Finite Group Databasebeta

← #11895990

Subgroups — #11895990

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594520C211yesmaximal, characteristic
2#10594318C211yesmaximal, characteristic, complemented
3#10592588C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4890C211yesmaximal, characteristic, complemented
6#10590888C211yesmaximal, characteristic, complemented
7#10590879C211yesmaximal, characteristic, complemented
8#10590879C211yesmaximal, characteristic, complemented
9#10590646C211yesmaximal, characteristic, complemented
10#10590590C211yesmaximal, characteristic, complemented
11#10590553C211yesmaximal, characteristic, complemented
12#10590550C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81153—31nomaximal
17#80995—31nomaximal
18C2×#3798—21no—
19C2×#3744C2211yescharacteristic
20#64102C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63914C2211yescharacteristic
28#63912—21no—
29#63911C2211yescharacteristic
30#63911C2211yescharacteristic
31#63906—21no—
32#63906—21no—
33#63872C2211yescharacteristic
34#63870—21no—
35#63847—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843—21no—
39#63839—21no—
40C2×#3716C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C32×#107C2211yescharacteristic
43#63642C2211yescharacteristic
44#63637C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63572C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5721—31no—
62#5685—31no—
63#5553—31no—
64#5553—31no—
65C3×#478—31no—
66C3×#474—31no—
67#5088—31no—
68#5067—31no—
69#5018—31no—
70C4×#214—31no—
71#4891—31no—
72#4891D311yescharacteristic, complemented
73#4890D311yescharacteristic, complemented
74#4889—31no—
75#4889—31no—
76#4889—31no—
77#4889—61no—
78#4871—31no—
79#4852—31no—
80#4848—31no—
81#4848—31no—
82#4831—31no—
83#4828—31no—
84#4764—31no—
85#4764—31no—
86#4764—31no—
87#4762—31no—
88#4762—31no—
89#4762—31no—
90#4762—31no—
91#4760—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×#627D411yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#625—21no—
106C2×#625—21no—
107#3798—44no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112#3750—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3744—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129#3724—21no—
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3716—22no—
139#3368—91noSylow
140C2×#235—61no—
141C2×#235—61no—
142C3×C4⋊Q8—31no—
143C3×#125—31no—
144C3×C4×D4—31no—
145C3×C4×D4—31no—
146Q8×Dic3—61no—
147#944—61no—
148#940—31no—
149#940—31no—
150#940—31no—
151#940—31no—
152C2×#214—31no—
153C2×#214—31no—
154#930—61no—
155#930—61no—
156C2×#204—31no—
157C2×#204—31no—
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—61no—
161#893—31no—
162#893—31no—
163#893—61no—
164#893C2×D311yescharacteristic
165#893C2×D311yescharacteristic
166#890—31no—
167#890—31no—
168#890C2×D311yescharacteristic
169#889—61no—
170#889—61no—
171#889—61no—
172#889—61no—
173#888—61no—
174#888C2×D311yescharacteristic
175#887—31no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—61no—
180#887—61no—
181#884—61no—
182#884—61no—
183#884—61no—
184#884—61no—
185#874—31no—
186#874—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#107—21no—
192C3×#107—31no—
193C3×#107C2×D311yescharacteristic
194C3×#107C2×D311yescharacteristic
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202#832—31no—
203#832—31no—
204#821—31no—
205#821—31no—
206#821C2×D311yescharacteristic
207#821C2×D311yescharacteristic
208#815—31no—
209#815—31no—
210#815—31no—
211#815—61no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8C2×D311yescharacteristic
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231#803—31no—
232C4×C3⋊C8—31no—
233C22×C3⋊D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C4×C3⋊D3—42no—
245#634—21no—
246#634#4112yescomplemented
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×C4×D3—42no—
258C3×C4×D3—42no—
259C3×Dic6—42no—
260#627—22no—
261#626—42no—
262#626—42no—
263#626—81no—
264#626—81no—
265#625—42no—
266#625—81no—
267C32×C8—21no—
268C3⋊(C3⋊C8)—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271#557—91no—
272#550—91no—
273#490—91no—
274#490—91no—
275#486—91no—
276#478—31no—
277#478—91no—
278#474—31no—
279#460—91no—
280#460—91no—
281#460—91no—
282#446—91no—
283#440—91no—
284#440—91no—
285C4×SD16—91no—
286C2×C3×Q8—61no—
287C2×C3×D4—31no—
288C2×C3×D4—31no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C2×#67—61no—
292C2×#67—61no—
293C2×#67—61no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—61no—
299#235—124no—
300#235—124no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—61no—
304C2×D12—61no—
305C2×D12—61no—
306C2×D12—61no—
307C2×D12—61no—
308C2×D12C22×D311yescharacteristic
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—121no—
315C2×Dic6—21no—
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—61no—
321C2×C3×C8—21no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—31no—
340C3×C42—31no—
341#214—62no—
342#214—62no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—121no—
348C4⋊Dic3—21no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—21no—
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—121no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—121no—
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—62no—
388#204—62no—
389#204—64no—
390#204—62no—
391#204—62no—
392C22×C32C22×D411yescharacteristic
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4C2×#4111yescharacteristic
405C32×C42−1+411yescharacteristic
406C3⋊Dic3—22no—
407C3⋊Dic3—21no—
408C3⋊Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3AGL(1,ℤ/8)12yes—
415C2×#41—181no—
416C2×SD16—91no—
417C2×SD16—91no—
418C2×SD16—91no—
