Finite Group Databasebeta

← #11865792

Subgroups — #11865792

Order 1152.

1071 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic, complemented
2#10595029C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592701C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590561C211yesmaximal, characteristic, complemented
9#10590559C211yesmaximal, characteristic, complemented
10#10590549C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590536C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic, complemented
14#10590532C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#82525—31nomaximal
17#78861—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×#67⋊C4—21no—
31C3×#872—21no—
32C3×C42×D3—21no—
33#63978—21no—
34#63978—21no—
35#63911C2211yescharacteristic
36C4×#626—21no—
37C4×#626—21no—
38#63866C2211yescharacteristic
39#63864C2211yescharacteristic
40#63860C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44#63829—24no—
45C2×#3716C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51#63637C2211yescharacteristic
52#63637C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59Dic3⋊(C3⋊C8)C2211yescharacteristic
60Dic3⋊(C3⋊C8)C2211yescharacteristic
61Dic3⋊(C3⋊C8)C2211yescharacteristic
62Dic3⋊(C3⋊C8)C2211yescharacteristic
63C3×C4×#41—31no—
64#5832—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—31no—
68C2×#904—31no—
69#5522D311yescharacteristic, complemented
70#5477—31no—
71C3×#416—31no—
72C2×Dic3⋊C8—31no—
73#5031—31no—
74#5028—31no—
75#5028—31no—
76#5027—31no—
77#5019—31no—
78#5016—31no—
79#5016—31no—
80#5015—31no—
81#5002—31no—
82#5002—31no—
83#5002—61no—
84#5002D311yescharacteristic, complemented
85C2×C4⋊(C3⋊C8)—31no—
86#4819—31no—
87#4818—31no—
88#4798—31no—
89#4795—31no—
90#4787—31no—
91#4786—31no—
92#4767—31no—
93#4762—31no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96#3828—22no—
97#3828—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3D411yescharacteristic
104C22×C3×Dic3D411yescharacteristic
105C3×#235—22no—
106C3×#235—22no—
107C3×#235—22no—
108C3×#235D414yescomplemented
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122C32×C42—21no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—22no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3719—22no—
146#3718—22no—
147#3717—22no—
148#3716—22no—
149#3715—22no—
150#3715—22no—
151#3714—22no—
152#3713—22no—
153#3035—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#235—31no—
157C2×#235—31no—
158C2×#235—61no—
159C2×#235C2×D311yescharacteristic
160C2×#235C2×D311yescharacteristic
161C22×C3×C8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×#117—21no—
169C3×#117—61no—
170C3×#117C2×D311yescharacteristic
171C3×#117C2×D311yescharacteristic
172C2×C3×C42—31no—
173C2×C3×C42—61no—
174#950—64no—
175#950—64no—
176#950—64no—
177#947—31no—
178#944—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940—31no—
186#939—61no—
187#939—61no—
188#936—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195#930—61no—
196#930—61no—
197C4×#67—61no—
198C4×#67—61no—
199C2×C4×Dic3C2×D311yescharacteristic
200C22×C3⋊C8—31no—
201C22×C3⋊C8—31no—
202C22×C3⋊C8—61no—
203C22×C3⋊C8C2×D311yescharacteristic
204C2×Dic12—31no—
205#904—64no—
206C2×D24—31no—
207C2×#204—31no—
208C2×#204—31no—
209#893C2×D311yescharacteristic
210#893C2×D311yescharacteristic
211#887C2×D311yescharacteristic
212#887C2×D311yescharacteristic
213#67⋊C4—21no—
214#67⋊C4—21no—
215#875—31no—
216#875—31no—
217#874—31no—
218C4×D12—61no—
219C4×D12—61no—
220#872—21no—
221C42×D3—21no—
222#869—31no—
223C3×#103—31no—
224C3×#103—31no—
225C3×#102—31no—
226C3×#102—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#810—61no—
236#810—61no—
237#810C2×D311yescharacteristic
238#810C2×D311yescharacteristic
239#809—31no—
240#809—31no—
241#809—31no—
242#809—31no—
243#809—61no—
244#809—61no—
245#809C2×D311yescharacteristic
246#809C2×D311yescharacteristic
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32C2×D411yescharacteristic
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4#4112yes—
260C2×C32×C4C2411yescharacteristic
261#638—42no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4×C3⋊D3—42no—
266#634—21no—
267#634—21no—
268C3×#67—24no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—41no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×C4×D3—24no—
283C3×C4×D3—42no—
