Finite Group Databasebeta

← #11884149

Subgroups — #11884149

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3#10595067C211yesmaximal, characteristic
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592748C211yesmaximal, characteristic, complemented
6C3×#5047C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591174C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590596C211yesmaximal, characteristic, complemented
13#10590536C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80241—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64139C2211yescharacteristic
25C2×#3748C2211yescharacteristic, complemented
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#896—21no—
32C3×#888—21no—
33C3×#887C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63983—21no—
37#63971—21no—
38D3×#215—24no—
39D3×(C2×D3)⋊C4—21no—
40Dic3×D12C2211yescharacteristic
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic
43#63850—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48#63827—24no—
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64#5829—31no—
65C2×#951—31no—
66C2×#942—31no—
67C22×#215—31no—
68C2×D3×SD16—31no—
69#5632D311yescharacteristic, complemented
70#5550—31no—
71C3×#452—31no—
72#5228—31no—
73#5227—31no—
74#5190—31no—
75#5186—31no—
76#5162—31no—
77#5086—31no—
78#5083—31no—
79#5051—31no—
80#5049—31no—
81#5049—31no—
82#5049—61no—
83#5047D311yescharacteristic, complemented
84#5046—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4813—31no—
89#4798—31no—
90#4776—31no—
91#4757—31no—
92#4738—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×#235—22no—
105C3×#235—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—22no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6—41no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3755—22no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3748—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217D411yescharacteristic
131C3×#216—41no—
132C3×#215—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3718—22no—
150#3718—22no—
151#3717—22no—
152#3717—41no—
153#3715—22no—
154#3715D414yescomplemented
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C2×D3×Q8C2×D311yescharacteristic
161C2×D3×D4—31no—
162C2×#235C2×D311yescharacteristic
163C22×D12—31no—
164C22×Dic6C2×D311yescharacteristic, complemented
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×C4⋊Q8—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—61no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8C2×D311yescharacteristic, complemented
174C3×C22⋊Q8C2×D311yescharacteristic, complemented
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178#951—64no—
179#947—31no—
180#946—31no—
181#944C2×D311yescharacteristic, complemented
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187#942—64no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—61no—
195C2×#215—64no—
196C2×#215C2×D311yescharacteristic
197#939—61no—
198#937—61no—
199#937—61no—
200D4×Dic3—31no—
201C2×#214—31no—
202C2×#214—31no—
203#930—31no—
204#930—31no—
205#930—61no—
206#929—61no—
207C4×#67C2×D311yescharacteristic
208C2×(C2×D3)⋊C4—61no—
209#924—31no—
210C2×#208—31no—
211C2×#208—31no—
212C2×#208—61no—
213C22×C3⋊C8—31no—
214D3×SD16—64no—
215C2×#204—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218#897C2×D311yescharacteristic
219#896—21no—
220#894—61no—
221#888—21no—
222#887C2×D311yescharacteristic, complemented
223#884—61no—
224#67⋊C4—21no—
225D3×C22⋊C4—61no—
226#878—21no—
227#875—31no—
228C4×D12—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#830—31no—
238#830C2×D311yescharacteristic, complemented
239(C2×D3)⋊C8—31no—
240#816—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269#638—81no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C3×#67—22no—
274C3×#67—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12C2×D412yes—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—42no—
294C3×Dic6—42no—
295C3×Dic6C2×D412yes—
296#626—42no—
297D3×Dic3—81no—
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—91no—
310#461—91no—
311#452—31no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×Q8—62no—
327C2×C3×Q8—61no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67#6711yescharacteristic
349C22×Dic3—21no—
350C22×Dic3—61no—
351D3×Q8—22no—
352D3×Q8—41no—
353D3×D4—62no—
354D3×D4—121no—
355#235—22no—
356#235—41no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12—121no—
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—22no—
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6—41no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C2×Dic6C22×D311yescharacteristic
375C3×Q16—121no—
376C3×SD16—62no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—41no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397C3×C42—61no—
398#217—61no—
399#217—61no—
400#217#6711yescharacteristic
401#216—41no—
402#216—62no—
403#216—62no—
404#216—62no—
405#216—62no—
406#215—22no—
407#215—34no—
408#215—62no—
409#215—62no—
410#215—62no—
411#215—62no—
412#215—122no—
413#215—121no—
414#214—34no—
415#214—62no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
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—61no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4#6711yescharacteristic
427C4⋊Dic3—21no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—61no—
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4#6711yescharacteristic
437C4×Dic3—21no—
438C4×Dic3C22×D311yescharacteristic
439#208—62no—
440#208—62no—
441#208—122no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—62no—
452#204—121no—
453D3×C8—62no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—31no—
498C4⋊Q8—61no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—61no—
504C22⋊Q8—91no—
505C22⋊Q8D3211yescharacteristic, complemented
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—61no—
