Finite Group Databasebeta

← #11002901

Subgroups — #11002901

Order 768.

1588 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2667C211yesmaximal, characteristic, complemented
2#78119C211yesmaximal, characteristic
3#78076C211yesmaximal, characteristic, complemented
4#78068C211yesmaximal, characteristic, complemented
5#78062C211yesmaximal, characteristic
6#78004C211yesmaximal, characteristic, complemented
7#77968C211yesmaximal, characteristic, complemented
8#77923C211yesmaximal, characteristic, complemented
9#77921C211yesmaximal, characteristic, complemented
10#77912C211yesmaximal, characteristic, complemented
11#77911C211yesmaximal, characteristic, complemented
12#77861C211yesmaximal, characteristic, complemented
13#77855C211yesmaximal, characteristic, complemented
14#77436C211yesmaximal, characteristic
15#77377C211yesmaximal, characteristic
16#77369C211yesmaximal, characteristic, complemented
17#77351C211yesmaximal, characteristic, complemented
18#76244C211yesmaximal, characteristic, complemented
19#76098C211yesmaximal, characteristic, complemented
20#76063C211yesmaximal, characteristic, complemented
21#76001C211yesmaximal, characteristic, complemented
22#75318C211yesmaximal, characteristic, complemented
23#75133C211yesmaximal, characteristic, complemented
24#75131C211yesmaximal, characteristic, complemented
25#75128C211yesmaximal, characteristic, complemented
26#74117C211yesmaximal, characteristic, complemented
27#74055C211yesmaximal, characteristic
28#74006C211yesmaximal, characteristic
29#74001C211yesmaximal, characteristic, complemented
30#73557C211yesmaximal, characteristic, complemented
31#73438C211yesmaximal, characteristic
32#36753—31nomaximal, Sylow
33C2×C4×#67C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C2×#897C2211yescharacteristic
36C2×#896C2211yescharacteristic
37C2×#896C2211yescharacteristic
38C2×#889C2211yescharacteristic
39C2×#889C2211yescharacteristic
40C2×#888C2211yescharacteristic
41C2×#888C2211yescharacteristic
42C2×#878C2211yescharacteristic
43C2×#878C2211yescharacteristic
44C2×#878C2211yescharacteristic
45C2×#872C2211yescharacteristic
46C3×#399C2211yescharacteristic
47C3×#399C2211yescharacteristic
48C3×#398C2211yescharacteristic
49C3×#398C2211yescharacteristic
50C3×#398C2211yescharacteristic
51C3×#398C2211yescharacteristic
52C3×#396C2211yescharacteristic
53C3×#396C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#387C2211yescharacteristic
57C3×#387C2211yescharacteristic
58C3×#381C2211yescharacteristic
59C3×#380C2211yescharacteristic
60C3×C4×C22⋊C4C2211yescharacteristic
61#5212C2211yescharacteristic
62#5211C2211yescharacteristic
63#4994C2211yescharacteristic
64#4994C2211yescharacteristic
65#4993C2211yescharacteristic
66#4993C2211yescharacteristic
67#4993C2211yescharacteristic
68#4993C2211yescharacteristic
69#4989C2211yescharacteristic
70#4989C2211yescharacteristic
71#4989C2211yescharacteristic
72#4989C2211yescharacteristic
73#4987C2211yescharacteristic
74#4984C2211yescharacteristic
75#4984C2211yescharacteristic
76#4983C2211yescharacteristic
77#4983C2211yescharacteristic
78#4983C2211yescharacteristic
79#4982C2211yescharacteristic
80#4982C2211yescharacteristic
81#4982C2211yescharacteristic
