Finite Group Databasebeta

← #11878380

Subgroups — #11878380

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic
3#10592742C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic, complemented
5#10591635C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591587C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591170C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591103C211yesmaximal, characteristic, complemented
12#10590520C211yesmaximal, characteristic, complemented
13#10590519C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590501C211yesmaximal, characteristic, complemented
16#83408—31nomaximal
17#80238—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#894—21no—
29C3×#892C2211yescharacteristic
30C3×#888—21no—
31C3×#885—21no—
32C3×#883—21no—
33#63980—21no—
34#63980—21no—
35#63908—21no—
36#63908C2211yescharacteristic
37#63908C2211yescharacteristic
38#63856—21no—
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63657C2211yescharacteristic
48#63635C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5833—31no—
63#5833—31no—
64#5628D311yescharacteristic, complemented
65C3×#452—31no—
66#5239—31no—
67#5234—31no—
68#5228—31no—
69#5227—31no—
70#5188—31no—
71#5186—31no—
72#5174—31no—
73#5170—31no—
74#5052—31no—
75#5051—31no—
76#5049—31no—
77#5048—31no—
78#5047—31no—
79#5047D311yescharacteristic, complemented
80#5044—31no—
81#5043—31no—
82#5043—31no—
83#5043—61no—
84#5003—31no—
85#4996—31no—
86#4816—31no—
87#4814—31no—
88#4784—31no—
89#4778—31no—
90#4727—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C2×C3×#67D411yescharacteristic
98C3×D3×Q8—41no—
99C3×D3×Q8—41no—
100C3×#235—41no—
101C3×#235—41no—
102C3×#235—41no—
103C3×#235—41no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6D411yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#625—21no—
115C2×#625—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#216—41no—
126C3×#215—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3718—41no—
144#3715—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C22×C3×Q8—31no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C3×C4⋊Q8—61no—
157C3×#124—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×#117—31no—
167#946—31no—
168#946—31no—
169#946—61no—
170#946C2×D311yescharacteristic
171C2×#216—31no—
172C2×#216—31no—
173C2×#216C2×D311yescharacteristic
174C2×#215—31no—
175C2×#215C2×D311yescharacteristic
176#939—61no—
177#939—61no—
178#939—61no—
179#939—61no—
180#938—31no—
181#938—31no—
182#938—61no—
183C2×#214—31no—
184#930—31no—
185#930—31no—
186#930—61no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—61no—
190#924—31no—
191#924—31no—
192#924—61no—
193#924C2×D311yescharacteristic
194C2×#208—31no—
195C22×C3⋊C8—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×D3×C8—31no—
198#897C2×D311yescharacteristic
199#894—21no—
200#892C2×D311yescharacteristic
201#888—21no—
202#885—21no—
203#883—21no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835—61no—
216#832—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#818—31no—
227#816—31no—
228#816—31no—
229#810—31no—
230#810C2×D311yescharacteristic
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238#808—61no—
239#807—31no—
240#807—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C3×#67—41no—
257C3×#67—41no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—41no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—41no—
278C3×Dic6—42no—
279#625—81no—
280#625—81no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—31no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—91no—
294#465—91no—
295#452—31no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—91no—
300C3×#41—121no—
301C3×#41—121no—
302C3×#41—121no—
303C3×#41—121no—
304C2×C3×Q8—21no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—61no—
309C2×C3×Q8—121no—
310C2×C3×Q8—121no—
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—61no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67#6711yescharacteristic
331C2×#67#6711yescharacteristic
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—121no—
335D3×Q8—41no—
336D3×Q8—41no—
337#235—41no—
338#235—41no—
339#235—41no—
340#235—41no—
341C2×D12#6711yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—21no—
348C2×Dic6#6711yescharacteristic
349C2×Dic6C22×D311yescharacteristic
350C2×Dic6C22×D311yescharacteristic
351C3×Q16—121no—
352C3×SD16—121no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—61no—
373#217—21no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#216—41no—
379#216—121no—
380#216—121no—
381#215—41no—
382#215—121no—
383#214—121no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—121no—
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408C4×Dic3—21no—
409#208—121no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—121no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419ΓL(1,𝔽25)—121no—
