Finite Group Databasebeta

← #33250336

Subgroups — #33250336

Order 18688.

2290 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613117C211yesmaximal, characteristic, complemented
2#22613088C211yesmaximal, characteristic, complemented
3#22613088C211yesmaximal, characteristic, complemented
4#22613079C211yesmaximal, characteristic, complemented
5#22613067C211yesmaximal, characteristic, complemented
6#22613037C211yesmaximal, characteristic, complemented
7#22612983C211yesmaximal, characteristic, complemented
8#22612983C211yesmaximal, characteristic, complemented
9#22612973C211yesmaximal, characteristic, complemented
10#22612951C211yesmaximal, characteristic, complemented
11#22612927C211yesmaximal, characteristic, complemented
12#22612927C211yesmaximal, characteristic, complemented
13#22612871C211yesmaximal, characteristic, complemented
14#22612860C211yesmaximal, characteristic, complemented
15#22612816C211yesmaximal, characteristic, complemented
16#22612791C211yesmaximal, characteristic, complemented
17#22612725C211yesmaximal, characteristic, complemented
18#22612725C211yesmaximal, characteristic, complemented
19#22612698C211yesmaximal, characteristic, complemented
20#22612698C211yesmaximal, characteristic, complemented
21#22612657C211yesmaximal, characteristic, complemented
22#22612657C211yesmaximal, characteristic, complemented
23#22612636C211yesmaximal, characteristic, complemented
24#22612636C211yesmaximal, characteristic, complemented
25#22612626C211yesmaximal, characteristic, complemented
26#22612603C211yesmaximal, characteristic, complemented
27#22612564C211yesmaximal, characteristic, complemented
28#123×Dic73C211yesmaximal, characteristic, complemented
29#121×Dic73C211yesmaximal, characteristic, complemented
30#22612376C211yesmaximal, characteristic, complemented
31C2×#540×C73C211yesmaximal, characteristic
32C2×D4×Dic73C2211yescharacteristic
33C2×D4×Dic73C2211yescharacteristic
34C2×D4×Dic73C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556550C2211yescharacteristic
41C2×#14556550C2211yescharacteristic
42C22×C4⋊Dic73C2211yescharacteristic
43C22×C4×Dic73C2211yescharacteristic
44#17988490C2211yescharacteristic
45#17988490C2211yescharacteristic
46#17988490C2211yescharacteristic
47#17988490C2211yescharacteristic
48#17988490C2211yescharacteristic
49#17988490C2211yescharacteristic
50#17988490C2211yescharacteristic
51#17988490C2211yescharacteristic
52#17988486C2211yescharacteristic
53#17988486C2211yescharacteristic
54#17988486C2211yescharacteristic
55#17988486C2211yescharacteristic
56#17988486C2211yescharacteristic
57#17988486C2211yescharacteristic
58#17988480C2211yescharacteristic
59#17988480C2211yescharacteristic
60#17988480C2211yescharacteristic
61#17988480C2211yescharacteristic
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#17988473C2211yescharacteristic
79#17988473C2211yescharacteristic
80#17988473C2211yescharacteristic
81#17988473C2211yescharacteristic
82#17988473C2211yescharacteristic
83#17988473C2211yescharacteristic
84#17988473C2211yescharacteristic
