Finite Group Databasebeta

← #11232943

Subgroups — #11232943

Order 768.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2738C211yesmaximal, characteristic, complemented
2#78376C211yesmaximal, characteristic, complemented
3#78253C211yesmaximal, characteristic, complemented
4#78182C211yesmaximal, characteristic, complemented
5#78181C211yesmaximal, characteristic, complemented
6#78079C211yesmaximal, characteristic, complemented
7#78022C211yesmaximal, characteristic
8#77988C211yesmaximal, characteristic, complemented
9#77793C211yesmaximal, characteristic, complemented
10#77783C211yesmaximal, characteristic, complemented
11#77741C211yesmaximal, characteristic, complemented
12#77606C211yesmaximal, characteristic, complemented
13#77495C211yesmaximal, characteristic
14#76056C211yesmaximal, characteristic, complemented
15#75982C211yesmaximal, characteristic, complemented
16#75590C211yesmaximal, characteristic, complemented
17#75588C211yesmaximal, characteristic, complemented
18#75554C211yesmaximal, characteristic
19#75501C211yesmaximal, characteristic
20#75183C211yesmaximal, characteristic, complemented
21#75066C211yesmaximal, characteristic, complemented
22#74964C211yesmaximal, characteristic, complemented
23#74950C211yesmaximal, characteristic, complemented
24#74471C211yesmaximal, characteristic, complemented
25#74386C211yesmaximal, characteristic
26#74273C211yesmaximal, characteristic, complemented
27#74264C211yesmaximal, characteristic, complemented
28#74101C211yesmaximal, characteristic, complemented
29#74061C211yesmaximal, characteristic
30#73942C211yesmaximal, characteristic
31#73931C211yesmaximal, characteristic, complemented
32#45318—31nomaximal, Sylow
33C2×C4×#67C2211yescharacteristic
34C2×#888C2211yescharacteristic
35C2×#887C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#885C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C3×#400C2211yescharacteristic
40C3×#400C2211yescharacteristic
41C3×#399C2211yescharacteristic
42C3×#398C2211yescharacteristic
43C3×#398C2211yescharacteristic
44C3×#397C2211yescharacteristic
45C3×#389C2211yescharacteristic
46C3×#388C2211yescharacteristic
47C3×#388C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#385C2211yescharacteristic
51C3×#383C2211yescharacteristic
52C3×#381C2211yescharacteristic
53C3×#380C2211yescharacteristic
54#5212C2211yescharacteristic
55#5210C2211yescharacteristic
56C4×#217C2211yescharacteristic
57#4993C2211yescharacteristic
58#4992C2211yescharacteristic
59#4992C2211yescharacteristic
60#4992C2211yescharacteristic
61#4990C2211yescharacteristic
62#4990C2211yescharacteristic
63#4990C2211yescharacteristic
64#4989C2211yescharacteristic
65#4987C2211yescharacteristic
66#4987C2211yescharacteristic
67#4986C2211yescharacteristic
68#4986C2211yescharacteristic
69#4986C2211yescharacteristic
70#4985C2211yescharacteristic
71#4985C2211yescharacteristic
72#4984C2211yescharacteristic
73#4982C2211yescharacteristic
74#4982C2211yescharacteristic
75#4981C2211yescharacteristic
76#4980C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4978C2211yescharacteristic
81#4978C2211yescharacteristic
82#4978C2211yescharacteristic
83#4977C2211yescharacteristic
84#4976C2211yescharacteristic
85#4976C2211yescharacteristic
86#4976C2211yescharacteristic
87#4975C2211yescharacteristic
88Dic3×C4⋊C4C2211yescharacteristic
89Dic3×C4⋊C4C2211yescharacteristic
90Dic3×C4⋊C4C2211yescharacteristic
