Finite Group Databasebeta

← #11885830

Subgroups — #11885830

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3#10594886C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592750C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591606C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10591172C211yesmaximal, characteristic, complemented
11#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17#80168—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#947C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×C4×#67C2211yescharacteristic
30C3×#895—21no—
31C3×#895C2211yescharacteristic, complemented
32C3×#894—21no—
33C3×#893C2211yescharacteristic, complemented
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36#63976—21no—
37D3×#217—21no—
38#63947—24no—
39#63908C2211yescharacteristic, complemented
40Dic3×D12C2211yescharacteristic, complemented
41#63885—21no—
42#63884—21no—
43#63860C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3713—24no—
47C2×#3713C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65#5806—31no—
66C22×#213—31no—
67C22×#213—31no—
68C2×#916—31no—
69#5630D311yescharacteristic, complemented
70#5550—31no—
71C3×#450—31no—
72#5238—31no—
73#5218—31no—
74#5172—31no—
75#5168—31no—
76#5165—31no—
77#5059—31no—
78#5057—31no—
79#5051—31no—
80#5051—31no—
81#5051—61no—
82#5046D311yescharacteristic, complemented
83#5038—31no—
84#5037—31no—
85#5016—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4787—31no—
89#4781—31no—
90#4775—31no—
91#4756—31no—
92#4731—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×#239—22no—
101C3×#239—41no—
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3795—22no—
122#3795—41no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126#3757—21no—
127#3756—22no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C2×C3⋊(C3⋊C8)—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217D411yescharacteristic
134C3×#215—22no—
135C3×#215—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3716—41no—
151#3713—22no—
152#3713—22no—
153#3713—22no—
154#3713D414yescomplemented
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×#235—31no—
163C22×D12C2×D311yescharacteristic
164C22×D12C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C22⋊C4—61no—
178#953—61no—
179C2×#217—61no—
180#950—64no—
181#947C2×D311yescharacteristic, complemented
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—61no—
185C2×#215C2×D311yescharacteristic, complemented
186C2×#215C2×D311yescharacteristic, complemented
187#939—61no—
188#938—31no—
189#937—61no—
190#936—31no—
191#935—61no—
192D4×Dic3—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—64no—
204C2×#213—64no—
205#930—31no—
206C4×#67C2×D311yescharacteristic
207#924—31no—
208#924—31no—
209#924—61no—
210C22×C3⋊C8—31no—
211C22×C3⋊C8—31no—
212C22×C3⋊C8—31no—
213C22×C3⋊C8—61no—
214#916—64no—
215C2×#204—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218#895—21no—
219#895C2×D311yescharacteristic, complemented
220#894—21no—
221#894—61no—
222#893C2×D311yescharacteristic, complemented
223#884—61no—
224#882—21no—
225D3×C22⋊C4—21no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#830—31no—
238#830C2×D311yescharacteristic
239#821—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242Dic3⋊C8—31no—
243C8×Dic3—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#809C2×D311yescharacteristic, complemented
248#809C2×D311yescharacteristic, complemented
249#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253C4×C3⋊C8—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C32×Q8—21no—
267C32×Q8—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276#634—21no—
277#634—21no—
278C3×#67—22no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×D12—42no—
291C3×D12—81no—
292C3×D12C2×D412yes—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297C3×C4×D3—81no—
298#625—42no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
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—31no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—91no—
320C8×D4—91no—
321C24×C3—61no—
322C24×C3—61no—
323C23×D3—21no—
324C23×D3—21no—
325C3×#41—62no—
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—31no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—121no—