82#4982C2211yescharacteristic
83#4981C2211yescharacteristic
84#4981C2211yescharacteristic
85#4981C2211yescharacteristic
86#4981C2211yescharacteristic
87#4980C2211yescharacteristic
88#4979C2211yescharacteristic
89#4979C2211yescharacteristic
90#4979C2211yescharacteristic
91#4979C2211yescharacteristic
92#4979C2211yescharacteristic
93#4979C2211yescharacteristic
94#4979C2211yescharacteristic
95#4978C2211yescharacteristic
96#4978C2211yescharacteristic
97#4978C2211yescharacteristic
98#4978C2211yescharacteristic
99#4978C2211yescharacteristic
100#4978C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103#4976C2211yescharacteristic
104#4976C2211yescharacteristic
105#4976C2211yescharacteristic
106#4975C2211yescharacteristic
107#4975C2211yescharacteristic
108#4973C2211yescharacteristic
109#4973C2211yescharacteristic
110#4972C2211yescharacteristic
111#4972C2211yescharacteristic
112#4958C2211yescharacteristic
113#4958C2211yescharacteristic
114#4957C2211yescharacteristic
115#4957C2211yescharacteristic
116#4956C2211yescharacteristic
117#4956C2211yescharacteristic
118#4950C2211yescharacteristic
119#4948C2211yescharacteristic
120#4948C2211yescharacteristic
121#4947C2211yescharacteristic
122#4947C2211yescharacteristic
123#4946C2211yescharacteristic
124#4946C2211yescharacteristic
125#4946C2211yescharacteristic
126#4945C2211yescharacteristic
127#4945C2211yescharacteristic
128#4945C2211yescharacteristic
129#4945C2211yescharacteristic
130#4942C2211yescharacteristic
131#4942C2211yescharacteristic
132#4942C2211yescharacteristic
133C4×(C2×D3)⋊C4C2211yescharacteristic
134#4933C2211yescharacteristic
135#4933C2211yescharacteristic
136#4932C2211yescharacteristic
137C4×Dic3⋊C4C2211yescharacteristic
138#4929C2211yescharacteristic
139#4929C2211yescharacteristic
140#4673C2211yescharacteristic
141#4673C2211yescharacteristic
142#4670C2211yescharacteristic
143#4670C2211yescharacteristic
144#4669C2211yescharacteristic
145#4669C2211yescharacteristic
146#4668C2211yescharacteristic
147#4668C2211yescharacteristic
148#4667C2211yescharacteristic
149#4666C2211yescharacteristic
150#4664C2211yescharacteristic
151D3×#95C2211yescharacteristic
152#4660C2211yescharacteristic
153#4660C2211yescharacteristic
154#4659C2211yescharacteristic
155#4658C2211yescharacteristic
156#4658C2211yescharacteristic
157#4658C2211yescharacteristic
158#4657C2211yescharacteristic
159#4656C2211yescharacteristic
160#4656C2211yescharacteristic
161#4656C2211yescharacteristic
162#4655C2211yescharacteristic
163#4655C2211yescharacteristic
164#4654C2211yescharacteristic
165#4654C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4652C2211yescharacteristic
171#4651C2211yescharacteristic
172#4650C2211yescharacteristic
173#4649C2211yescharacteristic
174#4648C2211yescharacteristic
175#4647C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2857—31no—
189#2855—31no—
190#2807—31no—
191#2806—31no—
192#2792—31no—
193#2791—31no—
194#2788—31no—
195#2748—31no—
196#2742—31no—
197#2732—31no—
198#2729—31no—
199#2720—31no—
200#2720—31no—
201#2713—31no—
202#2704—31no—
203#2692—31no—
204#2692—31no—
205#2677—31no—
206#2667D311yescharacteristic, complemented
207#2665—31no—
208#2612—31no—
209#2607—31no—
210#2606—31no—
