Finite Group Databasebeta

← #11864507

Subgroups — #11864507

Order 1152.

1474 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×D3×#216C211yesmaximal, characteristic, complemented
4#10594884C211yesmaximal, characteristic, complemented
5#10592927C211yesmaximal, characteristic, complemented
6C3×#5228C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591595C211yesmaximal, characteristic, complemented
10#10591594C211yesmaximal, characteristic, complemented
11#10591557C211yesmaximal, characteristic, complemented
12#10591556C211yesmaximal, characteristic, complemented
13#10591173C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84117—31nomaximal
17#80185—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C3×#1007—24no—
20C3×#1007—24no—
21C2×C3×#239—21no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic
24C2×C3×D3×Q8—21no—
25C2×C3×D3×Q8C2211yescharacteristic
26C2×C3×D3×Q8C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3756C2211yescharacteristic
33C2×#3756C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C3×#924C2211yescharacteristic
38#63969—21no—
39#63959—21no—
40#63943—24no—
41D3×#216—24no—
42#63884—21no—
43#63857C2211yescharacteristic
44#63856C2211yescharacteristic
45#63841C2211yescharacteristic
46#63839—21no—
47C2×#3719C2211yescharacteristic
48C2×#3718C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic
54#63662C2211yescharacteristic
55#63657C2211yescharacteristic
56C3×#835C2211yescharacteristic
57C3×#835C2211yescharacteristic
58C3×#830C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×C3×2−1+4—31no—
66C2×#1007D311yescharacteristic
67#5825—31no—
68C2×#951—31no—
69C22×#216—31no—
70C2×#918—31no—
71C2×D3×Q16—31no—
72#5628—31no—
73C3×#451—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—31no—
78#5234—31no—
79#5233—31no—
80#5228—31no—
81#5228—31no—
82#5228—31no—
83#5228—31no—
84#5228—61no—
85#5228D311yescharacteristic, complemented
86#5225—31no—
87#5187—31no—
88#5186—31no—
89#5047—31no—
90#4809—31no—
91#4808—31no—
92#4804—31no—
93#4802—31no—
94#4733—31no—
95#4727—31no—
96C2×C32×Q8—22no—
97C2×C32×Q8—22no—
98C2×C32×Q8—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C2×C3×#67D411yescharacteristic
107C3×#239—28no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239D414yes—
112C3×D3×Q8—28no—
113C3×D3×Q8—22no—
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8D414yes—
117C3×#235—28no—
118C3×#235—28no—
119C3×#235—22no—
120C3×#235—22no—
121C3×#235—22no—
122C3×#235—22no—
123C2×C3×D12—21no—
124C2×C3×D12—21no—
125C2×C3×D12D411yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3—21no—
128C2×C3×C4×D3—21no—
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×Dic6—21no—
135C2×C3×Dic6—21no—
136C2×C3×Dic6D411yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×#627—21no—
140C2×D3×Dic3—21no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143#3757—21no—
144#3756—22no—
145#3756—22no—
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147#3750—21no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C3×#217—21no—
151C3×#216—22no—
152C3×#216—22no—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×Dic3⋊C4—21no—
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157#3724—21no—
158Dic3⋊Dic3—21no—
159(C2×D3)⋊Dic3—21no—
160(C2×D3)⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162Dic32—21no—
163#3719—22no—
164#3718—22no—
165#3716—22no—
166#3715—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3011—91noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C22×C3×Q8—21no—