342C2×C3×D4—121no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67#6711yescharacteristic
354C22×Dic3—61no—
355C22×Dic3—61no—
356#239—22no—
357#239—41no—
358#237—62no—
359#237—121no—
360#235—62no—
361#235—121no—
362C2×D12—22no—
363C2×D12—22no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—41no—
369C2×D12—41no—
370C2×D12C22×D311yescharacteristic
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—21no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3C22×D311yescharacteristic
379C2×Dic6—31no—
380C2×Dic6—31no—
381C2×Dic6—61no—
382C3×SD16—62no—
383C3×SD16—121no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—41no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—31no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—121no—
410#217#6711yescharacteristic
411#216—62no—
412#216—62no—
413#216—122no—
414#215—22no—
415#215—41no—
416#214—62no—
417#214—121no—
418#213—34no—
419#213—34no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—62no—
425#213—62no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4#6711yescharacteristic
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—121no—
441Dic3⋊C4#6711yescharacteristic
442C4×Dic3C22×D311yescharacteristic
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⋊C8—62no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8—122no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—62no—
456#204—121no—
457D3×C8—62no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32#13512yescomplemented
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
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—
477C2×C3×D3—84no—
478C2×C3×D3—84no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—31no—
492C22×D4—31no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—91no—
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—91no—
511C22⋊Q8D3211yescharacteristic
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×D4—91no—
521C2×C22⋊C4—61no—
522C2×C22⋊C4—181no—
523#107—91no—
524C4⋊C8—91no—
525#103—91no—
526#103—91no—
527#102—31no—
528#102—31no—
529#102—91no—
530#102—91no—
531C22⋊C8—31no—
532C22⋊C8—91no—
533C4×C8—91no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—122no—
544C23×C3—241no—
545C23×C3—241no—
546C23×C3D3×D411yescharacteristic
547C23×C3C2×#6711yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—81no—
557C22×D3—81no—
558C22×D3C2×#6711yescharacteristic
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—41no—
564C3×Q8—41no—
565C3×D4—32no—
566C3×D4—32no—
567C3×D4—62no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—241no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—122no—
598C2×C3×C4—241no—
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4C2×#6711yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—22no—
604#67—122no—
605#67—122no—
606#67—241no—
607#67—241no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—122no—
615C2×Dic3—241no—
616C2×Dic3C2×#6711yescharacteristic
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—42no—
626D12—42no—
627D12—42no—
628D12—81no—
629D12D3×D412yes—
630D12D3×D412yes—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—42no—
634C4×D3—81no—
635C4×D3—122no—
636C4×D3—241no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—121no—
642Dic6—121no—
643C3×C8—61no—
644C3×C8—61no—
645C3⋊C8—21no—
646C3⋊C8—21no—
647C3⋊C8—32no—
648C3⋊C8—32no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C3⋊C8—121no—
653C2×C32—22no—
654C2×C32D4211yescharacteristic
655C2×C32C2×#13511yescharacteristic
656C2×C32#57611yescharacteristic
657C3×D3—41no—
658C3×D3—42no—
659C3×D3—42no—
660C3×D3—81no—
661C3×D3—81no—
662C24—61no—
663C24—61no—
664#41—62no—
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—31no—
675C2×D4—62no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—121no—
682C2×D4—121no—
683C2×D4—181no—
684C2×D4—181no—
685C22×C4—31no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—181no—
689C22×C4—181no—
690C22×C4C2×D3211yescharacteristic
691Q16—182no—
692SD16—62no—
693SD16—121no—
694SD16—182no—
695SD16—361no—
696D8—94no—
697D8—182no—
698D8—182no—
699D8—182no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—91no—
703C2×C8—91no—
704C2×C8—182no—
705C2×C8—182no—
706C4⋊C4—21no—
707C4⋊C4—31no—
708C4⋊C4—91no—
709C4⋊C4—181no—
710C4⋊C4C2×D3211yescharacteristic