85#17988473C2211yescharacteristic
86#17988473C2211yescharacteristic
87#17988473C2211yescharacteristic
88#17988473C2211yescharacteristic
89#17988473C2211yescharacteristic
90#17988473C2211yescharacteristic
91#17988473C2211yescharacteristic
92#17988473C2211yescharacteristic
93#17988473C2211yescharacteristic
94#17988473C2211yescharacteristic
95#17988473C2211yescharacteristic
96#17988473C2211yescharacteristic
97#17988473C2211yescharacteristic
98#17988467C2211yescharacteristic
99#17988467C2211yescharacteristic
100#17988467C2211yescharacteristic
101#17988467C2211yescharacteristic
102#17988467C2211yescharacteristic
103#17988467C2211yescharacteristic
104#17988467C2211yescharacteristic
105#17988467C2211yescharacteristic
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
119#17988467C2211yescharacteristic
120#17988467C2211yescharacteristic
121#17988467C2211yescharacteristic
122#17988462C2211yescharacteristic
123#17988462C2211yescharacteristic
124#17988462C2211yescharacteristic
125#17988462C2211yescharacteristic
126#17988462C2211yescharacteristic
127#17988462C2211yescharacteristic
128#17988462C2211yescharacteristic
129#17988462C2211yescharacteristic
130#17988462C2211yescharacteristic
131#17988462C2211yescharacteristic
132#17988455C2211yescharacteristic
133#17988453C2211yescharacteristic
134#17988453C2211yescharacteristic
135#17988453C2211yescharacteristic
136#17988450C2211yescharacteristic
137#17988450C2211yescharacteristic
138#17988450C2211yescharacteristic
139#17988447C2211yescharacteristic
140#17988447C2211yescharacteristic
141#17988447C2211yescharacteristic
142#17988447C2211yescharacteristic
143#17988447C2211yescharacteristic
144C4⋊C4×Dic73C2211yescharacteristic
145C4⋊C4×Dic73C2211yescharacteristic
146C4⋊C4×Dic73C2211yescharacteristic
147C4⋊C4×Dic73C2211yescharacteristic
148C4⋊C4×Dic73C2211yescharacteristic
149C4⋊C4×Dic73C2211yescharacteristic
150C4×C4⋊Dic73C2211yescharacteristic
151C22⋊C4×Dic73C2211yescharacteristic
152C22⋊C4×Dic73C2211yescharacteristic
153C22⋊C4×Dic73C2211yescharacteristic
154C22⋊C4×Dic73C2211yescharacteristic
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C4×C22⋊Dic73C2211yescharacteristic
162C4×C22⋊Dic73C2211yescharacteristic
163C4×C22⋊Dic73C2211yescharacteristic
164C4×C22⋊Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166#17988433C2211yescharacteristic
167#17988433C2211yescharacteristic
168#17988433C2211yescharacteristic
169C2×#14556498C2211yescharacteristic
170C2×#14556498C2211yescharacteristic
171C2×#14556498C2211yescharacteristic
172#540×C73C4116yescomplemented
173C2×#127×C73C2211yescharacteristic
174C2×#125×C73C2211yescharacteristic
175C2×#123×C73C2211yescharacteristic
176C2×#123×C73C2211yescharacteristic
177C2×#123×C73C2211yescharacteristic
178C2×#123×C73C2211yescharacteristic
179C2×#121×C73C2211yescharacteristic
180C2×#121×C73C2211yescharacteristic
181C2×#121×C73C2211yescharacteristic
182C2×#121×C73C2211yescharacteristic
183C2×#121×C73C2211yescharacteristic
184C2×#121×C73C2211yescharacteristic
185C2×C4×D4×C73C2211yescharacteristic
186C2×C4×D4×C73C2211yescharacteristic
