Finite Group Databasebeta

← #11895850

Subgroups — #11895850

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593942C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3#10592400C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic, complemented
5C3×#4710C211yesmaximal, characteristic, complemented
6#10590901C211yesmaximal, characteristic, complemented
7#10590866C211yesmaximal, characteristic, complemented
8#10590817C211yesmaximal, characteristic, complemented
9#10590778C211yesmaximal, characteristic, complemented
10#10590750C211yesmaximal, characteristic
11#10590748C211yesmaximal, characteristic, complemented
12#10590743C211yesmaximal, characteristic, complemented
13#10590740C211yesmaximal, characteristic
14#10590348C211yesmaximal, characteristic
15#10590310C211yesmaximal, characteristic, complemented
16#81670—31nomaximal
17#79751—31nomaximal
18C2×D3×Dic6—21no—
19C4×#634C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#875C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2211yescharacteristic
26#63919C2211yescharacteristic
27#63899—21no—
28#63899—21no—
29#63898C2211yescharacteristic
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63896—21no—
33#63877—21no—
34#63873C2211yescharacteristic
35#63863C2211yescharacteristic
36#63861—21no—
37#63859—21no—
38#63856—21no—
39#63843C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×#97C2211yescharacteristic
43#63642C2211yescharacteristic
44#63641C2211yescharacteristic
45#63641C2211yescharacteristic
46C8×C3⋊Dic3C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63576C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61#5727—31no—
62#5671—31no—
63#5568—31no—
64D4×Dic6—31no—
65C3×#489—31no—
66C3×#440—31no—
67#5165—31no—
68#5162—31no—
69#5091—31no—
70#5057—31no—
71#5021—31no—
72#5016—31no—
73#4890—31no—
74#4875—31no—
75#4818—31no—
76#4817—31no—
77#4794—31no—
78#4793—31no—
79#4792—31no—
80#4792—31no—
81#4787—31no—
82#4765—31no—
83#4759—31no—
84#4757—31no—
85#4756—31no—
86#4756—31no—
87#4714D311yescharacteristic, complemented
88#4710D311yescharacteristic, complemented
89#4701—31no—
90#4701—31no—
91#4701—61no—
92C2×#634D411yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C42C2311yescharacteristic
108C4⋊(C3⋊Dic3)D411yescharacteristic
109#3750D411yescharacteristic
110#3750D411yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×#204—22no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3715—22no—
138#3713—22no—
139#3367—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C3×C4⋊Q8—31no—
144C3×#124—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147#947—31no—
148#946—61no—
149Q8×Dic3—31no—
150#944—31no—
151#944—31no—
152C2×#215—31no—
153#936—31no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157C2×#214—31no—
158C2×#213—31no—
159C2×#213—31no—
160#924—61no—
161C2×#204C2×D311yescharacteristic
162#898—61no—
163#896—61no—
164#896—61no—
165#896—61no—
166#893—31no—
167#893—31no—
168#893—31no—
169#888—31no—
170#888—31no—
171#888—31no—
172#888—31no—
173#887—31no—
174#879—61no—
175#879—61no—
176#878—61no—
177#878—61no—
178#878—61no—
179#877—61no—
180#876—61no—
181#875C2×D311yescharacteristic
182C4×D12C2×D311yescharacteristic
183#872—61no—
184#869C2×D311yescharacteristic
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C4×Dic6C2×D311yescharacteristic
189C3×#107—31no—
190C3×#103—31no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#97—21no—
197C3×#97C2×D311yescharacteristic
198C3×#97C2×D311yescharacteristic
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#821C2×D311yescharacteristic
204#821C2×D311yescharacteristic
205#821C2×D311yescharacteristic
206#818C2×D311yescharacteristic
207#816C2×D311yescharacteristic
208#816C2×D311yescharacteristic
209#816C2×D311yescharacteristic
210#815—31no—
211#815—31no—
212#815—61no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—61no—
218Dic3⋊C8—61no—
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—61no—
222#810—31no—
223#810—31no—
224#810—31no—
225#809—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—61no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—22no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C3×D12—21no—
250C3×D12—21no—
251C3×D12—21no—
252C3×D12#4112yes—
253C3×C4×D3—42no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—42no—
259#627—42no—
260#627—42no—
261D3×Dic3—42no—
262D3×Dic3—42no—
263D3×Dic3—42no—
264C32×C8—21no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3⋊(C3⋊C8)—21no—
268#556—91no—
269D4×Q8—91no—
270#489—31no—
271#489—91no—
272#487—91no—
273#477—91no—
274#477—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#461—91no—
279#446—91no—
280#440—31no—
281#440—91no—
282C4×D8—91no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—31no—
287C2×C3×D4—31no—
288C22×C3×C4—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292D3×Q8—124no—
293C2×D12C22×D311yescharacteristic
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×Dic6—21no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—124no—
308C2×Dic6C22×D311yescharacteristic
309C2×Dic6C22×D311yescharacteristic
310C3×SD16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C22⋊C4—61no—
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C42—21no—
327C3×C42—61no—
328C3×C42C22×D311yescharacteristic
