Finite Group Databasebeta

← #33300379

Subgroups — #33300379

Order 18688.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618319C211yesmaximal, characteristic, complemented
2#22618315C211yesmaximal, characteristic, complemented
3#22617850C211yesmaximal, characteristic, complemented
4#22617828C211yesmaximal, characteristic, complemented
5#22617740C211yesmaximal, characteristic, complemented
6#22617701C211yesmaximal, characteristic, complemented
7#22617532C211yesmaximal, characteristic, complemented
8#22617457C211yesmaximal, characteristic, complemented
9#22617450C211yesmaximal, characteristic, complemented
10#22617320C211yesmaximal, characteristic, complemented
11#22617199C211yesmaximal, characteristic
12#22617171C211yesmaximal, characteristic, complemented
13#22617033C211yesmaximal, characteristic, complemented
14#22617003C211yesmaximal, characteristic, complemented
15#22616796C211yesmaximal, characteristic, complemented
16#22616641C211yesmaximal, characteristic, complemented
17#22616637C211yesmaximal, characteristic, complemented
18#22616626C211yesmaximal, characteristic
19#22615979C211yesmaximal, characteristic, complemented
20#22615934C211yesmaximal, characteristic, complemented
21#22615394C211yesmaximal, characteristic, complemented
22#22615274C211yesmaximal, characteristic, complemented
23#22615247C211yesmaximal, characteristic, complemented
24#22614099C211yesmaximal, characteristic, complemented
25#22614024C211yesmaximal, characteristic, complemented
26#22613644C211yesmaximal, characteristic, complemented
27#22613339C211yesmaximal, characteristic, complemented
28#22612725C211yesmaximal, characteristic, complemented
29#22612531C211yesmaximal, characteristic, complemented
30#22612396C211yesmaximal, characteristic, complemented
31C73×#2602C211yesmaximal, characteristic
32C2×#14556583C2211yescharacteristic
33C2×#14556581C2211yescharacteristic
34C2×#14556572C2211yescharacteristic
35C2×#14556572C2211yescharacteristic
36C2×#14556550C2211yescharacteristic
37C2×#14556550C2211yescharacteristic
38C22×#11924007C2211yescharacteristic
39#17988529C2211yescharacteristic
40#17988529C2211yescharacteristic
41#17988529C2211yescharacteristic
42#17988529C2211yescharacteristic
43#17988528C2211yescharacteristic
44#17988528C2211yescharacteristic
45#17988528C2211yescharacteristic
46#17988526C2211yescharacteristic
47#17988525C2211yescharacteristic
48#17988523C2211yescharacteristic
49#17988523C2211yescharacteristic
50#17988523C2211yescharacteristic
51#17988521C2211yescharacteristic
52#17988520C2211yescharacteristic
53#17988520C2211yescharacteristic
54#17988520C2211yescharacteristic
55#17988520C2211yescharacteristic
56#17988520C2211yescharacteristic
57#17988519C2211yescharacteristic
58#17988519C2211yescharacteristic
59#17988517C2211yescharacteristic
60#17988517C2211yescharacteristic
61#17988515C2211yescharacteristic
62#17988515C2211yescharacteristic
63#17988515C2211yescharacteristic
64#17988515C2211yescharacteristic
65#17988515C2211yescharacteristic
66#17988512C2211yescharacteristic
67#17988512C2211yescharacteristic
68#17988512C2211yescharacteristic
69#17988512C2211yescharacteristic
70#17988510C2211yescharacteristic
71#17988510C2211yescharacteristic
72#17988510C2211yescharacteristic
73#17988510C2211yescharacteristic
74#17988510C2211yescharacteristic
75#17988510C2211yescharacteristic
76#17988510C2211yescharacteristic
77#17988510C2211yescharacteristic
78#17988510C2211yescharacteristic
79#17988510C2211yescharacteristic
80#17988501C2211yescharacteristic
81#17988501C2211yescharacteristic
82#17988501C2211yescharacteristic
83#17988490C2211yescharacteristic
84#17988490C2211yescharacteristic
