Finite Group Databasebeta

← #11884142

Subgroups — #11884142

Order 1152.

1064 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10595403C211yesmaximal, characteristic, complemented
3C2×#63945C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8#10591635C211yesmaximal, characteristic, complemented
9#10591590C211yesmaximal, characteristic, complemented
10#10591578C211yesmaximal, characteristic, complemented
11#10591565C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590824C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590728C211yesmaximal, characteristic, complemented
16#81881—31nomaximal
17#80204—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3797C2211yescharacteristic, complemented
22C2×C32×Q16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic
32#63945—24no—
33D3×#215—24no—
34#63923—21no—
35#63921—21no—
36#63916C2211yescharacteristic
37#63910—21no—
38#63904—21no—
39C4×#626C2211yescharacteristic
40#63894C2211yescharacteristic
41#63888—21no—
42#63856C2211yescharacteristic
43#63853—21no—
44#63851—21no—
45Dic3×Dic6C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63Q8×#67—31no—
64C22×#215—31no—
65C2×#918—31no—
66C2×#918—31no—
67C2×D3×SD16—31no—
68#5727—31no—
69#5676—31no—
70#5630—31no—
71C3×#497—31no—
72C3×#451—31no—
73#5190D311yescharacteristic, complemented
74#5188—31no—
75#5187—31no—
76#5187—31no—
77#5187—61no—
78#5186D311yescharacteristic, complemented
79#5185—31no—
80#5174—31no—
81#5170—31no—
82#5169—31no—
83#5083—31no—
84#5054—31no—
85#5051—31no—
86#4818—31no—
87#4817—31no—
88#4812—31no—
89#4806—31no—
90#4731—31no—
91#4730—31no—
92#4710—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—41no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#624—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3797—22no—
120#3797—41no—
121C32×Q16—41no—
122C2×C32×C8C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#216—22no—
129C3×#216—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—41no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3717—22no—
152#3717D414yescomplemented
153#3715—22no—
154#3712—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—61no—
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C2×D3×Q8C2×D311yescharacteristic
164C2×D3×D4—31no—
165C22×D12—31no—
166C2×C3×Q16—21no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C3×C4⋊Q8—31no—
174C3×#124—31no—
175C3×C22⋊Q8—31no—
176#947C2×D311yescharacteristic
177#946—31no—
178#946—31no—
179#946—31no—
180#946—61no—
181#946—61no—
182#946C2×D311yescharacteristic
183Q8×Dic3—31no—
184#944—61no—
185#944C2×D311yescharacteristic, complemented
186C2×#216C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215—64no—
195C2×#215C2×D311yescharacteristic
196#938—31no—
197C2×#214—31no—
198C4×#67—31no—
199C4×#67—61no—
200#924—31no—
201#924—61no—
202C22×C3⋊C8—31no—
203#918—64no—
204#918—64no—
205D3×SD16—64no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204C2×D311yescharacteristic
209C2×ΓL(1,𝔽25)—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#896—61no—
213#896—61no—
214#895—31no—
215#895—61no—
216#894—61no—
217#893—31no—
218#893—61no—
219#888—61no—
220#884—61no—
221#883—61no—
222#882—61no—
223#882—61no—
224D3×C22⋊C4—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×C22⋊C8—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—61no—
246(C2×D3)⋊C8C2×D311yescharacteristic
247#818—31no—
248#816C2×D311yescharacteristic, complemented
249#815C2×D311yescharacteristic, complemented
250Dic3⋊C8—31no—
251#810—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—42no—
272C4⋊(C3⋊D3)C2×D412yes—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#626—22no—
294#626—42no—
295#626—81no—
296#624—42no—
297#624—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—31no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—31no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—62no—
325C2×C3×Q8—121no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C2×#67—31no—
334C2×#67—61no—
335C2×#67—61no—
336#239—62no—
337#239—62no—
338#239—122no—
339#239—121no—
340#239—121no—
341#239—122no—
342D3×Q8—22no—
343D3×Q8—41no—
344D3×Q8—62no—
345D3×Q8—62no—
346D3×Q8—121no—
347D3×Q8—121no—
348D3×D4—62no—
349D3×D4—121no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—121no—
373C2×C4×D3C22×D311yescharacteristic
374C2×Dic6—21no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—41no—
380C3×Q16—41no—
381C3×Q16—42no—
382C3×Q16—62no—
383C3×Q16—62no—
384C3×SD16—62no—
385C3×SD16—121no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399#217—31no—
400#217—61no—
401#217—61no—
402#216—22no—
403#216—22no—
404#215—22no—
405#215—34no—
406#215—62no—
407#215—62no—
408#215—62no—
409#215—62no—
410#215—122no—
411#214—62no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—31no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—121no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450#204—34no—
451#204—41no—
452#204—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—31no—
489C2×Q16D3211yescharacteristic, complemented
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—91no—
499C4⋊Q8—31no—
500C4⋊Q8—181no—
501#124—31no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—91no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8—91no—
526#97—31no—
527C23×C3—31no—
528C23×C3—61no—
529C22×D3—21no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3D3×D411yescharacteristic
543C3×Q8—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—32no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—122no—
