Finite Group Databasebeta

← #11884270

Subgroups — #11884270

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2#10595078C211yesmaximal, characteristic, complemented
3#10594834C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591184C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590897C211yesmaximal, characteristic, complemented
12#10590860C211yesmaximal, characteristic, complemented
13#10590853C211yesmaximal, characteristic, complemented
14#10590768C211yesmaximal, characteristic, complemented
15#10590760C211yesmaximal, characteristic, complemented
16#80675—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C2×#3746C2211yescharacteristic, complemented
24#64113—24no—
25C2×#3745C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic, complemented
28C3×#930C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C2×C3×#204C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63975—21no—
35#63958—21no—
36#63958—21no—
37#63921—21no—
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic, complemented
40#63883—21no—
41#63866C2211yescharacteristic, complemented
42#63860C2211yescharacteristic
43#63857C2211yescharacteristic
44#63857C2211yescharacteristic
45#63853—21no—
46#63853—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52C3×#830C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#817C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#908—31no—
65C2×#904—31no—
66C2×#904—31no—
67C2×#904—61no—
68#5631—31no—
69#5612—31no—
70#5551—31no—
71#5550—31no—
72C3×#465—31no—
73C3×#435—31no—
74#5167—31no—
75#5137—31no—
76#5114D311yescharacteristic, complemented
77#5111D311yescharacteristic, complemented
78#5047—31no—
79#5037—31no—
80#4869—31no—
81#4867—31no—
82#4844—31no—
83#4841—31no—
84#4818—31no—
85#4808—31no—
86#4787—31no—
87#4776—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—22no—
100#3828—41no—
101#3828—41no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×#624—21no—
117C2×#624—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3799—22no—
121#3799—41no—
122C2×C32×C8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125#3746—22no—
126#3745D414yescomplemented
127#3744—22no—
128#3744—22no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×ΓL(1,𝔽25)—22no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3717—22no—
154#3716—41no—
155#3714—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×D3×D4—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C2×#235—61no—
166C22×D12—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—21no—
170C22×C3×C8C2×D311yescharacteristic, complemented
171C22×C3×C8C2×D311yescharacteristic, complemented
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#944—31no—
176C2×#216—31no—
177C2×#215—31no—
178#938—61no—
179#938—61no—
180#937—61no—
181#937—61no—
182#936—31no—
183C2×#214—31no—
184C2×#213—31no—
185#930C2×D311yescharacteristic
186C4×#67C2×D311yescharacteristic
187#924—31no—
188#924—31no—
189#924C2×D311yescharacteristic, complemented
190#914—64no—
191#908—64no—
192C2×Dic12—31no—
193C2×Dic12—31no—
194C2×Dic12—31no—
195C2×Dic12—61no—
196#904—64no—
197#904—64no—
198#904—68no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—61no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—61no—
210C2×#204—61no—
211C2×#204C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic
213#897—31no—
214#897—31no—
215#894—61no—
216#894—61no—
217#893—31no—
218#893—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4—61no—
221#884—61no—
222#884—61no—
223#883—61no—
224#883—61no—
225#883—61no—
226#883—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229#875—31no—
230C4×D12—31no—
231C4×D12—31no—
232#869—31no—
233C3×#106—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#830C2×D311yescharacteristic, complemented
241#821—31no—
242#821—31no—
243#821C2×D311yescharacteristic
244(C2×D3)⋊C8C2×D311yescharacteristic
245#817C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#816C2×D311yescharacteristic, complemented
249#815C2×D311yescharacteristic, complemented
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#810—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—42no—