211#2605—31no—
212#2550—31no—
213#2549—31no—
214#2441—31no—
215#2438—31no—
216#2319—31no—
217#2318—31no—
218#2290—31no—
219C23×C3×C4C2311yescharacteristic
220C22×#67C2311yescharacteristic
221C23×Dic3C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
228C22×Dic6C2311yescharacteristic
229C22×Dic6C2311yescharacteristic
230C22×Dic6C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C4⋊C4C2311yescharacteristic
243C2×C3×C4⋊C4C2311yescharacteristic
244C2×C3×C4⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C22⋊C4C2311yescharacteristic
247C2×C3×C22⋊C4C2311yescharacteristic
248C2×C3×C22⋊C4C2311yescharacteristic
249C2×C3×C22⋊C4C2311yescharacteristic
250C2×C3×C22⋊C4C2311yescharacteristic
251C2×C3×C42C2311yescharacteristic
252C2×C3×C42C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C4×#67Q818yescomplemented
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×(C2×D3)⋊C4C2311yescharacteristic
265C2×(C2×D3)⋊C4C2311yescharacteristic
266C2×(C2×D3)⋊C4C2311yescharacteristic
267C2×(C2×D3)⋊C4C2311yescharacteristic
268C2×(C2×D3)⋊C4C2311yescharacteristic
269C2×(C2×D3)⋊C4C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
273C2×C4⋊Dic3C2311yescharacteristic
274C2×C4⋊Dic3C2311yescharacteristic
275C2×C4⋊Dic3C2311yescharacteristic
276C2×C4⋊Dic3C2311yescharacteristic
277C2×C4⋊Dic3C2311yescharacteristic
278C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×Dic3⋊C4C2311yescharacteristic
298C2×Dic3⋊C4C2311yescharacteristic
299C2×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
301C2×Dic3⋊C4C2311yescharacteristic
302C2×Dic3⋊C4C2311yescharacteristic
303C2×Dic3⋊C4C2311yescharacteristic
304C2×Dic3⋊C4C2311yescharacteristic
305C2×Dic3⋊C4C2311yescharacteristic
306C2×Dic3⋊C4C2311yescharacteristic
307C2×Dic3⋊C4C2311yescharacteristic
308C2×C4×Dic3—42no—
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316C2×C4×Dic3C2311yescharacteristic
317C2×C4×Dic3C2311yescharacteristic
318C2×C4×Dic3C2311yescharacteristic
319C2×C4×Dic3C2311yescharacteristic
320#897—42no—
321#896—42no—
322#896—42no—
323#889—42no—
324#889—42no—
325#888—42no—
326#888—42no—
327#878—42no—
328#878—42no—
329#878—42no—
330#872—42no—
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
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C3⋊#95C2311yescharacteristic
385C3⋊#95C2311yescharacteristic
386C3⋊#95C2311yescharacteristic
387C2×C4⋊Q8—31no—
388C2×C4⋊Q8—31no—
389C2×#125—31no—
390C2×#125—31no—
391C2×C22⋊Q8—31no—
392C2×C22⋊Q8—31no—
393C2×C22⋊Q8—31no—
394C2×C22⋊Q8—31no—
395C2×C22⋊Q8—31no—
396C2×C22⋊Q8—31no—
397C2×C4×D4—31no—
398C2×#117—31no—
399C22×C42—31no—
400#400—31no—
401#400—31no—
402#400—31no—
403#400—31no—
404#400—31no—
405#400—31no—
406#399—31no—
407#399—31no—
408#399—31no—
409#399—31no—
410#399C2×D311yescharacteristic
411#399C2×D311yescharacteristic
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398—31no—
419#398—31no—
420#398—31no—
421#398—31no—
422#398—31no—
423#398—31no—
424#398C2×D311yescharacteristic
425#398C2×D311yescharacteristic
426#398C2×D311yescharacteristic
427#398C2×D311yescharacteristic
428#396—31no—
429#396—31no—
430#396—31no—
431#396—31no—
432#396C2×D311yescharacteristic
433#396C2×D311yescharacteristic
434#395—31no—
435#395—31no—
436#395—31no—
