Finite Group Databasebeta

← #11889706

Subgroups — #11889706

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595982C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic
3C3×#4970C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591157C211yesmaximal, characteristic, complemented
8#10590618C211yesmaximal, characteristic, complemented
9#10590612C211yesmaximal, characteristic, complemented
10#10590541C211yesmaximal, characteristic, complemented
11#10590538C211yesmaximal, characteristic, complemented
12#10590510C211yesmaximal, characteristic, complemented
13#10590506C211yesmaximal, characteristic, complemented
14#10590471C211yesmaximal, characteristic, complemented
15#10590461C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#78763—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C4×#638—21no—
22C4×#638C2211yescharacteristic
23#64133—21no—
24#64133C2211yescharacteristic
25#64106C2211yescharacteristic, complemented
26#64105—21no—
27C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
28#64098—21no—
29#64097C2211yescharacteristic, complemented
30#64096C2211yescharacteristic, complemented
31C3×#924C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63977—21no—
34D3×#217—21no—
35#63916C2211yescharacteristic
36#63898C2211yescharacteristic
37#63886—21no—
38#63884—21no—
39#63863C2211yescharacteristic
40C2×#3719C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5806—31no—
62#5630—31no—
63#5511—31no—
64#5511—31no—
65#5511—61no—
66C3×#484—31no—
67C2×C3×#102—31no—
68#5218—31no—
69#5116—31no—
70#5111—31no—
71#5051—31no—
72#4970D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4890—31no—
75#4889—31no—
76#4886—31no—
77#4882—31no—
78#4808—31no—
79#4803—31no—
80#4798—31no—
81#4794—31no—
82#4783—31no—
83#4780—31no—
84#4774—31no—
85#4771—31no—
86#4767—31no—
87#4765—31no—
88#4759—31no—
89#4757—31no—
90#4731—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3757D411yescharacteristic
117#3752—21no—
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123#3750—21no—
124#3750—21no—
125#3750D411yescharacteristic
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#217—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3719—41no—
141#3716—22no—
142#3716—41no—
143#3712—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154#953—61no—
155C2×#217—61no—
156#947—31no—
157C2×#216—31no—
158#939—61no—
159#938—31no—
160#936—31no—
161#935—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164C2×#214—31no—
165C4×#67—31no—
166C4×#67—31no—
167C4×#67—61no—
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—62no—
171#924—31no—
172#924—31no—
173#924—61no—
174#924—61no—
175#924—61no—
176#924—62no—
177#924C2×D311yescharacteristic
178C22×C3⋊C8C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×#204—31no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184#897—31no—
185#897—31no—
186#897—61no—
187#896—61no—
188#896—61no—
189#896—62no—
190#895—31no—
191#895—61no—
192#894—61no—
193#893—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—61no—
197#889—61no—
198#889—61no—
199#889—62no—
200#888—31no—
201#888—31no—
202#888—61no—
203#887—31no—
204#887—31no—
205#887—61no—
206#882—61no—
207D3×C22⋊C4—61no—
208C3×#107—31no—
209C3×#107—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#835—31no—
218#832—31no—
219#832—31no—
220#830C2×D311yescharacteristic
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229#815—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232#810—31no—
233#810C2×D311yescharacteristic, complemented
234#810C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic
239#807—31no—
240#807C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—81no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—22no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—81no—
265#634—21no—
266#634—21no—
267#634—81no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×D12#4112yes—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—81no—
279D3×Dic3—42no—
280D3×Dic3—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—91no—
287#489—91no—
288#484—31no—
289#480—91no—
290#474—91no—
291#468—91no—
292#467—91no—
293#464—91no—
294#452—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#417—91no—
299C2×#102—31no—
300C24×C3—61no—
301C23×D3—21no—
302C2×C3×Q8—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321#239—62no—
322#239—121no—
323#237—62no—
324#237—121no—
325C2×D12—22no—
326C2×D12—21no—
327C2×D12—41no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—62no—
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—62no—
346C2×Dic6C22×D311yescharacteristic
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364#217—21no—
365#217—31no—
366#217—31no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—62no—
373#217—61no—
374#217—61no—
375#216—121no—
376#214—62no—
377#214—121no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—62no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—62no—
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—62no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—121no—
423#204—62no—
424#204—121no—
425ΓL(1,𝔽25)—121no—
426ΓL(1,𝔽25)—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32#13712yes—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—84no—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4C2×#4111yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—91no—
454C22×D4—31no—
455C2×Q16—91no—
456C2×SD16—91no—
457C2×SD16—91no—
458C2×M16—91no—
459C22×C8—31no—
460C4⋊Q8—91no—
461#125—181no—
462#124—91no—
463#123—181no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—181no—