276C4×C3⋊D3—42no—
277#634—21no—
278#634—21no—
279#634—21no—
280#634—21no—
281C3×#67—41no—
282C3×#67—81no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296#626—42no—
297#624—42no—
298#624—42no—
299#624—81no—
300C32×C8—21no—
301C32×C8C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—91no—
306#547—91no—
307#546—91no—
308#497—91no—
309#470—91no—
310#465—31no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—91no—
318#435—31no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—121no—
337C2×#67—121no—
338C2×#67D1211yescharacteristic
339#239—62no—
340#239—121no—
341D3×D4—62no—
342D3×D4—121no—
343#235—62no—
344#235—62no—
345#235—62no—
346#235—62no—
347#235—62no—
348#235—64no—
349#235—64no—
350#235—121no—
351#235—121no—
352#235—121no—
353#235—121no—
354#235—121no—
355#235—122no—
356#235—122no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—121no—
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6—31no—
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—61no—
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—62no—
389C3×M16—62no—
390C2×C3×C8—24no—
391C2×C3×C8—22no—
392C2×C3×C8—22no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—21no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217D1211yescharacteristic
416#216—121no—
417#215—62no—
418#214—121no—
419#213—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4D1211yescharacteristic
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4D1211yescharacteristic
442C4×Dic3C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444C2×C3⋊C8C22×D311yescharacteristic
445Dic12—64no—
446Dic12—62no—
447Dic12—62no—
448Dic12—121no—
449D24—34no—
450D24—34no—
451D24—64no—
452D24—62no—
453#204—22no—
454#204—62no—
455#204—62no—
456#204—62no—
457#204—62no—
458#204—64no—
459#204—64no—
460#204—62no—
461#204—121no—
462ΓL(1,𝔽25)—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—91no—
492C2×#41—91no—
493C2×#41—91no—
494C22×D4—91no—
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—91no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8—91no—
506C2×M16—31no—
507C22×C8D3211yescharacteristic, complemented
508C4⋊Q8—91no—
509#124—91no—
510#123—181no—
511#123—181no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—91no—
515C22⋊Q8—91no—
516#121—31no—
517#121—181no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—181no—
525#106—31no—
526C4⋊C8—31no—
527#103—31no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—91no—
532#102—91no—
533C22⋊C8—31no—
534C22⋊C8—31no—
535#97—31no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—61no—
539C23×C3C2×D1211yescharacteristic
540C23×C3D3×D411yescharacteristic
541C22×D3—21no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3C2×D1211yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—121no—
560C3×D4—241no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4C2×D1211yescharacteristic
578C2×C3×C4D3×D411yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—41no—
582#67—81no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—124no—
590#67—124no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3C2×D1211yescharacteristic
601C2×Dic3C2×D1211yescharacteristic
602C2×Dic3C2×D1211yescharacteristic
603D12—21no—
604D12—21no—
605D12—32no—
606D12—32no—
607D12—32no—
608D12—32no—
609D12—62no—
610D12—62no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—121no—
616D12—121no—
617D12—122no—
618D12—122no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—124no—
630C4×D3—124no—
631C4×D3—241no—
632C4×D3—241no—
633Dic6—21no—
634Dic6—21no—
635Dic6—62no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—121no—
646Dic6—121no—
647C3×C8—22no—
648C3×C8—21no—
649C3×C8—21no—
650C3×C8—22no—
651C3×C8—61no—
652C3×C8—61no—
653C3×C8D3×D412yes—
654C3×C8D3×D412yes—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C2×C32—41no—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57711yescharacteristic
661C3⋊D3—42no—
662C3⋊D3—42no—
663C3×D3—41no—
664C3×D3—81no—
665C24—181no—
666#41—182no—
667#41—182no—
668#41—182no—
669#41—361no—
670#41—361no—
671#41—361no—
672C2×Q8—31no—
673C2×Q8—91no—
674C2×Q8—91no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—181no—
