Finite Group Databasebeta

← #11896046

Subgroups — #11896046

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593942C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592527C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4845C211yesmaximal, characteristic
6#10590901C211yesmaximal, characteristic, complemented
7#10590866C211yesmaximal, characteristic
8#10590819C211yesmaximal, characteristic, complemented
9#10590816C211yesmaximal, characteristic, complemented
10#10590798C211yesmaximal, characteristic, complemented
11#10590796C211yesmaximal, characteristic
12#10590776C211yesmaximal, characteristic
13#10590775C211yesmaximal, characteristic
14#10590381C211yesmaximal, characteristic, complemented
15#10590280C211yesmaximal, characteristic
16#81004—31nomaximal
17#80582—31nomaximal
18C4×#634C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#875C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2211yescharacteristic
26#63919C2211yescharacteristic
27#63918—21no—
28#63898C2211yescharacteristic
29#63896—21no—
30#63877—21no—
31#63873C2211yescharacteristic
32#63863C2211yescharacteristic
33#63861—21no—
34#63859—21no—
35#63844—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39#63839—21no—
40#63839—21no—
41C2×#3718C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43#63642C2211yescharacteristic
44#63641C2211yescharacteristic
45#63641C2211yescharacteristic
46C8×C3⋊Dic3C2211yescharacteristic
47#63630C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63574C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5722—31no—
62#5671—31no—
63#5568—31no—
64Q8×Dic6—31no—
65C3×#475—31no—
66C3×#464—31no—
67#5184—31no—
68#5182—31no—
69#5166—31no—
70Dic3×SD16—31no—
71#5089—31no—
72#5055—31no—
73#5030—31no—
74#5030—31no—
75#4870—31no—
76#4854—31no—
77#4853—31no—
78#4852—31no—
79#4851D311yescharacteristic, complemented
80#4845D311yescharacteristic
81#4828—31no—
82#4828—31no—
83#4828—61no—
84#4798—31no—
85#4795—31no—
86#4794—31no—
87#4792—31no—
88#4792—31no—
89#4791—31no—
90#4765—31no—
91#4761—31no—
92C2×#634D411yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×Dic6—21no—
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)D411yescharacteristic
105#3750D411yescharacteristic
106#3750D411yescharacteristic
107C4×C3⋊Dic3C2311yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×Dic12—22no—
123C3×#204—22no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3718—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×#124—31no—
143C3×C4×Q8—31no—
144C3×C4×Q8—31no—
145#947—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149#944—31no—
150#944—31no—
151#944—61no—
152#944—61no—
153C2×#216—31no—
154C2×#216—31no—
155#936—31no—
156D4×Dic3—31no—
157C2×Dic12C2×D311yescharacteristic
158C2×#204C2×D311yescharacteristic
159#898—61no—
160#896—61no—
161#893—31no—
162#888—31no—
163#888—31no—
164#888—31no—
165#888—31no—
166#888—61no—
167#888—61no—
168#888—61no—
169#887—31no—
170#887—31no—
171#887—31no—
172#887—61no—
173#879—61no—
174#879—61no—
175#878—61no—
176#877—61no—
177#876—61no—
178#875C2×D311yescharacteristic
179#872—61no—
180#869—61no—
181#869C2×D311yescharacteristic
182C4×Dic6—31no—
183C4×Dic6—31no—
184C4×Dic6—61no—
185C4×Dic6—61no—
186C4×Dic6C2×D311yescharacteristic
187C4×Dic6C2×D311yescharacteristic
188C3×#106—31no—
189C3×#106—31no—
190C3×C4⋊C8—21no—
191C3×C4⋊C8C2×D311yescharacteristic
192C3×C4⋊C8C2×D311yescharacteristic
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#102—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#821C2×D311yescharacteristic
204#817C2×D311yescharacteristic
205#817C2×D311yescharacteristic
206#816C2×D311yescharacteristic
207#816C2×D311yescharacteristic
208#816C2×D311yescharacteristic
209#815—31no—
210#815—31no—
211#815—61no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—61no—
217Dic3⋊C8—61no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#803—31no—
230#803—31no—
231#803—61no—
232C22×C3×D3—21no—
233C2×C32×C4C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3C2×D411yescharacteristic
237C2×C3⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240#634—22no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C3×D12—21no—
249C3×D12—21no—
250C3×Dic6—21no—
251C3×Dic6—21no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—81no—
256C3×Dic6#4112yes—
257#627—81no—
258#627—81no—
259D3×Dic3—42no—
260C32×C8—21no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264Q82—91no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—31no—
271#475—91no—
272#464—31no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×D4—31no—
284C22×Dic3—61no—
285C2×D12C22×D311yescharacteristic
286C2×C4×D3—61no—
287C2×Dic6—21no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6C22×D311yescharacteristic
296C2×Dic6C22×D311yescharacteristic
297C2×Dic6C22×D311yescharacteristic
298C3×Q16—62no—
299C3×SD16—62no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—21no—