91Dic3×C4⋊C4C2211yescharacteristic
92Dic3×C4⋊C4C2211yescharacteristic
93#4973C2211yescharacteristic
94#4957C2211yescharacteristic
95#4957C2211yescharacteristic
96#4957C2211yescharacteristic
97#4957C2211yescharacteristic
98#4957C2211yescharacteristic
99#4953C2211yescharacteristic
100#4953C2211yescharacteristic
101#4952C2211yescharacteristic
102#4952C2211yescharacteristic
103#4952C2211yescharacteristic
104#4951C2211yescharacteristic
105#4951C2211yescharacteristic
106#4951C2211yescharacteristic
107#4951C2211yescharacteristic
108#4949C2211yescharacteristic
109#4947C2211yescharacteristic
110#4947C2211yescharacteristic
111#4945C2211yescharacteristic
112#4945C2211yescharacteristic
113#4945C2211yescharacteristic
114#4944C2211yescharacteristic
115#4944C2211yescharacteristic
116#4944C2211yescharacteristic
117#4940C2211yescharacteristic
118#4940C2211yescharacteristic
119#4932C2211yescharacteristic
120#4932C2211yescharacteristic
121C4×Dic3⋊C4C2211yescharacteristic
122C4×Dic3⋊C4C2211yescharacteristic
123#4929C2211yescharacteristic
124#4677C2211yescharacteristic
125#4675C2211yescharacteristic
126#4675C2211yescharacteristic
127#4675C2211yescharacteristic
128#4673C2211yescharacteristic
129#4673C2211yescharacteristic
130#4670C2211yescharacteristic
131#4670C2211yescharacteristic
132#4670C2211yescharacteristic
133#4669C2211yescharacteristic
134#4669C2211yescharacteristic
135#4669C2211yescharacteristic
136#4669C2211yescharacteristic
137#4668C2211yescharacteristic
138#4666C2211yescharacteristic
139#4664C2211yescharacteristic
140#4661C2211yescharacteristic
141#4661C2211yescharacteristic
142#4660C2211yescharacteristic
143#4660C2211yescharacteristic
144#4660C2211yescharacteristic
145#4659C2211yescharacteristic
146#4659C2211yescharacteristic
147#4657C2211yescharacteristic
148#4655C2211yescharacteristic
149#4654C2211yescharacteristic
150#4654C2211yescharacteristic
151#4654C2211yescharacteristic
152#4653C2211yescharacteristic
153#4653C2211yescharacteristic
154#4653C2211yescharacteristic
155#4652C2211yescharacteristic
156#4652C2211yescharacteristic
157#4652C2211yescharacteristic
158#4652C2211yescharacteristic
159#4651C2211yescharacteristic
160#4651C2211yescharacteristic
161#4651C2211yescharacteristic
162#4650C2211yescharacteristic
163#4650C2211yescharacteristic
164#4650C2211yescharacteristic
165#4650C2211yescharacteristic
166#4650C2211yescharacteristic
167#4650C2211yescharacteristic
168#4649C2211yescharacteristic
169#4649C2211yescharacteristic
170#4649C2211yescharacteristic
171#4649C2211yescharacteristic
172#4649C2211yescharacteristic
173#4648C2211yescharacteristic
174#4648C2211yescharacteristic
175#4648C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4646C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2754—31no—
189#2754—31no—
190#2754—31no—
191#2754—31no—
192#2738—31no—
193#2738—31no—
194#2738—31no—
195#2738D311yescharacteristic, complemented
196#2570—31no—
197#2570—31no—
198#2568—31no—
199#2563—31no—
200#2532—31no—
201#2532—31no—
202#2532—31no—
203#2532—31no—
204#2530—31no—
205#2530—31no—
206#2530—31no—
207#2530—31no—
208#2513—31no—
209#2513—31no—
210#2448—31no—
211#2448—31no—
212#2402—31no—
213#2357—31no—
214#2356—31no—
215#2356—31no—
216#2351—31no—
217#2331—31no—
218#2326—31no—
219C23×C3×C4C2311yescharacteristic
220C22×#67C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×#217C2311yescharacteristic
