Finite Group Databasebeta

← #11884100

Subgroups — #11884100

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic
5#10592725C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10590616C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590518C211yesmaximal, characteristic, complemented
12#10590503C211yesmaximal, characteristic, complemented
13#10590379C211yesmaximal, characteristic, complemented
14#10590376C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80627—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#897—21no—
28C3×#897—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic
32C3×C4×D12—21no—
33C3×C4×D12C2211yescharacteristic
34C3×#869—21no—
35C3×#869C2211yescharacteristic, complemented
36#63948—24no—
37D3×#215—24no—
38#63922—21no—
39#63921—21no—
40#63912—21no—
41#63908C2211yescharacteristic
42#63856C2211yescharacteristic
43#63854—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#918—31no—
67C2×D3×SD16—31no—
68#5676—31no—
69Q8×D12D311yescharacteristic, complemented
70#5550—31no—
71C3×#464—31no—
72#5228—31no—
73#5227—31no—
74#5186—31no—
75#5170—31no—
76#5086—31no—
77#5083—31no—
78#5060—31no—
79#5051—31no—
80#5049—31no—
81#5047—31no—
82#5046—31no—
83#5028D311yescharacteristic, complemented
84#5026—31no—
85#5026—31no—
86#5026—61no—
87#5011—31no—
88#4841—31no—
89#4836—31no—
90#4813—31no—
91#4808—31no—
92#4780—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—41no—
101C3×D3×Q8—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C42—21no—
124C32×C42C2311yescharacteristic
125#3755D414yescomplemented
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#216—22no—
131C3×#215—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3D411yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3718—22no—
149#3718—41no—
150#3717—22no—
151#3717—22no—
152#3715—22no—
153#3715—41no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic
161C2×D3×Q8C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×C4⋊Q8—61no—
169C3×#124—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8—61no—
174C3×C4×Q8—21no—
175C3×C4×Q8C2×D311yescharacteristic, complemented
176C3×C4×Q8C2×D311yescharacteristic, complemented
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#946—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216C2×D311yescharacteristic, complemented
185#942—64no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215—64no—
194C2×#215C2×D311yescharacteristic
195#938—31no—
196#937—61no—
197C2×#214—31no—
198C2×#214—31no—
199#930—31no—
200#924—31no—
201C2×#208—31no—
202C22×C3⋊C8—31no—
203#918—64no—
204D3×SD16—64no—
205C2×#204—31no—
206C2×#204—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×D3×C8—31no—
209#897—21no—
210#897—21no—
211#897C2×D311yescharacteristic
212#897C2×D311yescharacteristic, complemented
213#894—61no—
214#884—61no—
215#884—61no—
216#883—61no—
217#882—61no—
218D3×C22⋊C4—61no—
219D3×C22⋊C4—61no—
220#875C2×D311yescharacteristic
221C4×D12—21no—
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225C4×D12C2×D311yescharacteristic
226#869—21no—
227#869C2×D311yescharacteristic, complemented
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#816—31no—
241#816—31no—
242#810C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—61no—
246#809C2×D311yescharacteristic
247#807—31no—
248#807—31no—
249#807—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—22no—
278C3×D12—21no—
279C3×D12—21no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—42no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6—42no—
294#626—42no—
295#626—42no—
296#625—81no—
297#624—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—31no—
310#461—91no—
311#452—91no—
312#451—91no—
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—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8—121no—
328C2×C3×Q8—121no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341#239—62no—
342#239—121no—
343D3×Q8—22no—
344D3×Q8—22no—
345D3×Q8—41no—
346D3×Q8—41no—
347D3×D4—62no—
348D3×D4—121no—
349#235—62no—
350#235—121no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12#6711yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×SD16—62no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—41no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—21no—
398C3×C42—41no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—61no—
402#217—61no—
403#216—22no—
404#216—62no—
405#216—62no—
406#216—121no—
407#216—121no—
408#215—22no—
409#215—34no—
410#215—34no—
411#215—64no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—121no—
416#214—62no—
417#214—121no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4#6711yescharacteristic
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—21no—
430C4⋊Dic3—21no—
431C4⋊Dic3—21no—
432C4⋊Dic3—21no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3#6711yescharacteristic
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449#204—62no—
450#204—62no—
451ΓL(1,𝔽25)—62no—
452D3×C8—62no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#13712yescomplemented
466D32—84no—
467C32×C4—22no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—91no—
480C22×Q8—31no—
481C22×Q8—31no—
482C22×D4—91no—
483#137—184no—
484C2×Q16—31no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—184no—
494C2×M16—91no—
495C22×C8—91no—
496C4⋊Q8—31no—
497C4⋊Q8—61no—
498#124—31no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—61no—
504C22⋊Q8—91no—
505#121—91no—
506#121—181no—
507#120—181no—
508C4×Q8D3211yescharacteristic, complemented
509C4×D4—31no—
510C4×D4—61no—
511C4×D4—91no—
512C2×C22⋊C4—181no—
513#107—91no—
514C4⋊C8—31no—
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—241no—
536C22×D3—241no—
537C22×D3C2×#6711yescharacteristic
