Finite Group Databasebeta

← #11897596

Subgroups — #11897596

Order 1152.

802 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594484C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4876C211yesmaximal, characteristic, complemented
6#10590789C211yesmaximal, characteristic, complemented
7#10590776C211yesmaximal, characteristic, complemented
8#10590759C211yesmaximal, characteristic, complemented
9#10590746C211yesmaximal, characteristic
10#10590589C211yesmaximal, characteristic
11#10590467C211yesmaximal, characteristic, complemented
12#10590466C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic
14#10590418C211yesmaximal, characteristic, complemented
15#10590416C211yesmaximal, characteristic, complemented
16#81964—31nomaximal
17#81158—31nomaximal
18C2×D3×Dic6—21no—
19#64102C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63919C2211yescharacteristic
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63900—21no—
29#63898C2211yescharacteristic
30#63896—21no—
31#63895—21no—
32#63895—21no—
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63887—21no—
37#63865—21no—
38#63851—21no—
39C2×#3714C2211yescharacteristic
40C32×#107C2211yescharacteristic
41#63648C2211yescharacteristic
42#63641C2211yescharacteristic
43#63636C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×#815C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60#63553C2211yescharacteristic
61#5727—31no—
62#5690—31no—
63#5690—31no—
64D4×Dic6—31no—
65C3×#501—31no—
66C3×#478—31no—
67#5084—31no—
68#5066—31no—
69#5064—31no—
70#5014—31no—
71#4891D311yescharacteristic, complemented
72#4890—31no—
73#4890—31no—
74#4890—61no—
75#4876—31no—
76#4876D311yescharacteristic, complemented
77#4872—31no—
78#4870—31no—
79#4870—31no—
80#4870—31no—
81#4869—31no—
82#4855—31no—
83#4855—31no—
84#4842—31no—
85#4828—31no—
86#4785—31no—
87#4763—31no—
88#4761—31no—
89#4756—31no—
90#4711—31no—
91#4701—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×#624—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105D3×Dic6—44no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109#3752—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
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⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3714Q814yescomplemented
137#3384—91noSylow
138C2×D3×Q8—61no—
139C22×Dic6—61no—
140C3×C4⋊Q8—31no—
141C3×#125—31no—
142C3×#125—31no—
143C3×C4×D4—31no—
144#946—61no—
145D4×Dic3—31no—
146D4×Dic3—31no—
147C2×#213—31no—
148#924—61no—
149C2×D24—31no—
150#897—61no—
151#897—61no—
152#896—61no—
153#896—61no—
154#896—61no—
155#896—61no—
156#896—61no—
157#896—61no—
158#893—31no—
159#893—31no—
160#893—31no—
161#893—31no—
162#893—31no—
163#893—61no—
164#893C2×D311yescharacteristic
165D3×C4⋊C4—61no—
166D3×C4⋊C4—61no—
167#890C2×D311yescharacteristic
168#890C2×D311yescharacteristic
169#888—31no—
170#888—31no—
171#888—31no—
172#888—31no—
173#888—31no—
174#888—61no—
175#888C2×D311yescharacteristic
176#878—61no—
177#878—61no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—31no—
181#869—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C3×#107—21no—
185C3×#107—31no—
186C3×#107C2×D311yescharacteristic
187C3×#107C2×D311yescharacteristic
188C3×#106—31no—
189C3×#106—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#97—31no—
195#832—31no—
196#821—31no—
197#821—31no—
198#821—31no—
199#821—61no—
200#821C2×D311yescharacteristic
201#817—31no—
202#817—31no—
203#817C2×D311yescharacteristic
204#815—31no—
205#815C2×D311yescharacteristic
206Dic3⋊C8—31no—
207Dic3⋊C8—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—61no—
210Dic3⋊C8C2×D311yescharacteristic
211C8×Dic3—31no—
212C8×Dic3—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#809C2×D311yescharacteristic
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808C2×D311yescharacteristic
224#808C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230#803—31no—
231C22×C3⋊D3—21no—
232C22×C3×D3—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)C2×Q812yescomplemented
241C4×C3⋊D3—42no—
242#634—42no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12C2×Q812yes—
252C3×C4×D3—42no—
253C3×Dic6—42no—
254#627—22no—
255#627—42no—
256#627—81no—
257#624—81no—
258#624—81no—
259D3×Dic3—42no—
260D3×Dic3—42no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yescomplemented
265#554—91no—
266D4×Q8—91no—
267#501—31no—
268#501—91no—
269#498—91no—
270#478—31no—
271#478—91no—
272#476—91no—
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—31no—
282C22×C3×C4—61no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285D3×Q8—124no—
286C2×D12—31no—
287C2×D12—31no—
288C2×D12—61no—
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—21no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—121no—
300C2×Dic6—21no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—121no—
310C2×Dic6—124no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C22⋊C4—61no—
331C3×C42—31no—
332C3×C42—31no—
333#217—61no—
334#217—61no—
335#213—34no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
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—21no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
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×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380D24—34no—
381C22×C32C22×D411yescharacteristic
382C2×C3⋊D3—22no—
383C2×C3⋊D3—41no—