187C2×#117×C73C2211yescharacteristic
188C23×Dic73C2311yescharacteristic
189C23×Dic73C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192C23×Dic73C2311yescharacteristic
193C23×Dic73C2311yescharacteristic
194C23×Dic73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198D4×Dic73—42no—
199D4×Dic73—42no—
200D4×Dic73—42no—
201D4×Dic73—42no—
202D4×Dic73—42no—
203D4×Dic73—42no—
204D4×Dic73—42no—
205D4×Dic73—42no—
206#14556550—42no—
207#14556550—42no—
208C2×C4⋊Dic73—42no—
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×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
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×C4×Dic73—42no—
258C2×C4×Dic73C2311yescharacteristic
259C2×C4×Dic73C2311yescharacteristic
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
276#14556498C2311yescharacteristic
277#14556498C2311yescharacteristic
278#14556498C2311yescharacteristic
279#14556498C2311yescharacteristic
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
320C22×D4×C73C2311yescharacteristic
321C22×D4×C73C2311yescharacteristic
322C22×D4×C73C2311yescharacteristic
323C22×D4×C73C2311yescharacteristic
324C22×D4×C73C2311yescharacteristic
325C22×D4×C73C2311yescharacteristic
326C22×D4×C73C2311yescharacteristic
327C22×D4×C73C2311yescharacteristic
328C22×D4×C73C2311yescharacteristic
329C22×D4×C73C2311yescharacteristic
330C23×C4×C73C2311yescharacteristic
331C23×C4×C73C2311yescharacteristic
332C23×C4×C73C2311yescharacteristic
333C23×C4×C73C2311yescharacteristic
334C23×C4×C73C2311yescharacteristic
335#127×C73C2×C418yescomplemented
336#125×C73C2×C418yescomplemented
337#123×C73C2×C418yescomplemented
338#123×C73C2×C418yescomplemented
339#123×C73C2×C418yescomplemented
340#123×C73C2×C418yescomplemented
341#121×C73C2×C418yescomplemented
342#121×C73C2×C418yescomplemented
343#121×C73C2×C418yescomplemented
344#121×C73C2×C418yescomplemented
345#121×C73C2×C418yescomplemented
346#121×C73C2×C418yescomplemented
347C4×D4×C73C2×C418yescomplemented
348C4×D4×C73C2×C418yescomplemented
349#117×C73C2×C418yescomplemented
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C4⋊C4×C73C2311yescharacteristic
354C2×C4⋊C4×C73C2311yescharacteristic
355C2×C4⋊C4×C73C2311yescharacteristic
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C4⋊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×Dic73—41no—
395C22×Dic73—41no—
396C22×Dic73—41no—
397C22×Dic73—41no—
398C22×Dic73—41no—
399C22×Dic73—41no—
400C22×Dic73C2411yescharacteristic
401C22×Dic73C2411yescharacteristic
402C22×Dic73C2411yescharacteristic
403C22×Dic73C2411yescharacteristic
404C22×Dic73C2411yescharacteristic
405C22×Dic73C2411yescharacteristic
406C22×Dic73C2411yescharacteristic
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C4⋊Dic73—22no—
417C4⋊Dic73—22no—
418C4⋊Dic73—22no—
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—
430C4⋊Dic73—41no—
431C4⋊Dic73—41no—
432C4⋊Dic73—41no—
433C4⋊Dic73—41no—
434C22⋊Dic73—22no—
435C22⋊Dic73—22no—
436C22⋊Dic73—22no—
437C22⋊Dic73—22no—
438C22⋊Dic73—22no—
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—
462C22⋊Dic73—41no—
