Finite Group Databasebeta

← #11864060

Subgroups — #11864060

Order 1152.

1961 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×#63937C211yesmaximal, characteristic, complemented
4#10594922C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591602C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591562C211yesmaximal, characteristic, complemented
10#10591466C211yesmaximal, characteristic, complemented
11#10591457C211yesmaximal, characteristic, complemented
12#10591426C211yesmaximal, characteristic, complemented
13#10591184C211yesmaximal, characteristic, complemented
14#10591182C211yesmaximal, characteristic, complemented
15#10591159C211yesmaximal, characteristic, complemented
16#80227—31nomaximal
17#80083—31nomaximal
18C2×C32×#41C2211yescharacteristic
19#41×C3⋊D3—24no—
20#41×C3⋊D3—24no—
21C2×#3832C2211yescharacteristic
22C2×Q8×C3⋊D3C2211yescharacteristic
23C2×#3830—21no—
24C2×#3830C2211yescharacteristic
25C2×D4×C3⋊D3—21no—
26C2×D4×C3⋊D3C2211yescharacteristic
27C2×#3828—21no—
28C2×#3828C2211yescharacteristic
29C22×C4×C3⋊D3—21no—
30C22×C4×C3⋊D3C2211yescharacteristic
31C2×#3796C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C3×#930C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38#63981—21no—
39#67⋊Dic3—21no—
40#63951—24no—
41#63937—24no—
42#63916C2211yescharacteristic, complemented
43#63881—21no—
44#63871C2211yescharacteristic, complemented
45#63853—21no—
46#63849C2211yescharacteristic
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic
52C2×#3712C2211yescharacteristic
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#830C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64#63557C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×D3×#41—61no—
68C2×#918—31no—
69C2×#915—31no—
70C2×#914—31no—
71C2×#911—31no—
72#5627—31no—
73#5606—31no—
74C3×#452—31no—
75C3×#449—31no—
76#5239D311yescharacteristic, complemented
77#5238D311yescharacteristic, complemented
78#5187—31no—
79#5173—31no—
80#5172—31no—
81#5158—31no—
82#5047—31no—
83#5037—31no—
84#4810—31no—
85#4808—31no—
86#4802—31no—
87#4802—31no—
88#4783—31no—
89#4781—31no—
90#4770—31no—
91#4770—31no—
92#4734—31no—
93#4733—31no—
94#4726—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C23×C3⋊D3D411yescharacteristic
98C32×#41—22no—
99C32×#41—22no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C2×#638—21no—
106C2×#638—21no—
107C2×#638—21no—
108C22×C3⋊Dic3—21no—
109C22×C3⋊Dic3D411yescharacteristic
110#3832—22no—
111#3832—22no—
112Q8×C3⋊D3—22no—
113Q8×C3⋊D3D414yescomplemented
114#3830—28no—
115#3830—22no—
116#3830—22no—
117D4×C3⋊D3—28no—
118D4×C3⋊D3—22no—
119D4×C3⋊D3D414yescomplemented
120#3828—28no—
121#3828—22no—
122#3828—22no—
123C2×C4⋊(C3⋊D3)—21no—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3—28no—
126C2×C4×C3⋊D3—21no—
127C2×C4×C3⋊D3—21no—
128C2×C4×C3⋊D3—21no—
129C2×C4×C3⋊D3—22no—
130C2×C4×C3⋊D3—22no—
131C2×C4×C3⋊D3D411yescharacteristic
