Finite Group Databasebeta

← #11864512

Subgroups — #11864512

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 957 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3C2×#63929C211yesmaximal, characteristic, complemented
4#10594884C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6C3×#5239C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591557C211yesmaximal, characteristic, complemented
10#10591463C211yesmaximal, characteristic, complemented
11#10591461C211yesmaximal, characteristic, complemented
12#10591420C211yesmaximal, characteristic, complemented
13#10591186C211yesmaximal, characteristic, complemented
14#10591185C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84117—31nomaximal
17#80230—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C3×#1010—24no—
20C3×#1010—24no—
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237—21no—
24C2×C3×#237—21no—
25C2×C3×#237C2211yescharacteristic
26C2×C3×#237C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×Dic6—21no—
30C22×C3×Dic6C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3756C2211yescharacteristic
33C2×#3754C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C3×#924C2211yescharacteristic
38#63969—21no—
39#63959—21no—
40D3×#216—24no—
41#63929—24no—
42#63884—21no—
43#63857C2211yescharacteristic
44#63856C2211yescharacteristic
45#63841C2211yescharacteristic
46#63839—21no—
47C2×#3719C2211yescharacteristic
48C2×#3719C2211yescharacteristic
49C2×#3718C2211yescharacteristic
50C2×#3718C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic
54#63659C2211yescharacteristic
55#63657C2211yescharacteristic
56C3×#835C2211yescharacteristic
57C3×#832C2211yescharacteristic
58C3×#830C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#63565C2211yescharacteristic
62#63565C2211yescharacteristic
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×C3×2−1+4—31no—
66C2×#1010D311yescharacteristic
67#5825—31no—
68C2×#951—31no—
69C22×#216—31no—
70C2×D3×Q16—31no—
71C2×#915—31no—
72#5628—31no—
73C3×#452—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—31no—
78#5239—61no—
79#5239D311yescharacteristic, complemented
80#5234—31no—
81#5233—31no—
82#5228—31no—
83#5228—31no—
84#5228—31no—
85#5228—31no—
86#5225—31no—
87#5186—31no—
88#5173—31no—
89#5050—31no—
90#4809—31no—
91#4802—31no—
92#4783—31no—
93#4772—31no—
94#4739—31no—
95#4727—31no—
96C32×#41—22no—
97C32×#41—22no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C2×C3×#67D411yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C3×D3×Q8—22no—
112C3×D3×Q8—22no—
113C3×D3×Q8—22no—
114C3×D3×Q8D414yes—
115C3×#237—28no—
116C3×#237—28no—
117C3×#237—22no—
118C3×#237—22no—
119C3×#237—22no—
120C3×#237D414yes—
121C3×#235—28no—
122C3×#235—22no—
123C3×#235—22no—
124C2×C3×D12D411yescharacteristic
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3—21no—
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6—28no—
130C2×C3×Dic6—21no—
131C2×C3×Dic6—21no—
132C2×C3×Dic6—21no—
133C2×C3×Dic6—22no—
134C2×C3×Dic6—22no—
135C2×C3×Dic6D411yescharacteristic
136C2×C3×Dic6C2311yescharacteristic
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#3754—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×#214—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#3719—22no—
165#3718—22no—
166#3718—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3011—91noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C2×C3×#41C2×D311yescharacteristic
180C2×C3×#41C2×D311yescharacteristic
181C22×C3×Q8—31no—
182C22×C3×Q8—31no—
183C22×C3×Q8—31no—
184C22×C3×Q8—61no—
185#1010—24no—
186#1010—24no—
187C2×D3×Q8—31no—
188C2×D3×Q8C2×D311yescharacteristic
189C2×D3×Q8C2×D311yescharacteristic
190C2×#237—21no—
191C2×#237—21no—
192C2×#237C2×D311yescharacteristic
193C2×#237C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235C2×D311yescharacteristic