284C3×C4×D3—42no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6C2×D412yes—
290#626—42no—
291#626—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—91no—
297C2×#135—91no—
298#532—91no—
299C4×#41—31no—
300#464—91no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—91no—
306#460—91no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—31no—
310#416—91no—
311C3×#41—34no—
312C3×#41—62no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—121no—
337C22×Dic3#6711yescharacteristic
338C22×Dic3#6711yescharacteristic
339#235—22no—
340#235—22no—
341#235—22no—
342#235—64no—
343#235—62no—
344#235—62no—
345#235—62no—
346#235—62no—
347#235—122no—
348#235D1214yescomplemented
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—121no—
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—61no—
366C2×Dic6C22×D311yescharacteristic
367C2×Dic6C22×D311yescharacteristic
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—62no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—21no—
385C3×C42—21no—
386C3×C42—31no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—31no—
390C3×C42—41no—
391C3×C42—61no—
392C3×C42—61no—
393#217—61no—
394#217—61no—
395#216—62no—
396#216—62no—
397#216—62no—
398#215—62no—
399#215—62no—
400#215—62no—
401#214—62no—
402#214—62no—
403#214—62no—
404#213—62no—
405#213—62no—
406#213—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415C4⋊Dic3—61no—
416C4⋊Dic3—61no—
417Dic3⋊C4—21no—
418Dic3⋊C4—21no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421C4×Dic3—21no—
422C4×Dic3—21no—
423C4×Dic3#6711yescharacteristic
424C4×Dic3#6711yescharacteristic
425C4×Dic3C22×D311yescharacteristic
426C4×Dic3C22×D311yescharacteristic
427C2×C3⋊C8—22no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8—122no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439Dic12—62no—
440D24—62no—
441#204—62no—
442#204—62no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32#12112yes—
446C22×C32C22×D411yescharacteristic
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3×D3—22no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C32×C4—41no—
457C32×C4—41no—
458C32×C4#12112yes—
459C32×C4C22×D411yescharacteristic
460C32×C4C2×#4111yescharacteristic
461C3⋊Dic3—41no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#13512yescomplemented
468C2×#41—31no—
469C2×#41—31no—
470C2×#41—91no—
471#135—184no—
472#135—184no—
473C2×Q16—91no—
474C2×Q16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×D8—91no—
480C2×D8—91no—
481C22×C8—31no—
482C22×C8—91no—
483C4⋊Q8—91no—
484#127—91no—
485#124—91no—
486#124—91no—
487#121—181no—
488#121—181no—
489C4×Q8—31no—
490C4×Q8—31no—
491C4×D4—31no—
492C4×D4—31no—
493C4×D4—61no—
494C4×D4—61no—
495C4×D4—181no—
496C4×D4—181no—
497#117—61no—
498#117D3211yescharacteristic
499C2×C42—31no—
500C2×C42—61no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#102—31no—
510#102—31no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3D3×D411yescharacteristic
517C23×C3C2×#6711yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—121no—
523C3×Q8—32no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—32no—
528C3×D4—64no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—122no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—62no—
548C2×C3×C4—61no—
549C2×C3×C4—64no—
550C2×C3×C4—61no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4—121no—
554C2×C3×C4—122no—
555C2×C3×C4C2×D1212yes—
556C2×C3×C4#23512yes—
557C2×C3×C4#23512yes—
558C2×C3×C4D3×D412yes—
559C2×C3×C4D3×D411yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563#67—24no—
564#67—42no—
565#67—122no—
566#67—124no—
567#67—122no—
568#67—122no—
569#67—122no—
570C2×Dic3—21no—
571C2×Dic3—22no—
572C2×Dic3—21no—
573C2×Dic3—41no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577C2×Dic3C2×#6711yescharacteristic
578C2×Dic3C2×#6711yescharacteristic
579C2×Dic3C2×#6711yescharacteristic
580C2×Dic3C2×#6711yescharacteristic
581D12—21no—
582D12—21no—
583D12—21no—
584D12—62no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—121no—
590D12—122no—
591D12—122no—
592D12C2×D1212yes—
593C4×D3—24no—
594C4×D3—42no—
595C4×D3—42no—
596C4×D3—42no—
597C4×D3—124no—
598C4×D3—122no—
599C4×D3—122no—
600Dic6—21no—
601Dic6—21no—
602Dic6—21no—
603Dic6—62no—
604Dic6—61no—
605Dic6—61no—
606Dic6—61no—
607Dic6—61no—
608Dic6—121no—