132C2×C4×C3⋊D3D411yescharacteristic
133C2×C4×C3⋊D3C2311yescharacteristic
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×#634—21no—
136C2×#634C2311yescharacteristic
137C2×C3×#67—21no—
138C2×C3×D12C2311yescharacteristic
139C2×C3×Dic6C2311yescharacteristic
140C2×#626—21no—
141C2×#626—21no—
142C2×D3×Dic3—21no—
143#3796—22no—
144#3796—22no—
145C3×#217—21no—
146C3×#216—22no—
147C3×#215—22no—
148C3×#214—22no—
149C3×#213—22no—
150C3×(C2×D3)⋊C4—21no—
151C3×C4⋊Dic3C2311yescharacteristic
152C3×C4⋊Dic3C2311yescharacteristic
153C3×Dic3⋊C4—21no—
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158Dic3⋊Dic3—21no—
159#3722—21no—
160#3722—21no—
161(C2×D3)⋊Dic3—21no—
162Dic32—21no—
163#3719—22no—
164#3717—22no—
165#3716—22no—
166#3714—22no—
167#3712—22no—
168#3712—22no—
169#3005—91noSylow
170C2×C3×#41—21no—
171C2×C3×#41C2×D311yescharacteristic
172C2×C3×#41C2×D311yescharacteristic
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176D3×#41—64no—
177D3×#41—68no—
178D3×#41—68no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—31no—
182C2×#239—61no—
183C2×D3×Q8—31no—
184C2×D3×Q8—31no—
185C2×D3×Q8—61no—
186C2×#237—31no—
187C2×#237—31no—
188C2×#237—31no—
189C2×#237—61no—
190C2×#237—61no—
191C2×#237—61no—
192C2×#237—62no—
193C2×D3×D4—31no—
194C2×D3×D4—31no—
195C2×D3×D4—61no—
196C2×D3×D4—61no—
197C2×D3×D4—61no—
198C2×D3×D4—62no—
199C2×#235—31no—
200C2×#235—31no—
201C2×#235—61no—
202C2×#235—61no—
203C2×#235—61no—
204C2×#235—62no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3—61no—
208C22×C4×D3—61no—
209C22×C4×D3—61no—
210C22×C4×D3—62no—
211C2×C3×Q16—31no—
212C2×C3×SD16—31no—
213C2×C3×SD16—31no—
214C2×C3×D8—31no—
215C3×C22⋊Q8—31no—
216C3×#121—31no—
217#946—31no—
218C2×#216—31no—
219C2×#216C2×D311yescharacteristic, complemented
220C2×#215—31no—
221C2×#215C2×D311yescharacteristic, complemented
222#938—31no—
223#937—61no—
224D4×Dic3—61no—
225C2×#214—31no—
226C2×#214C2×D311yescharacteristic, complemented
227C2×#213—31no—
228C2×#213C2×D311yescharacteristic, complemented
229#930C2×D311yescharacteristic, complemented
230#924C2×D311yescharacteristic, complemented
231#918—64no—
232#915—64no—
233#914—64no—
234#911—64no—
235C2×Dic12—31no—
236C2×D24—31no—
237C2×#204—31no—
238C2×#204—31no—
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)—31no—
241C2×ΓL(1,𝔽25)—31no—
242C2×ΓL(1,𝔽25)—31no—
243#897—31no—
244#895—31no—
245#894—61no—
246#893—61no—
247#892—31no—
248#892—31no—
249#883—61no—
250#882—61no—
251#67⋊C4—61no—
252#67⋊C4—61no—
253C3×#103—31no—
254C3×#103—31no—
255C3×#102—31no—
256C3×#102—31no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259#835C2×D311yescharacteristic, complemented
260#835C2×D311yescharacteristic, complemented
261#832C2×D311yescharacteristic, complemented
262#832C2×D311yescharacteristic, complemented
263#830C2×D311yescharacteristic, complemented
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266#821—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269(C2×D3)⋊C8—31no—