437#395—31no—
438#395—31no—
439#395—31no—
440#395—31no—
441#395—31no—
442#395—31no—
443#395—31no—
444#393—31no—
445#393—31no—
446#393—31no—
447#393—31no—
448#391—31no—
449#391—31no—
450#391—31no—
451#391—31no—
452#391—31no—
453#391—31no—
454#391—31no—
455#391—31no—
456#391—31no—
457#391—31no—
458#391—31no—
459#390—31no—
460#390—31no—
461#389—31no—
462#389—31no—
463#389—31no—
464#389—31no—
465#389—31no—
466#389—31no—
467#389—31no—
468#389—31no—
469#389—31no—
470#389—31no—
471#389—31no—
472#389—31no—
473#389—31no—
474#389—31no—
475#389—31no—
476#389C2×D311yescharacteristic
477#389C2×D311yescharacteristic
478#388—31no—
479#388—31no—
480#388—31no—
481#388—31no—
482#388—31no—
483#388—31no—
484#388—31no—
485#388—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387—31no—
490#387—31no—
491#387—31no—
492#387—31no—
493#387—31no—
494#387—31no—
495#387—31no—
496#387—31no—
497#387—31no—
498#387—31no—
499#387—31no—
500#387—31no—
501#387—31no—
502#387—31no—
503#387—31no—
504#387C2×D311yescharacteristic
505#387C2×D311yescharacteristic
506#386—31no—
507#386—31no—
508#386—31no—
509#386—31no—
510#385—31no—
511#385—31no—
512#385—31no—
513#385—31no—
514#385—31no—
515#385—31no—
516#385—31no—
517#385—31no—
518#385—31no—
519#385—31no—
520#384—31no—
521#384—31no—
522#383—31no—
523#382—31no—
524#381—31no—
525#381—31no—
526#381C2×D311yescharacteristic
527#380—31no—
528#380—31no—
529#380—31no—
530#380—31no—
531#380—31no—
532#380—31no—
533#380C2×D311yescharacteristic
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C22⋊C4—31no—
537C4×C22⋊C4—31no—
538C4×C22⋊C4C2×D311yescharacteristic
539#376—31no—
540#376—31no—
541C2×#95—31no—
542C24×C3C2411yescharacteristic
543C23×D3C2411yescharacteristic
544C22×C3×C4—41no—
545C22×C3×C4—41no—
546C22×C3×C4C2×Q814yes—
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C2×#67—41no—
562C2×#67—41no—
563C2×#67C2×Q814yes—
564C22×Dic3—22no—
565C22×Dic3—22no—
566C22×Dic3—22no—
567C22×Dic3—41no—
568C22×Dic3—41no—
569C22×Dic3—41no—
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C22×Dic3C2411yescharacteristic
582C22×Dic3C2411yescharacteristic
583C22×Dic3C2411yescharacteristic
584C22×Dic3C2411yescharacteristic
585C2×C4×D3—41no—
586C2×C4×D3—41no—
587C2×C4×D3—41no—
588C2×C4×D3—41no—
589C2×C4×D3—41no—
590C2×C4×D3—41no—
591C2×C4×D3—41no—
592C2×C4×D3—41no—
593C2×C4×D3C2×Q814yes—
594C2×Dic6—22no—
595C2×Dic6—22no—
596C2×Dic6—22no—
597C2×Dic6—41no—
598C2×Dic6—41no—
599C2×Dic6—41no—
600C2×Dic6—41no—
601C2×Dic6—41no—
602C2×Dic6—41no—
603C2×Dic6—41no—
604C2×Dic6—41no—
605C2×Dic6—41no—
606C2×Dic6—41no—
607C2×Dic6—41no—
608C2×Dic6—41no—
609C3×C4⋊C4—41no—
610C3×C4⋊C4—41no—
611C3×C4⋊C4—41no—
612C3×C4⋊C4—41no—
613C3×C4⋊C4—41no—
614C3×C4⋊C4—41no—
615C3×C4⋊C4—41no—
616C3×C4⋊C4—41no—
617C3×C4⋊C4—41no—
618C3×C4⋊C4—41no—
619C3×C4⋊C4—41no—
620C3×C4⋊C4—41no—
621C3×C4⋊C4—41no—
622C3×C4⋊C4—41no—
623C3×C22⋊C4—41no—
624C3×C22⋊C4—41no—
625C3×C22⋊C4—41no—
626C3×C22⋊C4—41no—
627C3×C22⋊C4—41no—
628C3×C22⋊C4—41no—
629C3×C42—41no—
630C3×C42—41no—
631#217—41no—
632#217—41no—
633#217—41no—
634#217—41no—
635#217C2×Q814yes—
636(C2×D3)⋊C4—22no—
637(C2×D3)⋊C4—22no—
638(C2×D3)⋊C4—22no—
639(C2×D3)⋊C4—41no—
640(C2×D3)⋊C4—41no—
641(C2×D3)⋊C4—41no—
642(C2×D3)⋊C4—41no—
