Finite Group Databasebeta

← #11884411

Subgroups — #11884411

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic, complemented
5#10592727C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10590613C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590588C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590371C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#79796—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25#64084C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#895—21no—
28C3×#895—21no—
29C3×#895C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31C3×#874—21no—
32C3×#874C2211yescharacteristic, complemented
33C3×C4×D12—21no—
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36#63947—24no—
37#63939—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic
41#63906—21no—
42#63890—21no—
43#63857C2211yescharacteristic
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#807C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#550—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#916—31no—
67C2×#914—31no—
68#5577D311yescharacteristic, complemented
69#5554—31no—
70#5550—31no—
71C3×#440—31no—
72#5239—31no—
73#5238—31no—
74#5074—31no—
75#5072—31no—
76#5042—31no—
77#5038—31no—
78#5037—31no—
79#5036—31no—
80#5028—31no—
81#5028—31no—
82#5028—61no—
83#5026D311yescharacteristic, complemented
84#5015—31no—
85#5011—31no—
86#4886—31no—
87#4883—31no—
88#4810—31no—
89#4808—31no—
90#4781—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3795—22no—
124#3795—41no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C42—21no—
128C32×C42C2311yescharacteristic
129#3756—22no—
130#3755—22no—
131#3752—21no—
132#3752—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#215D414yescomplemented
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×(C2×D3)⋊C4D411yescharacteristic
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#3716—22no—
149#3716—41no—
150#3714—22no—
151#3714—41no—
152#3713—22no—
153#3713—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×#239C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C3×#127—31no—
167C3×#127—61no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—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—
178#950—64no—
179#949—64no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186C2×#215C2×D311yescharacteristic
187#937—61no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196#930—31no—
197#930—61no—
198C2×(C2×D3)⋊C4—61no—
199#924—31no—
200C2×#208—31no—
201C22×C3⋊C8—31no—
202#916—64no—
203#914—64no—
204C2×D24—31no—
205C2×D24—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×D3×C8—31no—
210#897—31no—
211#895—21no—
212#895—21no—
213#895—31no—
214#895C2×D311yescharacteristic
215#895C2×D311yescharacteristic, complemented
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—
224#874—21no—
225#874C2×D311yescharacteristic, complemented
226C4×D12—21no—
227C4×D12C2×D311yescharacteristic
228C4×D12C2×D311yescharacteristic
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×#97—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#832—31no—
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—61no—
243#809—31no—
244#809—31no—
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×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—41no—
284C3×D12—42no—
285C3×D12—42no—
286C3×D12—42no—
287C3×D12—81no—
288C3×D12—81no—
289C3×D12—81no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×C4×D3—81no—
298#626—42no—
299#626—81no—
300#625—42no—
301D3×Dic3—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—31no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—31no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—21no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C22×Dic3—61no—
350#239—22no—
351#239—22no—
352#239—41no—
353#239—41no—
354#237—62no—
355#237—121no—
356D3×D4—62no—
357D3×D4—121no—
358#235—62no—
359#235—121no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—121no—
373C2×D12#6711yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C3×SD16—34no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—41no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—21no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—41no—
406C3×C42C22×D311yescharacteristic
407C3×C42C22×D311yescharacteristic
408#217—61no—
409#216—62no—
410#216—62no—
411#216—122no—
412#215—62no—
413#215—62no—
414#215—122no—
415#215D1214yescomplemented
416#214—62no—
417#214—121no—
418#213—62no—
419#213—62no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—121no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4—121no—
436(C2×D3)⋊C4#6711yescharacteristic
437(C2×D3)⋊C4#6711yescharacteristic
438C4⋊Dic3—61no—
439C4⋊Dic3#6711yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—61no—
442#208—62no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—62no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452D24—62no—
453D24—121no—
454#204—62no—
455#204—121no—
456ΓL(1,𝔽25)—62no—
457D3×C8—62no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—22no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—31no—
506#127—61no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510#121—31no—
511#121—31no—
512#121—61no—
513#121—61no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8D3211yescharacteristic, complemented
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—61no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3C2×#6711yescharacteristic
551C22×D3C2×#6711yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—22no—
555C3×Q8—41no—
556C3×Q8C2×D1212yes—
557C3×Q8D3×D412yes—
