Finite Group Databasebeta

← #11884479

Subgroups — #11884479

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic, complemented
2#10595431C211yesmaximal, characteristic, complemented
3#10595410C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5C3×#5187C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10591589C211yesmaximal, characteristic, complemented
11#10591540C211yesmaximal, characteristic, complemented
12#10590947C211yesmaximal, characteristic, complemented
13#10590839C211yesmaximal, characteristic, complemented
14#10590765C211yesmaximal, characteristic, complemented
15#10590737C211yesmaximal, characteristic, complemented
16#80628—31nomaximal
17#80266—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25#64128—24no—
26C2×#3745C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic, complemented
33#63939—24no—
34#63923—21no—
35#63921—21no—
36#63916—21no—
37#63916C2211yescharacteristic
38#63916C2211yescharacteristic, complemented
39#63911—21no—
40#63911C2211yescharacteristic, complemented
41#63910—21no—
42#63909—21no—
43#63909C2211yescharacteristic
44C4×#626—21no—
45C4×#626C2211yescharacteristic
46#63894C2211yescharacteristic
47#63853—21no—
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63576C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63#5834—31no—
64C2×#949—31no—
65C2×#919—31no—
66C2×#919—31no—
67C2×#919—61no—
68C2×#914—31no—
69#5676—31no—
70#5630—31no—
71#5577—31no—
72C3×#464—31no—
73C3×#452—31no—
74#5187D311yescharacteristic, complemented
75#5185D311yescharacteristic, complemented
76#5176—31no—
77#5172—31no—
78#5172—31no—
79#5058—31no—
80#5049—31no—
81#5026—31no—
82#4843—31no—
83#4836—31no—
84#4817—31no—
85#4812—31no—
86#4810—31no—
87#4810—31no—
88#4786—31no—
89#4775—31no—
90#4775—31no—
91#4773—31no—
92#4732—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—22no—
99#3832—41no—
100#3832—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C3×#239—22no—
109C3×#239—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626D411yescharacteristic
122C2×#624—21no—
123D3×D12—22no—
124D3×D12—41no—
125C32×Q16—22no—
126C2×C32×C8C2311yescharacteristic
127#3755—22no—
128#3755D414yescomplemented
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—22no—
131C8×C3⋊D3—22no—
132C3×#215—22no—
133C3×#215—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3714—22no—
153#3714—41no—
154#3713—22no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—31no—
162C2×#239—61no—
163C2×#239—61no—
164C2×#239C2×D311yescharacteristic
165C2×D3×D4—31no—
166C22×D12—31no—
167C2×C3×Q16—21no—
168C2×C3×Q16C2×D311yescharacteristic, complemented
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C3×#124—31no—
173C3×C22⋊Q8—31no—
174C3×C4×Q8—31no—
175#949—64no—
176#947C2×D311yescharacteristic
177#946C2×D311yescharacteristic
178Q8×Dic3C2×D311yescharacteristic, complemented
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—61no—
184C2×#215—61no—
185C2×#215C2×D311yescharacteristic
186C2×#215C2×D311yescharacteristic, complemented
187#940—31no—
188#940—61no—
189#938—31no—
190#938—31no—
191#938—61no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196#930—31no—
197#930—61no—
198C4×#67—31no—
199C4×#67—61no—
200C2×#208—31no—
201#919—64no—
202#919—64no—
203#919—68no—
204#914—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—61no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212C2×D3×C8—31no—
213C2×D3×C8—61no—
214#895—31no—
215#895—31no—
216#895—31no—
217#895—61no—
218#895—61no—
219#895—61no—
220#894—61no—
221#893—31no—
222#884—61no—
223#883—61no—
224#882—61no—
225#882—61no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228#874—31no—
229#874—61no—
230C4×D12—31no—
231C4×D12—31no—
232C4×D12—61no—
233C3×C4⋊C8—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835C2×D311yescharacteristic, complemented
240#835C2×D311yescharacteristic, complemented
241#821—31no—
242#821—31no—
243#821C2×D311yescharacteristic
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8C2×D311yescharacteristic
248#815—31no—
249Dic3⋊C8C2×D311yescharacteristic, complemented
250#809—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254#803—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—81no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×Q8—21no—
267C32×Q8C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—42no—