512C4×D4—91no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3D3×D411yescharacteristic
529C23×C3C2×#6711yescharacteristic
530C22×D3—21no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—121no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3C2×#6711yescharacteristic
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—32no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8—122no—
554C3×Q8—122no—
555C3×D4—32no—
556C3×D4—62no—
557C3×D4—61no—
558C3×D4—122no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
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—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4—122no—
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—22no—
589#67—42no—
590#67—122no—
591#67—241no—
592#67—241no—
593#67—242no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—42no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—121no—
601C2×Dic3—241no—
602C2×Dic3C2×#6711yescharacteristic
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605D12—21no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12D3×D412yes—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—42no—
617C4×D3—42no—
618C4×D3—241no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625Dic6—42no—
626Dic6D3×D412yes—
627C3×C8—61no—
628C3×C8—61no—
629C3⋊C8—21no—
630C3⋊C8—21no—
631C3⋊C8—32no—
632C3⋊C8—32no—
633C3⋊C8—62no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—121no—
637C2×C32—41no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3⋊D3—81no—
642C3×D3—22no—
643C3×D3—42no—
644C24—181no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—61no—
653C2×Q8—62no—
654C2×Q8—121no—
655C2×Q8—121no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—181no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—361no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671Q16—121no—
672Q16—182no—
673Q16—182no—
674SD16—62no—
675SD16—94no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—91no—
684C2×C8—91no—
685C2×C8—182no—
686C4⋊C4—21no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—91no—
693C4⋊C4—181no—
694C4⋊C4C2×D3211yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—31no—
697C22⋊C4—31no—
698C22⋊C4—61no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—31no—
705C42—61no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—62no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C22×#6711yescharacteristic
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—244no—
739C2×D3—244no—
740C2×D3#94212yescomplemented
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—62no—
754C3×C4—81no—
755C3×C4—81no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×D3×D411yescharacteristic
760C3×C4#100411yescharacteristic
761C3×C4#100411yescharacteristic
762Dic3—22no—
763Dic3—21no—
764Dic3—21no—
765Dic3—21no—
766Dic3—41no—
767Dic3—41no—
768Dic3—121no—
769Dic3—121no—
770Dic3—241no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—31no—
773C23—61no—
774C23—181no—
775C23—362no—
776C23—362no—
777C23—721no—
778C23D3×#6711yescharacteristic
779Q8—21no—
780Q8—21no—
781Q8—32no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—122no—
789D4—32no—
790D4—62no—
791D4—61no—
792D4—122no—
793D4—181no—
794D4—181no—
795D4—362no—
796D4—721no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4—122no—
812C2×C4—181no—
813C2×C4—721no—
814C2×C4D3×#6711yescharacteristic
815C2×C4C22×D3211yescharacteristic
816C8—61no—
817C8—61no—
818C8—92no—
819C8—181no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—62no—
826C2×C3—81no—
827C2×C3—122no—
828C2×C3#559011yescharacteristic
829C2×C3#577011yescharacteristic
830C2×C3D3×#13711yescharacteristic
831C2×C3D4×#6711yescharacteristic
832C2×C3C2×#94211yescharacteristic
833C2×C3#583711yescharacteristic
834D3—22no—
835D3—42no—
836D3—241no—
837D3—241no—
838D3—481no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—32no—
843C22—61no—
844C22—61no—
845C22—62no—
846C22—121no—
847C22—121no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—724no—
852C22C2×D3×#6711yescharacteristic
853C4—21no—
854C4—41no—
855C4—41no—
856C4—61no—
857C4—61no—
858C4—62no—
859C4—61no—
860C4—121no—
861C4—121no—
862C4—361no—
863C4D32×D411yescharacteristic
864C4#6431311yescharacteristic
865C3—21no—
866C3#8024111yescharacteristic, complemented
867C3#8355911yescharacteristic, complemented
868C2—41no—
869C2—62no—
870C2—122no—
871C2—721no—
872C2#1059528711yescharacteristic
873C2D3×#94211yescharacteristic
874C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595067C2
hypercenterC22⋊Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5632C2semidirect
2. C2×D3×#215C2semidirect
4. C2×#63827C2semidirect
5. #10592748C2semidirect
6. C3×#5047C2semidirect
7. #10591608C2semidirect
8. #10591594C2semidirect
9. #10591564C2semidirect
10. #10591174C2semidirect
11. #10591151C2semidirect
12. #10590596C2semidirect
13. #10590536C2semidirect
14. #10590518C2semidirect
15. #10590454C2semidirect
20. C22×C3×Dic6C22semidirect
22. C32×C22⋊Q8C22semidirect
25. C2×#3748C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#216C22semidirect
33. C3×#887C22semidirect
44. C2×#3718C22semidirect
45. C2×#3718C22semidirect
52. #63662C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. #63554C22semidirect
69. #5632D3semidirect
83. #5047D3semidirect
154. #3715D4semidirect
164. C22×Dic6C2×D3semidirect
173. C3×C22⋊Q8C2×D3semidirect
174. C3×C22⋊Q8C2×D3semidirect
181. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
222. #887C2×D3semidirect
238. #830C2×D3semidirect
244. #810C2×D3semidirect
466. C2×C3×D3#137semidirect
505. C22⋊Q8D32semidirect
740. C2×D3#942semidirect
771. C32#3266semidirect
866. C3#80241semidirect
867. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
C2×D3×#2152
#105950672
C2×#638272
#105927482
C3×#50472
#105916082
#105915942
#105915642
#105911742
#105911512
#105905962
#105905362
#105905182
#105904542
#835593
#802413