Finite Group Databasebeta

← #11889216

Subgroups — #11889216

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5641C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592751C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591634C211yesmaximal, characteristic, complemented
7#10591604C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591151C211yesmaximal, characteristic, complemented
10#10591134C211yesmaximal, characteristic, complemented
11#10591085C211yesmaximal, characteristic, complemented
12#10590608C211yesmaximal, characteristic, complemented
13#10590531C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#83665—31nomaximal
17#80162—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C3×#898—21no—
31C3×#892C2211yescharacteristic, complemented
32C3×#888C2211yescharacteristic, complemented
33C3×#887—21no—
34C3×#885—21no—
35C3×#879—21no—
36#63976—21no—
37D3×#217—21no—
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63885—21no—
41#63884—21no—
42#63860C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#556—31no—
62#5806—31no—
63#5641D311yescharacteristic, complemented
64#5550—31no—
65C3×#450—31no—
66#5215—31no—
67#5173—31no—
68#5171—31no—
69#5166—31no—
70#5164—31no—
71#5089—31no—
72#5084—31no—
73#5052—31no—
74#5052—31no—
75#5052—61no—
76#5048—31no—
77#5047—31no—
78#5046D311yescharacteristic, complemented
79#5028—31no—
80#5026—31no—
81#5011—31no—
82#5003—31no—
83#5002—31no—
84#5001—31no—
85#4996—31no—
86#4784—31no—
87#4772—31no—
88#4765—31no—
89#4761—31no—
90#4728—31no—
91#4723—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×#625—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114#3756—41no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3748—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#215—22no—
123C3×#215—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#126—61no—
153C3×#126—61no—
154C3×#124—61no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8C2×D311yescharacteristic
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C4×Q8—31no—
160C3×C4×Q8—61no—
161C3×C4×D4—31no—
162C3×#117—31no—
163C3×#117—31no—
164#953—61no—
165C2×#217—61no—
166#946C2×D311yescharacteristic, complemented
167Q8×Dic3C2×D311yescharacteristic, complemented
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#215C2×D311yescharacteristic
172C2×#215C2×D311yescharacteristic
173#939—61no—
174#938—31no—
175#937—61no—
176#936—31no—
177#935—61no—
178D4×Dic3—31no—
179#930—31no—
180C4×#67C2×D311yescharacteristic
181#926C2×D311yescharacteristic
182#924—31no—
183#924—31no—
184#924—61no—
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C22×C3⋊C8—31no—
189C2×D3×C8—31no—
190#898—21no—
191#894—61no—
192#892C2×D311yescharacteristic, complemented
193#888C2×D311yescharacteristic, complemented
194#887—21no—
195#885—21no—
196#884—61no—
197D3×C22⋊C4—61no—
198#879—21no—
199#875—31no—
200C4×D12—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#818—31no—
215#817—31no—
216#816—31no—
217#816—31no—
218#815—31no—
219Dic3⋊C8—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
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—
255#634—21no—
256#634—21no—
257C3×#67—41no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—42no—
271#625—42no—
272#625—81no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—31no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—61no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—121no—
306C22×C3×C4—21no—
307C22×C3×C4—31no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67#6711yescharacteristic
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—121no—
319#235—62no—
320#235—121no—
321C2×D12—22no—
322C2×D12—21no—
323C2×D12—41no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361#217—21no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#217#6711yescharacteristic
370#216—121no—
371#216—121no—
372#216—122no—
373#215—22no—
374#215—41no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3C22×D311yescharacteristic
398#208—121no—
399#208—121no—
400#208—122no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—31no—
445#126—61no—
446#126—61no—
447#124—61no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8D3211yescharacteristic
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×Q8—61no—
458C4×D4—31no—
459C4×D4—91no—
460#117—31no—
461#117—31no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×#6711yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—122no—
502C3×D4—32no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—122no—
507C3×D4—121no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—41no—
534#67—122no—
535#67—122no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—241no—
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551D12—21no—
552D12—21no—
553D12—21no—
554D12—42no—
555D12#23712yes—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—122no—
559C4×D3—241no—
560Dic6—42no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—62no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32—41no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—42no—
583C3×D3—81no—
584C24—61no—
585#41—182no—
586#41—361no—
587C2×Q8—61no—
588C2×Q8—91no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—62no—
594C2×D4—61no—
595C2×D4—121no—
596C2×D4—181no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4C2×D3211yescharacteristic
602Q16—361no—
603SD16—62no—
604SD16—121no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—91no—
610C2×C8—361no—
611C4⋊C4—21no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—31no—
633C42—61no—
634C42—61no—
635C42—61no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—244no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×#6711yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23711yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—122no—
704C23—122no—
705C23—241no—
706C23D3×#6711yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—122no—
710Q8—181no—
711Q8—181no—
712D4—32no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—121no—
718D4—362no—
719D4—721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4D3×#6711yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—61no—
738C8—61no—
739C8—181no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—81no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3—241no—
750C2×C3#559111yescharacteristic
751C2×C3#576211yescharacteristic
752C2×C3#577311yescharacteristic
753C2×C3#582211yescharacteristic
754C2×C3#582911yescharacteristic
755C2×C3#583711yescharacteristic
756D3—42no—
757D3—41no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—61no—
763C22—61no—
764C22—62no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22C2×D3×#6711yescharacteristic
773C4—21no—
774C4—41no—
775C4—41no—
776C4—61no—
777C4—61no—
778C4—61no—
779C4—121no—
780C4—121no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#8016211yescharacteristic, complemented
787C3#8366511yescharacteristic, complemented
788C2—41no—
789C2—121no—
790C2—122no—
791C2—241no—
792C2#1059530411yescharacteristic
793C2#1059531811yescharacteristic
794C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22⋊Q8D32
hypocenterC32#3311
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×#5641C2semidirect
3. #10592751C2semidirect
4. C3×#5046C2semidirect
5. #10591655C2semidirect
6. #10591634C2semidirect
7. #10591604C2semidirect
8. #10591566C2semidirect
9. #10591151C2semidirect
10. #10591134C2semidirect
11. #10591085C2semidirect
12. #10590608C2semidirect
13. #10590531C2semidirect
14. #10590505C2semidirect
15. #10590465C2semidirect
21. C2×#3756C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
31. C3×#892C22semidirect
32. C3×#888C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63637C22semidirect
46. #63635C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
63. #5641D3semidirect
78. #5046D3semidirect
166. #946C2×D3semidirect
167. Q8×Dic3C2×D3semidirect
192. #892C2×D3semidirect
193. #888C2×D3semidirect
699. C32#3311semidirect
786. C3#80162semidirect
787. C3#83665semidirect

Maximal subgroups

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

subgroupindex
C3×#56412
#105948862
#105927512
C3×#50462
#105916552
#105916342
#105916042
#105915662
#105911512
#105911342
#105910852
#105906082
#105905312
#105905052
#105904652
#836653
#801623