538C22×D3C2×#6711yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—22no—
542C3×Q8—41no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×Q8—122no—
551C3×Q8D3×D412yes—
552C3×Q8D3×D412yes—
553C3×D4—62no—
554C3×D4—61no—
555C3×D4—61no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—122no—
583#67—122no—
584#67—241no—
585#67—241no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3C2×#6711yescharacteristic
593C2×Dic3C2×#6711yescharacteristic
594D12—22no—
595D12—21no—
596D12—21no—
597D12—32no—
598D12—32no—
599D12—62no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—122no—
604D12—122no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—42no—
610C4×D3—42no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—241no—
614C4×D3—241no—
615C4×D3—242no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624C3×C8—61no—
625C3×C8—61no—
626C3⋊C8—21no—
627C3⋊C8—21no—
628C3⋊C8—32no—
629C3⋊C8—32no—
630C3⋊C8—62no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—121no—
634C2×C32D4211yescharacteristic
635C2×C32C2×#13711yescharacteristic
636C2×C32#57711yescharacteristic
637C3⋊D3—42no—
638C3×D3—22no—
639C3×D3—41no—
640C3×D3—81no—
641C24—181no—
642#41—182no—
643#41—361no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—31no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—62no—
651C2×Q8—121no—
652C2×Q8—121no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—91no—
657C2×D4—181no—
658C2×D4—182no—
659C2×D4—181no—
660C2×D4—181no—
661C2×D4—361no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4—181no—
668Q16—62no—
669Q16—182no—
670Q16—361no—
671SD16—62no—
672SD16—94no—
673SD16—182no—
674SD16—182no—
675SD16—182no—
676SD16—361no—
677M16—182no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—91no—
681C2×C8—91no—
682C2×C8—182no—
683C4⋊C4—21no—
684C4⋊C4—31no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4C2×D3211yescharacteristic
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C42—21no—
702C42C2×D3211yescharacteristic
703C22×C3—21no—
704C22×C3—32no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C22×#6711yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—122no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3#94212yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—22no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—42no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—61no—
749C3×C4—61no—
750C3×C4—81no—
751C3×C4—121no—
752C3×C4—121no—
753C3×C4—121no—
754C3×C4C2×D3×D411yescharacteristic
755C3×C4C2×D3×D411yescharacteristic
756C3×C4#100411yescharacteristic
757C3×C4#100911yescharacteristic
758Dic3—21no—
759Dic3—21no—
760Dic3—41no—
761Dic3—41no—
762Dic3—41no—
763Dic3—121no—
764Dic3—121no—
765Dic3—241no—
766C32#326611yescharacteristic, complemented, Sylow
767C23—31no—
768C23—31no—
769C23—61no—
770C23—181no—
771C23—362no—
772C23—362no—
773C23—721no—
774Q8—21no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—122no—
782Q8—122no—
783Q8#380212yes—
784D4—62no—
785D4—61no—
786D4—61no—
787D4—92no—
788D4—181no—
789D4—362no—
790D4—362no—
791D4—721no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—181no—
806C2×C4—362no—
807C2×C4—721no—
808C2×C4D3×#6711yescharacteristic
809C2×C4D3×#6711yescharacteristic
810C2×C4C22×D3211yescharacteristic
811C8—61no—
812C8—61no—
813C8—92no—
814C8—181no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—62no—
819C2×C3—121no—
820C2×C3—241no—
821C2×C3#560911yescharacteristic
822C2×C3#577011yescharacteristic
823C2×C3D3×#13711yescharacteristic
824C2×C3D4×#6711yescharacteristic
825C2×C3C2×#94211yescharacteristic
826C2×C3#583711yescharacteristic
827D3—22no—
828D3—41no—
829D3—81no—
830D3—122no—
831D3—122no—
832D3—242no—
833C22—32no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—182no—
843C22—361no—
844C22—361no—
845C22—724no—
846C22C2×D3×#6711yescharacteristic
847C4—21no—
848C4—21no—
849C4—22no—
850C4—41no—
851C4—61no—
852C4—61no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—361no—
857C4C2×#380211yescharacteristic
858C4#6430711yescharacteristic
859C3—21no—
860C3#8062711yescharacteristic, complemented
861C3#8355911yescharacteristic, complemented
862C2—62no—
863C2—121no—
864C2—241no—
865C2—362no—
866C2#1059506911yescharacteristic
867C2D3×#94211yescharacteristic
868C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4×Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
2. C2×#63948C2semidirect
3. C2×D3×#215C2semidirect
5. #10592725C2semidirect
6. C3×#5028C2semidirect
7. #10591594C2semidirect
8. #10591583C2semidirect
9. #10590616C2semidirect
10. #10590596C2semidirect
11. #10590518C2semidirect
12. #10590503C2semidirect
13. #10590379C2semidirect
14. #10590376C2semidirect
15. #10590330C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C32×C4×Q8C22semidirect
25. C2×C3×#216C22semidirect
30. C3×#897C22semidirect
35. C3×#869C22semidirect
44. C2×#3718C22semidirect
45. C2×#3718C22semidirect
50. C2×#3711C22semidirect
52. #63662C22semidirect
54. #63634C22semidirect
55. #63630C22semidirect
56. C3×#810C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. Q8×D12D3semidirect
83. #5028D3semidirect
125. #3755D4semidirect
161. C2×D3×Q8C2×D3semidirect
175. C3×C4×Q8C2×D3semidirect
176. C3×C4×Q8C2×D3semidirect
184. C2×#216C2×D3semidirect
212. #897C2×D3semidirect
227. #869C2×D3semidirect
242. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
465. C2×C3×D3#137semidirect
508. C4×Q8D32semidirect
734. C2×D3#942semidirect
766. C32#3266semidirect
860. C3#80627semidirect
861. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C2×#639482
C2×D3×#2152
#105940072
#105927252
C3×#50282
#105915942
#105915832
#105906162
#105905962
#105905182
#105905032
#105903792
#105903762
#105903302
#835593
#806273