270(C2×D3)⋊C8—31no—
271#816—31no—
272#816—31no—
273#810—31no—
274#810—31no—
275#809—31no—
276#809—31no—
277C23×C32—21no—
278C23×C32C2×D411yescharacteristic
279C22×C3⋊D3—21no—
280C22×C3⋊D3—24no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—41no—
283C22×C3⋊D3—41no—
284C22×C3⋊D3—42no—
285C22×C3⋊D3—42no—
286C22×C3⋊D3C2×D411yescharacteristic
287C22×C3⋊D3C2×D411yescharacteristic
288C22×C3×D3—21no—
289C32×Q8—21no—
290C32×Q8C2×D412yes—
291C32×D4—24no—
292C32×D4—21no—
293C32×D4C2×D412yes—
294C2×C32×C4—24no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2×D411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300#638—24no—
301#638—24no—
302#638—24no—
303C2×C3⋊Dic3—24no—
304C2×C3⋊Dic3—21no—
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3C2×D411yescharacteristic
307C2×C3⋊Dic3C2×D411yescharacteristic
308C4⋊(C3⋊D3)—24no—
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)C2×D412yes—
311C4×C3⋊D3—24no—
312C4×C3⋊D3—24no—
313C4×C3⋊D3—22no—
314C4×C3⋊D3—24no—
315C4×C3⋊D3—21no—
316C4×C3⋊D3—21no—
317C4×C3⋊D3—22no—
318C4×C3⋊D3C2×D412yes—
319C4×C3⋊D3C2×D412yes—
320#634—21no—
321#634—24no—
322#634C2×D412yes—
323C3×#67—42no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—21no—
327C3×D12—21no—
328C3×D12—21no—
329C3×Dic6—21no—
330C3×Dic6—21no—
331#626—42no—
332#626—42no—
333D3×Dic3—42no—
334C3×C3⋊C8—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×#137—91no—
340C2×AGL(1,ℤ/8)—91no—
341#525—91no—
342#452—31no—
343#452—91no—
344#452—91no—
345#452—91no—
346#449—31no—
347#449—91no—
348#449—91no—
349#449—91no—
350#419—91no—
351#418—91no—
352#407—91no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—62no—
359C3×#41—24no—
360C3×#41—24no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—22no—
364C3×#41—22no—
365C2×C3×Q8—21no—
366C2×C3×Q8—31no—
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×Q8C22×D311yescharacteristic
369C2×C3×D4—22no—
370C2×C3×D4—21no—
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—31no—
374C2×C3×D4—61no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—22no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—21no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—61no—
394C2×#67—61no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—62no—
402#239—62no—
403#239—62no—
404#239—62no—
405#239—62no—
406#239—64no—
407#239—64no—
408#239—62no—
409#239—62no—
410D3×Q8—34no—
411D3×Q8—34no—
412D3×Q8—64no—
413D3×Q8—62no—
414D3×Q8—62no—
415D3×Q8—64no—
416#237—62no—
417#237—62no—
418#237—62no—
419#237—62no—
420#237—64no—
421#237—68no—
422#237—68no—
423#237—616no—
424#237—64no—
425#237—62no—
426#237—62no—
427D3×D4—34no—
428D3×D4—34no—
429D3×D4—64no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—64no—
433D3×D4—68no—
434D3×D4—68no—
435D3×D4—616no—
436#235—62no—
437#235—62no—
438#235—62no—
439#235—62no—
440#235—64no—
441#235—64no—
442#235—68no—
443#235—68no—
444#235—616no—
445C2×D12—31no—
