Finite Group Databasebeta

← #11868970

Subgroups — #11868970

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic
2#10593855C211yesmaximal, characteristic, complemented
3C3×#5009C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591494C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591426C211yesmaximal, characteristic
8#10591416C211yesmaximal, characteristic
9#10590584C211yesmaximal, characteristic, complemented
10#10590574C211yesmaximal, characteristic, complemented
11#10590435C211yesmaximal, characteristic, complemented
12#10590433C211yesmaximal, characteristic, complemented
13#10590332C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81169—31nomaximal
17#81062—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C4×#638—21no—
22C2×#3752—21no—
23#64102C2211yescharacteristic
24#64101C2211yescharacteristic
25#64090—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081C2211yescharacteristic
29C3×#870C2211yescharacteristic, complemented
30C3×#869C2211yescharacteristic, complemented
31#63919C2211yescharacteristic, complemented
32#63900C2211yescharacteristic
33#63895—21no—
34#63888—21no—
35#63872C2211yescharacteristic, complemented
36#63849C2211yescharacteristic
37#63847—21no—
38#63839—21no—
39C2×#3712C2211yescharacteristic
40C2×#3710C2211yescharacteristic
41C3×#832C2211yescharacteristic
42C3×#832C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#808C2211yescharacteristic, complemented
46C3×#808C2211yescharacteristic, complemented
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5729—31no—
62#5689—31no—
63#5545—31no—
64#5545—31no—
65#5545—61no—
66C3×#478—31no—
67C3×#476—31no—
68#5087—31no—
69#5066—31no—
70#5009D311yescharacteristic, complemented
71#5008D311yescharacteristic, complemented
72#4891—31no—
73#4880—31no—
74#4871—31no—
75#4870—31no—
76#4870—31no—
77#4861—31no—
78#4861—31no—
79#4860—31no—
80#4847—31no—
81#4846—31no—
82#4839—31no—
83#4839—31no—
84#4770—31no—
85#4770—31no—
86D3×#102—31no—
87D3×#102—31no—
88#4766—31no—
89#4763—31no—
90#4759—31no—
91#4759—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3Q814yescomplemented
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×#627—21no—
105C2×#624—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C42C2311yescharacteristic
109#3757—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752D411yescharacteristic
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136Dic32—21no—
137#3712—22no—
138#3710—22no—
139#3081—91noSylow
140C2×D3×D4—31no—
141C2×D3×D4—31no—
142C2×D3×D4—61no—
143C3×C4⋊Q8—31no—
144C3×#125—31no—
145C3×C4×D4—21no—
146C3×C4×D4C2×D311yescharacteristic
147C3×C4×D4C2×D311yescharacteristic
148#946—61no—
149#944—61no—
150D4×Dic3—31no—
151D4×Dic3—31no—
152D4×Dic3—61no—
153C4×#67—61no—
154C4×#67—61no—
155C4×#67—62no—
156C2×(C2×D3)⋊C4—61no—
157C2×(C2×D3)⋊C4—61no—
158C2×(C2×D3)⋊C4—62no—
159C2×ΓL(1,𝔽25)—31no—
160C2×ΓL(1,𝔽25)—31no—
161C2×D3×C8—31no—
162C2×D3×C8—31no—
163#897—61no—
164#896—61no—
165#896—61no—
166#893—31no—
167#893—31no—
168#893—61no—
169#892—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—61no—
174D3×C4⋊C4—31no—
175D3×C4⋊C4—31no—
176#890—31no—
177#890—31no—
178#889—61no—
179#889—61no—
180#888—31no—
181#888—31no—
182#888—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—62no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—62no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192#872—31no—
193#872—31no—
194#872—61no—
195#870C2×D311yescharacteristic, complemented
196#869C2×D311yescharacteristic, complemented
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#818—31no—
216#818—31no—
217#818—31no—
218#817—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808C2×D311yescharacteristic, complemented
229#808C2×D311yescharacteristic, complemented
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—24no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3—81no—
242C22×C3⋊D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4C2×Q812yes—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—24no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—81no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C2×Q812yes—
258C4×C3⋊D3—81no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3C2×Q812yes—
261C4×C3⋊D3#4112yes—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C3×Dic6—81no—
267#627—81no—
268#624—81no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273#544—91no—
274#518—91no—
275#478—31no—
276#478—91no—
277#478—91no—
278#478—91no—
279#476—31no—
280#476—91no—
281#474—91no—
282#474—91no—
283#428—91no—
284#427—91no—
285#424—91no—
286#418—91no—
287C2×#102—91no—
288C23×D3—61no—
289C23×D3—61no—
290C23×D3—62no—
291C2×C3×Q8—61no—
292C2×C3×D4—21no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C22×D311yescharacteristic
295C22×C3×C4—22no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—62no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—62no—
304D3×D4—34no—
305D3×D4—34no—
306D3×D4—64no—
307D3×D4—62no—
308D3×D4—62no—
309D3×D4—64no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×Dic6—21no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—22no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C42—21no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347#217—61no—
348#217—61no—
349#217—62no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—62no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403ΓL(1,𝔽25)—62no—
404ΓL(1,𝔽25)—62no—
405D3×C8—62no—
406D3×C8—62no—
407C22×C32—22no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—84no—
417C2×C3⋊D3C22⋊Q812yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4C22×Q811yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—41no—