180C22×C3×Q8—31no—
181C22×C3×Q8—31no—
182C22×C3×Q8—61no—
183C22×C3×Q8C2×D311yescharacteristic
184C22×C3×Q8C2×D311yescharacteristic
185#1007—24no—
186#1007—24no—
187C2×#239—21no—
188C2×#239C2×D311yescharacteristic
189C2×#239C2×D311yescharacteristic
190C2×D3×Q8—21no—
191C2×D3×Q8—31no—
192C2×D3×Q8C2×D311yescharacteristic
193C2×D3×Q8C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235—21no—
196C2×#235C2×D311yescharacteristic
197C2×#235C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×Q16—31no—
201C3×C22⋊Q8—31no—
202#951—64no—
203#946—31no—
204#944—61no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#216—31no—
210C2×#216—31no—
211C2×#216—31no—
212C2×#216—61no—
213C2×#216—61no—
214C2×#216—64no—
215C2×#216C2×D311yescharacteristic
216C2×#216C2×D311yescharacteristic
217C2×#215—31no—
218#936—61no—
219#935—61no—
220#935—61no—
221C2×#214—31no—
222C2×#214—31no—
223#926—31no—
224#924—31no—
225#924—31no—
226#924—31no—
227#924—31no—
228#924—61no—
229#924C2×D311yescharacteristic
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#918—64no—
233D3×Q16—64no—
234C2×Dic12—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#897—31no—
239#894—61no—
240#892—31no—
241#888—61no—
242#885—61no—
243#883—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—31no—
253#835—61no—
254#835—61no—
255#835C2×D311yescharacteristic
256#835C2×D311yescharacteristic
257#832—31no—
258#832—31no—
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic
265#821—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3×D3—21no—
273C22×C3×D3C2×D411yescharacteristic
274C22×C3×D3C2×D411yescharacteristic
275C32×Q8—24no—
276C32×Q8—21no—
277C32×Q8—21no—
278C32×Q8C2×D412yes—
279C32×Q8C2×D412yes—
280C2×C32×C4—24no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4C2×D411yescharacteristic
286C2×C32×C4C2411yescharacteristic
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289#634—21no—
290#634—21no—
291C3×#67—24no—
292C3×#67—22no—
293C3×#67—22no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3C2×D411yescharacteristic
298C2×C3×Dic3C2×D411yescharacteristic
299C3×D12—24no—
300C3×D12—24no—
301C3×D12—22no—
302C3×D12—21no—
303C3×D12C2×D412yes—
304C3×C4×D3—24no—
305C3×C4×D3—24no—
306C3×C4×D3—24no—
307C3×C4×D3—24no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3—24no—
311C3×C4×D3C2×D412yes—
312C3×C4×D3C2×D412yes—
313C3×Dic6—24no—
314C3×Dic6—21no—
315C3×Dic6—24no—
316C3×Dic6—22no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6C2×D412yes—
320#627—42no—
321D3×Dic3—42no—
322C3⋊(C3⋊C8)—21no—
323C3⋊(C3⋊C8)—21no—
324C3×C3⋊C8—21no—
325C3×C3⋊C8—21no—
326C2×2−1+4—31no—
327C2×#137—91no—
328C22×Q16—91no—
329#536—91no—
330#452—91no—
331#452—91no—
332#452—91no—
333#452—91no—
334#451—31no—
335#451—91no—
336#451—91no—
337#451—91no—
338#419—91no—
339#416—91no—
340#408—91no—
341C3×#41—34no—
342C3×#41—62no—
343C3×#41—62no—
344C3×#41—62no—
345C3×#41—62no—
346C3×#41—68no—
347C3×#41—68no—
348C3×#41—62no—
349C3×#41—62no—
350C3×#41—68no—
351C3×#41—62no—
352C2×C3×Q8—22no—
353C2×C3×Q8—22no—
354C2×C3×Q8—22no—
355C2×C3×Q8—22no—
356C2×C3×Q8—21no—
357C2×C3×Q8—21no—
358C2×C3×Q8—21no—
359C2×C3×Q8—21no—
360C2×C3×Q8—31no—
361C2×C3×Q8—34no—
362C2×C3×Q8—31no—
363C2×C3×Q8—31no—
364C2×C3×Q8—41no—
365C2×C3×Q8—42no—
366C2×C3×Q8—42no—
367C2×C3×Q8—61no—
368C2×C3×Q8—61no—
369C2×C3×Q8—62no—
370C2×C3×Q8—62no—
371C2×C3×Q8—68no—
372C2×C3×Q8—62no—
373C2×C3×Q8C22×D311yescharacteristic