446C2×D12—31no—
447C2×D12—61no—
448C2×D12—61no—
449C2×D12—61no—
450C2×D12—62no—
451C2×D12—61no—
452C2×D12—61no—
453C2×D12C22×D311yescharacteristic
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—61no—
463C2×C4×D3—61no—
464C2×C4×D3—61no—
465C2×C4×D3—61no—
466C2×C4×D3—62no—
467C2×C4×D3—62no—
468C2×C4×D3—62no—
469C2×C4×D3—62no—
470C2×C4×D3—61no—
471C2×C4×D3—61no—
472C2×C4×D3—61no—
473C2×C4×D3—61no—
474C2×C4×D3—62no—
475C2×C4×D3—62no—
476C2×C4×D3—62no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—68no—
480C2×C4×D3—68no—
481C2×C4×D3—616no—
482C2×C4×D3—61no—
483C2×C4×D3—61no—
484C2×C4×D3—61no—
485C2×Dic6—31no—
486C2×Dic6—31no—
487C2×Dic6—61no—
488C2×Dic6—61no—
489C2×Dic6—61no—
490C2×Dic6—62no—
491C2×Dic6C22×D311yescharacteristic
492C3×Q16—62no—
493C3×SD16—62no—
494C3×SD16—62no—
495C3×D8—62no—
496C2×C3×C8—31no—
497C2×C3×C8—31no—
498C2×C3×C8—31no—
499C2×C3×C8—31no—
500C3×C4⋊C4—31no—
501C3×C4⋊C4—31no—
502C3×C4⋊C4—61no—
503C3×C22⋊C4—61no—
504C3×C22⋊C4—61no—
505#217—21no—
506#217—61no—
507#216—22no—
508#216—62no—
509#215—22no—
510#215—62no—
511#214—22no—
512#214—62no—
513#213—22no—
514#213—62no—
515(C2×D3)⋊C4—21no—
516(C2×D3)⋊C4—61no—
517(C2×D3)⋊C4—61no—
518(C2×D3)⋊C4—61no—
519(C2×D3)⋊C4—61no—
520(C2×D3)⋊C4—61no—
521C4⋊Dic3—61no—
522C4⋊Dic3C22×D311yescharacteristic
523C4⋊Dic3C22×D311yescharacteristic
524Dic3⋊C4—21no—
525Dic3⋊C4—61no—
526C4×Dic3—61no—
527C4×Dic3—61no—
528C2×C3⋊C8C22×D311yescharacteristic
529C2×C3⋊C8C22×D311yescharacteristic
530C2×C3⋊C8C22×D311yescharacteristic
531C2×C3⋊C8C22×D311yescharacteristic
532Dic12—62no—
533D24—62no—
534#204—62no—
535#204—62no—
536ΓL(1,𝔽25)—62no—
537ΓL(1,𝔽25)—62no—
538ΓL(1,𝔽25)—62no—
539ΓL(1,𝔽25)—62no—
540C22×C32—21no—
541C22×C32—22no—
542C22×C32—21no—
543C22×C32—21no—
544C22×C32—41no—
545C22×C32—41no—
546C22×C32C22×D411yescharacteristic
547C2×C3⋊D3—21no—
548C2×C3⋊D3—21no—
549C2×C3⋊D3—21no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—44no—
554C2×C3⋊D3—48no—
555C2×C3⋊D3—41no—
556C2×C3⋊D3—41no—
557C2×C3⋊D3#12012yes—
558C2×C3×D3—41no—
559C2×C3×D3—41no—
560C2×C3×D3—41no—
561C32×C4—22no—
562C32×C4—21no—
563C32×C4C22×D411yescharacteristic
564C32×C4C22×D411yescharacteristic
565C3⋊Dic3—22no—
566C3⋊Dic3—21no—
567C3⋊Dic3#12012yes—
568C3×Dic3—41no—
569C3×Dic3—41no—
570C3×Dic3—41no—
571C2×#41—91no—
572C2×#41—91no—
573C2×#41—91no—
574C2×#41—91no—
575C2×#41—181no—
576C2×#41—181no—
577C2×#41—184no—
578C2×#41—184no—
579C2×#41D3211yescharacteristic
580C22×Q8—91no—
581C22×D4—91no—
582C22×D4—181no—
583C23×C4—91no—
584C23×C4—181no—
585#137—184no—
586AGL(1,ℤ/8)—184no—
587C2×Q16—31no—
588C2×Q16—91no—
589C2×SD16—31no—
590C2×SD16—31no—
591C2×SD16—91no—
592C2×SD16—91no—
593C2×D8—31no—
594C2×D8—91no—
595C2×M16—91no—
596C2×M16—91no—
597#123—181no—
598C22⋊Q8—31no—
599C22⋊Q8—91no—
600#121—31no—
601#121—91no—
602#120—181no—
603C4×D4—181no—
604C4×D4—181no—
605#117—91no—
606#103—31no—
607#103—31no—
608#103—91no—
609#103—91no—