196C22×Dic6—21no—
197C22×Dic6—31no—
198C22×Dic6C2×D311yescharacteristic
199C2×C3×Q16—31no—
200C2×C3×SD16—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—31no—
213C2×#216—61no—
214C2×#216—64no—
215C2×#216C2×D311yescharacteristic
216#936—61no—
217#935—61no—
218#935—61no—
219C2×#214—31no—
220C2×#214—31no—
221C2×#214—61no—
222C2×#214C2×D311yescharacteristic
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—
232D3×Q16—64no—
233#915—64no—
234C2×Dic12—31no—
235C2×Dic12—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×#102—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#835C2×D311yescharacteristic
255#832—31no—
256#832—31no—
257#832—61no—
258#832C2×D311yescharacteristic
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267#816—31no—
268#816—31no—
269#810—31no—
270#810—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3C2×D411yescharacteristic
274C22×C3×D3C2×D411yescharacteristic
275C32×Q8—21no—
276C32×Q8C2×D412yes—
277C32×D4—24no—
278C32×D4—21no—
279C32×D4C2×D412yes—
280C2×C32×C4—24no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2411yescharacteristic
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288#634—21no—
289#634—21no—
290C3×#67—24no—
291C3×#67—22no—
292C3×#67—24no—
293C3×#67—22no—
294C2×C3×Dic3—24no—
295C2×C3×Dic3—24no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—24no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—22no—
304C3×C4×D3—24no—
305C3×C4×D3—24no—
306C3×C4×D3—21no—
307C3×C4×D3—21no—
308C3×C4×D3C2×D412yes—
309C3×C4×D3C2×D412yes—
310C3×Dic6—24no—
311C3×Dic6—24no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—22no—
315C3×Dic6—24no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
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—31no—
331#452—91no—
332#452—91no—
333#452—91no—
334#451—91no—
335#451—91no—
336#451—91no—
337#451—91no—
338#419—91no—
339#416—91no—
340#408—91no—
341C3×#41—22no—
342C3×#41—22no—
343C3×#41—22no—
344C3×#41—22no—
345C3×#41—34no—
346C3×#41—42no—
347C3×#41—42no—
348C3×#41—62no—
349C3×#41—62no—
350C3×#41—68no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—68no—
354C3×#41—68no—
355C3×#41—62no—
356C2×C3×Q8—21no—
357C2×C3×Q8—31no—
358C2×C3×Q8—34no—
359C2×C3×Q8—31no—
360C2×C3×Q8—31no—
361C2×C3×Q8—31no—
362C2×C3×Q8—61no—
363C2×C3×Q8—61no—
364C2×C3×Q8—62no—
365C2×C3×Q8—62no—
366C2×C3×Q8—68no—
367C2×C3×Q8—62no—
368C2×C3×Q8—62no—
369C2×C3×Q8—62no—
370C2×C3×Q8—61no—
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×Q8C22×D311yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—31no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—41no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4C22×D311yescharacteristic
383C2×C3×D4C22×D311yescharacteristic
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—21no—
399C2×#67#6711yescharacteristic
400C2×#67#6711yescharacteristic
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3—21no—
404C22×Dic3—61no—
405D3×Q8—22no—
406D3×Q8—22no—
407D3×Q8—22no—
408D3×Q8—62no—
409D3×Q8—62no—
410D3×Q8#6714yes—
411#237—28no—
412#237—28no—
413#237—22no—
414#237—22no—
415#237—22no—
416#237#6714yes—
417#235—28no—
418#235—22no—
419#235—22no—
420C2×D12#6711yescharacteristic
421C2×C4×D3—21no—
422C2×C4×D3—21no—
423C2×C4×D3—61no—
424C2×C4×D3C22×D311yescharacteristic
425C2×C4×D3C22×D311yescharacteristic
426C2×Dic6—28no—
427C2×Dic6—21no—
428C2×Dic6—21no—
429C2×Dic6—21no—
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—61no—
435C2×Dic6—62no—
436C2×Dic6—62no—
437C2×Dic6—61no—
438C2×Dic6—61no—
439C2×Dic6#6711yescharacteristic
440C2×Dic6C22×D311yescharacteristic
441C2×Dic6C22×D311yescharacteristic
442C2×Dic6C22×D311yescharacteristic
443C3×Q16—62no—
444C3×SD16—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—62no—
