Finite Group Databasebeta

← #11884614

Subgroups — #11884614

Order 1152.

1016 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5598C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3#10594887C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592741C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591491C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591431C211yesmaximal, characteristic, complemented
10#10591186C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590561C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83543—31nomaximal
17#80097—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C3×#939—21no—
27C3×#936C2211yescharacteristic
28C3×D4×Dic3—21no—
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#887C2211yescharacteristic
34C3×#885—21no—
35C3×#878—21no—
36#63970—21no—
37#63969—21no—
38#63933—24no—
39#63905—21no—
40Dic3×D12C2211yescharacteristic
41D3×Dic3⋊C4—21no—
42#63866C2211yescharacteristic
43#63856C2211yescharacteristic
44C2×#3719C2211yescharacteristic
45C2×#3719C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47C2×#3718C2211yescharacteristic
48#63827—24no—
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63659C2211yescharacteristic
53#63637C2211yescharacteristic
54#63634C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#548—31no—
64#5824—31no—
65C2×#951—31no—
66C2×#950—31no—
67C2×#942—31no—
68C2×#912—31no—
69#5598D311yescharacteristic, complemented
70#5551—31no—
71C3×#449—31no—
72#5239—31no—
73#5228—31no—
74#5173—31no—
75#5167—31no—
76#5153—31no—
77#5060—31no—
78#5057—31no—
79#5051—31no—
80#5047—31no—
81#5042—31no—
82#5042—31no—
83#5042—61no—
84#5037D311yescharacteristic, complemented
85#5031—31no—
86#5026—31no—
87#5011—31no—
88#4813—31no—
89#4795—31no—
90#4783—31no—
91#4757—31no—
92#4739—31no—
93#4728—31no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C3×#235—22no—
106C3×#235—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—22no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—41no—
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3795—22no—
120#3795—41no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123#3757—21no—
124#3754—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3748—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×#214—41no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3719—22no—
150#3719—41no—
151#3718—22no—
152#3718—22no—
153#3715—22no—
154#3715D414yescomplemented
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C2×#237—31no—
161C2×#237C2×D311yescharacteristic
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—31no—
168C3×#124—61no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—61no—
171C3×#121—21no—
172C3×#121—61no—
173C3×#121C2×D311yescharacteristic
174C3×#121C2×D311yescharacteristic
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178#951—64no—
179#950—64no—
180#946—31no—
181#944—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188#942—64no—
189C2×#215—31no—
190C2×#215—31no—
191#939—21no—
192#939—61no—
193#938—61no—
194#936C2×D311yescharacteristic
195#935—61no—
196D4×Dic3—21no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—61no—
203C2×#214C2×D311yescharacteristic
204C2×#213C2×D311yescharacteristic
205#929—61no—
206C4×#67C2×D311yescharacteristic
207#924—31no—
208#924—31no—
209#924—31no—
210#924—61no—
211C2×Dic3⋊C4—61no—
212C2×#208—31no—
213C2×#208—31no—
214C2×#208—61no—
215C22×C3⋊C8—31no—
216#912—64no—
217C2×Dic12—31no—
218C2×Dic12—31no—
219C2×D3×C8—31no—
220#897C2×D311yescharacteristic
221D3×C4⋊C4—61no—
222#887C2×D311yescharacteristic
223#885—21no—
224#883—61no—
225#883—61no—
226#878—21no—
227C4×D12—31no—
228#869—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#830—31no—
238#830C2×D311yescharacteristic
239(C2×D3)⋊C8—31no—
240#816—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic
248#809C2×D311yescharacteristic
249#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C32×D4—21no—
259C32×D4—21no—
260C32×D4—42no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268#634—21no—
269#634—21no—
270C3×#67—41no—
271C3×#67—42no—
272C3×#67—42no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12C2×D412yes—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6C2×D412yes—
293#625—42no—