643(C2×D3)⋊C4—41no—
644(C2×D3)⋊C4—41no—
645(C2×D3)⋊C4—41no—
646(C2×D3)⋊C4C2×Q814yes—
647C4⋊Dic3—22no—
648C4⋊Dic3—22no—
649C4⋊Dic3—41no—
650C4⋊Dic3—41no—
651C4⋊Dic3—41no—
652C4⋊Dic3—41no—
653C4⋊Dic3—41no—
654C4⋊Dic3—41no—
655C4⋊Dic3—41no—
656Dic3⋊C4—22no—
657Dic3⋊C4—22no—
658Dic3⋊C4—22no—
659Dic3⋊C4—22no—
660Dic3⋊C4—22no—
661Dic3⋊C4—22no—
662Dic3⋊C4—22no—
663Dic3⋊C4—22no—
664Dic3⋊C4—22no—
665Dic3⋊C4—22no—
666Dic3⋊C4—41no—
667Dic3⋊C4—41no—
668Dic3⋊C4—41no—
669Dic3⋊C4—41no—
670Dic3⋊C4—41no—
671Dic3⋊C4—41no—
672Dic3⋊C4—41no—
673Dic3⋊C4—41no—
674Dic3⋊C4—41no—
675Dic3⋊C4—41no—
676Dic3⋊C4—41no—
677Dic3⋊C4—41no—
678Dic3⋊C4—41no—
679Dic3⋊C4—41no—
680Dic3⋊C4—41no—
681Dic3⋊C4—41no—
682Dic3⋊C4—41no—
683Dic3⋊C4—41no—
684Dic3⋊C4C2×Q814yes—
685C4×Dic3—22no—
686C4×Dic3—22no—
687C4×Dic3—41no—
688C4×Dic3—41no—
689C4×Dic3—41no—
690C4×Dic3—41no—
691C4×Dic3—41no—
692C4×Dic3—41no—
693C4×Dic3—41no—
694C4×Dic3—41no—
695C4×Dic3C2×Q814yes—
696C22×Q8—31no—
697C22×Q8—31no—
698C22×Q8—31no—
699C22×Q8—31no—
700C22×Q8—31no—
701C22×D4—31no—
702C23×C4—31no—
703C23×C4—31no—
704C23×C4—31no—
705C23×C4—31no—
706C23×C4—31no—
707C23×C4C22×D311yescharacteristic
708C4⋊Q8—122no—
709C4⋊Q8—122no—
710#125—122no—
711#125—122no—
712C22⋊Q8—122no—
713C22⋊Q8—122no—
714C22⋊Q8—122no—
715C22⋊Q8—122no—
716C22⋊Q8—122no—
717C22⋊Q8—122no—
718C4×D4—38no—
719#117—122no—
720C2×C4⋊C4—31no—
721C2×C4⋊C4—31no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—31no—
734C2×C4⋊C4—31no—
735C2×C4⋊C4—31no—
736C2×C4⋊C4—31no—
737C2×C4⋊C4—31no—
738C2×C4⋊C4—31no—
739C2×C4⋊C4—31no—
740C2×C4⋊C4—31no—
741C2×C4⋊C4—31no—
742C2×C4⋊C4—31no—
743C2×C4⋊C4—31no—
744C2×C4⋊C4—31no—
745C2×C4⋊C4—31no—
746C2×C4⋊C4—31no—
747C2×C4⋊C4—31no—
748C2×C4⋊C4—31no—
749C2×C4⋊C4—31no—
750C2×C4⋊C4—31no—
751C2×C4⋊C4—31no—
752C2×C4⋊C4—31no—
753C2×C4⋊C4—31no—
754C2×C4⋊C4—31no—
755C2×C4⋊C4—31no—
756C2×C4⋊C4—31no—
757C2×C4⋊C4—31no—
758C2×C4⋊C4C22×D311yescharacteristic
759C2×C4⋊C4C22×D311yescharacteristic
760C2×C4⋊C4C22×D311yescharacteristic
761C2×C4⋊C4C22×D311yescharacteristic
762C2×C4⋊C4C22×D311yescharacteristic
763C2×C4⋊C4C22×D311yescharacteristic
764C2×C4⋊C4C22×D311yescharacteristic
765C2×C4⋊C4C22×D311yescharacteristic
766C2×C4⋊C4C22×D311yescharacteristic
767C2×C4⋊C4C22×D311yescharacteristic
768C2×C4⋊C4C22×D311yescharacteristic
769C2×C4⋊C4C22×D311yescharacteristic
770C2×C4⋊C4C22×D311yescharacteristic
771C2×C4⋊C4C22×D311yescharacteristic
772C2×C22⋊C4—31no—
773C2×C22⋊C4—31no—
774C2×C22⋊C4—31no—
775C2×C22⋊C4—31no—
776C2×C22⋊C4—31no—
777C2×C22⋊C4—31no—
778C2×C22⋊C4—31no—
779C2×C22⋊C4—31no—
780C2×C22⋊C4—31no—
781C2×C22⋊C4—31no—
782C2×C22⋊C4—31no—
783C2×C22⋊C4—31no—
784C2×C22⋊C4—31no—
785C2×C22⋊C4—31no—
786C2×C22⋊C4—31no—
787C2×C22⋊C4—31no—
788C2×C22⋊C4C22×D311yescharacteristic
789C2×C22⋊C4C22×D311yescharacteristic
790C2×C22⋊C4C22×D311yescharacteristic
791C2×C22⋊C4C22×D311yescharacteristic
792C2×C22⋊C4C22×D311yescharacteristic
793C2×C22⋊C4C22×D311yescharacteristic
794C2×C42—31no—
795C2×C42—31no—
796C2×C42—31no—
797C2×C42—31no—
798C2×C42—31no—
799C2×C42—31no—
800C2×C42—31no—
801C2×C42—31no—
802C2×C42—31no—
803C2×C42—31no—
804C2×C42—31no—
805C2×C42—122no—
806C2×C42C22×D311yescharacteristic
807C2×C42C22×D311yescharacteristic