463C22⋊Dic73—41no—
464C4×Dic73—22no—
465C4×Dic73—22no—
466C4×Dic73—22no—
467C4×Dic73—22no—
468C4×Dic73—22no—
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×C73C2411yescharacteristic
483C24×C73C2411yescharacteristic
484C24×C73C2411yescharacteristic
485C24×C73C2411yescharacteristic
486C24×C73C2411yescharacteristic
487C2×D4×C73—41no—
488C2×D4×C73—41no—
489C2×D4×C73—41no—
490C2×D4×C73—41no—
491C2×D4×C73—41no—
492C2×D4×C73—41no—
493C2×D4×C73—41no—
494C2×D4×C73—41no—
495C2×D4×C73—41no—
496C2×D4×C73—41no—
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×C73C22×C414yes—
508C2×D4×C73C22×C414yes—
509C2×D4×C73C22×C414yes—
510C2×D4×C73C22×C414yes—
511C2×D4×C73C22×C414yes—
512C2×D4×C73C22×C414yes—
513C2×D4×C73C22×C414yes—
514C2×D4×C73C22×C414yes—
515C2×D4×C73C22×C414yes—
516C2×D4×C73C22×C414yes—
517C22×C4×C73—41no—
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×C73—41no—
527C22×C4×C73C22×C414yes—
528C22×C4×C73C22×C414yes—
529C22×C4×C73C22×C414yes—
530C22×C4×C73C22×C414yes—
531C22×C4×C73C22×C414yes—
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C22×C4×C73C2411yescharacteristic
537C22×C4×C73C2411yescharacteristic
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2411yescharacteristic
540C22×C4×C73C2411yescharacteristic
541C22×C4×C73C2411yescharacteristic
542C4⋊C4×C73C22×C414yes—
543C4⋊C4×C73C22×C414yes—
544C4⋊C4×C73C22×C414yes—
545C4⋊C4×C73C22×C414yes—
546C4⋊C4×C73C22×C414yes—
547C4⋊C4×C73C22×C414yes—
548C4⋊C4×C73C22×C414yes—
549C4⋊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×C73C23×C412yes—
593C23×C73C23×C412yes—
594C23×C73C23×C412yes—
595C23×C73C23×C412yes—
596C23×C73C23×C412yes—
597C23×C73C2511yescharacteristic
598D4×C73—44no—
599D4×C73—44no—
600D4×C73—44no—
601D4×C73—44no—
602D4×C73—44no—
603D4×C73—44no—
604D4×C73—44no—
605D4×C73—44no—
606D4×C73—44no—
607D4×C73—44no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
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—44no—
629C2×C4×C73—44no—
630C2×C4×C73—44no—
631C2×C4×C73—44no—
632C2×C4×C73—44no—
633C2×C4×C73C23×C412yes—
634C2×C4×C73C23×C412yes—
635C2×C4×C73C23×C412yes—
636C2×C4×C73C23×C412yes—
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×Dic73—21no—
644C2×Dic73—21no—
645C2×Dic73—21no—
646C2×Dic73—21no—
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—44no—
690C2×Dic73—44no—
691C2×Dic73—82no—
692C2×Dic73—82no—
693C2×Dic73—82no—
694C2×Dic73—82no—
695C2×Dic73—82no—
696C2×Dic73—82no—
697C2×Dic73—82no—
698C2×Dic73—82no—
699C2×Dic73H(5,𝔽2)12yes—
700C2×Dic73H(5,𝔽2)12yes—
701C22×C73—22no—
702C22×C73—22no—
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—41no—
717C22×C73—41no—
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×C73C24×C411yescharacteristic
737C22×C73C2×H(5,𝔽2)11yescharacteristic
738C22×C73C2×H(5,𝔽2)11yescharacteristic
739C22×C73#58511yescharacteristic
740C22×C73#58511yescharacteristic
741C22×C73#58511yescharacteristic
742C22×C73#58511yescharacteristic
743C4×C73—22no—
744C4×C73—22no—
745C4×C73—22no—
746C4×C73—22no—
747C4×C73—22no—
748C4×C73—22no—
749C4×C73—22no—
750C4×C73—22no—
