Finite Group Databasebeta

← #11885827

Subgroups — #11885827

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×C4×#213C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591452C211yesmaximal, characteristic, complemented
9#10590613C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590579C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590370C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15C3⋊C8×D12C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17#79606—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25#64084C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic, complemented
36#63933—24no—
37D3×#213—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic, complemented
41#63906—21no—
42#63890—21no—
43#63857C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58C3×C4×C3⋊C8C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C22×#213—31no—
66C2×#912—31no—
67C2×D3×D8—31no—
68#5554—31no—
69#5554D311yescharacteristic, complemented
70#5550—31no—
71C3×C4×D8—31no—
72#5238—31no—
73#5218—31no—
74#5059—31no—
75#5057—31no—
76#5051—31no—
77#5046—31no—
78#5038—31no—
79#5037—31no—
80#5016—31no—
81#5016—31no—
82#5016—31no—
83#5016—61no—
84C4×#213D311yescharacteristic, complemented
85D4×C3⋊C8—31no—
86#4887—31no—
87#4883—31no—
88#4781—31no—
89#4781—31no—
90#4776—31no—
91#4776—31no—
92#4696—31no—
93C8×D12—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3795—22no—
122#3795—41no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126#3754—22no—
127#3753—22no—
128#3752—21no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#213D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×(C2×D3)⋊C4D411yescharacteristic
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#3717—41no—
150#3716—41no—
151#3715—22no—
152#3714—22no—
153#3713—22no—
154D3×C3⋊C8—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#237—31no—
160C2×#237C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×D8—31no—
166C3×#124—31no—
167C3×#123—61no—
168C3×C22⋊Q8—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#120—61no—
172C3×C4×D4—21no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4C2×D311yescharacteristic, complemented
176C3×C4×D4C2×D311yescharacteristic, complemented
177C2×C3×C22⋊C4—61no—
178#950—64no—
179C2×#216—31no—
180C2×#215—31no—
181C2×#215—31no—
182#937—61no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—61no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—61no—
194C2×#213—64no—
195C2×#213C2×D311yescharacteristic
196#930—21no—
197#930—31no—
198#930—61no—
199C2×(C2×D3)⋊C4—21no—
200C2×(C2×D3)⋊C4—61no—
201#924—31no—
202C22×C3⋊C8—31no—
203C22×C3⋊C8—31no—
204#912—64no—
205D3×D8—64no—
206C2×Dic12—31no—
207C2×D24—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897C2×D311yescharacteristic
214#895—31no—
215#895C2×D311yescharacteristic, complemented
216#894—61no—
217#886—21no—
218#886—61no—
219#884—61no—
220#882—21no—
221#882—61no—
222D3×C22⋊C4—61no—
223#875—31no—
224#875—31no—
225#875—61no—
226#875C2×D311yescharacteristic, complemented
227C4×D12C2×D311yescharacteristic
228C4×D12C2×D311yescharacteristic, complemented
229C3×#107—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C4×C8—31no—
233#835—31no—
234#832—31no—
235#832C2×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—61no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic, complemented
249#807C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253C4×C3⋊C8C2×D311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×D4—21no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—81no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276#634—21no—
277#634—21no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—22no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
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—81no—
296C3×Dic6—21no—
297C3×Dic6—21no—
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×#135—91no—
307C22×D8—91no—
308#546—31no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—91no—
314#463—91no—
315#450—91no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—31no—
320C8×D4—91no—
321C24×C3—61no—
322C23×D3—21no—
323C23×D3—61no—
324C23×D3—61no—
325C3×#41—62no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—41no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C22×Dic3—21no—
353C22×Dic3—61no—
354#237—22no—
355#237—41no—
356#237—62no—
357#237—121no—
358D3×D4—22no—
359D3×D4—41no—
360D3×D4—62no—
361D3×D4—121no—