85#17988490C2211yescharacteristic
86#17988486C2211yescharacteristic
87#17988486C2211yescharacteristic
88#17988486C2211yescharacteristic
89#17988485C2211yescharacteristic
90#17988485C2211yescharacteristic
91#17988484C2211yescharacteristic
92#17988484C2211yescharacteristic
93#17988484C2211yescharacteristic
94#17988484C2211yescharacteristic
95#17988482C2211yescharacteristic
96#17988482C2211yescharacteristic
97#17988482C2211yescharacteristic
98#17988482C2211yescharacteristic
99#17988481C2211yescharacteristic
100#17988481C2211yescharacteristic
101#17988481C2211yescharacteristic
102#17988480C2211yescharacteristic
103#17988480C2211yescharacteristic
104#17988480C2211yescharacteristic
105#17988480C2211yescharacteristic
106#17988480C2211yescharacteristic
107#17988480C2211yescharacteristic
108#17988480C2211yescharacteristic
109#17988480C2211yescharacteristic
110#17988480C2211yescharacteristic
111#17988480C2211yescharacteristic
112#17988475C2211yescharacteristic
113#17988475C2211yescharacteristic
114#17988475C2211yescharacteristic
115#17988475C2211yescharacteristic
116#17988474C2211yescharacteristic
117#17988474C2211yescharacteristic
118#17988473C2211yescharacteristic
119#17988473C2211yescharacteristic
120#17988473C2211yescharacteristic
121#17988473C2211yescharacteristic
122#17988472C2211yescharacteristic
123#17988472C2211yescharacteristic
124#17988472C2211yescharacteristic
125#17988472C2211yescharacteristic
126#17988471C2211yescharacteristic
127#17988471C2211yescharacteristic
128#17988471C2211yescharacteristic
129#17988471C2211yescharacteristic
130#17988471C2211yescharacteristic
131#17988471C2211yescharacteristic
132#17988470C2211yescharacteristic
133#17988470C2211yescharacteristic
134#17988470C2211yescharacteristic
135#17988470C2211yescharacteristic
136#17988470C2211yescharacteristic
137#17988469C2211yescharacteristic
138#17988469C2211yescharacteristic
139#17988469C2211yescharacteristic
140#17988469C2211yescharacteristic
141#17988468C2211yescharacteristic
142#17988468C2211yescharacteristic
143#17988467C2211yescharacteristic
144#17988467C2211yescharacteristic
145#17988467C2211yescharacteristic
146#17988467C2211yescharacteristic
147#17988462C2211yescharacteristic
148#17988462C2211yescharacteristic
149#17988462C2211yescharacteristic
150#17988460C2211yescharacteristic
151#17988460C2211yescharacteristic
152#17988459C2211yescharacteristic
153#17988459C2211yescharacteristic
154#17988459C2211yescharacteristic
155#17988457C2211yescharacteristic
156#17988454C2211yescharacteristic
157#17988451C2211yescharacteristic
158#17988451C2211yescharacteristic
159#17988448C2211yescharacteristic
160#17988448C2211yescharacteristic
161#17988448C2211yescharacteristic
162#17988447C2211yescharacteristic
163#17988445C2211yescharacteristic
164#17988445C2211yescharacteristic
165#17988445C2211yescharacteristic
166C4⋊C4×Dic73C2211yescharacteristic
167C4×C4⋊Dic73C2211yescharacteristic
168C22⋊C4×Dic73C2211yescharacteristic
169C4×C22⋊Dic73C2211yescharacteristic
170C4×C22⋊Dic73C2211yescharacteristic
171C42×Dic73C2211yescharacteristic
172C2×#123×C73C2211yescharacteristic
173C2×C4×D4×C73C2211yescharacteristic
174#397×C73C2211yescharacteristic
175#394×C73C2211yescharacteristic
176#394×C73C2211yescharacteristic
177#392×C73C2211yescharacteristic
178#390×C73C2211yescharacteristic
179#389×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#387×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C23×Dic73C2311yescharacteristic
188C23×Dic73C2311yescharacteristic
189C23×Dic73C2311yescharacteristic
190#14556583—42no—
191#14556581—42no—
192#14556572—42no—
193#14556572—42no—
194#14556550—42no—
195#14556550—42no—
196C2×C4⋊Dic73C2311yescharacteristic