244C2×#217C2311yescharacteristic
245C2×#217C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C4×#67—24no—
251C2×(C2×D3)⋊C4C2311yescharacteristic
252C2×(C2×D3)⋊C4C2311yescharacteristic
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×C4×Dic3C2311yescharacteristic
293C2×C4×Dic3C2311yescharacteristic
294C2×C4×Dic3C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311#888—24no—
312#887—24no—
313#887—24no—
314#885—24no—
315C4×Dic6—24no—
316C3×#95C2311yescharacteristic
317C3×#95C2311yescharacteristic
318C3×#95C2311yescharacteristic
319C3×#95C2311yescharacteristic
320C3×#95C2311yescharacteristic
321C3×#95C2311yescharacteristic
322C3×#95C2311yescharacteristic
323C3×#95C2311yescharacteristic
324C3×#95C2311yescharacteristic
325C3×#95C2311yescharacteristic
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3×#95C2311yescharacteristic
331C3×#95C2311yescharacteristic
332C3⋊#95C2311yescharacteristic
333C3⋊#95C2311yescharacteristic
334C3⋊#95C2311yescharacteristic
335C3⋊#95C2311yescharacteristic
336C3⋊#95C2311yescharacteristic
337C3⋊#95C2311yescharacteristic
338C3⋊#95C2311yescharacteristic
339C3⋊#95C2311yescharacteristic
340C3⋊#95C2311yescharacteristic
341C3⋊#95C2311yescharacteristic
342C3⋊#95C2311yescharacteristic
343C3⋊#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C2×C4⋊Q8—31no—
381C2×#124—31no—
382C2×C4×Q8—31no—
383C2×C4×Q8—31no—
384C2×C4×Q8—31no—
385C2×C4×D4—31no—
386#400—31no—
387#400—31no—
388#400—31no—
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400—31no—
396#400C2×D311yescharacteristic
397#400C2×D311yescharacteristic
398#399—31no—
399#399—31no—
400#399—31no—
401#399C2×D311yescharacteristic
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398C2×D311yescharacteristic
409#398C2×D311yescharacteristic
410#397—31no—
411#397—31no—
412#397—31no—
413#397—31no—
414#397—31no—
415#397—31no—
416#397—31no—
417#397—31no—
418#397—31no—
419#397—31no—
420#397—31no—
421#397C2×D311yescharacteristic
422#393—31no—
423#393—31no—
424#393—31no—
425#393—31no—
426#391—31no—
427#391—31no—
428#391—31no—
429#391—31no—
430#391—31no—
431#391—31no—
432#391—31no—
433#391—31no—
434#391—31no—
435#391—31no—
436#391—31no—
437#390—31no—
438#390—31no—
439#390—31no—
440#390—31no—
441#390—31no—
442#389—31no—
443#389—31no—
444#389—31no—
445#389—31no—
446#389—31no—
447#389—31no—
448#389—31no—
449#389C2×D311yescharacteristic
450#388—31no—
451#388—31no—
452#388—31no—
453#388—31no—
454#388—31no—
455#388—31no—
456#388—31no—
457#388—31no—
458#388—31no—
459#388—31no—
460#388—31no—
461#388—31no—
462#388—31no—
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—31no—
469#388—31no—
470#388—31no—
471#388—31no—
472#388C2×D311yescharacteristic
473#388C2×D311yescharacteristic
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387—31no—
490#387—31no—
491#387—31no—
492#387C2×D311yescharacteristic
493#387C2×D311yescharacteristic
494#385—31no—
495#385—31no—
496#385—31no—
497#385C2×D311yescharacteristic
498#384—31no—
499#383—31no—
500#383—31no—
501#383—31no—
502#383C2×D311yescharacteristic
503#382—31no—
504#382—31no—
505#382—31no—
506#382—31no—
507#382—31no—
508#382—31no—
509#382—31no—
510#381—31no—
511#381C2×D311yescharacteristic
512#380—31no—
513#380—31no—
514#380—31no—
515#380C2×D311yescharacteristic
516C4×C4⋊C4—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530#376—31no—
531#376—31no—
532#376—31no—
533#376—31no—
534#376—31no—
