Finite Group Databasebeta

← #11888598

Subgroups — #11888598

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5618C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic, complemented
3#10592736C211yesmaximal, characteristic, complemented
4C3×#5042C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591460C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10591147C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11#10591101C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590562C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#83615—31nomaximal
17#80819—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#939—21no—
24C3×#938C2211yescharacteristic
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C3×#892C2211yescharacteristic
33C3×#890C2211yescharacteristic
34C3×#886—21no—
35C3×#879—21no—
36#63975—21no—
37#63958—21no—
38#63894C2211yescharacteristic
39#63883—21no—
40#63866C2211yescharacteristic
41#63857C2211yescharacteristic
42#63853—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#807C2211yescharacteristic
50#63574C2211yescharacteristic
51#63574C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#553—31no—
62#5631—31no—
63#5618D311yescharacteristic, complemented
64#5551—31no—
65C3×#468—31no—
66#5172—31no—
67#5162—31no—
68#5133—31no—
69#5127—31no—
70#5069—31no—
71#5066—31no—
72#5043—31no—
73#5042D311yescharacteristic, complemented
74#5041—31no—
75#5037—31no—
76#5037—31no—
77#5037—31no—
78#5037—61no—
79#5019—31no—
80#5014—31no—
81#5011—31no—
82#5002—31no—
83#4996—31no—
84#4971—31no—
85#4966—31no—
86#4891—31no—
87#4888—31no—
88#4804—31no—
89#4797—31no—
90#4785—31no—
91#4778—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96#3828—22no—
97#3828—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114#3754—41no—
115#3753—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#214—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×#208—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×#121—21no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#121C2×D311yescharacteristic
160C3×#121C2×D311yescharacteristic
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C3×#117—31no—
165C2×C3×C4⋊C4—31no—
166#944—31no—
167#939—21no—
168#938—61no—
169#938C2×D311yescharacteristic
170D4×Dic3—21no—
171D4×Dic3C2×D311yescharacteristic
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175C2×#214C2×D311yescharacteristic
176C2×#213—31no—
177C2×#213—31no—
178C2×#213—61no—
179C4×#67C2×D311yescharacteristic
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924—31no—
182#924C2×D311yescharacteristic
183C2×#208C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C2×D3×C8—31no—
186#897—31no—
187#894—61no—
188#893—31no—
189#892C2×D311yescharacteristic
190D3×C4⋊C4—61no—
191D3×C4⋊C4—61no—
192#890C2×D311yescharacteristic
193#886—21no—
194#884—61no—
195#883—61no—
196#883—61no—
197#883—61no—
198#879—21no—
199C4×D12—31no—
200#869—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#102—31no—
204#835—31no—
205#835—31no—
206#832C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214#816—31no—
215#816—31no—
216#815—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—42no—
255#634—21no—
256#634—21no—
257C3×#67—41no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#624—42no—
274#624—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—31no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C2×#67#6711yescharacteristic
315C22×Dic3—21no—
316C22×Dic3—21no—
317#239—62no—
318#239—121no—
319#235—62no—
320#235—62no—
321#235—62no—
322#235—122no—
323#235—121no—
324#235—121no—
325#235—121no—
326#235—122no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—121no—
344C3×M16—121no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—61no—
369#217—21no—
370#217—21no—
371#217—21no—
372#217—61no—
373#217#6711yescharacteristic
374#214—41no—
375#214—121no—
376#214—121no—
377#214—122no—
378#213—62no—
379#213—62no—
380#213—122no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4#6711yescharacteristic
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4#6711yescharacteristic
400C4×Dic3—21no—
401C4×Dic3C22×D311yescharacteristic
402#208—41no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D3×C8—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—22no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C2×#41—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×D8—91no—
443C2×M16—31no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#126—61no—
447#125—31no—
448#123—61no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453#121—31no—
454#121—61no—
455#121—181no—
456#121D3211yescharacteristic
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—61no—
460C4×D4—91no—
461#117—31no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—181no—
464#107—31no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3C2×#6711yescharacteristic
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—42no—
501C3×D4—42no—
502C3×D4—82no—
503C3×D4—121no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—41no—
532#67—81no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—124no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—81no—
544C2×Dic3—81no—
545C2×Dic3—121no—
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549D12—32no—
550D12—32no—
551D12—62no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—122no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—124no—
565Dic6—21no—
566Dic6—21no—
567Dic6—62no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—41no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32#57511yescharacteristic
587C2×C32#57711yescharacteristic
588C3⋊D3—42no—
589C3×D3—41no—
590#41—182no—
591#41—182no—
592#41—361no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—91no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610SD16—121no—
611SD16—361no—
612D8—182no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—361no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4#100411yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4D3×#4111yescharacteristic
696C3×C4#100911yescharacteristic
697Dic3—21no—
698Dic3—21no—
699Dic3—21no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707C32#330711yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—181no—
711C23D3×#6711yescharacteristic
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716D4—21no—
717D4—21no—
718D4—42no—
719D4—92no—
720D4—121no—
721D4—181no—
722D4—241no—
723D4—362no—
724D4—362no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4—362no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—81no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—121no—
758C2×C3—161no—
759C2×C3#561011yescharacteristic
760C2×C3#577311yescharacteristic
761C2×C3#577811yescharacteristic
762C2×C3#582211yescharacteristic
763C2×C3#582911yescharacteristic
764C2×C3#583611yescharacteristic
765D3—41no—
766D3—122no—
767D3—122no—
768D3—242no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—182no—
779C22—361no—
780C22—361no—
781C22C2×D3×#6711yescharacteristic
782C4—21no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—361no—
792C4#6431211yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#8081911yescharacteristic, complemented
796C3#8361511yescharacteristic, complemented
797C2—41no—
798C2—81no—
799C2—121no—
800C2—362no—
801C2#1059509511yescharacteristic
802C2#1059530511yescharacteristic
803C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5618C2semidirect
2. #10594834C2semidirect
3. #10592736C2semidirect
4. C3×#5042C2semidirect
5. #10591521C2semidirect
6. #10591489C2semidirect
7. #10591460C2semidirect
8. #10591404C2semidirect
9. #10591147C2semidirect
10. #10591106C2semidirect
11. #10591101C2semidirect
12. #10590610C2semidirect
13. #10590562C2semidirect
14. #10590468C2semidirect
15. #10590429C2semidirect
63. #5618D3semidirect
73. #5042D3semidirect
707. C32#3307semidirect
795. C3#80819semidirect
796. C3#83615semidirect

Maximal subgroups

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

subgroupindex
C3×#56182
#105948342
#105927362
C3×#50422
#105915212
#105914892
#105914602
#105914042
#105911472
#105911062
#105911012
#105906102
#105905622
#105904682
#105904292
#836153
#808193