197C2×C4⋊Dic73C2311yescharacteristic
198C2×C4⋊Dic73C2311yescharacteristic
199C2×C4⋊Dic73C2311yescharacteristic
200C2×C4⋊Dic73C2311yescharacteristic
201C2×C4⋊Dic73C2311yescharacteristic
202C2×C4⋊Dic73C2311yescharacteristic
203C2×C4⋊Dic73C2311yescharacteristic
204C2×C4⋊Dic73C2311yescharacteristic
205C2×C4⋊Dic73C2311yescharacteristic
206C2×C4⋊Dic73C2311yescharacteristic
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×C4⋊Dic73C2311yescharacteristic
210C2×C4⋊Dic73C2311yescharacteristic
211C2×#11924007—24no—
212C2×#11924007C2311yescharacteristic
213C2×#11924007C2311yescharacteristic
214C2×#11924007C2311yescharacteristic
215C2×#11924007C2311yescharacteristic
216C2×#11924007C2311yescharacteristic
217C2×#11924007C2311yescharacteristic
218C2×#11924007C2311yescharacteristic
219C2×#11924007C2311yescharacteristic
220C2×#11924007C2311yescharacteristic
221C2×#11924007C2311yescharacteristic
222C2×#11924007C2311yescharacteristic
223C2×#11924007C2311yescharacteristic
224C2×#11924007C2311yescharacteristic
225C2×#11924007C2311yescharacteristic
226C2×#11924007C2311yescharacteristic
227C2×#11924007C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
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×Dic73C2311yescharacteristic
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
268#14556498C2311yescharacteristic
269#14556498C2311yescharacteristic
270#14556498C2311yescharacteristic
271#14556498C2311yescharacteristic
272#14556498C2311yescharacteristic
273#14556498C2311yescharacteristic
274#14556498C2311yescharacteristic
275#14556498C2311yescharacteristic
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
314C22×D4×C73C2311yescharacteristic
315C22×D4×C73C2311yescharacteristic
316C22×D4×C73C2311yescharacteristic
317C23×C4×C73C2311yescharacteristic
318C23×C4×C73C2311yescharacteristic
319#123×C73—24no—
320C4×D4×C73—24no—
321C2×C4⋊C4×C73C2311yescharacteristic
322C2×C4⋊C4×C73C2311yescharacteristic
323C2×C4⋊C4×C73C2311yescharacteristic
324C2×C4⋊C4×C73C2311yescharacteristic
325C2×C4⋊C4×C73C2311yescharacteristic
326C2×C4⋊C4×C73C2311yescharacteristic
327C2×C22⋊C4×C73C2311yescharacteristic
328C2×C22⋊C4×C73C2311yescharacteristic
329C2×C22⋊C4×C73C2311yescharacteristic
330C2×C22⋊C4×C73C2311yescharacteristic
331C2×C22⋊C4×C73C2311yescharacteristic
332C2×C22⋊C4×C73C2311yescharacteristic
333C2×C22⋊C4×C73C2311yescharacteristic
334C2×C22⋊C4×C73C2311yescharacteristic
335C2×C22⋊C4×C73C2311yescharacteristic
336C2×C22⋊C4×C73C2311yescharacteristic
337C2×C22⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C42×C73C2311yescharacteristic
341C2×C42×C73C2311yescharacteristic
342C2×C42×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351C22×Dic73—22no—
352C22×Dic73—22no—
353C22×Dic73—41no—
354C22×Dic73—41no—
355C22×Dic73—41no—
356C22×Dic73—41no—
357C22×Dic73—41no—
358C22×Dic73—41no—
359C22×Dic73—41no—
360C22×Dic73C2411yescharacteristic
361C22×Dic73C2411yescharacteristic
362C22×Dic73C2411yescharacteristic
363C22×Dic73C2411yescharacteristic
364C22×Dic73C2411yescharacteristic
365C22×Dic73C2411yescharacteristic
366C22×Dic73C2411yescharacteristic
367C22×Dic73C2411yescharacteristic
368C22×Dic73C2411yescharacteristic
369C22×Dic73C2411yescharacteristic
370C22×Dic73C2411yescharacteristic
371C22×Dic73C2411yescharacteristic
372C22×Dic73C2411yescharacteristic
373C22×Dic73C2411yescharacteristic
374C22×Dic73C2411yescharacteristic
375C22×Dic73C2411yescharacteristic
376C4⋊Dic73—22no—
377C4⋊Dic73—22no—
378C4⋊Dic73—22no—
379C4⋊Dic73—41no—
380C4⋊Dic73—41no—
381C4⋊Dic73—41no—
382C4⋊Dic73—41no—
383C4⋊Dic73—41no—
384C4⋊Dic73—41no—
385C4⋊Dic73—41no—
386C4⋊Dic73—41no—
387C4⋊Dic73—41no—
388C4⋊Dic73—41no—
389C4⋊Dic73—41no—
390C4⋊Dic73—41no—