535C24×C3C2411yescharacteristic
536C23×D3C2411yescharacteristic
537C22×C3×C4—22no—
538C22×C3×C4—41no—
539C22×C3×C4—41no—
540C22×C3×C4C2411yescharacteristic
541C22×C3×C4C2411yescharacteristic
542C22×C3×C4C2411yescharacteristic
543C22×C3×C4C2411yescharacteristic
544C22×C3×C4C2411yescharacteristic
545C22×C3×C4C2411yescharacteristic
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C2×#67—22no—
555C2×#67—22no—
556C2×#67—22no—
557C22×Dic3C2411yescharacteristic
558C22×Dic3C2411yescharacteristic
559C22×Dic3C2411yescharacteristic
560C22×Dic3C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C2×C4×D3—22no—
573C2×C4×D3—41no—
574C2×C4×D3—41no—
575C2×Dic6—22no—
576C2×Dic6—22no—
577C2×Dic6—22no—
578C2×Dic6—22no—
579C2×Dic6—41no—
580C2×Dic6—41no—
581C2×Dic6—41no—
582C2×Dic6—41no—
583C2×Dic6#4114yes—
584C3×C4⋊C4—22no—
585C3×C4⋊C4—22no—
586C3×C4⋊C4—22no—
587C3×C4⋊C4—41no—
588C3×C4⋊C4—41no—
589C3×C4⋊C4—41no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C4⋊C4—41no—
593C3×C4⋊C4—41no—
594C3×C22⋊C4—22no—
595C3×C22⋊C4—41no—
596C3×C22⋊C4—41no—
597C3×C22⋊C4—41no—
598C3×C22⋊C4—41no—
599C3×C22⋊C4—41no—
600C3×C42—22no—
601C3×C42—41no—
602#217—22no—
603#217—22no—
604#217—41no—
605#217—41no—
606#217—41no—
607#217—41no—
608#217—41no—
609(C2×D3)⋊C4—22no—
610(C2×D3)⋊C4—22no—
611(C2×D3)⋊C4—22no—
612(C2×D3)⋊C4—41no—
613(C2×D3)⋊C4—41no—
614(C2×D3)⋊C4—41no—
615(C2×D3)⋊C4—41no—
616(C2×D3)⋊C4—41no—
617(C2×D3)⋊C4—41no—
618(C2×D3)⋊C4—41no—
619(C2×D3)⋊C4—41no—
620(C2×D3)⋊C4—41no—
621(C2×D3)⋊C4—41no—
622C4⋊Dic3—22no—
623C4⋊Dic3—22no—
624C4⋊Dic3—41no—
625C4⋊Dic3—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
628C4⋊Dic3—41no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
631Dic3⋊C4—22no—
632Dic3⋊C4—22no—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—41no—
641Dic3⋊C4—41no—
642Dic3⋊C4—41no—
643Dic3⋊C4—41no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650C4×Dic3—22no—
651C4×Dic3—22no—
652C4×Dic3—22no—
653C4×Dic3—22no—
654C4×Dic3—22no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—22no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3—41no—
668C4×Dic3#4114yes—
669C22×Q8—31no—
670C22×Q8—31no—
671C22×Q8—31no—
672C22×D4—31no—
673C23×C4—31no—
674C23×C4C22×D311yescharacteristic
675C4⋊Q8—64no—
676#124—64no—
677C4×Q8—64no—
678C4×Q8—64no—
679C4×Q8—64no—
680C4×D4—64no—
681C2×C4⋊C4—31no—
682C2×C4⋊C4—31no—
683C2×C4⋊C4—31no—
684C2×C4⋊C4—31no—
685C2×C4⋊C4—31no—
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—31no—
691C2×C4⋊C4—31no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—31no—
697C2×C4⋊C4—31no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—31no—
701C2×C4⋊C4—31no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—31no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—31no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4C22×D311yescharacteristic
710C2×C4⋊C4C22×D311yescharacteristic
711C2×C4⋊C4C22×D311yescharacteristic
712C2×C4⋊C4C22×D311yescharacteristic
713C2×C4⋊C4C22×D311yescharacteristic
714C2×C4⋊C4C22×D311yescharacteristic
715C2×C4⋊C4C22×D311yescharacteristic
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C22⋊C4—31no—
720C2×C22⋊C4—31no—
721C2×C22⋊C4—31no—
722C2×C22⋊C4—31no—
723C2×C22⋊C4—31no—
724C2×C22⋊C4—31no—
725C2×C22⋊C4—31no—
726C2×C22⋊C4—31no—
727C2×C22⋊C4—31no—
728C2×C22⋊C4—31no—
729C2×C22⋊C4—31no—
730C2×C22⋊C4—31no—
731C2×C22⋊C4—31no—
732C2×C22⋊C4—31no—
733C2×C22⋊C4—31no—