294D3×Dic3—42no—
295D3×Dic3—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)C2×D412yes—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C2×#137—91no—
301C2×#135—91no—
302#548—31no—
303#547—91no—
304#497—91no—
305#468—91no—
306#467—91no—
307#463—91no—
308#462—91no—
309#452—91no—
310#452—91no—
311#451—91no—
312#449—31no—
313#440—91no—
314#435—91no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—121no—
318C3×#41—121no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—62no—
323C2×C3×Q8—61no—
324C2×C3×Q8—121no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—41no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67#6711yescharacteristic
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351#237—22no—
352#237—41no—
353#237—62no—
354#237—121no—
355#235—22no—
356#235—41no—
357#235—62no—
358#235—121no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—41no—
369C2×Dic6—61no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C3×SD16—121no—
374C3×D8—62no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4C22×D311yescharacteristic
382C3×C4⋊C4C22×D311yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—41no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C42—31no—
392C3×C42—61no—
393#217—21no—
394#217—21no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—121no—
400#217#6711yescharacteristic
401#216—62no—
402#216—62no—
403#216—62no—
404#216—62no—
405#216—62no—
406#216—121no—
407#215—34no—
408#215—62no—
409#214—34no—
410#214—41no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—122no—
415#213—22no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4#6711yescharacteristic
420C4⋊Dic3—21no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426Dic3⋊C4—21no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—121no—
434Dic3⋊C4#6711yescharacteristic
435C4×Dic3—21no—
436C4×Dic3C22×D311yescharacteristic
437#208—62no—
438#208—62no—
439#208—122no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450Dic12—121no—
451D3×C8—62no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C32×C4—21no—
466C32×C4—41no—
467C32×C4C22×D411yescharacteristic
468C32×C4H(5,𝔽2)11yescharacteristic
469C3⋊Dic3—41no—
470C3⋊Dic3—41no—
471C3×Dic3—21no—
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—31no—
479C2×#41—91no—
480C22×Q8—31no—
481#137—184no—
482#135—184no—
483C2×Q16—91no—
484C2×Q16—91no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×D8—31no—
492C2×M16—91no—
493C22×C8—91no—
494C4⋊Q8—91no—
495#124—31no—
496#124—61no—
497#123—181no—
498#123—181no—
499C22⋊Q8—31no—
500C22⋊Q8—61no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503#121—61no—
504#121—181no—
505#121D3211yescharacteristic
506C4×Q8—31no—
507C4×D4—31no—
508C4×D4—61no—
509C4×D4—91no—
510C2×C4⋊C4—181no—
511#107—91no—
512C4⋊C8—91no—
513#103—31no—
514#103—91no—
515#103—91no—
516#103—91no—
517#102—31no—
518#102—91no—
519C22⋊C8—31no—
520C22⋊C8—91no—
521#97—91no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—41no—
527C23×C3—61no—
528C23×C3D3×D411yescharacteristic
529C23×C3C2×#6711yescharacteristic
530C22×D3—21no—
531C22×D3C2×#6711yescharacteristic
532C3×Q8—32no—
533C3×Q8—61no—
534C3×Q8—61no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—122no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—32no—
544C3×D4—41no—
545C3×D4—41no—
546C3×D4—42no—
547C3×D4—42no—
548C3×D4—61no—
549C3×D4—82no—
550C3×D4—121no—
551C3×D4—122no—
552C3×D4—122no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C2×#6711yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—41no—
580#67—42no—
581#67—42no—
582#67—122no—
583#67—122no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—42no—
588C2×Dic3—42no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—122no—
596C2×Dic3—122no—
597C2×Dic3C2×#6711yescharacteristic
598C2×Dic3C2×#6711yescharacteristic
599C2×Dic3C2×#6711yescharacteristic
600D12—21no—
601D12D3×D412yes—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—122no—
606C4×D3—122no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—21no—
611Dic6—21no—
612Dic6—42no—
613Dic6—61no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—121no—
618Dic6—121no—
619Dic6D3×D412yes—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C3⋊C8—32no—
625C3⋊C8—32no—