384C2×C3⋊D3—41no—
385C2×C3×D3—22no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4C22×Q811yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—21no—
393C3⋊Dic3—41no—
394C3⋊Dic3AGL(1,ℤ/8)12yes—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C22×Q8—181no—
403C2×D8—91no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408#125—31no—
409#125—31no—
410C22⋊Q8—181no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C22⋊Q8—181no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—91no—
417C4×D4—31no—
418C4×D4—91no—
419C4×D4—91no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—91no—
423C2×C4⋊C4—181no—
424#107—31no—
425#107—91no—
426#107D3211yescharacteristic
427#106—31no—
428#106—31no—
429#106—31no—
430#106—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#102—31no—
437#102—31no—
438#102—91no—
439#102—91no—
440#102—91no—
441#102—91no—
442#97—31no—
443#97—91no—
444C4×C8—91no—
445C23×C3—61no—
446C22×D3—21no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—121no—
450C3×Q8—122no—
451C3×D4—32no—
452C3×D4—61no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—122no—
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—121no—
482C2×Dic3—122no—
483C2×Dic3—122no—
484C2×Dic3D3×D411yescharacteristic
485C2×Dic3D3×D411yescharacteristic
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488D12—21no—
489D12—32no—
490D12—32no—
491D12—62no—
492D12—61no—
493D12—61no—
494D12—121no—
495D12D3×Q812yes—
496C4×D3—42no—
497C4×D3—122no—
498C4×D3—122no—
499C4×D3—122no—
500C4×D3—122no—
501C4×D3—242no—
502C4×D3—241no—
503C4×D3—241no—
504C4×D3—241no—
505C4×D3—241no—
506Dic6—42no—
507Dic6—62no—
508Dic6—62no—
509Dic6—122no—
510Dic6—122no—
511Dic6—122no—
512Dic6—122no—
513Dic6—242no—
514Dic6—241no—
515Dic6—241no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—32no—
519C3×C8—41no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C3⋊C8D3×Q812yescomplemented
526C2×C32D4×Q811yescharacteristic
527C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
528C2×C32#57711yescharacteristic
529C3⋊D3—42no—
530C3×D3—42no—
531C2×Q8—61no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×Q8—181no—
535C2×Q8—181no—
536C2×Q8—364no—
537C2×D4—31no—
538C2×D4—91no—
539C22×C4—61no—
540C22×C4—181no—
541C22×C4—181no—
542C22×C4—181no—
543C22×C4—181no—
544C22×C4—181no—
545D8—94no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C42—31no—
574C42—31no—
575C42—91no—
576C22×C3—21no—
577C22×C3—62no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3C2×D3×D411yescharacteristic
581C22×C3C2×D3×D411yescharacteristic
582C2×D3—22no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—122no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—241no—
593C2×D3—241no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×D3×Q811yescharacteristic
610C3×C4C2×D3×Q811yescharacteristic
611C3×C4#100711yescharacteristic
612C3×C4#101011yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—21no—
617Dic3—32no—
618Dic3—32no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—62no—
623Dic3—61no—
624Dic3—61no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629C32#338411yescharacteristic, complemented, Sylow
630C23—61no—
631C23—181no—
632Q8—122no—
633Q8—182no—
634Q8—362no—
635Q8—362no—
636Q8—721no—
637D4—32no—
638D4—61no—
639D4—92no—
640D4—181no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—122no—
653C2×C4—181no—
654C2×C4—362no—
655C2×C4—362no—
656C2×C4—362no—
657C2×C4—721no—
658C2×C4—721no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—32no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—122no—
668C2×C3#563211yescharacteristic
669C2×C3#572711yescharacteristic
670C2×C3#577011yescharacteristic
671C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
672C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
673C2×C3#577811yescharacteristic
674D3—42no—
675D3—122no—
676D3—122no—
677D3—242no—
678C22—62no—
679C22—121no—
680C22—121no—
681C22—182no—
682C22—361no—
683C22—361no—
684C22D32×D411yescharacteristic
685C4—41no—
686C4—41no—
687C4—61no—
688C4—61no—
689C4—61no—
690C4—61no—
691C4—92no—
692C4—121no—
693C4—121no—
694C4—121no—
695C4—181no—
696C4—361no—
697C4#6429711yescharacteristic
698C4D32×Q811yescharacteristic
699C3—21no—
700C3#8115811yescharacteristic, complemented
701C3#8196411yescharacteristic, complemented
702C2—122no—
703C2—362no—
704C2#1059437811yescharacteristic
705C2#1059472611yescharacteristic
706C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenter#107D32
hypocenterC32#3384
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
1. #10594484C2semidirect
2. #10594376C2semidirect
3. #10592589C2semidirect
4. C3×#4891C2semidirect
5. C3×#4876C2semidirect
6. #10590789C2semidirect
7. #10590776C2semidirect
8. #10590759C2semidirect
11. #10590467C2semidirect
12. #10590466C2semidirect
14. #10590418C2semidirect
15. #10590416C2semidirect
71. #4891D3semidirect
76. #4876D3semidirect
136. #3714Q8semidirect
240. C4⋊(C3⋊D3)C2×Q8semidirect
264. C3×C3⋊C8C2×Q8semidirect
525. C3⋊C8D3×Q8semidirect
629. C32#3384semidirect
700. C3#81158semidirect
701. C3#81964semidirect

Maximal subgroups

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

subgroupindex
#105944842
#105943762
#105925892
C3×#48912
C3×#48762
#105907892
#105907762
#105907592
#105907462
#105905892
#105904672
#105904662
#105904592
#105904182
#105904162
#819643
#811583