558C3×D4—32no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—121no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C3×D4—241no—
569C3×D4—241no—
570C3×D4—241no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4—241no—
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4C2×#6711yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—122no—
597#67—122no—
598#67—122no—
599#67—241no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—122no—
605C2×Dic3C2×#6711yescharacteristic
606C2×Dic3C2×#6711yescharacteristic
607D12—21no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—21no—
612D12—41no—
613D12—42no—
614D12—42no—
615D12—42no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—81no—
621D12—81no—
622D12—81no—
623D12—121no—
624D12—121no—
625D12—122no—
626D12—241no—
627D12C2×D1212yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—42no—
634C4×D3—81no—
635C4×D3—122no—
636Dic6—61no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—121no—
641Dic6—121no—
642C3×C8—32no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—121no—
650C3⋊C8—121no—
651C3⋊C8C2×D1212yes—
652C2×C32D4211yescharacteristic
653C2×C32#57511yescharacteristic
654C2×C32#57611yescharacteristic
655C3⋊D3—81no—
656C3×D3—41no—
657C3×D3—42no—
658C3×D3—41no—
659C3×D3—81no—
660C3×D3—81no—
661C24—181no—
662#41—62no—
663#41—62no—
664#41—121no—
665#41—121no—
666#41—182no—
667#41—361no—
668C2×Q8—91no—
669C2×Q8C2×D3211yescharacteristic
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—181no—
692Q16—182no—
693SD16—34no—
694SD16—182no—
695SD16—182no—
696SD16—361no—
697D8—182no—
698D8—182no—
699D8—182no—
700D8—361no—
701M16—182no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—91no—
705C2×C8—91no—
706C2×C8—182no—
707C4⋊C4—21no—
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—181no—
711C4⋊C4C2×D3211yescharacteristic
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—21no—
722C42C2×D3211yescharacteristic
723C22×C3—21no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—62no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C22×#6711yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—22no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—244no—
766C2×D3—244no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—42no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—81no—
783C3×C4—121no—
784C3×C4C22×D1211yescharacteristic
785C3×C4C2×D3×D411yescharacteristic
786C3×C4#100411yescharacteristic
787C3×C4#100911yescharacteristic
788Dic3—21no—
789Dic3—21no—
790Dic3—41no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—31no—
796C23—31no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—181no—
801C23—362no—
802C23—362no—
803C23—721no—
804Q8—21no—
805Q8—181no—
806Q8—181no—
807Q8D3×D1212yes—
808D4—32no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—121no—
815D4—122no—
816D4—122no—
817D4—122no—
818D4—181no—
819D4—181no—
820D4—241no—
821D4—241no—
822D4—241no—
823D4—362no—
824D4—362no—
825D4—721no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—181no—
838C2×C4—241no—
839C2×C4—362no—
840C2×C4D3×#6711yescharacteristic
841C2×C4D3×#6711yescharacteristic
842C2×C4C22×D3211yescharacteristic
843C8—32no—
844C8—61no—
845C8—181no—
846C8—181no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—122no—
851C2×C3—121no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3D4×D1211yescharacteristic
856C2×C3#577411yescharacteristic
857C2×C3#577711yescharacteristic
858C2×C3D4×#6711yescharacteristic
859C2×C3#582211yescharacteristic
860C2×C3#583511yescharacteristic
861D3—41no—
862D3—41no—
863D3—42no—
864D3—81no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—481no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—62no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—361no—
885C22—361no—
886C22—361no—
887C22—724no—
888C22C2×D3×#6711yescharacteristic
889C4—21no—
890C4—21no—
891C4—22no—
892C4—41no—
893C4—61no—
894C4—61no—
895C4—121no—
896C4—361no—
897C4C2×D3×D1211yescharacteristic
898C4#6430711yescharacteristic
899C3—21no—
900C3#7979611yescharacteristic, complemented
901C3#8357711yescharacteristic, complemented
902C2—121no—
903C2—121no—
904C2—122no—
905C2—241no—
906C2—241no—
907C2—721no—
908C2D12×#6711yescharacteristic
909C2#1059531711yescharacteristic
910C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3268
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×#5577C2semidirect
2. C2×#63947C2semidirect
3. C2×#63939C2semidirect
4. #10594003C2semidirect
5. #10592727C2semidirect
6. C3×#5026C2semidirect
7. #10591599C2semidirect
8. #10591588C2semidirect
9. #10590613C2semidirect
10. #10590595C2semidirect
11. #10590588C2semidirect
12. #10590576C2semidirect
13. #10590371C2semidirect
14. #10590347C2semidirect
15. #10590326C2semidirect
19. C2×C3×#239C22semidirect
22. C32×C4×Q8C22semidirect
23. C2×#3756C22semidirect
30. C3×#895C22semidirect
32. C3×#874C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63637C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#835C22semidirect
57. C3×#807C22semidirect
58. C3×#803C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5577D3semidirect
83. #5026D3semidirect
135. C3×#215D4semidirect
160. C2×#239C2×D3semidirect
173. C3×C4×Q8C2×D3semidirect
174. C3×C4×Q8C2×D3semidirect
215. #895C2×D3semidirect
225. #874C2×D3semidirect
233. #835C2×D3semidirect
249. #807C2×D3semidirect
253. #803C2×D3semidirect
415. #215D12semidirect
517. C4×Q8D32semidirect
794. C32#3268semidirect
900. C3#79796semidirect
901. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C2×#639472
C2×#639392
#105940032
#105927272
C3×#50262
#105915992
#105915882
#105906132
#105905952
#105905882
#105905762
#105903712
#105903472
#105903262
#835773
#797963