626C3⋊C8—62no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—121no—
630C2×C32—41no—
631C2×C32—81no—
632C2×C32D4211yescharacteristic
633C2×C32#57511yescharacteristic
634C2×C32#57811yescharacteristic
635C3×D3—41no—
636C3×D3—42no—
637#41—62no—
638#41—62no—
639#41—121no—
640#41—121no—
641#41—182no—
642#41—361no—
643C2×Q8—31no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—62no—
647C2×Q8—61no—
648C2×Q8—91no—
649C2×Q8—121no—
650C2×D4—21no—
651C2×D4—31no—
652C2×D4—31no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—181no—
656C2×D4C2×D3211yescharacteristic
657C22×C4—31no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664Q16—182no—
665Q16—182no—
666Q16—182no—
667Q16—361no—
668SD16—94no—
669SD16—121no—
670SD16—182no—
671SD16—182no—
672D8—62no—
673M16—182no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—91no—
677C2×C8—91no—
678C2×C8—182no—
679C4⋊C4—31no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—91no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C4⋊C4C2×D3211yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—31no—
690C22⋊C4—31no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—181no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C42—31no—
698C42—61no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—62no—
718C22×C3—61no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C22×#6711yescharacteristic
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—41no—
731C2×D3—41no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—62no—
743C3×C4—81no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4C2×D3×D411yescharacteristic
747C3×C4C2×D3×D411yescharacteristic
748C3×C4#100411yescharacteristic
749C3×C4#100411yescharacteristic
750Dic3—22no—
751Dic3—21no—
752Dic3—21no—
753Dic3—21no—
754Dic3—41no—
755Dic3—41no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—241no—
761Dic3—241no—
762C32#326911yescharacteristic, complemented, Sylow
763C23—21no—
764C23—31no—
765C23—61no—
766C23D3×#6711yescharacteristic
767Q8—32no—
768Q8—61no—
769Q8—61no—
770Q8—61no—
771Q8—61no—
772Q8—61no—
773Q8—122no—
774Q8—181no—
775Q8—181no—
776D4—21no—
777D4—21no—
778D4—32no—
779D4—42no—
780D4—61no—
781D4—121no—
782D4—122no—
783D4—122no—
784D4—362no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—362no—
802C2×C4—362no—
803C2×C4D3×#6711yescharacteristic
804C2×C4C22×D3211yescharacteristic
805C8—61no—
806C8—61no—
807C8—92no—
808C8—181no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—41no—
813C2×C3—41no—
814C2×C3—81no—
815C2×C3—81no—
816C2×C3—81no—
817C2×C3—122no—
818C2×C3—121no—
819C2×C3—161no—
820C2×C3#559011yescharacteristic
821C2×C3#577111yescharacteristic
822C2×C3#577311yescharacteristic
823C2×C3D4×#6711yescharacteristic
824C2×C3#582211yescharacteristic
825C2×C3#583811yescharacteristic
826D3—41no—
827D3—42no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—62no—
838C22—121no—
839C22—121no—
840C22C2×D3×#6711yescharacteristic
841C4—21no—
842C4—41no—
843C4—61no—
844C4—61no—
845C4—61no—
846C4—62no—
847C4—121no—
848C4—121no—
849C4—361no—
850C4—361no—
851C4D32×D411yescharacteristic
852C4#6431311yescharacteristic
853C3—21no—
854C3#8009711yescharacteristic, complemented
855C3#8354311yescharacteristic, complemented
856C2—41no—
857C2—81no—
858C2—121no—
859C2—122no—
860C2#1059509511yescharacteristic
861C2#1059528711yescharacteristic
862C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3269
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×#5598C2semidirect
2. C2×#63933C2semidirect
3. #10594887C2semidirect
4. C2×#63827C2semidirect
5. #10592741C2semidirect
6. C3×#5037C2semidirect
7. #10591491C2semidirect
8. #10591461C2semidirect
9. #10591431C2semidirect
10. #10591186C2semidirect
11. #10591151C2semidirect
12. #10590614C2semidirect
13. #10590561C2semidirect
14. #10590518C2semidirect
15. #10590454C2semidirect
69. #5598D3semidirect
84. #5037D3semidirect
154. #3715D4semidirect
762. C32#3269semidirect
854. C3#80097semidirect
855. C3#83543semidirect

Maximal subgroups

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

subgroupindex
C3×#55982
C2×#639332
#105948872
C2×#638272
#105927412
C3×#50372
#105914912
#105914612
#105914312
#105911862
#105911512
#105906142
#105905612
#105905182
#105904542
#835433
#800973