391#11924007—22no—
392#11924007—22no—
393#11924007—22no—
394#11924007—22no—
395#11924007—22no—
396#11924007—22no—
397#11924007—22no—
398#11924007—41no—
399#11924007—41no—
400#11924007—41no—
401#11924007—41no—
402#11924007—41no—
403#11924007—41no—
404#11924007—41no—
405#11924007—41no—
406#11924007—41no—
407#11924007—41no—
408#11924007—41no—
409#11924007—41no—
410#11924007—41no—
411#11924007—41no—
412#11924007—41no—
413#11924007—41no—
414#11924007—41no—
415C22⋊Dic73—22no—
416C22⋊Dic73—22no—
417C22⋊Dic73—22no—
418C22⋊Dic73—41no—
419C22⋊Dic73—41no—
420C22⋊Dic73—41no—
421C22⋊Dic73—41no—
422C22⋊Dic73—41no—
423C22⋊Dic73—41no—
424C22⋊Dic73—41no—
425C22⋊Dic73—41no—
426C22⋊Dic73—41no—
427C22⋊Dic73—41no—
428C22⋊Dic73—41no—
429C22⋊Dic73—41no—
430C22⋊Dic73—41no—
431C22⋊Dic73—41no—
432C22⋊Dic73—41no—
433C22⋊Dic73—41no—
434C22⋊Dic73—41no—
435C22⋊Dic73—41no—
436C4×Dic73—22no—
437C4×Dic73—22no—
438C4×Dic73—41no—
439C4×Dic73—41no—
440C4×Dic73—41no—
441C4×Dic73—41no—
442C4×Dic73—41no—
443C4×Dic73—41no—
444C4×Dic73—41no—
445C4×Dic73—41no—
446C4×Dic73—41no—
447C24×C73C2411yescharacteristic
448C24×C73C2411yescharacteristic
449C24×C73C2411yescharacteristic
450C2×D4×C73—22no—
451C2×D4×C73—22no—
452C2×D4×C73—22no—
453C2×D4×C73—41no—
454C2×D4×C73—41no—
455C2×D4×C73—41no—
456C2×D4×C73—41no—
457C2×D4×C73—41no—
458C2×D4×C73—41no—
459C22×C4×C73—22no—
460C22×C4×C73—41no—
461C22×C4×C73—41no—
462C22×C4×C73—41no—
463C22×C4×C73—41no—
464C22×C4×C73#4114yes—
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C4⋊C4×C73—22no—
478C4⋊C4×C73—22no—
479C4⋊C4×C73—22no—
480C4⋊C4×C73—22no—
481C4⋊C4×C73—41no—
482C4⋊C4×C73—41no—
483C22⋊C4×C73—22no—
484C22⋊C4×C73—22no—
485C22⋊C4×C73—22no—
486C22⋊C4×C73—22no—
487C22⋊C4×C73—22no—
488C22⋊C4×C73—22no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C42×C73—22no—
497C42×C73—41no—
498C42×C73—41no—
499C23×C73—21no—
500C23×C73—21no—
501C23×C73—21no—
502C23×C73—21no—
503C23×C73—21no—
504C23×C73—21no—
505C23×C73—21no—
506C23×C73—21no—
507C23×C73—21no—
508C23×C73—21no—
509C23×C73—21no—
510C23×C73—21no—
511C23×C73—21no—
512C23×C73—21no—
513C23×C73—21no—
514C23×C73—21no—
515C23×C73—21no—
516C23×C73—21no—
517C23×C73—21no—
518C23×C73—21no—
519C23×C73C2×#4112yes—
520C23×C73C2511yescharacteristic
521D4×C73—44no—
522D4×C73—82no—
523D4×C73—82no—
524C2×C4×C73—21no—
525C2×C4×C73—21no—
526C2×C4×C73—21no—
527C2×C4×C73—21no—
528C2×C4×C73—21no—
529C2×C4×C73—21no—
530C2×C4×C73—21no—
531C2×C4×C73—21no—
532C2×C4×C73—21no—
533C2×C4×C73—21no—
534C2×C4×C73—21no—
535C2×C4×C73—21no—
536C2×C4×C73—21no—
537C2×C4×C73—21no—
538C2×C4×C73—21no—
539C2×C4×C73—21no—
540C2×C4×C73—21no—
541C2×C4×C73—21no—
542C2×C4×C73—21no—
543C2×C4×C73—21no—
544C2×C4×C73—21no—
545C2×C4×C73—21no—
546C2×C4×C73—21no—
547C2×C4×C73—21no—
548C2×C4×C73—21no—
549C2×C4×C73—21no—
550C2×C4×C73—21no—
551C2×C4×C73—21no—
552C2×C4×C73—21no—
553C2×C4×C73—21no—
554C2×C4×C73—21no—
555C2×C4×C73—21no—
556C2×C4×C73—21no—
557C2×C4×C73—44no—
558C2×C4×C73—44no—
559C2×C4×C73C2×#4112yes—
560C2×C4×C73C2×#4112yes—
561C2×C4×C732−1+412yes—
562C2×Dic73—21no—
563C2×Dic73—21no—
564C2×Dic73—21no—
565C2×Dic73—21no—
566C2×Dic73—21no—
567C2×Dic73—21no—
568C2×Dic73—21no—
569C2×Dic73—21no—
570C2×Dic73—21no—
571C2×Dic73—21no—
572C2×Dic73—21no—
573C2×Dic73—21no—
574C2×Dic73—21no—
575C2×Dic73—21no—
576C2×Dic73—21no—
577C2×Dic73—21no—
578C2×Dic73—21no—
579C2×Dic73—21no—
580C2×Dic73—21no—
581C2×Dic73—21no—
582C2×Dic73—21no—
583C2×Dic73—21no—
584C2×Dic73—21no—
585C2×Dic73—21no—
586C2×Dic73—21no—
587C2×Dic73—21no—
588C2×Dic73—21no—
589C2×Dic73—21no—
590C2×Dic73—21no—
591C2×Dic73—21no—
592C2×Dic73—21no—
593C2×Dic73—21no—
594C2×Dic73—21no—
595C2×Dic73—21no—
596C2×Dic73—21no—