362#235—62no—
363#235—121no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12#6711yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×C4×D3—21no—
376C2×C4×D3—61no—
377C2×C4×D3C22×D311yescharacteristic
378C2×C4×D3C22×D311yescharacteristic
379C2×Dic6—31no—
380C2×Dic6—31no—
381C2×Dic6—61no—
382C2×Dic6C22×D311yescharacteristic
383C3×D8—34no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—21no—
403C3×C42C22×D311yescharacteristic
404C3×C42C22×D311yescharacteristic
405#217—61no—
406#216—62no—
407#215—62no—
408#215—121no—
409#214—62no—
410#214—62no—
411#214—62no—
412#214—122no—
413#214—121no—
414#213—62no—
415#213—62no—
416#213—62no—
417#213—62no—
418#213—62no—
419#213—122no—
420#213D1214yescomplemented
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—61no—
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—121no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4#6711yescharacteristic
436(C2×D3)⋊C4#6711yescharacteristic
437C4⋊Dic3—21no—
438C4⋊Dic3—61no—
439C4⋊Dic3#6711yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—61no—
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⋊C8—62no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—62no—
453D24—62no—
454#204—121no—
455#204—121no—
456D3×C8—62no—
457D3×C8—62no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—84no—
477C2×C3×D3#13512yescomplemented
478D32—84no—
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—
488C3×Dic3—41no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—31no—
492C22×D4—91no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—184no—
504C22×C8—91no—
505C22×C8—91no—
506#124—31no—
507#124—91no—
508#123—61no—
509#123—181no—
510C22⋊Q8—31no—
511C22⋊Q8—91no—
512#121—31no—
513#121—61no—
514#121—91no—
515#121—181no—
516#120—61no—
517#120—181no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4D3211yescharacteristic, complemented
521C2×C22⋊C4—61no—
522C2×C22⋊C4—181no—
523#107—31no—
524C4⋊C8—91no—
525#103—91no—
526#103—91no—
527#102—31no—
528#102—31no—
529#102—91no—
530#102—91no—
531C22⋊C8—91no—
532C22⋊C8—91no—
533C4×C8—31no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—31no—
538C23×C3—41no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—81no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—241no—
557C22×D3—241no—
558C22×D3C2×#6711yescharacteristic
559C22×D3C2×#6711yescharacteristic
560C3×Q8—61no—
561C3×Q8—61no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—22no—
565C3×D4—32no—
566C3×D4—41no—
567C3×D4—62no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C3×D4C2×D1212yes—
575C3×D4D3×D412yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—81no—
591C2×C3×C4—81no—
592C2×C3×C4—82no—
593C2×C3×C4—122no—
594C2×C3×C4—241no—
595C2×C3×C4D3×D411yescharacteristic
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C2×#6711yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—42no—
602#67—42no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—42no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—121no—
613C2×Dic3—122no—
614C2×Dic3C2×#6711yescharacteristic
615C2×Dic3C2×#6711yescharacteristic
616D12—22no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—81no—
625D12—121no—
626D12—121no—
627D12—122no—
628D12—241no—
629D12C2×D1212yes—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—81no—
635C4×D3—122no—
636Dic6—21no—
637Dic6—21no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—121no—
643Dic6—121no—
644C3×C8—32no—
645C3×C8—61no—
646C3⋊C8—21no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—61no—
651C3⋊C8—121no—
652C3⋊C8—121no—
653C3⋊C8C2×D1212yes—
654C2×C32—42no—
655C2×C32D4211yescharacteristic
656C2×C32C2×#13511yescharacteristic
657C2×C32#57611yescharacteristic
658C3⋊D3—81no—
659C3×D3—22no—
660C3×D3—42no—
661C3×D3—41no—
662C3×D3—81no—
663C24—61no—
664C24—181no—
665#41—62no—
666#41—121no—
667#41—182no—
668#41—361no—
669C2×Q8—31no—
670C2×Q8—91no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—121no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—361no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—21no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—181no—
692Q16—182no—
693SD16—182no—
694SD16—182no—
695SD16—361no—
696SD16—361no—
697D8—34no—
698D8—182no—
699D8—182no—
700D8—182no—
701C2×C8—31no—
702C2×C8—31no—
703C2×C8—91no—
704C2×C8—91no—
705C2×C8—182no—
706C2×C8—182no—
707C4⋊C4—31no—
708C4⋊C4—31no—
709C4⋊C4—61no—
710C4⋊C4—181no—
711C4⋊C4C2×D3211yescharacteristic