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95—31no—
819#95—31no—
820#95—31no—
821#95—31no—
822#95—31no—
823#95—31no—
824#95—31no—
825#95—31no—
826#95—31no—
827#95—31no—
828#95—31no—
829#95—31no—
830#95—31no—
831#95—31no—
832#95—31no—
833#95—31no—
834#95—31no—
835#95—31no—
836#95—31no—
837#95—31no—
838#95—31no—
839#95—31no—
840#95—31no—
841#95—31no—
842#95—31no—
843#95—31no—
844#95—31no—
845#95—31no—
846#95—31no—
847#95—31no—
848#95—31no—
849#95—31no—
850#95—31no—
851#95—31no—
852#95C22×D311yescharacteristic
853#95C22×D311yescharacteristic
854#95C22×D311yescharacteristic
855#95C22×D311yescharacteristic
856#95C22×D311yescharacteristic
857#95C22×D311yescharacteristic
858#95C22×D311yescharacteristic
859#95C22×D311yescharacteristic
860#95C22×D311yescharacteristic
861#95C22×D311yescharacteristic
862#95C22×D311yescharacteristic
863#95C22×D311yescharacteristic
864C23×C3—21no—
865C23×C3—21no—
866C23×C3—21no—
867C23×C3—21no—
868C23×C3—21no—
869C23×C3—21no—
870C23×C3C22×Q812yes—
871C23×C3C2511yescharacteristic
872C22×D3—21no—
873C22×D3—21no—
874C22×D3—21no—
875C22×D3—21no—
876C22×D3—21no—
877C22×D3—21no—
878C22×D3C22×Q812yes—
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—21no—
886C2×C3×C4—21no—
887C2×C3×C4—21no—
888C2×C3×C4—21no—
889C2×C3×C4—21no—
890C2×C3×C4—21no—
891C2×C3×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—21no—
912C2×C3×C4—21no—
913C2×C3×C4—21no—
914C2×C3×C4—21no—
915C2×C3×C4—21no—
916C2×C3×C4—21no—
917C2×C3×C4—21no—
918C2×C3×C4—21no—
919C2×C3×C4—44no—
920C2×C3×C4C22×Q812yes—
921C2×C3×C4C22×Q812yes—
922#67—44no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
937C2×Dic3—21no—
938C2×Dic3—21no—
939C2×Dic3—21no—
940C2×Dic3—21no—
941C2×Dic3—21no—
942C2×Dic3—21no—
943C2×Dic3—21no—
944C2×Dic3—21no—
945C2×Dic3—21no—
946C2×Dic3—21no—
947C2×Dic3—21no—
948C2×Dic3—21no—
949C2×Dic3—21no—
950C2×Dic3—21no—
951C2×Dic3—21no—
952C2×Dic3—21no—
953C2×Dic3—21no—
954C2×Dic3—21no—
955C2×Dic3—21no—
956C2×Dic3—21no—
957C2×Dic3—21no—
958C2×Dic3—21no—
959C2×Dic3—21no—
960C2×Dic3—21no—
961C2×Dic3—21no—
962C2×Dic3—44no—
963C2×Dic3—44no—
964C2×Dic3C22×Q812yes—
965C2×Dic3C22×Q812yes—
966C2×Dic3C22×Q812yes—
967C2×Dic3H(5,𝔽2)12yes—
968C2×Dic3H(5,𝔽2)12yes—
969C2×Dic32−1+412yes—
970C4×D3—44no—
971C4×D3—82no—
972C4×D3—82no—
973Dic6—82no—
974Dic6—82no—
975Dic6—82no—
976Dic6—82no—
977Dic6—82no—
978C24—31no—
979C24C23×D311yescharacteristic
980C2×Q8—62no—
981C2×Q8—62no—
982C2×Q8—62no—
983C2×Q8—121no—
984C2×Q8—121no—
985C2×Q8—121no—
986C2×Q8—121no—
987C2×Q8—121no—
988C2×Q8—121no—
989C2×Q8—121no—
990C2×Q8—121no—
991C2×Q8—121no—
992C2×Q8—121no—
993C2×Q8—121no—
994C2×Q8—121no—
995C2×D4—34no—
996C2×D4—121no—
997C2×D4—121no—
998C22×C4—31no—
999C22×C4—31no—
1000C22×C4—31no—
1001C22×C4—31no—
1002C22×C4—31no—
1003C22×C4—31no—
1004C22×C4—34no—
1005C22×C4—31no—
1006C22×C4—31no—
1007C22×C4—31no—
1008C22×C4—31no—
1009C22×C4—31no—
1010C22×C4—31no—
1011C22×C4—31no—
1012C22×C4—31no—
1013C22×C4—31no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—62no—
1017C22×C4—62no—
1018C22×C4—62no—
1019C22×C4—121no—
1020C22×C4—121no—
1021C22×C4—121no—
1022C22×C4—121no—
1023C22×C4—121no—
1024C22×C4—121no—
1025C22×C4—121no—
1026C22×C4—121no—
1027C22×C4—121no—