751C4×C73—22no—
752C4×C73—22no—
753Dic73—22no—
754Dic73—22no—
755Dic73—41no—
756Dic73—41no—
757Dic73—41no—
758Dic73—41no—
759Dic73—41no—
760Dic73—41no—
761Dic73—41no—
762Dic73—41no—
763Dic73—41no—
764Dic73—41no—
765Dic73—41no—
766Dic73—41no—
767Dic73—41no—
768Dic73—41no—
769#34450—731nomaximal, Sylow
770C2×C73—42no—
771C2×C73—42no—
772C2×C73—42no—
773C2×C73—42no—
774C2×C73—42no—
775C2×C73#342811yescharacteristic
776C2×C73C4×H(5,𝔽2)11yescharacteristic
777C2×C73C4×H(5,𝔽2)11yescharacteristic
778C2×C73#353311yescharacteristic
779C2×C73#354211yescharacteristic
780C2×C73#355111yescharacteristic
781C2×C73#356711yescharacteristic
782C2×#540D7311yescharacteristic
783#2382—731no—
784#2377—731no—
785#2377—731no—
786#2376—731no—
787#2374—731no—
788#2371—731no—
789#2364—731no—
790#2364—731no—
791#2363—731no—
792#2361—731no—
793#2359—731no—
794#2359—731no—
795#2353—731no—
796#2352—731no—
797#2346—731no—
798#2343—731no—
799#2335—731no—
800#2335—731no—
801#2333—731no—
802#2333—731no—
803#2328—731no—
804#2328—731no—
805#2325—731no—
806#2325—731no—
807#2324—731no—
808#2322—731no—
809#2318—731no—
810C4×#123—731no—
811C4×#121—731no—
812#2290—731no—
813C73#3445011yescharacteristic, complemented, Sylow
814#540Dic73116yescomplemented
815C2×#127C2×D7311yescharacteristic
816C2×#125C2×D7311yescharacteristic
817C2×#123C2×D7311yescharacteristic
818C2×#123C2×D7311yescharacteristic
819C2×#123C2×D7311yescharacteristic
820C2×#123C2×D7311yescharacteristic
821C2×#121C2×D7311yescharacteristic
822C2×#121C2×D7311yescharacteristic
823C2×#121C2×D7311yescharacteristic
824C2×#121C2×D7311yescharacteristic
825C2×#121C2×D7311yescharacteristic
826C2×#121C2×D7311yescharacteristic
827C2×C4×D4—731no—
828C2×C4×D4—731no—
829C2×C4×D4—731no—
830C2×C4×D4—731no—
831C2×C4×D4—731no—
832C2×C4×D4—731no—
833C2×C4×D4—731no—
834C2×C4×D4—731no—
835C2×C4×D4C2×D7311yescharacteristic
836C2×C4×D4C2×D7311yescharacteristic
837C2×#117—731no—
838C2×#117—731no—
839C2×#117C2×D7311yescharacteristic
840C22×C4⋊C4—731no—
841C22×C42—731no—
842#390—731no—
843#390—731no—
844#390—731no—
845#390—731no—
846#390—731no—
847#390—731no—
848#390—731no—
849#390—731no—
850#389—731no—
851#389—731no—
852#389—731no—
853#389—731no—
854#389—731no—
855#389—731no—
856#388—731no—
857#388—731no—
858#388—731no—
859#388—731no—
860#388—731no—
861#388—731no—
862#388—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#387—731no—
877#387—731no—
878#387—731no—
879#387—731no—
880#387—731no—
881#387—731no—
882#387—731no—
883#387—731no—
884#387—731no—
885#387—731no—
886#387—731no—
887#387—731no—
888#387—731no—
889#387—731no—
890#387—731no—
891#387—731no—
892#387—731no—
893#387—731no—
894#387—731no—
895#387—731no—
896#386—731no—
897#386—731no—
898#386—731no—
899#386—731no—
900#386—731no—
901#386—731no—
902#386—731no—
903#386—731no—
904#386—731no—
905#386—731no—
906#386—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#385—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#383—731no—
931#382—731no—
932#382—731no—
933#382—731no—
934#381—731no—
935#381—731no—
936#381—731no—
937#380—731no—