597C2×Dic73—21no—
598C2×Dic73—21no—
599C2×Dic73—21no—
600C2×Dic73—21no—
601C2×Dic73—21no—
602C2×Dic73—21no—
603C2×Dic73—21no—
604C2×Dic73—21no—
605C2×Dic73—21no—
606C2×Dic73—21no—
607C2×Dic73—21no—
608C2×Dic73—21no—
609C2×Dic73—44no—
610C2×Dic73—82no—
611C2×Dic73—82no—
612C2×Dic73H(5,𝔽2)12yes—
613C22×C73—22no—
614C22×C73—22no—
615C22×C73—22no—
616C22×C73—41no—
617C22×C73—41no—
618C22×C73—41no—
619C22×C73—41no—
620C22×C73—41no—
621C22×C73—41no—
622C22×C73—41no—
623C22×C73—41no—
624C22×C73—41no—
625C22×C73—41no—
626C22×C73—41no—
627C22×C73—41no—
628C22×C73—41no—
629C22×C73—41no—
630C22×C73—41no—
631C22×C73—41no—
632C22×C73—41no—
633C22×C73—41no—
634C22×C73C22×#4111yescharacteristic
635C22×C73C2×H(5,𝔽2)11yescharacteristic
636C22×C73C2×2−1+411yescharacteristic
637C22×C73#58511yescharacteristic
638C22×C73#58511yescharacteristic
639C22×C73#58511yescharacteristic
640C22×C73#58511yescharacteristic
641C4×C73—22no—
642C4×C73—22no—
643C4×C73—22no—
644C4×C73—41no—
645C4×C73—41no—
646C4×C73—41no—
647C4×C73—41no—
648C4×C73—41no—
649C4×C73—41no—
650C4×C73—41no—
651C4×C73—41no—
652C4×C73—41no—
653Dic73—22no—
654Dic73—41no—
655Dic73—41no—
656Dic73—41no—
657Dic73—41no—
658Dic73—41no—
659Dic73—41no—
660Dic73—41no—
661Dic73—41no—
662Dic73—41no—
663Dic73—41no—
664Dic73—41no—
665Dic73—41no—
666Dic73—41no—
667Dic73—41no—
668Dic73—41no—
669#36994—731nomaximal, Sylow
670C2×C73—42no—
671C2×C73—81no—
672C2×C73—81no—
673C2×C73#345511yescharacteristic
674C2×C73#349511yescharacteristic
675C2×C73#350511yescharacteristic
676C2×C73#355711yescharacteristic
677C2×C73#355911yescharacteristic
678C2×C73#356211yescharacteristic
679C2×C73#356711yescharacteristic
680#2865—731no—
681#2864—731no—
682#2802—731no—
683#2800—731no—
684#2793—731no—
685#2790—731no—
686#2777—731no—
687#2772—731no—
688#2771—731no—
689#2761—731no—
690#2752—731no—
691#2750—731no—
692#2740—731no—
693#2738—731no—
694#2719—731no—
695#2707—731no—
696#2707—731no—
697#2706—731no—
698#2652—731no—
699#2649—731no—
700#2602D7311yescharacteristic
701#2590—731no—
702#2579—731no—
703#2577—731no—
704#2475—731no—
705#2470—731no—
706#2441—731no—
707#2413—731no—
708#2335—731no—
709#2313—731no—
710#2293—731no—
711C73#3699411yescharacteristic, complemented, Sylow
712C2×#125—731no—
713C2×#125—731no—
714C2×#123—731no—
715C2×#123—731no—
716C2×#123C2×D7311yescharacteristic
717C2×C4×D4C2×D7311yescharacteristic
718C2×#117—731no—
719C2×#117—731no—
720C22×C4⋊C4—731no—
721#400—731no—
722#400—731no—
723#400—731no—
724#400—731no—
725#400—731no—
726#400—731no—
727#400—731no—
728#400—731no—
729#400—731no—
730#399—731no—
731#399—731no—
732#399—731no—
733#398—731no—
734#398—731no—
735#398—731no—
736#398—731no—
737#398—731no—
738#398—731no—
739#398—731no—
740#398—731no—
741#398—731no—
742#398—731no—
743#397—731no—
744#397—731no—
745#397—731no—
746#397—731no—
747#397—731no—
748#397—731no—
749#397—731no—
750#397—731no—
751#397—731no—
752#397C2×D7311yescharacteristic
753#396—731no—
754#396—731no—
755#396—731no—
756#396—731no—
757#396—731no—
758#396—731no—
759#396—731no—
760#396—731no—
761#396—731no—
762#396—731no—
763#394—731no—
764#394—731no—
765#394—731no—
766#394C2×D7311yescharacteristic
767#394C2×D7311yescharacteristic
768#392C2×D7311yescharacteristic
769#390—731no—
770#390—731no—
771#390—731no—
772#390C2×D7311yescharacteristic
773#389—731no—
774#389—731no—
775#389—731no—
776#389—731no—
777#389—731no—
778#389—731no—
779#389—731no—
780#389—731no—
781#389—731no—
782#389—731no—
783#389—731no—
784#389—731no—
785#389—731no—
786#389C2×D7311yescharacteristic
787#388—731no—
788#388—731no—
789#388—731no—
790#388—731no—
791#388—731no—
792#388—731no—
793#388—731no—
794#388—731no—