276C4⋊(C3⋊D3)—42no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C4×C3⋊D3—42no—
281C4×C3⋊D3—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295#626—41no—
296#626—42no—
297#626—42no—
298#626—81no—
299#626—81no—
300#626—81no—
301#626—81no—
302#624—81no—
303C32×C8—21no—
304C3⋊(C3⋊C8)C2×D412yes—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—91no—
309#550—91no—
310#546—91no—
311#496—91no—
312#468—91no—
313#466—91no—
314#464—31no—
315#459—91no—
316#452—31no—
317#449—91no—
318#449—91no—
319#447—91no—
320#440—91no—
321#435—91no—
322C23×D3—61no—
323C23×D3—61no—
324C3×#41—62no—
325C3×#41—121no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—31no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344#239—22no—
345#239—41no—
346#239—62no—
347#239—62no—
348#239—64no—
349#239—64no—
350#239—62no—
351#239—62no—
352#239—121no—
353#239—121no—
354#239—121no—
355#239—121no—
356#239—122no—
357#239—122no—
358D3×D4—62no—
359D3×D4—121no—
360C2×D12—21no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—121no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—121no—
395C2×C4×D3—121no—
396C2×C4×D3C22×D311yescharacteristic
397C3×Q16—24no—
398C3×Q16—22no—
399C3×Q16—22no—
400C3×SD16—62no—
401C3×SD16—121no—
402C2×C3×C8—21no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C42—31no—
415C3×C42—61no—
416#217—31no—
417#217—61no—
418#217—61no—
419#215—22no—
420#215—34no—
421#215—34no—
422#215—41no—
423#215—64no—
424#215—62no—
425#215—62no—
426#215—64no—
427#213—62no—
428#213—62no—
429#213—62no—
430#213—121no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443C4⋊Dic3—21no—
444C4⋊Dic3—31no—
445C4⋊Dic3C22×D311yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—31no—
449C4×Dic3—21no—
450C4×Dic3C22×D311yescharacteristic
451#208—62no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—62no—
458D24—62no—
459D24—64no—
460D24—62no—
461D24—121no—
462ΓL(1,𝔽25)—62no—
463D3×C8—62no—
464D3×C8—62no—
465D3×C8—64no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485D32—84no—
486C32×C4—22no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—31no—
497C2×#41—91no—
498C2×#41—91no—
499C22×D4—91no—
500AGL(1,ℤ/8)—184no—
501#135—184no—
502C2×Q16D3211yescharacteristic, complemented
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—91no—
512C22×C8—91no—
513#127—91no—
514#127—181no—
515#124—31no—
516#123—181no—
517C22⋊Q8—31no—
518#121—91no—
519#121—91no—
520#121—91no—
521#121—181no—
522#121—181no—
523#121—181no—
524#120—181no—
525C4×Q8—31no—
526C4×D4—91no—
527C4×D4—91no—
528C4×D4—181no—
529C2×C22⋊C4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—31no—
533#103—31no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—31no—
542C23×C3—61no—
543C23×C3—61no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3D3×D411yescharacteristic
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—22no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—22no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8D3×D412yes—
573C3×Q8D3×D412yes—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—122no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—121no—
597#67—122no—
598#67—122no—
599#67—241no—
600#67—241no—
601#67—241no—
602#67—241no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—61no—
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—32no—
616D12—32no—
617D12—42no—
618D12—62no—
619D12—62no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—121no—
627D12—121no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—124no—
633D12—124no—
634D12—121no—
635D12—122no—
636D12—122no—
637D12—241no—
638D12—241no—
639D12—241no—
640D12—241no—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—42no—
644C4×D3—62no—
645C4×D3—62no—
646C4×D3—61no—
647C4×D3—61no—
648C4×D3—61no—
649C4×D3—61no—
650C4×D3—122no—
651C4×D3—122no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—124no—
655C4×D3—124no—
656C4×D3—241no—
657C4×D3—241no—
658C3×C8—22no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—61no—
662C3×C8—61no—
663C3⋊C8—21no—
664C3⋊C8—21no—
665C3⋊C8—32no—
666C3⋊C8—32no—
667C3⋊C8—62no—
668C2×C32D4211yescharacteristic
669C2×C32#57511yescharacteristic
670C2×C32#57611yescharacteristic
671C3⋊D3—41no—
672C3⋊D3—42no—
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—81no—
676C3×D3—81no—
677C24—181no—
678#41—62no—