938#380—731no—
939#380—731no—
940#380—731no—
941#380—731no—
942C4×C4⋊C4—731no—
943C4×C4⋊C4—731no—
944C4×C4⋊C4—731no—
945C4×C4⋊C4—731no—
946C4×C4⋊C4—731no—
947C4×C4⋊C4—731no—
948C4×C4⋊C4—731no—
949C4×C22⋊C4—731no—
950C4×C22⋊C4—731no—
951C4×C22⋊C4—731no—
952C4×C22⋊C4—731no—
953C4×C22⋊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—
964#376—731no—
965#376—731no—
966#376—731no—
967C2×#95—731no—
968C2×#95—731no—
969C2×#95—731no—
970C22×D4C22×D7311yescharacteristic
971C22×D4C22×D7311yescharacteristic
972C22×D4C22×D7311yescharacteristic
973C22×D4C22×D7311yescharacteristic
974C22×D4C22×D7311yescharacteristic
975C22×D4C22×D7311yescharacteristic
976C22×D4C22×D7311yescharacteristic
977C22×D4C22×D7311yescharacteristic
978C22×D4C22×D7311yescharacteristic
979C22×D4C22×D7311yescharacteristic
980C23×C4—731no—
981C23×C4—731no—
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
994C23×C4C22×D7311yescharacteristic
995#127C2×Dic7318yescomplemented
996#125C2×Dic7318yescomplemented
997#123C2×Dic7318yescomplemented
998#123C2×Dic7318yescomplemented
999#123C2×Dic7318yescomplemented
1000#123C2×Dic7318yescomplemented
1001#121C2×Dic7318yescomplemented
1002#121C2×Dic7318yescomplemented
1003#121C2×Dic7318yescomplemented
1004#121C2×Dic7318yescomplemented
1005#121C2×Dic7318yescomplemented
1006#121C2×Dic7318yescomplemented
1007C4×D4—2922no—
1008C4×D4—2922no—
1009C4×D4—2922no—
1010C4×D4—2922no—
1011C4×D4—2922no—
1012C4×D4—2922no—
1013C4×D4—2922no—
1014C4×D4—2922no—
1015C4×D4C2×Dic7318yescomplemented
1016C4×D4C2×Dic7318yescomplemented
1017#117—2922no—
1018#117—2922no—
1019#117C2×Dic7318yescomplemented
1020C2×C4⋊C4—2922no—
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⋊C4—731no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4C22×D7311yescharacteristic
1040C2×C4⋊C4C22×D7311yescharacteristic
1041C2×C4⋊C4C22×D7311yescharacteristic
1042C2×C4⋊C4C22×D7311yescharacteristic
1043C2×C4⋊C4C22×D7311yescharacteristic
1044C2×C4⋊C4C22×D7311yescharacteristic
1045C2×C4⋊C4C22×D7311yescharacteristic
1046C2×C4⋊C4C22×D7311yescharacteristic
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⋊C4C22×D7311yescharacteristic
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×C42—2922no—
1088C2×C42—731no—
1089C2×C42—731no—
1090C2×C42—731no—
1091C2×C42—731no—
1092C2×C42—731no—
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×C42C22×D7311yescharacteristic
1107C2×C42C22×D7311yescharacteristic
1108#95—731no—
1109#95—731no—
1110#95—731no—
1111#95—731no—
1112#95—731no—
1113#95—731no—
1114#95—731no—
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—
1152C24C23×D7311yescharacteristic
1153C24C23×D7311yescharacteristic
1154C24C23×D7311yescharacteristic
1155C24C23×D7311yescharacteristic
1156C24C23×D7311yescharacteristic
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4C22×Dic7314yes—
1178C2×D4C22×Dic7314yes—
1179C2×D4C22×Dic7314yes—
1180C2×D4C22×Dic7314yes—
1181C2×D4C22×Dic7314yes—
1182C2×D4C22×Dic7314yes—
1183C2×D4C22×Dic7314yes—
1184C2×D4C22×Dic7314yes—
1185C2×D4C22×Dic7314yes—
