Finite Group Databasebeta

← #11895884

Subgroups — #11895884

Order 1152.

798 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595119C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic, complemented
3#10592458C211yesmaximal, characteristic, complemented
4C3×#4787C211yesmaximal, characteristic
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591488C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic
8#10591431C211yesmaximal, characteristic
9#10590804C211yesmaximal, characteristic, complemented
10#10590789C211yesmaximal, characteristic, complemented
11#10590766C211yesmaximal, characteristic, complemented
12#10590748C211yesmaximal, characteristic, complemented
13#10590567C211yesmaximal, characteristic, complemented
14#10590489C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#81670—31nomaximal
17#80518—31nomaximal
18C2×D3×Dic6—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C3×#936C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63982—21no—
28#63957—21no—
29#63956—21no—
30#63956—21no—
31#63918C2211yescharacteristic
32C4×#627C2211yescharacteristic
33#63898C2211yescharacteristic
34#63896—21no—
35Dic3×D12C2211yescharacteristic
36#63887—21no—
37#63873C2211yescharacteristic
38#63851—21no—
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63659C2211yescharacteristic
44#63645C2211yescharacteristic
45#63641C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63554C2211yescharacteristic
60#63553C2211yescharacteristic
61#5727—31no—
62#5671—31no—
63#5671—31no—
64D4×Dic6—31no—
65C3×#489—31no—
66C3×#463—31no—
67#5164—31no—
68#5162—31no—
69#5153—31no—
70Dic3×D8—31no—
71#5091—31no—
72#5057—31no—
73#5055—31no—
74#5018—31no—
75#4850—31no—
76#4828—31no—
77#4818—31no—
78#4817—31no—
79#4793—31no—
80#4793—31no—
81#4792—31no—
82#4792—31no—
83#4787D311yescharacteristic
84#4765—31no—
85#4765D311yescharacteristic, complemented
86#4759—31no—
87#4759—31no—
88#4759—61no—
89#4756—31no—
90#4710—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3757—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#213—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×#204—22no—
126#3724—21no—
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138#3715—22no—
139#3367—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C2×C3×D8—31no—
144C3×C4⋊Q8—31no—
145C3×#124—31no—
146C3×#124—31no—
147C3×C4×D4—31no—
148#946—61no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151#944—31no—
152#944—31no—
153C2×#215—31no—
154#936C2×D311yescharacteristic
155#936C2×D311yescharacteristic
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—61no—
161C2×#214—31no—
162C2×#213C2×D311yescharacteristic
163#924—61no—
164C2×#204C2×D311yescharacteristic
165#896—61no—
166#896—61no—
167#893—31no—
168#893C2×D311yescharacteristic
169#888—31no—
170#888—31no—
171#888—31no—
172#888—61no—
173#888C2×D311yescharacteristic
174#879—61no—
175#879—61no—
176#879—61no—
177#879—61no—
178#878—61no—
179#878—61no—
180#878—61no—
181#878—61no—
182#877—61no—
183#877—61no—
184C4×D12—31no—
185#869—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×C4⋊C8—31no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#102—21no—
195C3×#102—31no—
196C3×#102C2×D311yescharacteristic
197C3×#102C2×D311yescharacteristic
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832C2×D311yescharacteristic
207#821—31no—
208#818—31no—
209#818—31no—
210#818—31no—
211#818—61no—
212#816—31no—
213#816—31no—
214#816C2×D311yescharacteristic
215#815—31no—
216#815C2×D311yescharacteristic
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221Dic3⋊C8C2×D311yescharacteristic
222C8×Dic3—31no—
223C8×Dic3—31no—
224#810—31no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232#803—31no—
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—42no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244#634—42no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12#4112yes—
254C3×C4×D3—42no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—42no—
260#627—22no—
261#627—42no—
262D3×Dic3—42no—
263D3×Dic3—42no—
264C32×C8—21no—
265C3⋊(C3⋊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—31no—
277#463—91no—
278#461—91no—
279#446—91no—
280#440—91no—
281#440—91no—
282C4×D8—91no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C22×C3×C4—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—121no—
296D3×Q8—124no—
297C2×D12C22×D311yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×Dic6—21no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×Dic6C22×D311yescharacteristic
311C2×Dic6C22×D311yescharacteristic
312C3×SD16—62no—
313C3×D8—62no—
314C2×C3×C8—21no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331#217—21no—
332#217—21no—
333#217—21no—
334#217—21no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—61no—
339#217—121no—
340#215—62no—
341#214—62no—
342#213—22no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
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—
372Dic3⋊C4—121no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387#204—22no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—22no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C42−1+411yescharacteristic