468C22⋊Q8—181no—
469#121—91no—
470#121—181no—
471#120—181no—
472C4×Q8—91no—
473C4×D4—91no—
474C4×D4—91no—
475C4×D4—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4D3211yescharacteristic
478C2×C22⋊C4—181no—
479#107—31no—
480#107—31no—
481#107—91no—
482C4⋊C8—91no—
483#103—31no—
484#103—31no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102—31no—
491#102—91no—
492#102—91no—
493C22⋊C8—31no—
494C22⋊C8—91no—
495#97—91no—
496C23×C3—21no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—61no—
511C22×D3—81no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—32no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—122no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—81no—
536C2×C3×C4—81no—
537C2×C3×C4—82no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—64no—
543#67—62no—
544#67—62no—
545#67—122no—
546#67—241no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—122no—
565C2×Dic3—241no—
566D12—21no—
567D12—21no—
568D12—21no—
569D12—42no—
570D12—122no—
571D12—241no—
572D12#23512yes—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—121no—
578C4×D3—121no—
579C4×D3—122no—
580C4×D3—241no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—242no—
584Dic6—21no—
585Dic6—21no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—61no—
590Dic6—121no—
591Dic6—121no—
592Dic6—241no—
593Dic6—241no—
594Dic6—242no—
595C3×C8—61no—
596C3×C8—61no—
597C3×C8—61no—
598C3×C8—61no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32—22no—
604C2×C32#54611yescharacteristic
605C2×C32C2×#13711yescharacteristic
606C2×C32#57611yescharacteristic
607C3⋊D3—41no—
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611#41—182no—
612#41—361no—
613C2×Q8—31no—
614C2×Q8—91no—
615C2×Q8—181no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—62no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—121no—
622C2×D4—181no—
623C2×D4—181no—
624C22×C4—21no—
625C22×C4—91no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630Q16—361no—
631SD16—182no—
632SD16—361no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—121no—
639C4⋊C4—21no—
640C4⋊C4—31no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4C2×D3211yescharacteristic
650C4⋊C4C2×D3211yescharacteristic
651C22⋊C4—61no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C42—91no—
661C42—181no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—62no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—244no—
677C22×C3#91512yes—
678C22×C3#91812yes—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—22no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—62no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—84no—
695C2×D3—121no—
696C2×D3—121no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23511yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4#100911yescharacteristic
714Dic3—41no—
715Dic3—41no—
716Dic3—62no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—122no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#331411yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—91no—
735C23—122no—
736C23—122no—
737C23—241no—
738C23#381111yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—181no—
742Q8—181no—
743Q8—721no—
744D4—32no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—122no—
749D4—182no—
750D4—362no—
751D4—721no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—81no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—362no—
767C2×C4—721no—
768C2×C4—721no—
769C2×C4#381111yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—61no—
774C8—61no—
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—42no—
781C2×C3—122no—
782C2×C3—241no—
783C2×C3#549011yescharacteristic
784C2×C3#565411yescharacteristic
785C2×C3#575711yescharacteristic
786C2×C3C2×#91511yescharacteristic
787C2×C3C2×#91811yescharacteristic
788C2×C3#577411yescharacteristic
789D3—42no—
790D3—81no—
791D3—122no—
792D3—121no—
793D3—121no—
794C22—21no—
795C22—21no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—244no—
806C22#6395112yes—
807C22C2×#381111yescharacteristic
808C4—21no—
809C4—41no—
810C4—41no—
811C4—121no—
812C4—121no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—361no—
817C4—361no—
818C4D3×#23511yescharacteristic
819C4#6430711yescharacteristic
820C3—21no—
821C3#7876311yescharacteristic, complemented
822C3#8148611yescharacteristic, complemented
823C2—22no—
824C2—122no—
825C2—241no—
826C2—361no—
827C2#1059507711yescharacteristic
828C2#1059510211yescharacteristic
829C2C2×#6395111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595982C2semidirect
3. C3×#4970C2semidirect
4. C2×C3×#809C2semidirect
5. #10591187C2semidirect
6. #10591172C2semidirect
7. #10591157C2semidirect
8. #10590618C2semidirect
9. #10590612C2semidirect
10. #10590541C2semidirect
11. #10590538C2semidirect
12. #10590510C2semidirect
13. #10590506C2semidirect
14. #10590471C2semidirect
15. #10590461C2semidirect
25. #64106C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
29. #64097C22semidirect
30. #64096C22semidirect
40. C2×#3719C22semidirect
43. C2×#3712C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
72. #4970D3semidirect
73. C2×#809D3semidirect
233. #810C2×D3semidirect
234. #810C2×D3semidirect
240. #807C2×D3semidirect
241. #807C2×D3semidirect
731. C32#3314semidirect
821. C3#78763semidirect
822. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105959822
#105948892
C3×#49702
C2×C3×#8092
#105911872
#105911722
#105911572
#105906182
#105906122
#105905412
#105905382
#105905102
#105905062
#105904712
#105904612
#814863
#787633