419C4⋊Q8—31no—
420C4⋊Q8—181no—
421#127—91no—
422#127—91no—
423#127—91no—
424#125—31no—
425#125—91no—
426#125—181no—
427#125—181no—
428#121—181no—
429#121—181no—
430#121—181no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×Q8—91no—
434C4×Q8—91no—
435C4×Q8—181no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—91no—
439#107—31no—
440#107D3211yescharacteristic
441#106—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
444C4⋊C8—91no—
445#103—91no—
446#102—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—91no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#97—91no—
456#97—91no—
457C4×C8—91no—
458C23×C3—61no—
459C23×C3—61no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—121no—
465C3×Q8—122no—
466C3×D4—61no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—61no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—122no—
484C2×C3×C4—122no—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487#67—122no—
488#67—122no—
489#67—122no—
490#67—122no—
491#67—241no—
492#67—241no—
493#67—241no—
494#67—241no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—121no—
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509C2×Dic3D3×D411yescharacteristic
510D12—21no—
511D12—21no—
512D12—21no—
513D12—21no—
514D12—62no—
515D12—61no—
516D12—61no—
517D12—61no—
518D12—61no—
519D12—121no—
520D12—122no—
521D12—122no—
522D12—241no—
523D12—241no—
524C4×D3—42no—
525C4×D3—42no—
526C4×D3—122no—
527C4×D3—122no—
528C4×D3—242no—
529Dic6—32no—
530Dic6—32no—
531Dic6—42no—
532Dic6—62no—
533Dic6—62no—
534Dic6—61no—
535Dic6—61no—
536Dic6—62no—
537Dic6—121no—
538C3×C8—22no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—61no—
542C3×C8—61no—
543C3⋊C8—21no—
544C3⋊C8—21no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C2×C32#54811yescharacteristic
549C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
550C2×C32#57711yescharacteristic
551C3⋊D3—81no—
552C3×D3—81no—
553C3×D3—81no—
554#41—364no—
555C2×Q8—61no—
556C2×Q8—91no—
557C2×Q8—91no—
558C2×D4—31no—
559C2×D4—31no—
560C2×D4—91no—
561C2×D4—181no—
562C2×D4—181no—
563C2×D4—181no—
564C2×D4—181no—
565C2×D4—181no—
566C2×D4—181no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—181no—
570SD16—182no—
571SD16—182no—
572SD16—182no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—91no—
576C2×C8C2×D3211yescharacteristic
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4C2×D3211yescharacteristic
591C4⋊C4C2×D3211yescharacteristic
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—181no—
595C42—31no—
596C42—31no—
597C42—91no—
598C42—181no—
599C42—181no—
600C42—181no—
601C22×C3—21no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3—121no—
606C22×C3—121no—
607C22×C3—121no—
608C22×C3C2×D3×D411yescharacteristic
609C22×C3C2×D3×D411yescharacteristic
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—122no—
617C2×D3—121no—
618C2×D3—121no—
619C2×D3—121no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—241no—
624C2×D3—241no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—32no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—81no—
636C3×C4—81no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4#100711yescharacteristic
640C3×C4#100711yescharacteristic
641C3×C4D3×#4111yescharacteristic
642C3×C4D3×#4111yescharacteristic
643Dic3—21no—
644Dic3—21no—
645Dic3—21no—
646Dic3—41no—
647Dic3—41no—
648Dic3—62no—
649Dic3—62no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—122no—
655Dic3—121no—
656Dic3—121no—
657Dic3#91112yes—
658C32#336811yescharacteristic, complemented, Sylow
659C23—61no—
660C23—61no—
661C23—181no—
662Q8—92no—
663Q8—122no—
664Q8—182no—
665Q8—181no—
666D4—61no—
667D4—61no—
668D4—61no—
669D4—61no—
670D4—181no—
671D4—181no—
672D4—362no—
673D4—362no—
674D4—362no—
675D4—721no—
676D4—721no—
677D4—721no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—181no—
691C2×C4—362no—
692C2×C4C22×D3211yescharacteristic
693C8—21no—
694C8—61no—
695C8—61no—
696C8—181no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—241no—
701C2×C3—241no—
702C2×C3#563311yescharacteristic
703C2×C3#563311yescharacteristic
704C2×C3C2×#91111yescharacteristic
705C2×C3#577011yescharacteristic
706C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
707C2×C3#577811yescharacteristic
708D3—81no—
709D3—81no—
710D3—242no—
711D3—241no—
712D3—241no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22D32×D411yescharacteristic
723C4—32no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—181no—
732C4—181no—
733C4—182no—
734C4#6430611yescharacteristic
735C4#6431611yescharacteristic
736C3—21no—
737C3#8099511yescharacteristic, complemented
738C3#8115311yescharacteristic, complemented
739C2—241no—
740C2—241no—
741C2—721no—
742C2#1059452111yescharacteristic
743C2D3×#91111yescharacteristic
744C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594520C2
hypercenter#107D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594318C2semidirect
3. #10592588C2semidirect
4. C3×#4891C2semidirect
5. C3×#4890C2semidirect
6. #10590888C2semidirect
7. #10590879C2semidirect
8. #10590879C2semidirect
9. #10590646C2semidirect
10. #10590590C2semidirect
11. #10590553C2semidirect
12. #10590550C2semidirect
13. #10590548C2semidirect
14. #10590479C2semidirect
15. #10590435C2semidirect
72. #4891D3semidirect
73. #4890D3semidirect
246. #634#41semidirect
658. C32#3368semidirect
737. C3#80995semidirect
738. C3#81153semidirect

Maximal subgroups

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

subgroupindex
#105945202
#105943182
#105925882
C3×#48912
C3×#48902
#105908882
#105908792
#105906462
#105905902
#105905532
#105905502
#105905482
#105904792
#105904352
#811533
#809953