734C2×C22⋊C4—31no—
735C2×C22⋊C4—31no—
736C2×C22⋊C4—31no—
737C2×C22⋊C4—31no—
738C2×C22⋊C4—31no—
739C2×C22⋊C4C22×D311yescharacteristic
740C2×C22⋊C4C22×D311yescharacteristic
741C2×C22⋊C4C22×D311yescharacteristic
742C2×C22⋊C4C22×D311yescharacteristic
743C2×C22⋊C4C22×D311yescharacteristic
744C2×C22⋊C4C22×D311yescharacteristic
745C2×C42—31no—
746C2×C42—31no—
747C2×C42—31no—
748C2×C42—31no—
749C2×C42—31no—
750C2×C42—31no—
751C2×C42—31no—
752C2×C42—31no—
753C2×C42—31no—
754C2×C42—31no—
755C2×C42—31no—
756C2×C42—31no—
757C2×C42—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42—31no—
761C2×C42—31no—
762C2×C42—31no—
763C2×C42—31no—
764C2×C42C22×D311yescharacteristic
765C2×C42C22×D311yescharacteristic
766#95—31no—
767#95—31no—
768#95—31no—
769#95—31no—
770#95—31no—
771#95—31no—
772#95—31no—
773#95—31no—
774#95—31no—
775#95—31no—
776#95—31no—
777#95—31no—
778#95—31no—
779#95—31no—
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95C22×D311yescharacteristic
815#95C22×D311yescharacteristic
816#95C22×D311yescharacteristic
817#95C22×D311yescharacteristic
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—21no—
836C23×C3—21no—
837C23×C3C2511yescharacteristic
838C22×D3—21no—
839C22×D3—21no—
840C22×D3—21no—
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3—21no—
845C2×C3×C4—21no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—21no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—82no—
886C2×C3×C4C2×#4112yes—
887C2×C3×C4C2×#4112yes—
888#67—44no—
889C2×Dic3—21no—
890C2×Dic3—21no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3C2×#4112yes—
930C2×Dic3C2×#4112yes—
931C2×Dic3C2×#4112yes—
932C2×Dic3C2×#4112yes—
933C2×Dic32−1+412yes—
934C4×D3—82no—
935Dic6—28no—
936Dic6—82no—
937Dic6—82no—
938C24—31no—
939C24C23×D311yescharacteristic
940C2×Q8—34no—
941C2×Q8—62no—
942C2×Q8—62no—
943C2×Q8—62no—
944C2×Q8—62no—
945C2×Q8—121no—
946C2×Q8—121no—
947C2×Q8—121no—
948C2×Q8—121no—
949C2×D4—62no—
950C2×D4—62no—
951C2×D4—62no—
952C22×C4—22no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—31no—
967C22×C4—31no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—62no—
971C22×C4—121no—
972C22×C4—121no—
973C22×C4C23×D311yescharacteristic
974C22×C4C23×D311yescharacteristic
975C22×C4C23×D311yescharacteristic
976C22×C4C23×D311yescharacteristic
977C22×C4C23×D311yescharacteristic
978C22×C4C23×D311yescharacteristic
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—62no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—121no—
1009C4⋊C4—121no—
1010C4⋊C4—121no—
1011C4⋊C4—121no—
1012C4⋊C4—121no—
1013C4⋊C4—121no—
1014C4⋊C4—121no—
1015C4⋊C4—121no—
1016C4⋊C4—121no—
1017C4⋊C4—121no—
1018C4⋊C4—121no—
1019C4⋊C4—121no—
1020C4⋊C4—121no—
1021C4⋊C4—121no—
1022C4⋊C4—121no—
1023C4⋊C4—121no—
1024C4⋊C4—121no—
1025C22⋊C4—22no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—62no—
1032C22⋊C4—62no—
1033C22⋊C4—62no—
1034C22⋊C4—62no—
1035C22⋊C4—62no—
1036C22⋊C4—121no—
1037C22⋊C4—121no—
1038C22⋊C4—121no—
1039C22⋊C4—121no—
1040C22⋊C4—121no—
1041C22⋊C4—121no—
1042C22⋊C4—121no—
1043C22⋊C4—121no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C42—22no—
1052C42—34no—
1053C42—41no—
1054C42—62no—
1055C42—62no—
1056C42—62no—
1057C42—62no—
1058C42—62no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3C22×#4111yescharacteristic
1080C22×C3C22×#4111yescharacteristic
1081C22×C3C2×2−1+411yescharacteristic
1082C22×C3#58511yescharacteristic