712C22⋊C4—21no—
713C22⋊C4—31no—
714C22⋊C4—31no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C42C2×D3211yescharacteristic
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—32no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—62no—
739C22×C3—61no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—244no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C22×#6711yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—22no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—84no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—244no—
772C2×D3—244no—
773C2×D3#95012yescomplemented
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C22×D1211yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4#100911yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—41no—
797Dic3—121no—
798Dic3—121no—
799Dic3—241no—
800C32#328011yescharacteristic, complemented, Sylow
801C23—21no—
802C23—31no—
803C23—31no—
804C23—61no—
805C23—61no—
806C23—122no—
807C23—122no—
808C23—181no—
809C23—241no—
810C23—362no—
811C23—362no—
812C23—721no—
813Q8—61no—
814Q8—61no—
815Q8—181no—
816Q8—181no—
817D4—21no—
818D4—32no—
819D4—62no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—122no—
824D4—122no—
825D4—181no—
826D4—181no—
827D4—241no—
828D4—362no—
829D4—362no—
830D4—721no—
831D4D3×D1212yes—
832C2×C4—21no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—81no—
842C2×C4—122no—
843C2×C4—181no—
844C2×C4—241no—
845C2×C4—362no—
846C2×C4D3×#6711yescharacteristic
847C2×C4D3×#6711yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—32no—
850C8—61no—
851C8—181no—
852C8—181no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—62no—
859C2×C3—82no—
860C2×C3—122no—
861C2×C3—121no—
862C2×C3—241no—
863C2×C3D4×D1211yescharacteristic
864C2×C3#575711yescharacteristic
865C2×C3D3×#13511yescharacteristic
866C2×C3D4×#6711yescharacteristic
867C2×C3C2×#95011yescharacteristic
868C2×C3#583511yescharacteristic
869D3—22no—
870D3—41no—
871D3—42no—
872D3—81no—
873D3—241no—
874D3—241no—
875D3—481no—
876C22—22no—
877C22—32no—
878C22—41no—
879C22—41no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—62no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—244no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—724no—
896C22C2×D3×#6711yescharacteristic
897C4—21no—
898C4—21no—
899C4—41no—
900C4—61no—
901C4—61no—
902C4—121no—
903C4—121no—
904C4—361no—
905C4C2×D3×D1211yescharacteristic
906C4#6430711yescharacteristic
907C3—21no—
908C3#7960611yescharacteristic, complemented
909C3#8350511yescharacteristic, complemented
910C2—42no—
911C2—62no—
912C2—121no—
913C2—122no—
914C2—241no—
915C2—721no—
916C2D12×#6711yescharacteristic
917C2#1059509611yescharacteristic
918C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5554C2semidirect
2. C2×#63933C2semidirect
3. C2×D3×#213C2semidirect
4. #10594003C2semidirect
5. #10592715C2semidirect
6. C3×C4×#213C2semidirect
7. #10591459C2semidirect
8. #10591452C2semidirect
9. #10590613C2semidirect
10. #10590596C2semidirect
11. #10590579C2semidirect
12. #10590576C2semidirect
13. #10590370C2semidirect
14. #10590348C2semidirect
15. C3⋊C8×D12C2semidirect
18. C2×C3×#237C22semidirect
21. C2×#3795C22semidirect
22. C32×C4×D4C22semidirect
23. C2×#3754C22semidirect
25. #64084C22semidirect
30. C3×#895C22semidirect
33. C3×#875C22semidirect
35. C3×C4×D12C22semidirect
40. #63909C22semidirect
44. C2×#3719C22semidirect
45. C2×#3717C22semidirect
46. C2×#3716C22semidirect
47. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63637C22semidirect
53. #63636C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#832C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. C3×C4×C3⋊C8C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5554D3semidirect
84. C4×#213D3semidirect
132. C3×#213D4semidirect
160. C2×#237C2×D3semidirect
175. C3×C4×D4C2×D3semidirect
176. C3×C4×D4C2×D3semidirect
215. #895C2×D3semidirect
226. #875C2×D3semidirect
228. C4×D12C2×D3semidirect
235. #832C2×D3semidirect
248. #809C2×D3semidirect
249. #807C2×D3semidirect
253. C4×C3⋊C8C2×D3semidirect
420. #213D12semidirect
477. C2×C3×D3#135semidirect
520. C4×D4D32semidirect
773. C2×D3#950semidirect
800. C32#3280semidirect
908. C3#79606semidirect
909. C3#83505semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
C2×#639332
C2×D3×#2132
#105940032
#105927152
C3×C4×#2132
#105914592
#105914522
#105906132
#105905962
#105905792
#105905762
#105903702
#105903482
C3⋊C8×D122
#835053
#796063