Finite Group Databasebeta

← #11884101

Subgroups — #11884101

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic
5#10592727C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10590614C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590585C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590374C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#79795—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25#64084C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#897—21no—
28C3×#897—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×C4×D12—21no—
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×#869—21no—
35C3×#869C2211yescharacteristic, complemented
36#63946—24no—
37D3×#215—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic
41#63906—21no—
42#63890—21no—
43#63857C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#807C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, 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×#915—31no—
67C2×D3×SD16—31no—
68Q8×D12D311yescharacteristic, complemented
69#5554—31no—
70#5550—31no—
71C3×#440—31no—
72#5228—31no—
73#5227—31no—
74#5086—31no—
75#5083—31no—
76#5051—31no—
77#5049—31no—
78#5047—31no—
79#5046—31no—
80#5028—31no—
81#5028—31no—
82#5028—61no—
83#5026D311yescharacteristic, complemented
84#5019—31no—
85#5011—31no—
86#4887—31no—
87#4886—31no—
88#4809—31no—
89#4806—31no—
90#4783—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
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×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3795—22no—
120#3795—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C42—21no—
124C32×C42C2311yescharacteristic
125#3756—22no—
126#3755—22no—
127#3752—21no—
128#3752—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#215D414yescomplemented
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3719—41no—
150#3717—22no—
151#3717—41no—
152#3715—22no—
153#3715—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8C2×D311yescharacteristic
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C3×C4⋊Q8—31no—
167C3×C4⋊Q8—61no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8—61no—
172C3×C4×Q8—21no—
173C3×C4×Q8C2×D311yescharacteristic, complemented
174C3×C4×Q8C2×D311yescharacteristic, complemented
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183#942—64no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215—64no—
192C2×#215C2×D311yescharacteristic
193#937—61no—
194C2×#214—31no—
195C2×#214—31no—
196#930—31no—
197#930—61no—
198C2×(C2×D3)⋊C4—61no—
199#924—31no—
200C2×#208—31no—
201C22×C3⋊C8—31no—
202#915—64no—
203D3×SD16—64no—
204C2×Dic12—31no—
205C2×Dic12—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×D3×C8—31no—
210#897—21no—
211#897—21no—
212#897—31no—
213#897C2×D311yescharacteristic
214#897C2×D311yescharacteristic, complemented
215#895—31no—
216#894—61no—
217#886—61no—
218#884—61no—
219#882—61no—
220D3×C22⋊C4—61no—
221#875—31no—
222#875—31no—
223#875—61no—
224C4×D12—21no—
225C4×D12C2×D311yescharacteristic
226C4×D12C2×D311yescharacteristic
227#869—21no—
228#869C2×D311yescharacteristic, complemented
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#835C2×D311yescharacteristic, complemented
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—31no—
243#810—31no—
244#810—61no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#807C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
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)—21no—
271#634—21no—
272#634—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—22no—
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6—42no—
294#626—42no—
295#626—81no—
296#625—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
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—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—31no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8—61no—
324C2×C3×Q8—62no—
325C2×C3×Q8—62no—
326C2×C3×Q8—121no—
327C2×C3×Q8—121no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—61no—
342D3×Q8—22no—
343D3×Q8—22no—
344D3×Q8—41no—
345D3×Q8—41no—
346#237—62no—
347#237—121no—
348D3×D4—62no—
349D3×D4—121no—
350#235—62no—
351#235—121no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12#6711yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—21no—
368C2×Dic6—21no—
369C2×Dic6—31no—
370C2×Dic6—31no—
371C2×Dic6—61no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—34no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
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×C42—21no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—41no—
398C3×C42C22×D311yescharacteristic
399C3×C42C22×D311yescharacteristic
400#217—61no—
401#216—62no—
402#216—62no—
403#216—62no—
404#216—122no—
405#216—121no—
406#215—62no—
407#215—62no—
408#215—62no—
409#215—62no—
410#215—62no—
411#215—122no—
412#215—121no—
413#215D1214yescomplemented
414#214—62no—
415#214—62no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
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—61no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4#6711yescharacteristic
429(C2×D3)⋊C4#6711yescharacteristic
430C4⋊Dic3—21no—
431C4⋊Dic3—21no—
432C4⋊Dic3—21no—
433C4⋊Dic3—21no—
434C4⋊Dic3—61no—
435C4⋊Dic3#6711yescharacteristic
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—61no—
438#208—62no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—62no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448Dic12—62no—
449Dic12—121no—
450#204—62no—
451#204—121no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—22no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—91no—
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—31no—
503C22⋊Q8—61no—
504C22⋊Q8—61no—
505C22⋊Q8—91no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8D3211yescharacteristic, complemented
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—61no—
513C2×C22⋊C4—181no—
514#107—31no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8—91no—
524#97—31no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—241no—
537C22×D3—241no—