398C3⋊Dic3—21no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3AGL(1,ℤ/8)12yes—
402C3×Dic3—21no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—181no—
410C2×SD16—31no—
411C2×SD16—91no—
412C2×D8—31no—
413C4⋊Q8—31no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#124—31no—
420#124—31no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—91no—
434#107—91no—
435#107—91no—
436C4⋊C8—31no—
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—91no—
447#102—91no—
448#102D3211yescharacteristic
449#97—31no—
450#97—91no—
451C4×C8—91no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—41no—
455C23×C3—61no—
456C22×D3—21no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—122no—
462C3×D4—22no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—32no—
468C3×D4—41no—
469C3×D4—61no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—41no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—122no—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—122no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502C2×Dic3—122no—
503C2×Dic3—242no—
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—21no—
509D12#23712yes—
510C4×D3—42no—
511C4×D3—122no—
512C4×D3—122no—
513Dic6—21no—
514Dic6—21no—
515Dic6—21no—
516Dic6—21no—
517Dic6—42no—
518Dic6—62no—
519Dic6—62no—
520Dic6—122no—
521Dic6—122no—
522Dic6—122no—
523Dic6—122no—
524Dic6—242no—
525C3×C8—21no—
526C3×C8—21no—
527C3×C8—41no—
528C3×C8—61no—
529C3×C8—61no—
530C3⋊C8—21no—
531C3⋊C8—21no—
532C3⋊C8—61no—
533C3⋊C8—61no—
534C3⋊C8—121no—
535C2×C32—81no—
536C2×C32#54811yescharacteristic
537C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
538C2×C32#57811yescharacteristic
539C3×D3—42no—
540C2×Q8—31no—
541C2×Q8—31no—
542C2×Q8—61no—
543C2×Q8—91no—
544C2×Q8—181no—
545C2×Q8—181no—
546C2×Q8—364no—
547C2×D4—31no—
548C2×D4C2×D3211yescharacteristic
549C22×C4—61no—
550C22×C4—181no—
551C22×C4—181no—
552C22×C4—181no—
553SD16—62no—
554SD16—182no—
555D8—62no—
556C2×C8—31no—
557C2×C8—31no—
558C2×C8—91no—
559C2×C8C2×D3211yescharacteristic
560C4⋊C4—31no—
561C4⋊C4—61no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4C2×D3211yescharacteristic
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C42—31no—
583C42—31no—
584C42—91no—
585C42—181no—
586C42—181no—
587C22×C3—21no—
588C22×C3—42no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—62no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C2×D3×D411yescharacteristic
602C2×D3—22no—
603C2×D3—41no—
604C2×D3—41no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4C2×#23711yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4#101011yescharacteristic
620C3×C4#101011yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—32no—
626Dic3—32no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—62no—
631Dic3—61no—
632Dic3—61no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—121no—
638Dic3—241no—
639Dic3—241no—
640C32#336711yescharacteristic, complemented, Sylow
641C23—21no—
642C23—61no—
643Q8—61no—
644Q8—61no—
645Q8—61no—
646Q8—61no—
647Q8—122no—
648Q8—182no—
649Q8—362no—
650Q8—362no—
651D4—21no—
652D4—21no—
653D4—32no—
654D4—61no—
655C2×C4—21no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—122no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—362no—
669C2×C4—362no—
670C2×C4—362no—
671C2×C4C22×D3211yescharacteristic
672C8—21no—
673C8—61no—
674C8—61no—
675C8—181no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—82no—
680C2×C3—81no—
681C2×C3—81no—
682C2×C3—122no—
683C2×C3#559811yescharacteristic
684C2×C3#567711yescharacteristic
685C2×C3#577111yescharacteristic
686C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
687C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
688C2×C3#577911yescharacteristic
689D3—42no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—62no—
694C22—121no—
695C22—121no—
696C22D32×D411yescharacteristic
697C4—41no—
698C4—61no—
699C4—61no—
700C4—61no—
701C4—61no—
702C4—92no—
703C4—121no—
704C4—121no—
705C4—121no—
706C4—181no—
707C4—361no—
708C4—361no—
709C4#6429811yescharacteristic
710C4D3×#23711yescharacteristic
711C3—21no—
712C3#8051811yescharacteristic, complemented
713C3#8167011yescharacteristic, complemented
714C2—81no—
715C2—122no—
716C2#1059407611yescharacteristic
717C2#1059472611yescharacteristic
718C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenter#102D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595119C2semidirect
2. #10594376C2semidirect
3. #10592458C2semidirect
5. C3×#4765C2semidirect
6. #10591488C2semidirect
9. #10590804C2semidirect
10. #10590789C2semidirect
11. #10590766C2semidirect
12. #10590748C2semidirect
13. #10590567C2semidirect
14. #10590489C2semidirect
15. #10590478C2semidirect
85. #4765D3semidirect
640. C32#3367semidirect
712. C3#80518semidirect
713. C3#81670semidirect

Maximal subgroups

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

subgroupindex
#105951192
#105943762
#105924582
C3×#47872
C3×#47652
#105914882
#105914352
#105914312
#105908042
#105907892
#105907662
#105907482
#105905672
#105904892
#105904782
#816703
#805183