795#388—731no—
796#388—731no—
797#388—731no—
798#388—731no—
799#388—731no—
800#388—731no—
801#388—731no—
802#388—731no—
803#388—731no—
804#388C2×D7311yescharacteristic
805#388C2×D7311yescharacteristic
806#388C2×D7311yescharacteristic
807#387—731no—
808#387—731no—
809#387—731no—
810#387—731no—
811#387—731no—
812#387—731no—
813#387—731no—
814#387—731no—
815#387—731no—
816#387—731no—
817#387—731no—
818#387—731no—
819#387—731no—
820#387—731no—
821#387—731no—
822#387—731no—
823#387—731no—
824#387—731no—
825#387—731no—
826#387—731no—
827#387—731no—
828#387—731no—
829#387—731no—
830#387—731no—
831#387—731no—
832#387—731no—
833#387—731no—
834#387C2×D7311yescharacteristic
835#386—731no—
836#386—731no—
837#386—731no—
838#386—731no—
839#386C2×D7311yescharacteristic
840#385—731no—
841#385—731no—
842#385—731no—
843#385—731no—
844#385—731no—
845#385—731no—
846#385—731no—
847#385—731no—
848#385C2×D7311yescharacteristic
849#384—731no—
850#383—731no—
851#382—731no—
852#382—731no—
853#381—731no—
854#381—731no—
855#381—731no—
856#380—731no—
857#380—731no—
858#380—731no—
859#380—731no—
860C4×C4⋊C4—731no—
861C4×C4⋊C4—731no—
862C4×C22⋊C4—731no—
863C4×C22⋊C4—731no—
864C4×C22⋊C4—731no—
865C4×C22⋊C4C2×D7311yescharacteristic
866C43—731no—
867C22×D4C22×D7311yescharacteristic
868C22×D4C22×D7311yescharacteristic
869C22×D4C22×D7311yescharacteristic
870C23×C4—731no—
871C23×C4—731no—
872C23×C4—731no—
873C23×C4C22×D7311yescharacteristic
874C23×C4C22×D7311yescharacteristic
875#125—2922no—
876#125—2922no—
877#123—24no—
878#123—2922no—
879#123—2922no—
880C4×D4—24no—
881#117—2922no—
882#117—2922no—
883C2×C4⋊C4—731no—
884C2×C4⋊C4—731no—
885C2×C4⋊C4—731no—
886C2×C4⋊C4—731no—
887C2×C4⋊C4—731no—
888C2×C4⋊C4—731no—
889C2×C4⋊C4—731no—
890C2×C4⋊C4—731no—
891C2×C4⋊C4—731no—
892C2×C4⋊C4—731no—
893C2×C4⋊C4—731no—
894C2×C4⋊C4—731no—
895C2×C4⋊C4—731no—
896C2×C4⋊C4—731no—
897C2×C4⋊C4—731no—
898C2×C4⋊C4—731no—
899C2×C4⋊C4—731no—
900C2×C4⋊C4—731no—
901C2×C4⋊C4—731no—
902C2×C4⋊C4—731no—
903C2×C4⋊C4—731no—
904C2×C4⋊C4—731no—
905C2×C4⋊C4—731no—
906C2×C4⋊C4—731no—
907C2×C4⋊C4—731no—
908C2×C4⋊C4—731no—
909C2×C4⋊C4—731no—
910C2×C4⋊C4—731no—
911C2×C4⋊C4—731no—
912C2×C4⋊C4—731no—
913C2×C4⋊C4—731no—
914C2×C4⋊C4—731no—
915C2×C4⋊C4—731no—
916C2×C4⋊C4—731no—
917C2×C4⋊C4—731no—
918C2×C4⋊C4—731no—
919C2×C4⋊C4—731no—
920C2×C4⋊C4—731no—
921C2×C4⋊C4—731no—
922C2×C4⋊C4—1464no—
923C2×C4⋊C4C22×D7311yescharacteristic
924C2×C4⋊C4C22×D7311yescharacteristic
925C2×C4⋊C4C22×D7311yescharacteristic
926C2×C4⋊C4C22×D7311yescharacteristic
927C2×C4⋊C4C22×D7311yescharacteristic
928C2×C4⋊C4C22×D7311yescharacteristic
929C2×C22⋊C4—731no—
930C2×C22⋊C4—731no—
931C2×C22⋊C4—731no—
932C2×C22⋊C4—731no—
933C2×C22⋊C4—731no—
934C2×C22⋊C4—731no—
935C2×C22⋊C4—731no—
936C2×C22⋊C4—731no—
937C2×C22⋊C4—731no—
938C2×C22⋊C4—731no—
939C2×C22⋊C4—731no—
940C2×C22⋊C4—731no—
941C2×C22⋊C4—731no—
942C2×C22⋊C4—731no—
943C2×C22⋊C4—731no—
944C2×C22⋊C4—731no—
945C2×C22⋊C4—731no—
946C2×C22⋊C4—731no—
947C2×C22⋊C4—731no—
948C2×C22⋊C4—731no—
949C2×C22⋊C4—731no—
950C2×C22⋊C4C22×D7311yescharacteristic
951C2×C22⋊C4C22×D7311yescharacteristic
952C2×C22⋊C4C22×D7311yescharacteristic
953C2×C22⋊C4C22×D7311yescharacteristic
954C2×C22⋊C4C22×D7311yescharacteristic
955C2×C22⋊C4C22×D7311yescharacteristic
956C2×C22⋊C4C22×D7311yescharacteristic
957C2×C22⋊C4C22×D7311yescharacteristic
958C2×C22⋊C4C22×D7311yescharacteristic
959C2×C22⋊C4C22×D7311yescharacteristic
960C2×C22⋊C4C22×D7311yescharacteristic
961C2×C22⋊C4C22×D7311yescharacteristic
962C2×C22⋊C4C22×D7311yescharacteristic
963C2×C42—731no—
964C2×C42—731no—
965C2×C42—731no—
966C2×C42—731no—
967C2×C42—731no—
968C2×C42—731no—
969C2×C42—731no—
970C2×C42—731no—
971C2×C42—731no—