679#41—121no—
680#41—182no—
681#41—182no—
682#41—361no—
683#41—361no—
684C2×Q8C2×D3211yescharacteristic
685C2×Q8C2×D3211yescharacteristic
686C2×D4—31no—
687C2×D4—31no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—91no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C22×C4—31no—
703C22×C4—61no—
704C22×C4—91no—
705C22×C4—181no—
706C22×C4—181no—
707C22×C4—181no—
708Q16—22no—
709SD16—62no—
710SD16—94no—
711SD16—121no—
712SD16—182no—
713D8—182no—
714D8—182no—
715D8—182no—
716D8—361no—
717M16—182no—
718C2×C8—31no—
719C2×C8—31no—
720C2×C8—91no—
721C2×C8—182no—
722C2×C8C2×D3211yescharacteristic
723C4⋊C4—31no—
724C4⋊C4—31no—
725C4⋊C4—61no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C42—31no—
738C42—61no—
739C22×C3—21no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—62no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—62no—
767C2×D3—61no—
768C2×D3—62no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—122no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—244no—
788C2×D3—244no—
789C3×C4—22no—
790C3×C4—22no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100911yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812Dic3—61no—
813Dic3—61no—
814C32#326811yescharacteristic, complemented, Sylow
815C23—31no—
816C23—61no—
817C23—61no—
818C23—91no—
819C23—181no—
820C23—181no—
821C23—362no—
822C23—362no—
823C23—721no—
824Q8—21no—
825Q8—21no—
826Q8—21no—
827Q8#381112yes—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—92no—
833D4—122no—
834D4—181no—
835D4—181no—
836D4—181no—
837D4—362no—
838D4—362no—
839D4—361no—
840D4—362no—
841D4—362no—
842D4—721no—
843D4—721no—
844D4—721no—
845D4—721no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—91no—
856C2×C4—122no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—362no—
860C2×C4—362no—
861C2×C4—721no—
862C2×C4C22×D3211yescharacteristic
863C8—21no—
864C8—61no—
865C8—61no—
866C8—92no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—121no—
871C2×C3—241no—
872C2×C3—241no—
873C2×C3#559011yescharacteristic
874C2×C3#560911yescharacteristic
875C2×C3#576911yescharacteristic
876C2×C3#576911yescharacteristic
877C2×C3#577711yescharacteristic
878C2×C3#577711yescharacteristic
879D3—41no—
880D3—81no—
881D3—81no—
882D3—122no—
883D3—121no—
884D3—122no—
885D3—121no—
886D3—122no—
887D3—242no—
888D3—242no—
889D3—241no—
890D3—241no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—182no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—724no—
910C22D32×D411yescharacteristic
911C4—22no—
912C4—41no—
913C4—61no—
914C4—61no—
915C4—61no—
916C4—121no—
917C4—121no—
918C4—181no—
919C4#6431411yescharacteristic
920C4C2×#381111yescharacteristic
921C3—21no—
922C3#8026611yescharacteristic, complemented
923C3#8062811yescharacteristic, complemented
924C2—121no—
925C2—241no—
926C2—241no—
927C2—361no—
928C2—362no—
929C2—721no—
930C2#1059476211yescharacteristic
931C2#1059477111yescharacteristic
932C2#1059529211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. #10595431C2semidirect
3. #10595410C2semidirect
4. C2×#63939C2semidirect
5. C3×#5187C2semidirect
6. C3×#5185C2semidirect
7. #10591619C2semidirect
8. #10591593C2semidirect
9. #10591593C2semidirect
10. #10591589C2semidirect
11. #10591540C2semidirect
12. #10590947C2semidirect
13. #10590839C2semidirect
14. #10590765C2semidirect
15. #10590737C2semidirect
19. C2×#3832C22semidirect
22. C2×C32×Q16C22semidirect
24. C2×#3755C22semidirect
27. C2×C8×C3⋊D3C22semidirect
30. C3×Q8×Dic3C22semidirect
32. C2×C3×#215C22semidirect
38. #63916C22semidirect
40. #63911C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
55. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63576C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
74. #5187D3semidirect
75. #5185D3semidirect
128. #3755D4semidirect
168. C2×C3×Q16C2×D3semidirect
169. C2×C3×Q16C2×D3semidirect
178. Q8×Dic3C2×D3semidirect
186. C2×#215C2×D3semidirect
239. #835C2×D3semidirect
240. #835C2×D3semidirect
244. #821C2×D3semidirect
249. Dic3⋊C8C2×D3semidirect
502. C2×Q16D32semidirect
814. C32#3268semidirect
922. C3#80266semidirect
923. C3#80628semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
#105954312
#105954102
C2×#639392
C3×#51872
C3×#51852
#105916192
#105915932
#105915892
#105915402
#105909472
#105908392
#105907652
#105907372
#806283
#802663