426C3⋊Dic3C22⋊Q812yes—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—91no—
432C2×M16—91no—
433C22×C8—91no—
434C4⋊Q8—31no—
435C4⋊Q8—91no—
436C4⋊Q8—181no—
437#125—31no—
438#125—91no—
439#125—181no—
440C22⋊Q8—181no—
441C22⋊Q8—181no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447C4×D4D3211yescharacteristic
448#117—91no—
449#117—91no—
450#117—91no—
451C2×C4⋊C4—91no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454#107—31no—
455#107—91no—
456#107—91no—
457#107—91no—
458#106—31no—
459#106—31no—
460#106—31no—
461#106—91no—
462C4⋊C8—31no—
463C4⋊C8—31no—
464C4⋊C8—91no—
465C4⋊C8—91no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474C23×C3—22no—
475C23×C3—21no—
476C23×C3—21no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—61no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—62no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—68no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—242no—
491C22×D3—242no—
492C3×Q8—241no—
493C3×D4—22no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4D3×Q812yes—
498C3×D4D3×Q812yes—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—81no—
510C2×C3×C4—81no—
511C2×C3×C4—82no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—64no—
519#67—64no—
520#67—68no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—62no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—242no—
540D12—32no—
541D12—32no—
542D12—62no—
543D12—62no—
544D12—61no—
545D12—61no—
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—242no—
559C4×D3—242no—
560Dic6—81no—
561Dic6—241no—
562Dic6—241no—
563C3×C8—61no—
564C3×C8—61no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—42no—
572C2×C32C2×C22⋊Q811yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57711yescharacteristic
575C3⋊D3—22no—
576C3⋊D3—42no—
577C24—181no—
578C2×Q8—61no—
579C2×Q8—181no—
580C2×D4—94no—
581C2×D4—91no—
582C2×D4—182no—
583C2×D4—181no—
584C2×D4C2×D3211yescharacteristic
585C22×C4—21no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591M16—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—182no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—91no—
621C42—181no—
622C42—181no—
623C42C2×D3211yescharacteristic
624C22×C3—24no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—32no—
637C2×D3—32no—
638C2×D3—62no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—64no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—122no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—244no—
655C2×D3—244no—
656C2×D3—248no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×D3×Q811yescharacteristic
673C3×C4C2×D3×Q811yescharacteristic
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—32no—
677Dic3—32no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—121no—
688Dic3—121no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692C32#308111yescharacteristic, complemented, Sylow
693C23—21no—
694C23—91no—
695C23—184no—
696C23—181no—
697C23—721no—
698C23—721no—
699Q8—241no—
700Q8—721no—
701D4—21no—
702D4—92no—
703D4—184no—
704D4—181no—
705D4#379712yes—
706C2×C4—21no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—81no—
712C2×C4—91no—
713C2×C4—92no—
714C2×C4—92no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—181no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4#381111yescharacteristic
723C2×C4#381111yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—61no—
728C8—61no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—44no—
733C2×C3—42no—
734C2×C3—42no—
735C2×C3D3×C22⋊Q811yescharacteristic
736C2×C3D3×C22⋊Q811yescharacteristic
737C2×C3#576211yescharacteristic
738C2×C3#576911yescharacteristic
739C2×C3#577411yescharacteristic
740C2×C3#577511yescharacteristic
741D3—62no—
742D3—62no—
743D3—122no—
744D3—124no—
745D3—122no—
746D3—122no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—92no—
751C22—181no—
752C22—181no—
753C22—182no—
754C22—361no—
755C22—361no—
756C22—724no—
757C22C2×#381111yescharacteristic
758C4—21no—
759C4—21no—
760C4—41no—
761C4—92no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—361no—
769C4C2×#379711yescharacteristic
770C4#6430611yescharacteristic
771C3—21no—
772C3#8106211yescharacteristic, complemented
773C3#8116911yescharacteristic, complemented
774C2—42no—
775C2—182no—
776C2—362no—
777C2#1059492511yescharacteristic
778C2#1059511511yescharacteristic
779C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593855C2semidirect
3. C3×#5009C2semidirect
4. C3×#5008C2semidirect
5. #10591494C2semidirect
6. #10591479C2semidirect
9. #10590584C2semidirect
10. #10590574C2semidirect
11. #10590435C2semidirect
12. #10590433C2semidirect
13. #10590332C2semidirect
14. #10590313C2semidirect
15. #10590308C2semidirect
29. C3×#870C22semidirect
30. C3×#869C22semidirect
31. #63919C22semidirect
35. #63872C22semidirect
45. C3×#808C22semidirect
46. C3×#808C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×C4⋊(C3⋊C8)C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
55. #63572C22semidirect
56. #63572C22semidirect
70. #5009D3semidirect
71. #5008D3semidirect
98. D4×C3⋊D3Q8semidirect
195. #870C2×D3semidirect
196. #869C2×D3semidirect
228. #808C2×D3semidirect
229. #808C2×D3semidirect
230. #808C2×D3semidirect
234. #807C2×D3semidirect
235. C4⋊(C3⋊C8)C2×D3semidirect
236. C4⋊(C3⋊C8)C2×D3semidirect
692. C32#3081semidirect
772. C3#81062semidirect
773. C3#81169semidirect

Maximal subgroups

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

subgroupindex
#105960162
#105938552
C3×#50092
C3×#50082
#105914942
#105914792
#105914262
#105914162
#105905842
#105905742
#105904352
#105904332
#105903322
#105903132
#105903082
#811693
#810623