610#102—31no—
611#102—31no—
612#102—91no—
613#102—91no—
614C22⋊C8—31no—
615C22⋊C8—31no—
616C22⋊C8—91no—
617C22⋊C8—91no—
618C23×C3—22no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3—61no—
623C23×C3D3×D411yescharacteristic
624C23×C3D3×D411yescharacteristic
625C22×D3—21no—
626C22×D3—31no—
627C22×D3—31no—
628C22×D3—31no—
629C22×D3—31no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—64no—
633C22×D3—64no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—68no—
638C22×D3—64no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—121no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—122no—
646C22×D3—122no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3—122no—
653C3×Q8—22no—
654C3×Q8—21no—
655C3×Q8—21no—
656C3×Q8—22no—
657C3×Q8—61no—
658C3×Q8—61no—
659C3×Q8D3×D412yes—
660C3×Q8D3×D412yes—
661C3×D4—28no—
662C3×D4—24no—
663C3×D4—24no—
664C3×D4—22no—
665C3×D4—21no—
666C3×D4—21no—
667C3×D4—22no—
668C3×D4—61no—
669C3×D4—61no—
670C3×D4—122no—
671C3×D4D3×D412yes—
672C3×D4D3×D412yes—
673C2×C3×C4—22no—
674C2×C3×C4—28no—
675C2×C3×C4—24no—
676C2×C3×C4—24no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4D3×D411yescharacteristic
691C2×C3×C4D3×D411yescharacteristic
692C2×C3×C4C23×D311yescharacteristic
693C2×C3×C4C23×D311yescharacteristic
694#67—42no—
695#67—64no—
696#67—64no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—64no—
701#67—64no—
702#67—64no—
703#67—64no—
704#67—122no—
705#67—122no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—64no—
719C2×Dic3—68no—
720C2×Dic3—64no—
721C2×Dic3—64no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—122no—
725D12—21no—
726D12—21no—
727D12—32no—
728D12—32no—
729D12—62no—
730D12—68no—
731D12—64no—
732D12—64no—
733D12—62no—
734D12—61no—
735D12—61no—
736D12—122no—
737D12—122no—
738C4×D3—32no—
739C4×D3—32no—
740C4×D3—32no—
741C4×D3—32no—
742C4×D3—62no—
743C4×D3—62no—
744C4×D3—62no—
745C4×D3—62no—
746C4×D3—62no—
747C4×D3—62no—
748C4×D3—64no—
749C4×D3—64no—
750C4×D3—64no—
751C4×D3—64no—
752C4×D3—68no—
753C4×D3—64no—
754C4×D3—64no—
755C4×D3—68no—
756C4×D3—68no—
757C4×D3—64no—
758C4×D3—64no—
759C4×D3—62no—
760C4×D3—62no—
761C4×D3—61no—
762C4×D3—61no—
763C4×D3—61no—
764C4×D3—61no—
765C4×D3—122no—
766Dic6—21no—
767Dic6—21no—
768Dic6—32no—
769Dic6—32no—
770Dic6—62no—
771Dic6—64no—
772Dic6—64no—
773Dic6—68no—
774Dic6—62no—
775Dic6—61no—
776Dic6—61no—
777C3×C8—61no—
778C3×C8—61no—
779C3×C8—61no—
780C3×C8—61no—
781C3⋊C8—21no—
782C3⋊C8—21no—
783C3⋊C8—21no—
784C3⋊C8—21no—
785C2×C32—41no—
786C2×C32—42no—
787C2×C32C2×#12011yescharacteristic
788C2×C32#57511yescharacteristic
789C2×C32#57511yescharacteristic
790C3⋊D3—22no—
791C3⋊D3—41no—
792C3⋊D3—42no—
793C3×D3—81no—
794C24—91no—
795C24—181no—
796#41—22no—
797#41—22no—
798#41—182no—
799#41—182no—
800#41—188no—
801#41—182no—
802#41—182no—
803#41—182no—
804#41—188no—
805#41—182no—
806#41—182no—
807#41—182no—
808C2×Q8—31no—
809C2×Q8—94no—
810C2×Q8—91no—
