226126262
#226125922
#226125742
#123×Dic732
#121×Dic732
#226123762
C2×#538×C732
#3445173