1028C22×C4—121no—
1029C22×C4—121no—
1030C22×C4D3×Q814yes—
1031C22×C4C23×D311yescharacteristic
1032C22×C4C23×D311yescharacteristic
1033C22×C4C23×D311yescharacteristic
1034C22×C4C23×D311yescharacteristic
1035C22×C4C23×D311yescharacteristic
1036C22×C4C23×D311yescharacteristic
1037C22×C4C23×D311yescharacteristic
1038C22×C4C23×D311yescharacteristic
1039C22×C4C23×D311yescharacteristic
1040C22×C4C23×D311yescharacteristic
1041C22×C4C23×D311yescharacteristic
1042C22×C4C23×D311yescharacteristic
1043C22×C4C23×D311yescharacteristic
1044C22×C4C23×D311yescharacteristic
1045C4⋊C4—34no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—62no—
1061C4⋊C4—62no—
1062C4⋊C4—62no—
1063C4⋊C4—62no—
1064C4⋊C4—62no—
1065C4⋊C4—62no—
1066C4⋊C4—62no—
1067C4⋊C4—62no—
1068C4⋊C4—62no—
1069C4⋊C4—62no—
1070C4⋊C4—62no—
1071C4⋊C4—62no—
1072C4⋊C4—121no—
1073C4⋊C4—121no—
1074C4⋊C4—121no—
1075C4⋊C4—121no—
1076C4⋊C4—121no—
1077C4⋊C4—121no—
1078C4⋊C4—121no—
1079C4⋊C4—121no—
1080C4⋊C4—121no—
1081C4⋊C4—121no—
1082C4⋊C4—121no—
1083C4⋊C4—121no—
1084C4⋊C4—121no—
1085C4⋊C4—121no—
1086C4⋊C4—121no—
1087C4⋊C4—121no—
1088C4⋊C4—121no—
1089C4⋊C4—121no—
1090C4⋊C4—121no—
1091C4⋊C4—121no—
1092C4⋊C4—121no—
1093C4⋊C4—121no—
1094C4⋊C4—121no—
1095C4⋊C4—121no—
1096C4⋊C4—121no—
1097C22⋊C4—34no—
1098C22⋊C4—34no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—62no—
1106C22⋊C4—62no—
1107C22⋊C4—62no—
1108C22⋊C4—121no—
1109C22⋊C4—121no—
1110C22⋊C4—121no—
1111C22⋊C4—121no—
1112C22⋊C4—121no—
1113C22⋊C4—121no—
1114C22⋊C4—121no—
1115C22⋊C4—121no—
1116C22⋊C4—121no—
1117C22⋊C4—121no—
1118C22⋊C4—121no—
1119C42—34no—
1120C42—41no—
1121C42—41no—
1122C42—62no—
1123C42—62no—
1124C42—121no—
1125C42—121no—
1126C42—121no—
1127C42—121no—
1128C42—121no—
1129C42—121no—
1130C42—121no—
1131C42—121no—
1132C22×C3—22no—
1133C22×C3—22no—
1134C22×C3—22no—
1135C22×C3—41no—
1136C22×C3—41no—
1137C22×C3—41no—
1138C22×C3—41no—
1139C22×C3C23×Q811yescharacteristic
1140C22×C3C2×H(5,𝔽2)11yescharacteristic
1141C22×C3C2×H(5,𝔽2)11yescharacteristic
1142C22×C3C2×2−1+411yescharacteristic
1143C22×C3#58511yescharacteristic
1144C22×C3#58511yescharacteristic
1145C22×C3#58511yescharacteristic
1146C2×D3—22no—
1147C2×D3—22no—
1148C2×D3—22no—
1149C2×D3—41no—
1150C2×D3—41no—
1151C2×D3—41no—
1152C2×D3—41no—
1153C3×C4—22no—
1154C3×C4—22no—
1155C3×C4—41no—
1156C3×C4—41no—
1157C3×C4—41no—
1158C3×C4—41no—
1159C3×C4—41no—
1160C3×C4—41no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—41no—
1164C3×C4—41no—
1165C3×C4—41no—
1166C3×C4—41no—
1167Dic3—22no—
1168Dic3—22no—
1169Dic3—22no—
1170Dic3—22no—
1171Dic3—22no—
1172Dic3—22no—
1173Dic3—41no—
1174Dic3—41no—
1175Dic3—41no—
1176Dic3—41no—
1177Dic3—41no—
1178Dic3—41no—
1179Dic3—41no—
1180Dic3—41no—
1181Dic3—41no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—32no—
1189C23—61no—
1190C23—61no—
1191C23—61no—
1192C23—61no—
1193C23—61no—
1194C23—61no—
1195C23C2×D3×Q812yes—
1196C23C24×D311yescharacteristic
1197Q8—242no—
1198Q8—242no—
1199Q8—242no—
1200Q8—242no—
1201Q8—242no—
1202D4—124no—
1203C2×C4—21no—
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—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—32no—
1244C2×C4—32no—
1245C2×C4—32no—
1246C2×C4—32no—
1247C2×C4—32no—
1248C2×C4—32no—