811C2×Q8—181no—
812C2×Q8—182no—
813C2×Q8C2×D3211yescharacteristic
814C2×D4—21no—
815C2×D4—31no—
816C2×D4—61no—
817C2×D4—94no—
818C2×D4—91no—
819C2×D4—181no—
820C2×D4—181no—
821C2×D4—181no—
822C2×D4—182no—
823C2×D4—181no—
824C2×D4—188no—
825C2×D4—181no—
826C2×D4—181no—
827C2×D4C2×D3211yescharacteristic
828C22×C4—21no—
829C22×C4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—91no—
834C22×C4—182no—
835C22×C4—182no—
836C22×C4—181no—
837C22×C4—181no—
838C22×C4—188no—
839C22×C4—181no—
840C22×C4—181no—
841C22×C4—181no—
842C22×C4C2×D3211yescharacteristic
843Q16—62no—
844Q16—182no—
845SD16—62no—
846SD16—62no—
847SD16—182no—
848SD16—182no—
849D8—62no—
850D8—182no—
851M16—182no—
852M16—182no—
853C2×C8—31no—
854C2×C8—31no—
855C2×C8—31no—
856C2×C8—31no—
857C4⋊C4—31no—
858C4⋊C4—31no—
859C4⋊C4—61no—
860C4⋊C4—181no—
861C22⋊C4—61no—
862C22⋊C4—61no—
863C22⋊C4—181no—
864C22⋊C4—181no—
865C22⋊C4—181no—
866C42—181no—
867C22×C3—22no—
868C22×C3—24no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—41no—
885C22×C3—41no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3—121no—
889C22×C3C2×D3×D411yescharacteristic
890C22×C3C2×D3×D411yescharacteristic
891C2×D3—32no—
892C2×D3—32no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—64no—
904C2×D3—62no—
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—128no—
916C2×D3—1216no—
917C2×D3—124no—
918C2×D3—128no—
919C2×D3—124no—
920C2×D3—128no—
921C2×D3—122no—
922C2×D3—122no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C3×C4—24no—
928C3×C4—22no—
929C3×C4—22no—
930C3×C4—22no—
931C3×C4—21no—
932C3×C4—21no—
933C3×C4—21no—
934C3×C4—21no—
935C3×C4—121no—
936C3×C4—121no—
937C3×C4—121no—
938C3×C4C2×D3×D411yescharacteristic
939C3×C4C2×D3×D411yescharacteristic
940C3×C4C2×D3×D411yescharacteristic
941C3×C4C2×D3×D411yescharacteristic
942Dic3—32no—
943Dic3—32no—
944Dic3—41no—
945Dic3—41no—
946Dic3—41no—
947Dic3—62no—
948Dic3—64no—
949Dic3—62no—
950Dic3—62no—
951Dic3—62no—
952Dic3—61no—
953Dic3—61no—
954C32#300511yescharacteristic, complemented, Sylow
955C23—21no—
956C23—61no—
957C23—91no—
958C23—91no—
959C23—184no—
960C23—182no—
961C23—181no—
962C23—361no—
963C23—361no—
964C23—362no—
965C23—362no—
966C23#381111yescharacteristic
967Q8—21no—
968Q8—61no—
969Q8—61no—
970Q8—92no—
971Q8—184no—
972Q8—181no—
973Q8#381112yes—
974D4—24no—
975D4—21no—
976D4—61no—
977D4—61no—
978D4—92no—
979D4—122no—
980D4—184no—
981D4—184no—
982D4—184no—
983D4—184no—
984D4—181no—
985D4—362no—
986D4—362no—
987D4#381112yes—
988C2×C4—24no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—91no—
996C2×C4—92no—
997C2×C4—92no—
998C2×C4—91no—
999C2×C4—182no—
1000C2×C4—182no—
1001C2×C4—184no—
1002C2×C4—184no—
1003C2×C4—184no—
1004C2×C4—182no—
1005C2×C4—184no—
1006C2×C4—181no—
1007C2×C4—181no—
1008C2×C4—181no—
1009C2×C4—362no—
1010C2×C4#381111yescharacteristic
1011C2×C4C22×D3211yescharacteristic
1012C8—61no—
1013C8—61no—
1014C8—61no—