1186C2×D4C22×Dic7314yes—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—2921no—
1198C22×C4—2921no—
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—2921no—
1219C22×C4—2921no—
1220C22×C4—2921no—
1221C22×C4—2921no—
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—731no—
1235C22×C4—731no—
1236C22×C4—731no—
1237C22×C4—731no—
1238C22×C4—1462no—
1239C22×C4—1462no—
1240C22×C4—1462no—
1241C22×C4—1462no—
1242C22×C4—1462no—
1243C22×C4C22×Dic7314yes—
1244C22×C4C22×Dic7314yes—
1245C22×C4C22×Dic7314yes—
1246C22×C4C22×Dic7314yes—
1247C22×C4C22×Dic7314yes—
1248C22×C4C23×D7311yescharacteristic
1249C22×C4C23×D7311yescharacteristic
1250C22×C4C23×D7311yescharacteristic
1251C22×C4C23×D7311yescharacteristic
1252C22×C4C23×D7311yescharacteristic
1253C22×C4C23×D7311yescharacteristic
1254C22×C4C23×D7311yescharacteristic
1255C22×C4C23×D7311yescharacteristic
1256C22×C4C23×D7311yescharacteristic
1257C22×C4C23×D7311yescharacteristic
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—2921no—
1271C4⋊C4—2921no—
1272C4⋊C4—2921no—
1273C4⋊C4—1462no—
1274C4⋊C4—1462no—
1275C4⋊C4—1462no—
1276C4⋊C4C22×Dic7314yes—
1277C4⋊C4C22×Dic7314yes—
1278C4⋊C4C22×Dic7314yes—
1279C4⋊C4C22×Dic7314yes—
1280C4⋊C4C22×Dic7314yes—
1281C4⋊C4C22×Dic7314yes—
1282C4⋊C4C22×Dic7314yes—
1283C4⋊C4C22×Dic7314yes—
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—2921no—
1307C22⋊C4—2921no—
1308C22⋊C4—2921no—
1309C22⋊C4—1462no—
1310C22⋊C4—1462no—
1311C22⋊C4—1462no—
1312C22⋊C4—1462no—
1313C22⋊C4—1462no—
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—
1324C42—2921no—
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—1462no—
1338C42—1462no—
1339C42—1462no—
1340C42—1462no—
1341C42—1462no—
1342C42C22×Dic7314yes—
1343C42C22×Dic7314yes—
1344C23—21no—
1345C23—21no—
1346C23—21no—
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—
1374C23C23×Dic7312yes—
1375C23C23×Dic7312yes—
1376C23C23×Dic7312yes—
1377C23C23×Dic7312yes—
1378C23C23×Dic7312yes—
1379C23C24×D7311yescharacteristic
1380D4—44no—
1381D4—44no—
1382D4—44no—
1383D4—44no—
1384D4—44no—
1385D4—44no—
1386D4—44no—
1387D4—44no—
1388D4—44no—
1389D4—44no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
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—44no—
1411C2×C4—44no—
1412C2×C4—44no—
1413C2×C4—44no—
1414C2×C4—44no—
1415C2×C4—2924no—
1416C2×C4—2924no—
1417C2×C4—5842no—
1418C2×C4—5842no—
1419C2×C4—5842no—
1420C2×C4—5842no—
1421C2×C4—5842no—
1422C2×C4—5842no—
1423C2×C4—5842no—
1424C2×C4—5842no—
1425C2×C4—732no—
1426C2×C4—732no—
1427C2×C4—1461no—
1428C2×C4—1461no—
1429C2×C4—1461no—
1430C2×C4—1461no—
1431C2×C4—1461no—
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×C4C23×Dic7312yes—
1474C2×C4C23×Dic7312yes—
1475C2×C4C23×Dic7312yes—
1476C2×C4C23×Dic7312yes—
1477C2×C4C23×Dic7312yes—
1478C2×C4C23×Dic7312yes—
1479C2×C4C23×Dic7312yes—
1480C2×C4C23×Dic7312yes—
1481C2×C4C23×Dic7312yes—
1482C2×C4C23×Dic7312yes—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
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—
1518C22C24×Dic7311yescharacteristic
1519C22H(5,𝔽2)×D7311yescharacteristic
1520C22H(5,𝔽2)×D7311yescharacteristic