560C3×D4—61no—
561C3×D4—61no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—122no—
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—62no—
581#67—122no—
582#67—241no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3D3×D411yescharacteristic
593C2×Dic3D3×D411yescharacteristic
594C2×Dic3D3×D411yescharacteristic
595D12—21no—
596D12—21no—
597D12—32no—
598D12—32no—
599D12—62no—
600D12—62no—
601D12—61no—
602D12—61no—
603D12—121no—
604D12—122no—
605D12—122no—
606D12—124no—
607D12—122no—
608D12—241no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—42no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—121no—
617C4×D3—121no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—124no—
623C4×D3—241no—
624C4×D3—241no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—42no—
629Dic6—122no—
630Dic6—122no—
631Dic6D3×D412yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8D3×D412yes—
642C2×C32D4211yescharacteristic
643C2×C32C2×#13711yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—41no—
647C3×D3—22no—
648C3×D3—81no—
649C24—181no—
650#41—182no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—121no—
657C2×Q8—181no—
658C2×Q8—182no—
659C2×Q8—361no—
660C2×Q8C2×D3211yescharacteristic
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—91no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—41no—
677Q16—62no—
678Q16—62no—
679SD16—62no—
680SD16—94no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—182no—
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—31no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C22×C3—21no—
712C22×C3—32no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×D3×D411yescharacteristic
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—61no—
726C2×D3—62no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—62no—
733C2×D3—122no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—244no—
744C2×D3—244no—
745C2×D3#91812yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—42no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—62no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4C2×D3×D411yescharacteristic
761C3×C4C2×D3×D411yescharacteristic
762C3×C4#100411yescharacteristic
763C3×C4#100411yescharacteristic
764Dic3—21no—
765Dic3—21no—
766Dic3—22no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—61no—
771Dic3—61no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—241no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—31no—
778C23—61no—
779C23—91no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23—721no—
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—21no—
788Q8—32no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—122no—
793Q8—362no—
794D4—61no—
795D4—61no—
796D4—92no—
797D4—182no—
798D4—181no—
799D4—362no—
800D4—362no—
801D4—721no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—91no—
813C2×C4—122no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—721no—
820C2×C4C22×D3211yescharacteristic
821C8—21no—
822C8—32no—
823C8—61no—
824C8—181no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—62no—
829C2×C3—241no—
830C2×C3#559011yescharacteristic
831C2×C3#571711yescharacteristic
832C2×C3C2×#91811yescharacteristic
833C2×C3D3×#13711yescharacteristic
834C2×C3#577811yescharacteristic
835C2×C3#577811yescharacteristic
836D3—22no—
837D3—81no—
838D3—121no—
839D3—122no—
840D3—121no—
841D3—122no—
842D3—241no—
843D3—242no—
844C22—32no—
845C22—61no—
846C22—61no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—182no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—41no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—62no—
864C4—121no—
865C4—121no—
866C4—181no—
867C4—361no—
868C4D32×D411yescharacteristic
869C4#6433011yescharacteristic
870C3—21no—
871C3#8020411yescharacteristic, complemented
872C3#8188111yescharacteristic, complemented
873C2—62no—
874C2—241no—
875C2—361no—
876C2—362no—
877C2D3×#91811yescharacteristic
878C2#1059476711yescharacteristic
879C2#1059529511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenterC2×Q16D32
hypocenterC32#3266
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
2. #10595403C2semidirect
3. C2×#63945C2semidirect
4. C2×D3×#215C2semidirect
5. #10592886C2semidirect
6. C3×#5190C2semidirect
7. C3×#5186C2semidirect
8. #10591635C2semidirect
9. #10591590C2semidirect
10. #10591578C2semidirect
11. #10591565C2semidirect
12. #10590942C2semidirect
13. #10590824C2semidirect
14. #10590795C2semidirect
15. #10590728C2semidirect
21. C2×#3797C22semidirect
22. C2×C32×Q16C22semidirect
23. #64155C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
45. Dic3×Dic6C22semidirect
50. C2×#3712C22semidirect
52. #63662C22semidirect
54. #63647C22semidirect
55. C3×#835C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. #63575C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
73. #5190D3semidirect
78. #5186D3semidirect
152. #3717D4semidirect
169. C2×C3×Q16C2×D3semidirect
170. C2×C3×Q16C2×D3semidirect
185. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
187. C2×#216C2×D3semidirect
237. #835C2×D3semidirect
248. #816C2×D3semidirect
249. #815C2×D3semidirect
468. C2×C3×D3#137semidirect
489. C2×Q16D32semidirect
745. C2×D3#918semidirect
776. C32#3266semidirect
871. C3#80204semidirect
872. C3#81881semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105954032
C2×#639452
C2×D3×#2152
#105928862
C3×#51902
C3×#51862
#105916352
#105915902
#105915782
#105915652
#105909422
#105908242
#105907952
#105907282
#818813
#802043