420D3×C8—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C32×C4—21no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4H(5,𝔽2)11yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C2×#41—31no—
447C2×#41—31no—
448C22×Q8—31no—
449C2×Q16—31no—
450C2×Q16—91no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×M16—91no—
454C22×C8—91no—
455C4⋊Q8—61no—
456#124—61no—
457#123—61no—
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8D3211yescharacteristic
466#121—91no—
467#121—91no—
468#121—181no—
469#121—181no—
470#121—181no—
471#117—31no—
472C2×C4⋊C4—91no—
473#107—91no—
474#107—91no—
475#106—91no—
476#106—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482#103—91no—
483#102—31no—
484#102—91no—
485C22⋊C8—31no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3D3×D411yescharacteristic
494C23×C3C2×#6711yescharacteristic
495C22×D3—21no—
496C22×D3C2×#6711yescharacteristic
497C22×D3C2×#6711yescharacteristic
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—121no—
509C3×Q8—122no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—121no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—122no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4—122no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—41no—
546#67—41no—
547#67—42no—
548#67—241no—
549#67—241no—
550#67—241no—
551#67—241no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—241no—
562C2×Dic3—241no—
563C2×Dic3—242no—
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566D12—21no—
567D12—21no—
568D12—41no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—42no—
574C4×D3—42no—
575Dic6—21no—
576Dic6—21no—
577Dic6—21no—
578Dic6—21no—
579Dic6—41no—
580Dic6—42no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C3⋊C8—121no—
591C2×C32—41no—
592C2×C32#53411yescharacteristic
593C2×C32#57711yescharacteristic
594C2×C32#57811yescharacteristic
595C3×D3—41no—
596C3×D3—41no—
597C3×D3—81no—
598#41—121no—
599#41—121no—
600#41—121no—
601#41—121no—
602C2×Q8—31no—
603C2×Q8—31no—
604C2×Q8—31no—
605C2×Q8—61no—
606C2×Q8—121no—
607C2×Q8—121no—
608C2×Q8C2×D3211yescharacteristic
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—181no—
615C2×D4—181no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—181no—
621C22×C4C2×D3211yescharacteristic
622Q16—121no—
623Q16—361no—
624SD16—121no—
625SD16—361no—
626M16—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—91no—
631C2×C8—361no—
632C4⋊C4—21no—
633C4⋊C4—31no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4C2×D3211yescharacteristic
643C22⋊C4—21no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—61no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C22×#6711yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4#100411yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4#100411yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—241no—
713Dic3—241no—
714C32#320111yescharacteristic, complemented, Sylow
715C23—31no—
716C23—31no—
717C23—61no—
718C23D3×#6711yescharacteristic
719Q8—21no—
720Q8—21no—
721Q8—61no—
722Q8—61no—
723Q8—61no—
724Q8—61no—
725Q8—121no—
726Q8—122no—
727D4—61no—
728D4—61no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—122no—
733D4—721no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—721no—
753C2×C4D3×#6711yescharacteristic
754C2×C4C22×D3211yescharacteristic
755C8—61no—
756C8—61no—
757C8—181no—
758C8—181no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—121no—
766C2×C3—121no—
767C2×C3—241no—
768C2×C3#558911yescharacteristic
769C2×C3#577111yescharacteristic
770C2×C3#577811yescharacteristic
771C2×C3#580411yescharacteristic
772C2×C3#583711yescharacteristic
773C2×C3#583811yescharacteristic
774D3—41no—
775D3—41no—
776D3—81no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22C2×D3×#6711yescharacteristic
790C4—21no—
791C4—41no—
792C4—41no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—361no—
799C4—361no—
800C4#6431311yescharacteristic
801C4#6431311yescharacteristic
802C3—21no—
803C3#8023811yescharacteristic, complemented
804C3#8340811yescharacteristic, complemented
805C2—41no—
806C2—121no—
807C2—121no—
808C2—241no—
809C2#1059523011yescharacteristic
810C2#1059531911yescharacteristic
811C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC22⋊Q8D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5628C2semidirect
3. #10592742C2semidirect
4. C3×#5047C2semidirect
5. #10591635C2semidirect
6. #10591594C2semidirect
7. #10591587C2semidirect
8. #10591583C2semidirect
9. #10591170C2semidirect
10. #10591145C2semidirect
11. #10591103C2semidirect
12. #10590520C2semidirect
13. #10590519C2semidirect
14. #10590505C2semidirect
15. #10590501C2semidirect
64. #5628D3semidirect
79. #5047D3semidirect
714. C32#3201semidirect
803. C3#80238semidirect
804. C3#83408semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105950442
#105927422
C3×#50472
#105916352
#105915942
#105915872
#105915832
#105911702
#105911452
#105911032
#105905202
#105905192
#105905052
#105905012
#834083
#802383