1521C22#1798942211yescharacteristic
1522C22#1798942211yescharacteristic
1523C22#1798942311yescharacteristic
1524C22#1798942311yescharacteristic
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—22no—
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—2921no—
1536C4—2921no—
1537C4—2921no—
1538C4—2921no—
1539C4—2921no—
1540C4—2921no—
1541C4—2921no—
1542C4—2921no—
1543C4—2921no—
1544C4—2921no—
1545C4—2921no—
1546C4—2921no—
1547C4—2921no—
1548C4—2921no—
1549C4—1462no—
1550C4—1462no—
1551C2—42no—
1552C2—42no—
1553C2—42no—
1554C2—42no—
1555C2—42no—
1556C2#2262313411yescharacteristic
1557C2H(5,𝔽2)×Dic7311yescharacteristic
1558C2H(5,𝔽2)×Dic7311yescharacteristic
1559C2#2262409111yescharacteristic
1560C2#2262423811yescharacteristic
1561C2#2262435211yescharacteristic
1562C2#2262461611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
Fitting, prime radicalC2×#540×C73C2
socle, cosocleC23×C73C25
hypercenterC2×#540D73
hypocenterC73#34450
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #22613117C2semidirect
2. #22613088C2semidirect
3. #22613088C2semidirect
4. #22613079C2semidirect
5. #22613067C2semidirect
6. #22613037C2semidirect
7. #22612983C2semidirect
8. #22612983C2semidirect
9. #22612973C2semidirect
10. #22612951C2semidirect
11. #22612927C2semidirect
12. #22612927C2semidirect
13. #22612871C2semidirect
14. #22612860C2semidirect
15. #22612816C2semidirect
16. #22612791C2semidirect
17. #22612725C2semidirect
18. #22612725C2semidirect
19. #22612698C2semidirect
20. #22612698C2semidirect
21. #22612657C2semidirect
22. #22612657C2semidirect
23. #22612636C2semidirect
24. #22612636C2semidirect
25. #22612626C2semidirect
26. #22612603C2semidirect
27. #22612564C2semidirect
28. #123×Dic73C2semidirect
29. #121×Dic73C2semidirect
30. #22612376C2semidirect
172. #540×C73C4semidirect
335. #127×C73C2×C4semidirect
336. #125×C73C2×C4semidirect
337. #123×C73C2×C4semidirect
338. #123×C73C2×C4semidirect
339. #123×C73C2×C4semidirect
340. #123×C73C2×C4semidirect
341. #121×C73C2×C4semidirect
342. #121×C73C2×C4semidirect
343. #121×C73C2×C4semidirect
344. #121×C73C2×C4semidirect
345. #121×C73C2×C4semidirect
346. #121×C73C2×C4semidirect
347. C4×D4×C73C2×C4semidirect
348. C4×D4×C73C2×C4semidirect
349. #117×C73C2×C4semidirect
813. C73#34450semidirect
814. #540Dic73semidirect
995. #127C2×Dic73semidirect
996. #125C2×Dic73semidirect
997. #123C2×Dic73semidirect
998. #123C2×Dic73semidirect
999. #123C2×Dic73semidirect
1000. #123C2×Dic73semidirect
1001. #121C2×Dic73semidirect
1002. #121C2×Dic73semidirect
1003. #121C2×Dic73semidirect
1004. #121C2×Dic73semidirect
1005. #121C2×Dic73semidirect
1006. #121C2×Dic73semidirect
1015. C4×D4C2×Dic73semidirect
1016. C4×D4C2×Dic73semidirect
1019. #117C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
#226131172
#226130882
#226130792
#226130672
#226130372
#226129832
#226129732
#226129512
#226129272
#226128712
#226128602
#226128162
#226127912
#226127252
#226126982
#226126572
#226126362
#226126262
#226126032
#226125642
#123×Dic732
#121×Dic732
#226123762
C2×#540×C732
#3445073