1015C8—61no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—42no—
1020C2×C3—44no—
1021C2×C3—41no—
1022C2×C3—42no—
1023C2×C3—41no—
1024C2×C3—42no—
1025C2×C3—241no—
1026C2×C3D3×#12011yescharacteristic
1027C2×C3D3×#12011yescharacteristic
1028C2×C3#576811yescharacteristic
1029C2×C3#576811yescharacteristic
1030C2×C3#577311yescharacteristic
1031C2×C3#577711yescharacteristic
1032D3—64no—
1033D3—62no—
1034D3—62no—
1035D3—81no—
1036D3—122no—
1037D3—124no—
1038D3—121no—
1039D3—122no—
1040D3—121no—
1041D3—122no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—22no—
1046C22—41no—
1047C22—41no—
1048C22—92no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—181no—
1053C22—181no—
1054C22—181no—
1055C22—181no—
1056C22—182no—
1057C22—181no—
1058C22—364no—
1059C22—368no—
1060C22—361no—
1061C22—361no—
1062C22C2×#381111yescharacteristic
1063C4—21no—
1064C4—22no—
1065C4—92no—
1066C4—121no—
1067C4—121no—
1068C4—121no—
1069C4—181no—
1070C4—182no—
1071C4C2×#381111yescharacteristic
1072C4C2×#381111yescharacteristic
1073C3—21no—
1074C3#8008311yescharacteristic, complemented
1075C3#8022711yescharacteristic, complemented
1076C2—41no—
1077C2—42no—
1078C2—182no—
1079C2—241no—
1080C2—361no—
1081C2—362no—
1082C2#1059546011yescharacteristic
1083C2#1059547111yescharacteristic
1084C2#1059552711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3005
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
1. C2×#41×C3⋊D3C2semidirect
2. C2×#63951C2semidirect
3. C2×#63937C2semidirect
4. #10594922C2semidirect
5. C3×#5239C2semidirect
6. C3×#5238C2semidirect
7. #10591602C2semidirect
8. #10591593C2semidirect
9. #10591562C2semidirect
10. #10591466C2semidirect
11. #10591457C2semidirect
12. #10591426C2semidirect
13. #10591184C2semidirect
14. #10591182C2semidirect
15. #10591159C2semidirect
32. C2×C3×#216C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#213C22semidirect
36. C3×#930C22semidirect
37. C3×#924C22semidirect
42. #63916C22semidirect
44. #63871C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3716C22semidirect
50. C2×#3714C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#832C22semidirect
57. C3×#830C22semidirect
58. C3×#830C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
64. #63557C22semidirect
76. #5239D3semidirect
77. #5238D3semidirect
113. Q8×C3⋊D3D4semidirect
119. D4×C3⋊D3D4semidirect
219. C2×#216C2×D3semidirect
221. C2×#215C2×D3semidirect
226. C2×#214C2×D3semidirect
228. C2×#213C2×D3semidirect
229. #930C2×D3semidirect
230. #924C2×D3semidirect
259. #835C2×D3semidirect
260. #835C2×D3semidirect
261. #832C2×D3semidirect
262. #832C2×D3semidirect
263. #830C2×D3semidirect
264. #830C2×D3semidirect
954. C32#3005semidirect
1074. C3#80083semidirect
1075. C3#80227semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#639512
C2×#639372
#105949222
C3×#52392
C3×#52382
#105916022
#105915932
#105915622
#105914662
#105914572
#105914262
#105911842
#105911822
#105911592
#802273
#800833