374C2×C3×Q8C22×D311yescharacteristic
375C2×C3×Q8C22×D311yescharacteristic
376C2×C3×Q8C22×D311yescharacteristic
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—41no—
390C22×C3×C4—61no—
391C22×C3×C4—61no—
392C22×C3×C4—61no—
393C22×C3×C4—61no—
394C22×C3×C4—61no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C2×#67—21no—
398C2×#67#6711yescharacteristic
399C2×#67#6711yescharacteristic
400C22×Dic3—61no—
401#239—28no—
402#239—22no—
403#239—22no—
404#239—22no—
405#239#6714yes—
406D3×Q8—28no—
407D3×Q8—22no—
408D3×Q8—22no—
409D3×Q8—22no—
410D3×Q8—62no—
411D3×Q8—62no—
412D3×Q8#6714yes—
413#235—28no—
414#235—28no—
415#235—22no—
416#235—22no—
417#235—22no—
418#235—22no—
419C2×D12—21no—
420C2×D12—21no—
421C2×D12#6711yescharacteristic
422C2×D12C22×D311yescharacteristic
423C2×C4×D3—21no—
424C2×C4×D3—21no—
425C2×C4×D3—21no—
426C2×C4×D3—21no—
427C2×C4×D3—21no—
428C2×C4×D3—61no—
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D311yescharacteristic
431C2×Dic6—21no—
432C2×Dic6—21no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—61no—
436C2×Dic6—62no—
437C2×Dic6—62no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6#6711yescharacteristic
441C2×Dic6C22×D311yescharacteristic
442C2×Dic6C22×D311yescharacteristic
443C3×Q16—62no—
444C3×Q16—62no—
445C2×C3×C8—31no—
446C2×C3×C8—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—61no—
449C3×C22⋊C4—61no—
450#217—21no—
451#217—61no—
452#217—61no—
453#217—61no—
454#217—61no—
455#217—61no—
456#217—121no—
457#216—22no—
458#216—22no—
459#216—62no—
460#216—62no—
461#216—62no—
462#216—62no—
463#216—62no—
464#216—62no—
465#216—62no—
466#216—122no—
467#216—122no—
468#215—62no—
469#214—62no—
470#214—62no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—61no—
473(C2×D3)⋊C4—61no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—61no—
477C4⋊Dic3—61no—
478C4⋊Dic3C22×D311yescharacteristic
479Dic3⋊C4—21no—
480Dic3⋊C4—61no—
481Dic3⋊C4—61no—
482Dic3⋊C4—61no—
483Dic3⋊C4—61no—
484Dic3⋊C4—61no—
485Dic3⋊C4—121no—
486C4×Dic3—61no—
487C4×Dic3—61no—
488#208—62no—
489C2×C3⋊C8—31no—
490C2×C3⋊C8—31no—
491C2×C3⋊C8—31no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—61no—
494C2×C3⋊C8—61no—
495C2×C3⋊C8—62no—
496C2×C3⋊C8C22×D311yescharacteristic
497C2×C3⋊C8C22×D311yescharacteristic
498Dic12—62no—
499#204—62no—
500ΓL(1,𝔽25)—62no—
501D3×C8—62no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32C22×D411yescharacteristic
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—21no—
509C2×C3×D3—22no—
510C2×C3×D3—21no—
511C2×C3×D3—21no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3#12012yes—
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—21no—
518C32×C4C22×D411yescharacteristic
519C32×C4C22×D411yescharacteristic
520C3⋊Dic3—41no—
521C3⋊Dic3—41no—
522C3×Dic3—21no—
523C3×Dic3—22no—
524C3×Dic3—41no—
525C3×Dic3—41no—
526C3×Dic3#12012yes—
5272−1+4—64no—
5282−1+4—64no—
529C2×#41—31no—
530C2×#41—31no—
531C2×#41—31no—
532C2×#41—31no—
533C2×#41—61no—
534C2×#41—61no—
535C2×#41—61no—
536C22×Q8—31no—
537C22×Q8—31no—
538C22×Q8—61no—
539C22×Q8—91no—
540C22×Q8D3211yescharacteristic
541#137—184no—
542C2×Q16—31no—
543C2×Q16—31no—
544C2×Q16—91no—
545C2×Q16—91no—
546C2×Q16—91no—
547C2×Q16—91no—
548C2×Q16—184no—
549C2×SD16—91no—
550C2×SD16—91no—
551C2×M16—91no—
552C22×C8—91no—
553C4⋊Q8—181no—
554#124—181no—
555#123—181no—
556#123—181no—
557C22⋊Q8—31no—
558C22⋊Q8—91no—
559C22⋊Q8—91no—
560C22⋊Q8—91no—
561#117—91no—
562#103—31no—
563#103—31no—
564#103—91no—
565#103—91no—