1249C2×C4—44no—
1250C2×C4—61no—
1251C2×C4—61no—
1252C2×C4—61no—
1253C2×C4—61no—
1254C2×C4—61no—
1255C2×C4—61no—
1256C2×C4—61no—
1257C2×C4—61no—
1258C2×C4—61no—
1259C2×C4—61no—
1260C2×C4—61no—
1261C2×C4—61no—
1262C2×C4—61no—
1263C2×C4—61no—
1264C2×C4—61no—
1265C2×C4—61no—
1266C2×C4—61no—
1267C2×C4—61no—
1268C2×C4—61no—
1269C2×C4—61no—
1270C2×C4—61no—
1271C2×C4—61no—
1272C2×C4—61no—
1273C2×C4—61no—
1274C2×C4—61no—
1275C2×C4—61no—
1276C2×C4—61no—
1277C2×C4—61no—
1278C2×C4—61no—
1279C2×C4—61no—
1280C2×C4—61no—
1281C2×C4—61no—
1282C2×C4—61no—
1283C2×C4—61no—
1284C2×C4—61no—
1285C2×C4—61no—
1286C2×C4—61no—
1287C2×C4—61no—
1288C2×C4—61no—
1289C2×C4—124no—
1290C2×C4—124no—
1291C2×C4—124no—
1292C2×C4—242no—
1293C2×C4—242no—
1294C2×C4C2×D3×Q812yes—
1295C2×C4C2×D3×Q812yes—
1296C2×C3—42no—
1297C2×C3#345811yescharacteristic
1298C2×C3#350111yescharacteristic
1299C2×C3#350311yescharacteristic
1300C2×C3#353511yescharacteristic
1301C2×C3#354211yescharacteristic
1302C2×C3#355711yescharacteristic
1303C2×C3#356211yescharacteristic
1304D3—42no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—62no—
1313C22—62no—
1314C22—62no—
1315C22—121no—
1316C22—121no—
1317C22—121no—
1318C22—121no—
1319C22C22×D3×Q811yescharacteristic
1320C22#596411yescharacteristic
1321C22#596411yescharacteristic
1322C22D3×H(5,𝔽2)11yescharacteristic
1323C22D3×H(5,𝔽2)11yescharacteristic
1324C22#596611yescharacteristic
1325C22D3×2−1+411yescharacteristic
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—62no—
1341C4—62no—
1342C4—62no—
1343C4—62no—
1344C4—62no—
1345C4—62no—
1346C4—121no—
1347C4—121no—
1348C4—121no—
1349C4—121no—
1350C4—121no—
1351C4—121no—
1352C4—121no—
1353C4—121no—
1354C4—121no—
1355C3#3675311yescharacteristic, complemented, Sylow
1356C2—42no—
1357C2—122no—
1358C2#8627411yescharacteristic
1359C2#8644111yescharacteristic
1360C2#8646211yescharacteristic
1361C2#8647411yescharacteristic
1362C2#8648111yescharacteristic
1363C2#8657411yescharacteristic
1364C2#8658611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2667C2
prime radicalC22×#67C23
hypercenter#2667D3
hypocenterC3#36753
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2667

Complements

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

NH ≅ G/Ntype
1. C3×#2667C2semidirect
3. #78076C2semidirect
4. #78068C2semidirect
6. #78004C2semidirect
7. #77968C2semidirect
8. #77923C2semidirect
9. #77921C2semidirect
10. #77912C2semidirect
11. #77911C2semidirect
12. #77861C2semidirect
13. #77855C2semidirect
16. #77369C2semidirect
17. #77351C2semidirect
18. #76244C2semidirect
19. #76098C2semidirect
20. #76063C2semidirect
21. #76001C2semidirect
22. #75318C2semidirect
23. #75133C2semidirect
24. #75131C2semidirect
25. #75128C2semidirect
26. #74117C2semidirect
29. #74001C2semidirect
30. #73557C2semidirect
206. #2667D3semidirect
258. C4×#67Q8semidirect
1355. C3#36753semidirect

Maximal subgroups

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

subgroupindex
C3×#26672
#781192
#780762
#780682
#780622
#780042
#779682
#779232
#779212
#779122
#779112
#778612
#778552
#774362
#773772
#773692
#773512
#762442
#760982
#760632
#760012
#753182
#751332
#751312
#751282
#741172
#740552
#740062
#740012
#735572
#734382
#367533