538C22×D3C2×#6711yescharacteristic
539C22×D3C2×#6711yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—22no—
543C3×Q8—41no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—122no—
549C3×Q8—122no—
550C3×Q8C2×D1212yes—
551C3×Q8D3×D412yes—
552C3×D4—32no—
553C3×D4—62no—
554C3×D4—61no—
555C2×C3×C4—21no—
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—31no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
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—122no—
574C2×C3×C4—122no—
575C2×C3×C4—241no—
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—122no—
585#67—241no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—122no—
593C2×Dic3C2×#6711yescharacteristic
594C2×Dic3C2×#6711yescharacteristic
595D12—22no—
596D12—21no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—121no—
602D12—121no—
603D12—122no—
604D12—241no—
605D12C2×D1212yes—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—42no—
611C4×D3—42no—
612C4×D3—81no—
613C4×D3—122no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—42no—
619Dic6—42no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—121no—
625Dic6—121no—
626C3×C8—32no—
627C3×C8—61no—
628C3⋊C8—21no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—121no—
634C3⋊C8—121no—
635C3⋊C8C2×D1212yes—
636C2×C32D4211yescharacteristic
637C2×C32C2×#13711yescharacteristic
638C2×C32#57711yescharacteristic
639C3⋊D3—81no—
640C3×D3—22no—
641C3×D3—42no—
642C3×D3—41no—
643C24—181no—
644#41—182no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—61no—
649C2×Q8—61no—
650C2×Q8—62no—
651C2×Q8—62no—
652C2×Q8—91no—
653C2×Q8—121no—
654C2×Q8—121no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—91no—
659C2×D4—181no—
660C2×D4—182no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—361no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—181no—
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—34no—
674SD16—182no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—361no—
679M16—182no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—91no—
683C2×C8—91no—
684C2×C8—182no—
685C4⋊C4—21no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—181no—
693C4⋊C4C2×D3211yescharacteristic
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—21no—
704C42C2×D3211yescharacteristic
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—61no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C22×#6711yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—22no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—244no—
735C2×D3—244no—
736C2×D3#94212yescomplemented
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—42no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—81no—
753C3×C4—121no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4C22×D1211yescharacteristic
757C3×C4C2×D3×D411yescharacteristic
758C3×C4#100411yescharacteristic
759C3×C4#100911yescharacteristic
760Dic3—21no—
761Dic3—21no—
762Dic3—41no—
763Dic3—41no—
764Dic3—41no—
765Dic3—121no—
766Dic3—121no—
767Dic3—241no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—31no—
771C23—61no—
772C23—181no—
773C23—362no—
774C23—362no—
775C23—721no—
776Q8—21no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—122no—
782Q8—122no—
783Q8—181no—
784Q8—181no—
785Q8D3×D1212yes—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—181no—
790D4—181no—
791D4—362no—
792D4—362no—
793D4—721no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—241no—
809C2×C4—362no—
810C2×C4D3×#6711yescharacteristic
811C2×C4D3×#6711yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—32no—
814C8—61no—
815C8—181no—
816C8—181no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—62no—
821C2×C3—122no—
822C2×C3—121no—
823C2×C3D4×D1211yescharacteristic
824C2×C3#577511yescharacteristic
825C2×C3D3×#13711yescharacteristic
826C2×C3D4×#6711yescharacteristic
827C2×C3C2×#94211yescharacteristic
828C2×C3#583711yescharacteristic
829D3—22no—
830D3—41no—
831D3—42no—
832D3—241no—
833D3—241no—
834D3—481no—
835C22—32no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—62no—
842C22—121no—
843C22—121no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22C2×D3×#6711yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—41no—
853C4—61no—
854C4—61no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—361no—
859C4C2×D3×D1211yescharacteristic
860C4#6430711yescharacteristic
861C3—21no—
862C3#7979511yescharacteristic, complemented
863C3#8355911yescharacteristic, complemented
864C2—62no—
865C2—121no—
866C2—122no—
867C2—721no—
868C2D12×#6711yescharacteristic
869C2D3×#94211yescharacteristic
870C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594003C2
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×#63946C2semidirect
3. C2×D3×#215C2semidirect
5. #10592727C2semidirect
6. C3×#5026C2semidirect
7. #10591595C2semidirect
8. #10591584C2semidirect
9. #10590614C2semidirect
10. #10590596C2semidirect
11. #10590585C2semidirect
12. #10590579C2semidirect
13. #10590374C2semidirect
14. #10590363C2semidirect
15. #10590326C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C32×C4×Q8C22semidirect
23. C2×#3756C22semidirect
30. C3×#897C22semidirect
35. C3×#869C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
50. C2×#3711C22semidirect
52. #63637C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#835C22semidirect
57. C3×#807C22semidirect
58. C3×#803C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. Q8×D12D3semidirect
83. #5026D3semidirect
131. C3×#215D4semidirect
160. C2×D3×Q8C2×D3semidirect
173. C3×C4×Q8C2×D3semidirect
174. C3×C4×Q8C2×D3semidirect
214. #897C2×D3semidirect
228. #869C2×D3semidirect
235. #835C2×D3semidirect
249. #807C2×D3semidirect
253. #803C2×D3semidirect
413. #215D12semidirect
466. C2×C3×D3#137semidirect
509. C4×Q8D32semidirect
736. C2×D3#942semidirect
768. C32#3266semidirect
862. C3#79795semidirect
863. 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×#639462
C2×D3×#2152
#105940032
#105927272
C3×#50262
#105915952
#105915842
#105906142
#105905962
#105905852
#105905792
#105903742
#105903632
#105903262
#835593
#797953