1083C22×C3#58511yescharacteristic
1084C22×C3#58511yescharacteristic
1085C22×C3#58511yescharacteristic
1086C2×D3—41no—
1087C2×D3—41no—
1088C2×D3—41no—
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C3×C4—22no—
1094C3×C4—22no—
1095C3×C4—41no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—41no—
1105C3×C4—41no—
1106C3×C4—41no—
1107Dic3—22no—
1108Dic3—22no—
1109Dic3—41no—
1110Dic3—41no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3#55214yes—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23C24×D311yescharacteristic
1137Q8—68no—
1138Q8—242no—
1139Q8—242no—
1140D4—124no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—61no—
1194C2×C4—61no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—61no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—61no—
1213C2×C4—61no—
1214C2×C4—61no—
1215C2×C4—61no—
1216C2×C4—61no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—61no—
1225C2×C4—61no—
1226C2×C4—82no—
1227C2×C4—242no—
1228C2×C4D3×#4112yes—
1229C2×C4D3×#4112yes—
1230C2×C3—81no—
1231C2×C3C2×#55211yescharacteristic
1232C2×C3#351011yescharacteristic
1233C2×C3#351011yescharacteristic
1234C2×C3#352411yescharacteristic
1235C2×C3#352411yescharacteristic
1236C2×C3#356511yescharacteristic
1237C2×C3#356511yescharacteristic
1238D3—81no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—121no—
1247C22—121no—
1248C22—121no—
1249C22—121no—
1250C22—121no—
1251C22—121no—
1252C22—121no—
1253C22C2×D3×#4111yescharacteristic
1254C22C2×D3×#4111yescharacteristic
1255C22#596411yescharacteristic
1256C22#596611yescharacteristic
1257C22#596611yescharacteristic
1258C22D3×2−1+411yescharacteristic
1259C22#596811yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—34no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—62no—
1276C4—62no—
1277C4—121no—
1278C4—121no—
1279C4—121no—
1280C4—121no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C3#4531811yescharacteristic, complemented, Sylow
1290C2—81no—
1291C2—241no—
1292C2#8644711yescharacteristic
1293C2#8647111yescharacteristic
1294C2#8655211yescharacteristic
1295C2#8679411yescharacteristic
1296C2#8684311yescharacteristic
1297C2D3×#55211yescharacteristic
1298C2#8712411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2738C2
prime radicalC22×#67C23
hypercenter#2738D3
hypocenterC3#45318
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2738

Complements

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

NH ≅ G/Ntype
1. C3×#2738C2semidirect
2. #78376C2semidirect
3. #78253C2semidirect
4. #78182C2semidirect
5. #78181C2semidirect
6. #78079C2semidirect
8. #77988C2semidirect
9. #77793C2semidirect
10. #77783C2semidirect
11. #77741C2semidirect
12. #77606C2semidirect
14. #76056C2semidirect
15. #75982C2semidirect
16. #75590C2semidirect
17. #75588C2semidirect
20. #75183C2semidirect
21. #75066C2semidirect
22. #74964C2semidirect
23. #74950C2semidirect
24. #74471C2semidirect
26. #74273C2semidirect
27. #74264C2semidirect
28. #74101C2semidirect
31. #73931C2semidirect
195. #2738D3semidirect
1289. C3#45318semidirect

Maximal subgroups

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

subgroupindex
C3×#27382
#783762
#782532
#781822
#781812
#780792
#780222
#779882
#777932
#777832
#777412
#776062
#774952
#760562
#759822
#755902
#755882
#755542
#755012
#751832
#750662
#749642
#749502
#744712
#743862
#742732
#742642
#741012
#740612
#739422
#739312
#453183