566#103—91no—
567#103—91no—
568#102—91no—
569#102—91no—
570C22⋊C8—31no—
571C22⋊C8—91no—
572C22⋊C8—91no—
573C22⋊C8—91no—
574C23×C3—21no—
575C23×C3—31no—
576C23×C3—31no—
577C23×C3—61no—
578C23×C3D3×D411yescharacteristic
579C23×C3C2×#6711yescharacteristic
580C22×D3—21no—
581C22×D3C2×#6711yescharacteristic
582C22×D3C2×#6711yescharacteristic
583C3×Q8—24no—
584C3×Q8—24no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—21no—
588C3×Q8—21no—
589C3×Q8—22no—
590C3×Q8—22no—
591C3×Q8—32no—
592C3×Q8—41no—
593C3×Q8—41no—
594C3×Q8—44no—
595C3×Q8—64no—
596C3×Q8—62no—
597C3×Q8—64no—
598C3×Q8—61no—
599C3×Q8—61no—
600C3×Q8—61no—
601C3×Q8D3×D412yes—
602C3×Q8D3×D412yes—
603C3×Q8C2×#6712yes—
604C3×Q8C2×#6712yes—
605C3×D4—32no—
606C3×D4—62no—
607C3×D4—64no—
608C3×D4—64no—
609C3×D4—62no—
610C3×D4—62no—
611C3×D4—64no—
612C3×D4—61no—
613C2×C3×C4—24no—
614C2×C3×C4—24no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—31no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—31no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—44no—
634C2×C3×C4—64no—
635C2×C3×C4—64no—
636C2×C3×C4—64no—
637C2×C3×C4—64no—
638C2×C3×C4—64no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4D3×D411yescharacteristic
645C2×C3×C4C2×#6711yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648#67—24no—
649#67—22no—
650#67—22no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—122no—
661C2×Dic3C2×#6711yescharacteristic
662C2×Dic3C2×#6711yescharacteristic
663D12—24no—
664D12—24no—
665D12—22no—
666D12—21no—
667D12C2×#6712yes—
668C4×D3—24no—
669C4×D3—24no—
670C4×D3—24no—
671C4×D3—24no—
672C4×D3—21no—
673C4×D3—21no—
674C4×D3—24no—
675C4×D3—122no—
676C4×D3C2×#6712yes—
677C4×D3C2×#6712yes—
678Dic6—24no—
679Dic6—21no—
680Dic6—24no—
681Dic6—22no—
682Dic6—21no—
683Dic6—21no—
684Dic6—61no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—121no—
689Dic6—121no—
690Dic6—122no—
691Dic6—122no—
692Dic6C2×#6712yes—
693C3×C8—61no—
694C3×C8—61no—
695C3⋊C8—21no—
696C3⋊C8—21no—
697C3⋊C8—61no—
698C3⋊C8—61no—
699C3⋊C8—61no—
700C3⋊C8—61no—
701C3⋊C8—121no—
702C3⋊C8—121no—
703C2×C32—41no—
704C2×C32C2×#12011yescharacteristic
705C2×C32#57811yescharacteristic
706C2×C32#57811yescharacteristic
707C3×D3—22no—
708C3×D3—41no—
709C3×D3—42no—
710#41—34no—
711#41—62no—
712#41—62no—
713#41—62no—
714#41—62no—
715#41—68no—
716#41—68no—
717#41—62no—
718#41—62no—
719#41—68no—
720#41—62no—
721C2×Q8—22no—
722C2×Q8—22no—
723C2×Q8—21no—
724C2×Q8—31no—
725C2×Q8—34no—
726C2×Q8—31no—
727C2×Q8—31no—
728C2×Q8—61no—
729C2×Q8—61no—
730C2×Q8—62no—
731C2×Q8—62no—
732C2×Q8—68no—
733C2×Q8—62no—
734C2×Q8—91no—
735C2×Q8—181no—
736C2×Q8—182no—
737C2×Q8—182no—
738C2×Q8C2×D3211yescharacteristic
739C2×Q8C2×D3211yescharacteristic
740C2×D4—31no—
741C2×D4—31no—
742C2×D4—31no—
743C2×D4—31no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4—61no—
747C22×C4—21no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—181no—
756C22×C4C2×D3211yescharacteristic
757Q16—62no—
758Q16—62no—
759Q16—182no—
760Q16—182no—
761Q16—182no—
762Q16—182no—
763SD16—182no—
764SD16—182no—
765M16—182no—
766C2×C8—31no—
767C2×C8—31no—
768C2×C8—91no—
769C2×C8—91no—
770C2×C8—182no—
771C4⋊C4—31no—
772C4⋊C4—61no—
773C4⋊C4—91no—
774C4⋊C4—181no—
775C4⋊C4—181no—
776C4⋊C4—181no—
777C22⋊C4—61no—
778C22⋊C4—181no—
779C22⋊C4—181no—
780C22⋊C4—181no—
781C22⋊C4—181no—
782C42—181no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—32no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—61no—
797C22×C3—61no—