972C2×C42—731no—
973C2×C42—731no—
974C2×C42C22×D7311yescharacteristic
975C2×C42C22×D7311yescharacteristic
976C2×C42C22×D7311yescharacteristic
977#95—731no—
978#95—731no—
979#95—731no—
980#95—731no—
981#95—731no—
982#95—731no—
983#95—731no—
984#95—731no—
985#95—731no—
986#95—731no—
987#95—731no—
988#95—731no—
989#95—731no—
990#95—731no—
991#95—731no—
992#95—731no—
993#95—731no—
994#95—731no—
995#95—731no—
996#95—731no—
997#95—731no—
998#95—731no—
999#95—731no—
1000#95—731no—
1001#95—731no—
1002#95—731no—
1003#95—731no—
1004#95—731no—
1005#95—731no—
1006#95—731no—
1007#95—731no—
1008#95—731no—
1009#95—731no—
1010#95—731no—
1011#95—731no—
1012#95—731no—
1013#95—731no—
1014#95—731no—
1015#95—731no—
1016#95—731no—
1017#95—731no—
1018#95—731no—
1019#95—731no—
1020#95—731no—
1021#95—731no—
1022#95—731no—
1023#95C22×D7311yescharacteristic
1024#95C22×D7311yescharacteristic
1025#95C22×D7311yescharacteristic
1026#95C22×D7311yescharacteristic
1027#95C22×D7311yescharacteristic
1028#95C22×D7311yescharacteristic
1029#95C22×D7311yescharacteristic
1030#95C22×D7311yescharacteristic
1031C24C23×D7311yescharacteristic
1032C24C23×D7311yescharacteristic
1033C24C23×D7311yescharacteristic
1034C2×D4—22no—
1035C2×D4—22no—
1036C2×D4—22no—
1037C2×D4—41no—
1038C2×D4—41no—
1039C2×D4—41no—
1040C2×D4—41no—
1041C2×D4—41no—
1042C2×D4—41no—
1043C22×C4—22no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—2921no—
1049C22×C4—2921no—
1050C22×C4—2921no—
1051C22×C4—2921no—
1052C22×C4—2921no—
1053C22×C4—2921no—
1054C22×C4—2921no—
1055C22×C4—731no—
1056C22×C4—731no—
1057C22×C4—731no—
1058C22×C4—731no—
1059C22×C4—731no—
1060C22×C4—731no—
1061C22×C4—731no—
1062C22×C4—731no—
1063C22×C4—731no—
1064C22×C4—731no—
1065C22×C4—731no—
1066C22×C4—731no—
1067C22×C4—731no—
1068C22×C4—731no—
1069C22×C4—731no—
1070C22×C4—731no—
1071C22×C4—1462no—
1072C22×C4—1462no—
1073C22×C4#1192402714yes—
1074C22×C4C23×D7311yescharacteristic
1075C22×C4C23×D7311yescharacteristic
1076C22×C4C23×D7311yescharacteristic
1077C22×C4C23×D7311yescharacteristic
1078C22×C4C23×D7311yescharacteristic
1079C22×C4C23×D7311yescharacteristic
1080C22×C4C23×D7311yescharacteristic
1081C22×C4C23×D7311yescharacteristic
1082C22×C4C23×D7311yescharacteristic
1083C22×C4C23×D7311yescharacteristic
1084C22×C4C23×D7311yescharacteristic
1085C22×C4C23×D7311yescharacteristic
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—2921no—
1093C4⋊C4—2921no—
1094C4⋊C4—2921no—
1095C4⋊C4—2921no—
1096C4⋊C4—2921no—
1097C4⋊C4—2921no—
1098C4⋊C4—2921no—
1099C4⋊C4—2921no—
1100C4⋊C4—2921no—
1101C4⋊C4—2921no—
1102C4⋊C4—2921no—
1103C4⋊C4—2921no—
1104C4⋊C4—2921no—
1105C4⋊C4—2921no—
1106C4⋊C4—2921no—
1107C4⋊C4—2921no—
1108C4⋊C4—2921no—
1109C4⋊C4—2921no—
1110C4⋊C4—2921no—
1111C4⋊C4—2921no—
1112C4⋊C4—2921no—
1113C4⋊C4—2921no—
1114C4⋊C4—2921no—
1115C4⋊C4—2921no—
1116C4⋊C4—2921no—
1117C4⋊C4—2921no—
1118C4⋊C4—2921no—
1119C4⋊C4—2921no—
1120C4⋊C4—2921no—
1121C4⋊C4—1462no—
1122C4⋊C4—1462no—
1123C4⋊C4—1462no—
1124C4⋊C4—1462no—
1125C4⋊C4—1462no—
1126C4⋊C4—1462no—
1127C4⋊C4—1462no—
1128C4⋊C4—1462no—
1129C4⋊C4—1462no—
1130C4⋊C4—1462no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—22no—
1136C22⋊C4—22no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—2921no—
1145C22⋊C4—2921no—
1146C22⋊C4—2921no—
1147C22⋊C4—2921no—
1148C22⋊C4—2921no—
1149C22⋊C4—2921no—
1150C22⋊C4—2921no—
1151C22⋊C4—2921no—
1152C22⋊C4—2921no—
1153C22⋊C4—2921no—
1154C22⋊C4—2921no—
1155C22⋊C4—2921no—
1156C22⋊C4—2921no—
1157C22⋊C4—2921no—
1158C22⋊C4—2921no—
1159C22⋊C4—2921no—
1160C22⋊C4—2921no—
1161C22⋊C4—2921no—
1162C22⋊C4—1462no—
1163C22⋊C4—1462no—
1164C22⋊C4—1462no—
1165C42—22no—
1166C42—41no—
1167C42—41no—
1168C42—2921no—