329C3×C42C22×D311yescharacteristic
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#215—62no—
336#214—62no—
337#213—62no—
338#213—62no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347C4⋊Dic3—21no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372C4×Dic3—21no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—61no—
386C2×C3⋊C8—61no—
387#204—22no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—21no—
402C3⋊Dic3AGL(1,ℤ/8)12yes—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—181no—
410C2×SD16—31no—
411C2×SD16—91no—
412C2×D8—91no—
413C4⋊Q8—31no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#124—31no—
420#124—91no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C4×Q8—31no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—31no—
434#107—91no—
435#107—91no—
436C4⋊C8—91no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102—91no—
449#97—91no—
450#97D3211yescharacteristic
451C4×C8—91no—
452C23×C3—61no—
453C23×C3—61no—
454C22×D3—21no—
455C22×D3—21no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—122no—
461C3×D4—32no—
462C3×D4—61no—
463C3×D4—61no—
464C3×D4—61no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—122no—
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4D3×D411yescharacteristic
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—122no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502D12—21no—
503D12—21no—
504D12—21no—
505D12#23512yes—
506C4×D3—42no—
507C4×D3—122no—
508C4×D3—122no—
509C4×D3—122no—
510Dic6—21no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6—42no—
515Dic6—62no—
516Dic6—62no—
517Dic6—122no—
518Dic6—122no—
519Dic6—122no—
520Dic6—122no—
521Dic6—122no—
522C3×C8—22no—
523C3×C8—21no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—21no—
527C3×C8—41no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—61no—
531C3⋊C8—61no—
532C3⋊C8—121no—
533C3⋊C8—121no—
534C2×C32#54811yescharacteristic
535C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
536C2×C32#57811yescharacteristic
537C3×D3—42no—
538C3×D3—81no—
539C2×Q8—31no—
540C2×Q8—31no—
541C2×Q8—61no—
542C2×Q8—91no—
543C2×Q8—181no—
544C2×Q8—181no—
545C2×Q8—364no—
546C2×D4—31no—
547C2×D4—31no—
548C22×C4—61no—
549C22×C4—181no—
550C22×C4—181no—
551C22×C4—181no—
552SD16—62no—
553SD16—182no—
554D8—182no—
555C2×C8—91no—
556C2×C8—91no—
557C2×C8C2×D3211yescharacteristic
558C2×C8C2×D3211yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—181no—
577C22⋊C4—181no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C42—61no—
582C42—91no—
583C42—91no—
584C42—181no—
585C42C2×D3211yescharacteristic
586C22×C3—21no—
587C22×C3—62no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C2×D3—22no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4C2×#23511yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4#101011yescharacteristic
618C3×C4#101011yescharacteristic
619Dic3—32no—
620Dic3—32no—
621Dic3—41no—
622Dic3—41no—
623Dic3—41no—
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3—62no—
628Dic3—61no—
629Dic3—61no—
630Dic3—61no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637C32#336711yescharacteristic, complemented, Sylow
638C23—61no—
639C23—61no—
640Q8—61no—
641Q8—61no—
642Q8—61no—
643Q8—61no—
644Q8—122no—
645Q8—182no—
646Q8—362no—
647Q8—362no—
648D4—32no—
649D4—61no—
650D4—61no—
651D4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—122no—
663C2×C4—362no—
664C2×C4—362no—
665C2×C4—362no—
666C2×C4#380211yescharacteristic
667C2×C4#380211yescharacteristic
668C2×C4C22×D3211yescharacteristic
669C8—21no—
670C8—21no—
671C8—181no—
672C8—181no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—122no—
677C2×C3—241no—
678C2×C3#555211yescharacteristic
679C2×C3#567711yescharacteristic
680C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
681C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
682C2×C3#577911yescharacteristic
683C2×C3#577911yescharacteristic
684D3—42no—
685D3—81no—
686C22—62no—
687C22—121no—
688C22—121no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22C2×#380211yescharacteristic
693C4—21no—
694C4—21no—
695C4—92no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—121no—
700C4—121no—
701C4—121no—
702C4—181no—
703C4—181no—
704C4—181no—
705C4#6429811yescharacteristic
706C4D3×#23511yescharacteristic
707C3—21no—
708C3#7975111yescharacteristic, complemented
709C3#8167011yescharacteristic, complemented
710C2—122no—
711C2—241no—
712C2#1059390511yescharacteristic
713C2#1059471611yescharacteristic
714C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenter#97D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593942C2semidirect
2. #10593904C2semidirect
3. #10592400C2semidirect
4. C3×#4714C2semidirect
5. C3×#4710C2semidirect
6. #10590901C2semidirect
7. #10590866C2semidirect
8. #10590817C2semidirect
9. #10590778C2semidirect
11. #10590748C2semidirect
12. #10590743C2semidirect
15. #10590310C2semidirect
87. #4714D3semidirect
88. #4710D3semidirect
637. C32#3367semidirect
708. C3#79751semidirect
709. C3#81670semidirect

Maximal subgroups

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

subgroupindex
#105939422
#105939042
#105924002
C3×#47142
C3×#47102
#105909012
#105908662
#105908172
#105907782
#105907502
#105907482
#105907432
#105907402
#105903482
#105903102
#816703
#797513