Finite Group Databasebeta

← #11897584

Subgroups — #11897584

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#627C211yesmaximal, characteristic, complemented
2#10594470C211yesmaximal, characteristic, complemented
3#10592484C211yesmaximal, characteristic
4C3×#4766C211yesmaximal, characteristic, complemented
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic
8#10591400C211yesmaximal, characteristic
9#10590903C211yesmaximal, characteristic, complemented
10#10590764C211yesmaximal, characteristic, complemented
11#10590759C211yesmaximal, characteristic, complemented
12#10590646C211yesmaximal, characteristic, complemented
13#10590433C211yesmaximal, characteristic, complemented
14#10590419C211yesmaximal, characteristic, complemented
15#10590412C211yesmaximal, characteristic, complemented
16#81158—31nomaximal
17#81089—31nomaximal
18C22×#627—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#888C2211yescharacteristic
26#63982—21no—
27#63964—21no—
28#63964—21no—
29#63919C2211yescharacteristic
30#63918C2211yescharacteristic
31#63918C2211yescharacteristic
32C4×#627C2211yescharacteristic
33#63895—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63888—21no—
37#63883—21no—
38#63872C2211yescharacteristic
39#63871—21no—
40C32×#102C2211yescharacteristic
41#63648C2211yescharacteristic
42#63642C2211yescharacteristic
43#63635C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5690—31no—
63D4×Dic6—31no—
64D4×Dic6—31no—
65C3×#478—31no—
66C3×#476—31no—
67#5080—31no—
68#5064—31no—
69#5014—31no—
70C4×#213—31no—
71#4890—31no—
72#4876—31no—
73#4870—31no—
74#4870—31no—
75#4870—31no—
76#4856—31no—
77#4856—31no—
78#4855—31no—
79#4846—31no—
80#4842—31no—
81#4831—31no—
82#4828—31no—
83#4785—31no—
84#4785—31no—
85#4785—31no—
86#4785—61no—
87#4766—31no—
88#4766D311yescharacteristic, complemented
89#4763—31no—
90#4761D311yescharacteristic, complemented
91#4756—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×Dic6—21no—
99C2×#627—21no—
100C2×#627—21no—
101C2×#627—21no—
102C2×#627—44no—
103C2×#627D411yescharacteristic
104C2×#624—21no—
105C2×#624—21no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3757—21no—
109#3753Q814yescomplemented
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3384—91noSylow
138C22×Dic6—61no—
139C22×Dic6—61no—
140C3×C4⋊Q8—31no—
141C3×#125—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144#946—61no—
145#946—61no—
146D4×Dic3—31no—
147D4×Dic3—31no—
148D4×Dic3—61no—
149D4×Dic3C2×D311yescharacteristic
150D4×Dic3C2×D311yescharacteristic
151C2×#213—31no—
152C2×#213—31no—
153C2×#213—61no—
154#924—61no—
155#924—61no—
156#897—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#893—31no—
161#893—31no—
162#893—31no—
163#893—31no—
164#893—61no—
165D3×C4⋊C4—61no—
166D3×C4⋊C4—61no—
167#890—31no—
168#890—31no—
169#890C2×D311yescharacteristic
170#888—31no—
171#888—31no—
172#888—31no—
173#888—31no—
174#888C2×D311yescharacteristic
175#878—61no—
176#878—61no—
177#878—61no—
178#878—61no—
179C4×D12—31no—
180C4×D12—31no—
181#869—31no—
182#869—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C3×#107—31no—
186C3×#106—31no—
187C3×#106—31no—
188C3×#106—31no—
189C3×C4⋊C8—31no—
190C3×C4⋊C8—31no—
191C3×#102—21no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102C2×D311yescharacteristic
195C3×#102C2×D311yescharacteristic
196#832C2×D311yescharacteristic
197#832C2×D311yescharacteristic
198#821—31no—
199#821—31no—
200#821—31no—
201#821—31no—
202#821—61no—
203#818—31no—
204#818C2×D311yescharacteristic
205#817—31no—
206#817C2×D311yescharacteristic
207#815—31no—
208#815—31no—
209#815—31no—
210#815—61no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8C2×D311yescharacteristic
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216#809—31no—
217#809—31no—
218#808—31no—
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic
225#808C2×D311yescharacteristic
226#807—31no—
227#807—31no—
228#807—31no—
229#803—31no—
230C4×C3⋊C8—31no—
231C23×C32—21no—
232C22×C3⋊D3—21no—
233C32×D4—21no—
234C32×D4C2×Q812yes—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—42no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)C2×Q812yescomplemented
243C4×C3⋊D3—81no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—42no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—81no—
255#627—22no—
256#627—42no—
257#627—42no—
258#627—42no—
259#624—42no—
260#624—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)C2×Q812yescomplemented
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#554—91no—
266D4×Q8—91no—
267#501—91no—
268#501—91no—
269#498—91no—
270#478—31no—
271#478—91no—
272#476—31no—
273#476—91no—
274#476—91no—
275#474—91no—
276#446—91no—
277#442—91no—
278#442—91no—
279C4×D8—91no—
280C2×C3×Q8—61no—
281C2×C3×D4—21no—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C22×D311yescharacteristic
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3—121no—
291C2×D12—31no—
292C2×D12—31no—
293C2×D12—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—121no—
301C2×Dic6—21no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—124no—
311C2×Dic6—124no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331#217—21no—
332#217—21no—
333#217—61no—
334#217—61no—
335#217—121no—
336#213—34no—
337#213—34no—
338#213—64no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—121no—
346C4⋊Dic3—21no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359C4⋊Dic3C22×D311yescharacteristic
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—61no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C22×C32—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32C22×D411yescharacteristic