1169C42—2921no—
1170C42—2921no—
1171C42—2921no—
1172C42—2921no—
1173C42—2921no—
1174C42—2921no—
1175C42—2921no—
1176C42—2921no—
1177C42—1462no—
1178C42—1462no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23C2×#1192402712yes—
1200C23C24×D7311yescharacteristic
1201D4—44no—
1202D4—82no—
1203D4—82no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—2924no—
1240C2×C4—5842no—
1241C2×C4—5842no—
1242C2×C4—732no—
1243C2×C4—1461no—
1244C2×C4—1461no—
1245C2×C4—1461no—
1246C2×C4—1461no—
1247C2×C4—1461no—
1248C2×C4—1461no—
1249C2×C4—1461no—
1250C2×C4—1461no—
1251C2×C4—1461no—
1252C2×C4—1461no—
1253C2×C4—1461no—
1254C2×C4—1461no—
1255C2×C4—1461no—
1256C2×C4—1461no—
1257C2×C4—1461no—
1258C2×C4—1461no—
1259C2×C4—1461no—
1260C2×C4—1461no—
1261C2×C4—1461no—
1262C2×C4—1461no—
1263C2×C4—1461no—
1264C2×C4—1461no—
1265C2×C4—1461no—
1266C2×C4—1461no—
1267C2×C4—1461no—
1268C2×C4—1461no—
1269C2×C4—1461no—
1270C2×C4—1461no—
1271C2×C4—1461no—
1272C2×C4—1461no—
1273C2×C4—1461no—
1274C2×C4—1461no—
1275C2×C4—1461no—
1276C2×C4—1461no—
1277C2×C4—1461no—
1278C2×C4—1461no—
1279C2×C4—1461no—
1280C2×C4—1461no—
1281C2×C4—1461no—
1282C2×C4—1461no—
1283C2×C4—1461no—
1284C2×C4—1461no—
1285C2×C4—1461no—
1286C2×C4—1461no—
1287C2×C4—1461no—
1288C2×C4—1461no—
1289C2×C4—1461no—
1290C2×C4C2×#1192402712yes—
1291C2×C4C2×#1192402712yes—
1292C2×C4#1455663812yes—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22C22×#1192402711yescharacteristic
1315C22H(5,𝔽2)×D7311yescharacteristic
1316C22C2×#1455663811yescharacteristic
1317C22#1798942211yescharacteristic
1318C22#1798942311yescharacteristic
1319C22#1798942311yescharacteristic
1320C22#1798942311yescharacteristic
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—2921no—
1334C4—2921no—
1335C4—2921no—
1336C4—2921no—
1337C4—2921no—
1338C4—2921no—
1339C4—2921no—
1340C4—2921no—
1341C4—2921no—
1342C4—2921no—
1343C4—2921no—
1344C4—2921no—
1345C4—2921no—
1346C4—2921no—
1347C4—2921no—
1348C4—1462no—
1349C2—42no—
1350C2—81no—
1351C2—81no—
1352C2#2262332011yescharacteristic
1353C2#2262368511yescharacteristic
1354C2#2262376811yescharacteristic
1355C2#2262442811yescharacteristic
1356C2#2262445511yescharacteristic
1357C2#2262451211yescharacteristic
1358C2#2262461511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2602C2
prime radical#392×C73C22
hypercenter#2602D73
hypocenterC73#36994
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2602

Complements

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

NH ≅ G/Ntype
1. #22618319C2semidirect
2. #22618315C2semidirect
3. #22617850C2semidirect
4. #22617828C2semidirect
5. #22617740C2semidirect
6. #22617701C2semidirect
7. #22617532C2semidirect
8. #22617457C2semidirect
9. #22617450C2semidirect
10. #22617320C2semidirect
12. #22617171C2semidirect
13. #22617033C2semidirect
14. #22617003C2semidirect
15. #22616796C2semidirect
16. #22616641C2semidirect
17. #22616637C2semidirect
19. #22615979C2semidirect
20. #22615934C2semidirect
21. #22615394C2semidirect
22. #22615274C2semidirect
23. #22615247C2semidirect
24. #22614099C2semidirect
25. #22614024C2semidirect
26. #22613644C2semidirect
27. #22613339C2semidirect
28. #22612725C2semidirect
29. #22612531C2semidirect
30. #22612396C2semidirect
711. C73#36994semidirect

Maximal subgroups

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

subgroupindex
#226183192
#226183152
#226178502
#226178282
#226177402
#226177012
#226175322
#226174572
#226174502
#226173202
#226171992
#226171712
#226170332
#226170032
#226167962
#226166412
#226166372
#226166262
#226159792
#226159342
#226153942
#226152742
#226152472
#226140992
#226140242
#226136442
#226133392
#226127252
#226125312
#226123962
C73×#26022
#3699473