711C22⋊C4—21no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C42—31no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—22no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—62no—
735C22×C3—61no—
736C22×C3—62no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—244no—
748C22×C3—244no—
749C22×C3#91612yescomplemented
750C22×C3#95012yescomplemented
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C22×#6711yescharacteristic
753C2×D3—21no—
754C2×D3—22no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—22no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—84no—
769C2×D3—84no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—81no—
783C3×C4—81no—
784C3×C4C2×D3×D411yescharacteristic
785C3×C4C2×D3×D411yescharacteristic
786C3×C4#100411yescharacteristic
787C3×C4#100411yescharacteristic
788Dic3—21no—
789Dic3—21no—
790Dic3—21no—
791Dic3—121no—
792Dic3—121no—
793Dic3—121no—
794Dic3—121no—
795Dic3—241no—
796Dic3—241no—
797C32#328011yescharacteristic, complemented, Sylow
798C23—31no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—122no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23—241no—
808C23—241no—
809C23D3×#6711yescharacteristic
810Q8—21no—
811Q8—21no—
812Q8—181no—
813Q8—181no—
814D4—32no—
815D4—32no—
816D4—62no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—122no—
824D4—122no—
825D4—122no—
826D4—241no—
827D4—362no—
828D4—721no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—122no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—241no—
842C2×C4—362no—
843C2×C4—721no—
844C2×C4D3×#6711yescharacteristic
845C2×C4C22×D3211yescharacteristic
846C8—61no—
847C8—61no—
848C8—92no—
849C8—181no—
850C2×C3—22no—
851C2×C3—22no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—42no—
856C2×C3—121no—
857C2×C3—122no—
858C2×C3—122no—
859C2×C3—241no—
860C2×C3—241no—
861C2×C3#559011yescharacteristic
862C2×C3C2×#91611yescharacteristic
863C2×C3#577411yescharacteristic
864C2×C3D4×#6711yescharacteristic
865C2×C3C2×#95011yescharacteristic
866C2×C3#583511yescharacteristic
867D3—42no—
868D3—41no—
869D3—42no—
870D3—81no—
871D3—81no—
872C22—21no—
873C22—21no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—62no—
878C22—62no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—244no—
890C22—244no—
891C22#6394712yescomplemented
892C22C2×D3×#6711yescharacteristic
893C4—21no—
894C4—41no—
895C4—41no—
896C4—61no—
897C4—61no—
898C4—61no—
899C4—361no—
900C4—361no—
901C4D32×D411yescharacteristic
902C4#6431311yescharacteristic
903C3—21no—
904C3#8016811yescharacteristic, complemented
905C3#8350511yescharacteristic, complemented
906C2—22no—
907C2—121no—
908C2—122no—
909C2—122no—
910C2—241no—
911C2—241no—
912C2#1059528711yescharacteristic
913C2C2×#6394711yescharacteristic
914C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3280
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×#5630C2semidirect
2. C2×#63947C2semidirect
3. #10594886C2semidirect
4. C22×#3713C2semidirect
5. #10592750C2semidirect
6. C3×#5046C2semidirect
7. #10591606C2semidirect
8. #10591586C2semidirect
9. #10591567C2semidirect
10. #10591172C2semidirect
11. #67⋊(C3⋊C8)C2semidirect
12. #10590613C2semidirect
13. #10590530C2semidirect
14. #10590499C2semidirect
15. #10590452C2semidirect
18. C2×C3×#239C22semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
26. C3×#947C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×#215C22semidirect
31. C3×#895C22semidirect
33. C3×#893C22semidirect
39. #63908C22semidirect
40. Dic3×D12C22semidirect
43. #63860C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
69. #5630D3semidirect
82. #5046D3semidirect
154. #3713D4semidirect
160. C2×#239C2×D3semidirect
181. #947C2×D3semidirect
185. C2×#215C2×D3semidirect
186. C2×#215C2×D3semidirect
219. #895C2×D3semidirect
222. #893C2×D3semidirect
247. #809C2×D3semidirect
248. #809C2×D3semidirect
460. C22×C32#135semidirect
749. C22×C3#916semidirect
750. C22×C3#950semidirect
797. C32#3280semidirect
891. C22#63947semidirect
904. C3#80168semidirect
905. C3#83505semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C2×#639472
#105948862
C22×#37132
#105927502
C3×#50462
#105916062
#105915862
#105915672
#105911722
#67⋊(C3⋊C8)2
#105906132
#105905302
#105904992
#105904522
#835053
#801683