386C2×C3⋊D3—22no—
387C2×C3⋊D3—41no—
388C2×C3⋊D3—41no—
389C32×C4—41no—
390C32×C4C22×Q811yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—21no—
393C3⋊Dic3—21no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3AGL(1,ℤ/8)12yes—
403C22×Q8—181no—
404C2×D8—91no—
405C4⋊Q8—31no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409#125—31no—
410#125—91no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C22⋊Q8—181no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C22⋊Q8—181no—
417C4×Q8—91no—
418C4×D4—31no—
419C4×D4—31no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—91no—
423C4×D4—91no—
424C2×C4⋊C4—181no—
425#107—31no—
426#107—91no—
427#107—91no—
428#106—31no—
429#106—31no—
430#106—31no—
431#106—91no—
432#106—91no—
433#106—91no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8—91no—
437#102—31no—
438#102—31no—
439#102—91no—
440#102—91no—
441#102—91no—
442#102D3211yescharacteristic
443#97—91no—
444#97—91no—
445C4×C8—91no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—41no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—241no—
453C3×D4—21no—
454C3×D4—21no—
455C3×D4—22no—
456C3×D4—41no—
457C3×D4D3×Q812yes—
458C3×D4D3×Q812yes—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—41no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—122no—
472C2×C3×C4—122no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—42no—
484C2×Dic3—42no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—122no—
491C2×Dic3—122no—
492C2×Dic3—242no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497D12—32no—
498D12—32no—
499D12—62no—
500D12—61no—
501D12—61no—
502D12—121no—
503C4×D3—122no—
504C4×D3—122no—
505C4×D3—241no—
506C4×D3—241no—
507C4×D3—241no—
508C4×D3—241no—
509C4×D3—242no—
510Dic6—62no—
511Dic6—62no—
512Dic6—81no—
513Dic6—122no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6—122no—
518Dic6—122no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—61no—
523C3×C8—61no—
524C3⋊C8—21no—
525C3⋊C8—21no—
526C3⋊C8—32no—
527C3⋊C8—32no—
528C3⋊C8—62no—
529C2×C32—42no—
530C2×C32D4×Q811yescharacteristic
531C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
532C2×C32#57711yescharacteristic
533C3⋊D3—42no—
534C2×Q8—61no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×Q8—181no—
538C2×Q8—181no—
539C2×Q8—364no—
540C2×D4—91no—
541C2×D4C2×D3211yescharacteristic
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—181no—
545C22×C4—181no—
546C22×C4—181no—
547C22×C4—181no—
548D8—94no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—91no—
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4C2×D3211yescharacteristic
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C42—31no—
577C42—31no—
578C42—91no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—21no—
582C22×C3—42no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C2×D3—62no—
592C2×D3—62no—
593C2×D3—122no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—241no—
599C2×D3—241no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—32no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4C2×D3×Q811yescharacteristic
614C3×C4C2×D3×Q811yescharacteristic
615C3×C4#101011yescharacteristic
616C3×C4#101011yescharacteristic
617Dic3—21no—
618Dic3—21no—
619Dic3—21no—
620Dic3—41no—
621Dic3—41no—
622Dic3—41no—
623Dic3—41no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—121no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—241no—
633Dic3#91412yes—
634C32#338411yescharacteristic, complemented, Sylow
635C23—21no—
636C23—181no—
637Q8—182no—
638Q8—241no—
639Q8—362no—
640Q8—362no—
641Q8—362no—
642D4—21no—
643D4—92no—
644D4—181no—
645D4#379712yes—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—122no—
658C2×C4—122no—
659C2×C4—181no—
660C2×C4—362no—
661C2×C4—362no—
662C2×C4—721no—
663C2×C4—721no—
664C2×C4C22×D3211yescharacteristic
665C8—21no—
666C8—61no—
667C8—61no—
668C8—92no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—82no—
675C2×C3#563211yescharacteristic
676C2×C3#563211yescharacteristic
677C2×C3C2×#91411yescharacteristic
678C2×C3#577011yescharacteristic
679C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
680C2×C3#577511yescharacteristic
681D3—122no—
682D3—122no—
683D3—242no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—182no—
688C22—361no—
689C22—361no—
690C22D32×D411yescharacteristic
691C4—32no—
692C4—41no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—121no—
700C4—181no—
701C4—181no—
702C4—361no—
703C4C2×#379711yescharacteristic
704C4#6430911yescharacteristic
705C3—21no—
706C3#8108911yescharacteristic, complemented
707C3#8115811yescharacteristic, complemented
708C2—42no—
709C2—362no—
710C2#1059407211yescharacteristic
711C2#1059473611yescharacteristic
712C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#102D32
hypocenterC32#3384
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. D4×#627C2semidirect
2. #10594470C2semidirect
4. C3×#4766C2semidirect
5. C3×#4761C2semidirect
6. #10591479C2semidirect
9. #10590903C2semidirect
10. #10590764C2semidirect
11. #10590759C2semidirect
12. #10590646C2semidirect
13. #10590433C2semidirect
14. #10590419C2semidirect
15. #10590412C2semidirect
88. #4766D3semidirect
90. #4761D3semidirect
109. #3753Q8semidirect
242. C4⋊(C3⋊D3)C2×Q8semidirect
262. C3⋊(C3⋊C8)C2×Q8semidirect
634. C32#3384semidirect
706. C3#81089semidirect
707. C3#81158semidirect

Maximal subgroups

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

subgroupindex
D4×#6272
#105944702
#105924842
C3×#47662
C3×#47612
#105914792
#105914042
#105914002
#105909032
#105907642
#105907592
#105906462
#105904332
#105904192
#105904122
#811583
#810893