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#214—22no—
468#214—62no—
469#214—62no—
470#214—122no—
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—
499Dic12—62no—
500ΓL(1,𝔽25)—62no—
501D3×C8—62no—
502C22×C32—21no—
503C22×C32—22no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—41no—
507C22×C32—41no—
508C22×C32C22×D411yescharacteristic
509C2×C3×D3—21no—
510C2×C3×D3—21no—
511C2×C3×D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3#12012yes—
515C32×C4—21no—
516C32×C4—22no—
517C32×C4C22×D411yescharacteristic
518C32×C4C22×D411yescharacteristic
519C3⋊Dic3—41no—
520C3⋊Dic3—41no—
521C3×Dic3—21no—
522C3×Dic3—22no—
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—61no—
533C2×#41—61no—
534C2×#41—61no—
535C2×#41D3211yescharacteristic
536C22×Q8—31no—
537C22×Q8—31no—
538C22×Q8—31no—
539C22×Q8—61no—
540C22×Q8—91no—
541#137—184no—
542C2×Q16—31no—
543C2×Q16—91no—
544C2×Q16—91no—
545C2×Q16—91no—
546C2×Q16—91no—
547C2×Q16—91no—
548C2×Q16—184no—
549C2×SD16—31no—
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—91no—
564#103—91no—
565#103—91no—
566#103—91no—
567#103—91no—
568#102—31no—
569#102—91no—
570C22⋊C8—31no—
571C22⋊C8—91no—
572C22⋊C8—91no—
573C22⋊C8—91no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—31no—
578C23×C3—31no—
579C23×C3—41no—
580C23×C3D3×D411yescharacteristic
581C23×C3C2×#6711yescharacteristic
582C22×D3C2×#6711yescharacteristic
583C22×D3C2×#6711yescharacteristic
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—22no—
587C3×Q8—32no—
588C3×Q8—32no—
589C3×Q8—41no—
590C3×Q8—62no—
591C3×Q8—64no—
592C3×Q8—64no—
593C3×Q8—64no—
594C3×Q8—61no—
595C3×Q8—61no—
596C3×Q8—61no—
597C3×Q8—61no—
598C3×Q8D3×D412yes—
599C3×Q8C2×#6712yes—
600C3×D4—24no—
601C3×D4—24no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—22no—
605C3×D4—41no—
606C3×D4—44no—
607C3×D4—62no—
608C3×D4—62no—
609C3×D4—62no—
610C3×D4—64no—
611C3×D4—64no—
612C3×D4D3×D412yes—
613C3×D4C2×#6712yes—
614C2×C3×C4—24no—
615C2×C3×C4—24no—
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—31no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—31no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—44no—
632C2×C3×C4—64no—
633C2×C3×C4—64no—
634C2×C3×C4—64no—
635C2×C3×C4—64no—
636C2×C3×C4—64no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4D3×D411yescharacteristic
644C2×C3×C4C2×#6711yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—24no—
648#67—22no—
649#67—24no—
650#67—22no—
651C2×Dic3—24no—
652C2×Dic3—24no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—24no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3—122no—
665C2×Dic3C2×#6711yescharacteristic
666C2×Dic3C2×#6711yescharacteristic
667D12—22no—
668C4×D3—24no—
669C4×D3—24no—
670C4×D3—21no—
671C4×D3—21no—
672C4×D3—122no—
673C4×D3C2×#6712yes—
674C4×D3C2×#6712yes—
675Dic6—24no—
676Dic6—24no—
677Dic6—21no—
678Dic6—21no—
679Dic6—22no—
680Dic6—24no—
681Dic6—21no—
682Dic6—21no—
683Dic6—61no—
684Dic6—61no—
685Dic6—61no—
686Dic6—61no—
687Dic6—121no—
688Dic6—121no—
689Dic6—122no—
690Dic6—122no—
691Dic6C2×#6712yes—
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×C32—42no—
705C2×C32C2×#12011yescharacteristic
706C2×C32#57811yescharacteristic
707C2×C32#57811yescharacteristic
708C3×D3—22no—
709C3×D3—41no—
710#41—22no—
711#41—22no—
712#41—34no—
713#41—62no—
714#41—62no—
715#41—68no—
716#41—62no—
717#41—62no—
718#41—68no—
719#41—68no—
720#41—62no—
721C2×Q8—31no—
722C2×Q8—34no—
723C2×Q8—31no—
724C2×Q8—31no—
725C2×Q8—31no—
726C2×Q8—61no—
727C2×Q8—61no—
728C2×Q8—62no—
729C2×Q8—62no—
730C2×Q8—68no—
731C2×Q8—62no—
732C2×Q8—62no—
733C2×Q8—62no—
734C2×Q8—61no—
735C2×Q8—91no—
736C2×Q8—181no—
737C2×Q8—182no—
738C2×Q8—182no—
739C2×Q8C2×D3211yescharacteristic
740C2×D4—21no—
741C2×D4—31no—
742C2×D4—31no—
743C2×D4—31no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4C2×D3211yescharacteristic