609Dic6C2×D1212yes—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C3⋊C8—121no—
620C2×C32—22no—
621C2×C32C2×#12111yescharacteristic
622C2×C32C2×#13511yescharacteristic
623C2×C32#57511yescharacteristic
624C3⋊D3—81no—
625C3×D3—42no—
626C3×D3—81no—
627#41—34no—
628#41—62no—
629#41—62no—
630#41—62no—
631#41—182no—
632#41—182no—
633C2×Q8—31no—
634C2×Q8—31no—
635C2×Q8—91no—
636C2×D4—31no—
637C2×D4—31no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—91no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—181no—
651C22×C4C2×D3211yescharacteristic
652Q16—182no—
653Q16—182no—
654SD16—182no—
655SD16—182no—
656SD16—182no—
657SD16—182no—
658D8—182no—
659D8—182no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—62no—
663C2×C8—91no—
664C2×C8—91no—
665C2×C8—182no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C4⋊C4C2×D3211yescharacteristic
672C22⋊C4—21no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—21no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—31no—
684C42—61no—
685C42—61no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—62no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3#88412yes—
701C22×C3#93012yes—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×#6711yescharacteristic
704C2×D3—22no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—122no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—241no—
718C2×D3—241no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—22no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—62no—
728C3×C4—61no—
729C3×C4—61no—
730C3×C4—61no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4—121no—
734C3×C4#88412yes—
735C3×C4#93012yes—
736C3×C4C22×D1211yescharacteristic
737C3×C4C2×#23511yescharacteristic
738C3×C4C2×#23511yescharacteristic
739C3×C4C2×D3×D411yescharacteristic
740Dic3—22no—
741Dic3—21no—
742Dic3—21no—
743Dic3—21no—
744Dic3—41no—
745Dic3—122no—
746Dic3—121no—
747Dic3—121no—
748Dic3#95012yescomplemented
749C32#303511yescharacteristic, complemented, Sylow
750C23—61no—
751C23—61no—
752C23—181no—
753C23D3×#6711yescharacteristic
754Q8—32no—
755Q8—61no—
756Q8—61no—
757Q8—61no—
758Q8—181no—
759Q8—181no—
760D4—32no—
761D4—64no—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—122no—
766D4—181no—
767D4—181no—
768D4—362no—
769D4—362no—
770D4—362no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—121no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—362no—
787C2×C4#379812yes—
788C2×C4D3×D1212yes—
789C2×C4D3×#6711yescharacteristic
790C2×C4C22×D3211yescharacteristic
791C8—61no—
792C8—61no—
793C8—181no—
794C8—181no—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—42no—
801C2×C3—122no—
802C2×C3—241no—
803C2×C3C2×#88411yescharacteristic
804C2×C3D3×#13511yescharacteristic
805C2×C3#576811yescharacteristic
806C2×C3C2×#93011yescharacteristic
807C2×C3C2×#95011yescharacteristic
808C2×C3#582211yescharacteristic
809D3—42no—
810D3—81no—
811D3—242no—
812D3—241no—
813D3—241no—
814C22—21no—
815C22—21no—
816C22—62no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22#6390612yes—
826C22C2×D3×#6711yescharacteristic
827C4—32no—
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—61no—
833C4—62no—
834C4—121no—
835C4—361no—
836C4#6390612yes—
837C4C2×#379811yescharacteristic
838C4C2×D3×D1211yescharacteristic
839C3—21no—
840C3#7886111yescharacteristic, complemented
841C3#8252511yescharacteristic, complemented
842C2—22no—
843C2—122no—
844C2—241no—
845C2—721no—
846C2C2×#6390611yescharacteristic
847C2D3×#95011yescharacteristic
848C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5522C2semidirect
2. #10595029C2semidirect
3. C2×#63829C2semidirect
4. C2×#63822C2semidirect
5. #10592701C2semidirect
6. C3×#5002C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590561C2semidirect
9. #10590559C2semidirect
10. #10590549C2semidirect
11. #10590547C2semidirect
12. #10590536C2semidirect
13. #10590534C2semidirect
14. #10590532C2semidirect
15. #10590530C2semidirect
69. #5522D3semidirect
84. #5002D3semidirect
108. C3×#235D4semidirect
348. #235D12semidirect
467. C3×Dic3#135semidirect
748. Dic3#950semidirect
749. C32#3035semidirect
840. C3#78861semidirect
841. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
#105950292
C2×#638292
C2×#638222
#105927012
C3×#50022
C2×Dic3⋊(C3⋊C8)2
#105905612
#105905592
#105905492
#105905472
#105905362
#105905342
#105905322
#105905302
#825253
#788613