798C22×C3—62no—
799C22×C3—61no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3C2×D3×D411yescharacteristic
803C22×C3C22×#6711yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—21no—
807C2×D3—21no—
808C2×D3—21no—
809C2×D3—22no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3#95312yes—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—21no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—32no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—61no—
826C3×C4—62no—
827C3×C4—121no—
828C3×C4—121no—
829C3×C4C2×D3×D411yescharacteristic
830C3×C4C2×D3×D411yescharacteristic
831C3×C4C22×#6711yescharacteristic
832C3×C4C22×#6711yescharacteristic
833Dic3—21no—
834Dic3—22no—
835Dic3—41no—
836Dic3—41no—
837Dic3—121no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841Dic3—241no—
842Dic3—241no—
843Dic3#95312yes—
844C32#301111yescharacteristic, complemented, Sylow
845C23—31no—
846C23—31no—
847C23—61no—
848C23D3×#6711yescharacteristic
849Q8—24no—
850Q8—21no—
851Q8—21no—
852Q8—32no—
853Q8—64no—
854Q8—62no—
855Q8—64no—
856Q8—61no—
857Q8—61no—
858Q8—61no—
859Q8—181no—
860Q8—181no—
861Q8—362no—
862Q8D3×#6712yes—
863Q8D3×#6712yes—
864D4—32no—
865D4—62no—
866D4—64no—
867D4—64no—
868D4—62no—
869D4—62no—
870D4—64no—
871D4—61no—
872C2×C4—24no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—31no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—31no—
881C2×C4—64no—
882C2×C4—64no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—64no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—362no—
894C2×C4D3×#6711yescharacteristic
895C2×C4C22×D3211yescharacteristic
896C8—61no—
897C8—61no—
898C8—181no—
899C8—181no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—42no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—62no—
907C2×C3—121no—
908C2×C3—122no—
909C2×C3D3×#12011yescharacteristic
910C2×C3#576611yescharacteristic
911C2×C3#577911yescharacteristic
912C2×C3#583811yescharacteristic
913C2×C3#583811yescharacteristic
914C2×C3C2×#95311yescharacteristic
915D3—22no—
916D3—41no—
917D3—42no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—32no—
922C22—61no—
923C22—61no—
924C22—61no—
925C22—62no—
926C22—61no—
927C22—61no—
928C22—121no—
929C22—121no—
930C22C2×D3×#6711yescharacteristic
931C4—22no—
932C4—22no—
933C4—21no—
934C4—32no—
935C4—61no—
936C4—62no—
937C4—121no—
938C4—121no—
939C4—361no—
940C4—361no—
941C4C2×D3×#6711yescharacteristic
942C4C2×D3×#6711yescharacteristic
943C3—21no—
944C3#8018511yescharacteristic, complemented
945C3#8411711yescharacteristic, complemented
946C2—41no—
947C2—62no—
948C2—121no—
949C2—122no—
950C2#1059532711yescharacteristic
951C2#1059532811yescharacteristic
952C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC22×Q8D32
hypocenterC32#3011
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
2. C2×#63943C2semidirect
3. C2×D3×#216C2semidirect
4. #10594884C2semidirect
5. #10592927C2semidirect
6. C3×#5228C2semidirect
7. #10591599C2semidirect
8. #10591597C2semidirect
9. #10591595C2semidirect
10. #10591594C2semidirect
11. #10591557C2semidirect
12. #10591556C2semidirect
13. #10591173C2semidirect
14. #10591170C2semidirect
15. #10591145C2semidirect
85. #5228D3semidirect
844. C32#3011semidirect
944. C3#80185semidirect
945. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#639432
C2×D3×#2162
#105948842
#105929272
C3×#52282
#105915992
#105915972
#105915952
#105915942
#105915572
#105915562
#105911732
#105911702
#105911452
#841173
#801853