688C22×C4—181no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4C2×D3211yescharacteristic
693Q16—182no—
694Q16—361no—
695SD16—62no—
696SD16—182no—
697SD16—182no—
698SD16—182no—
699SD16—361no—
700D8—94no—
701D8—182no—
702M16—62no—
703C2×C8—22no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8C2×D3211yescharacteristic
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—31no—
711C4⋊C4—61no—
712C4⋊C4—181no—
713C4⋊C4—181no—
714C4⋊C4—181no—
715C4⋊C4—181no—
716C22⋊C4—31no—
717C22⋊C4—31no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3C22×D1211yescharacteristic
744C22×C3C2×D3×D411yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—22no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—121no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4C2×D3×D411yescharacteristic
783C3×C4C2×D3×D411yescharacteristic
784C3×C4#100911yescharacteristic
785C3×C4#100911yescharacteristic
786Dic3—21no—
787Dic3—21no—
788Dic3—21no—
789Dic3—41no—
790Dic3—41no—
791Dic3—41no—
792Dic3—122no—
793Dic3—122no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797Dic3—121no—
798C32#326711yescharacteristic, complemented, Sylow
799C23—31no—
800C23—61no—
801C23—181no—
802C23—181no—
803C23—362no—
804C23—362no—
805C23—721no—
806C23D3×D1211yescharacteristic
807Q8—61no—
808Q8—61no—
809Q8—181no—
810Q8—181no—
811Q8—181no—
812Q8—181no—
813D4—61no—
814D4—61no—
815D4—92no—
816D4—92no—
817D4—121no—
818D4—181no—
819D4—181no—
820D4—241no—
821D4—362no—
822D4—362no—
823D4—362no—
824D4—362no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—362no—
838C2×C4—362no—
839C2×C4—362no—
840C2×C4—362no—
841C2×C4—721no—
842C2×C4D3×D1211yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—61no—
846C8—61no—
847C8#381112yes—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—42no—
852C2×C3—41no—
853C2×C3—41no—
854C2×C3—121no—
855C2×C3—241no—
856C2×C3D4×D1211yescharacteristic
857C2×C3#560911yescharacteristic
858C2×C3#574811yescharacteristic
859C2×C3#575111yescharacteristic
860C2×C3#576211yescharacteristic
861C2×C3#576811yescharacteristic
862D3—41no—
863D3—81no—
864D3—122no—
865D3—122no—
866D3—122no—
867D3—122no—
868D3—242no—
869D3—242no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—182no—
880C22—182no—
881C22—361no—
882C22—361no—
883C22—361no—
884C22—361no—
885C22—724no—
886C22C2×D3×D1211yescharacteristic
887C4—21no—
888C4—61no—
889C4—61no—
890C4—61no—
891C4—121no—
892C4—121no—
893C4—121no—
894C4—361no—
895C4—361no—
896C4#6430811yescharacteristic
897C4C2×#381111yescharacteristic
898C3—21no—
899C3#7949611yescharacteristic, complemented
900C3#8067511yescharacteristic, complemented
901C2—41no—
902C2—121no—
903C2—241no—
904C2—362no—
905C2—362no—
906C2#1059467611yescharacteristic
907C2#1059467711yescharacteristic
908C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. #10595078C2semidirect
3. #10594834C2semidirect
4. C2×#63794C2semidirect
5. C3×#5114C2semidirect
6. C3×#5111C2semidirect
7. #10591184C2semidirect
8. #10591182C2semidirect
9. #10590970C2semidirect
10. #10590946C2semidirect
11. #10590897C2semidirect
12. #10590860C2semidirect
13. #10590853C2semidirect
14. #10590768C2semidirect
15. #10590760C2semidirect
19. C2×#3828C22semidirect
22. C22×C32×C8C22semidirect
23. C2×#3746C22semidirect
27. C2×#3744C22semidirect
30. C3×#924C22semidirect
39. #63894C22semidirect
41. #63866C22semidirect
47. C2×#3719C22semidirect
52. C3×#830C22semidirect
55. C3×#817C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
62. #63564C22semidirect
76. #5114D3semidirect
77. #5111D3semidirect
126. #3745D4semidirect
170. C22×C3×C8C2×D3semidirect
171. C22×C3×C8C2×D3semidirect
189. #924C2×D3semidirect
240. #830C2×D3semidirect
245. #817C2×D3semidirect
248. #816C2×D3semidirect
249. #815C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
507. C22×C8D32semidirect
798. C32#3267semidirect
899. C3#79496semidirect
900. C3#80675semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105950782
#105948342
C2×#637942
C3×#51142
C3×#51112
#105911842
#105911822
#105909702
#105909462
#105908972
#105908602
#105908532
#105907682
#105907602
#806753
#794963