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—182no—
759Q16—182no—
760Q16—182no—
761Q16—182no—
762Q16—182no—
763SD16—62no—
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—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—22no—
789C22×C3—21no—
790C22×C3—22no—
791C22×C3—21no—
792C22×C3—32no—
793C22×C3—42no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—61no—
802C22×C3—61no—
803C22×C3—61no—
804C22×C3—61no—
805C22×C3—61no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3C2×D3×D411yescharacteristic
809C22×C3C22×#6711yescharacteristic
810C2×D3—21no—
811C2×D3—21no—
812C2×D3—21no—
813C2×D3—21no—
814C2×D3—21no—
815C2×D3#95312yes—
816C3×C4—21no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—22no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—32no—
823C3×C4—41no—
824C3×C4—42no—
825C3×C4—61no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4C2×D3×D411yescharacteristic
831C3×C4C2×D3×D411yescharacteristic
832C3×C4C22×#6711yescharacteristic
833C3×C4C22×#6711yescharacteristic
834Dic3—21no—
835Dic3—22no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—121no—
840Dic3—121no—
841Dic3—121no—
842Dic3—121no—
843Dic3—241no—
844Dic3—241no—
845Dic3#95312yes—
846C32#301111yescharacteristic, complemented, Sylow
847C23—21no—
848C23—31no—
849C23—31no—
850C23D3×#6711yescharacteristic
851Q8—21no—
852Q8—32no—
853Q8—32no—
854Q8—62no—
855Q8—64no—
856Q8—64no—
857Q8—64no—
858Q8—61no—
859Q8—61no—
860Q8—61no—
861Q8—61no—
862Q8—181no—
863Q8—181no—
864Q8—362no—
865Q8D3×#6712yes—
866D4—24no—
867D4—21no—
868D4—62no—
869D4—62no—
870D4—62no—
871D4—64no—
872D4—64no—
873D4D3×#6712yes—
874C2×C4—24no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—31no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—31no—
882C2×C4—64no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—64no—
886C2×C4—64no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—362no—
896C2×C4D3×#6711yescharacteristic
897C2×C4C22×D3211yescharacteristic
898C8—61no—
899C8—61no—
900C8—181no—
901C8—181no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—41no—
906C2×C3—42no—
907C2×C3—41no—
908C2×C3—42no—
909C2×C3—62no—
910C2×C3—81no—
911C2×C3—82no—
912C2×C3—121no—
913C2×C3D3×#12011yescharacteristic
914C2×C3#577111yescharacteristic
915C2×C3#577911yescharacteristic
916C2×C3#583811yescharacteristic
917C2×C3#583811yescharacteristic
918C2×C3C2×#95311yescharacteristic
919D3—22no—
920D3—41no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—32no—
926C22—41no—
927C22—41no—
928C22—61no—
929C22—61no—
930C22—61no—
931C22—61no—
932C22—61no—
933C22C2×D3×#6711yescharacteristic
934C4—21no—
935C4—22no—
936C4—32no—
937C4—61no—
938C4—62no—
939C4—62no—
940C4—121no—
941C4—121no—
942C4—361no—
943C4—361no—
944C4C2×D3×#6711yescharacteristic
945C4C2×D3×#6711yescharacteristic
946C3—21no—
947C3#8023011yescharacteristic, complemented
948C3#8411711yescharacteristic, complemented
949C2—41no—
950C2—42no—
951C2—62no—
952C2—121no—
953C2#1059546511yescharacteristic
954C2#1059546711yescharacteristic
955C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×#41D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
3. C2×#63929C2semidirect
4. #10594884C2semidirect
5. #10592938C2semidirect
6. C3×#5239C2semidirect
7. #10591595C2semidirect
8. #10591594C2semidirect
9. #10591557C2semidirect
10. #10591463C2semidirect
11. #10591461C2semidirect
12. #10591420C2semidirect
13. #10591186C2semidirect
14. #10591185C2semidirect
15. #10591145C2semidirect
79. #5239D3semidirect
846. C32#3011semidirect
947. C3#80230semidirect
948. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×D3×#2162
C2×#639292
#105948842
#105929382
C3×#52392
#105915952
#105915942
#105915572
#105914632
#105914612
#105914202
#105911862
#105911852
#105911452
#841173
#802303