316C3×C42—61no—
317C3×C42—61no—
318C3×C42C22×D311yescharacteristic
319C3×C42C22×D311yescharacteristic
320#217—61no—
321#217—61no—
322#217—61no—
323#216—62no—
324#216—62no—
325(C2×D3)⋊C4—21no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330C4⋊Dic3—21no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3C22×D311yescharacteristic
338C4⋊Dic3C22×D311yescharacteristic
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—31no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—31no—
347Dic3⋊C4—61no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360C4×Dic3—21no—
361C4×Dic3—21no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—61no—
380Dic12—22no—
381#204—22no—
382C22×C32C22×D411yescharacteristic
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4C2×#4111yescharacteristic
389C32×C42−1+411yescharacteristic
390C3⋊Dic3—21no—
391C3⋊Dic3—21no—
392C3⋊Dic3—21no—
393C3⋊Dic3#13712yes—
394C3×Dic3—22no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—31no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—181no—
412#126—181no—
413#124—31no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—91no—
424#117—181no—
425#106—31no—
426#106—31no—
427#106—91no—
428C4⋊C8—91no—
429C4⋊C8—91no—
430C4⋊C8D3211yescharacteristic
431#103—31no—
432#103—31no—
433#103—31no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#97—91no—
442#97—91no—
443C4×C8—91no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—32no—
447C3×Q8—61no—
448C3×Q8—61no—
449C3×Q8—61no—
450C3×Q8—61no—
451C3×Q8—61no—
452C3×Q8—241no—
453C3×D4—61no—
454C3×D4—61no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—122no—
491D12—21no—
492D12—21no—
493C4×D3—122no—
494Dic6—21no—
495Dic6—21no—
496Dic6—21no—
497Dic6—21no—
498Dic6—21no—
499Dic6—62no—
500Dic6—62no—
501Dic6—81no—
502Dic6—122no—
503Dic6—241no—
504Dic6—241no—
505Dic6—241no—
506Dic6—241no—
507Dic6#23712yes—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—41no—
513C3×C8—41no—
514C3⋊C8—62no—
515C3⋊C8—61no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—61no—
519C3⋊C8—121no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57711yescharacteristic
523C3×D3—81no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8—61no—
528C2×Q8—91no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×D4—31no—
532C22×C4—181no—
533Q16—62no—
534Q16—182no—
535SD16—62no—
536C2×C8—91no—
537C2×C8—91no—
538C2×C8C2×D3211yescharacteristic
539C2×C8C2×D3211yescharacteristic
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—91no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C22⋊C4—181no—
562C42—61no—
563C42—61no—
564C42—91no—
565C42—91no—
566C42—181no—
567C42—181no—
568C42—181no—
569C42C2×D3211yescharacteristic
570C22×C3—21no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—62no—
588C3×C4—121no—
589C3×C4—121no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×#23711yescharacteristic
595C3×C4#100711yescharacteristic
596C3×C4D3×#4111yescharacteristic
597C3×C4#101011yescharacteristic
598Dic3—22no—
599Dic3—32no—
600Dic3—32no—
601Dic3—41no—
602Dic3—41no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—41no—
607Dic3—62no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611Dic3—61no—
612Dic3—61no—
613Dic3—61no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617C32#336911yescharacteristic, complemented, Sylow
618C23—61no—
619Q8—32no—
620Q8—61no—
621Q8—61no—
622Q8—61no—
623Q8—61no—
624Q8—61no—
625Q8—182no—
626Q8—241no—
627Q8—721no—
628Q8—721no—
629D4—61no—
630D4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—91no—
639C2×C4—91no—
640C2×C4—91no—
641C2×C4—91no—
642C2×C4—362no—
643C2×C4#380211yescharacteristic
644C2×C4#380211yescharacteristic
645C2×C4C22×D3211yescharacteristic
646C8—21no—
647C8—21no—
648C8—181no—
649C8—181no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—241no—
654C2×C3#559811yescharacteristic
655C2×C3#563311yescharacteristic
656C2×C3#576211yescharacteristic
657C2×C3#577011yescharacteristic
658C2×C3D3×#13711yescharacteristic
659C2×C3D3×#13711yescharacteristic
660D3—81no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22C2×#380211yescharacteristic
665C4—21no—
666C4—21no—
667C4—62no—
668C4—92no—
669C4—121no—
670C4—121no—
671C4—121no—
672C4—121no—
673C4—121no—
674C4—121no—
675C4—181no—
676C4—181no—
677C4—181no—
678C4D3×#23711yescharacteristic
679C4#6431511yescharacteristic
680C3—21no—
681C3#8058211yescharacteristic, complemented
682C3#8100411yescharacteristic, complemented
683C2—241no—
684C2#1059452511yescharacteristic
685C2#1059468611yescharacteristic
686C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592527C2semidirect
4. C3×#4851C2semidirect
6. #10590901C2semidirect
8. #10590819C2semidirect
9. #10590816C2semidirect
10. #10590798C2semidirect
14. #10590381C2semidirect
79. #4851D3semidirect
617. C32#3369semidirect
681. C3#80582semidirect
682. C3#81004semidirect

Maximal subgroups

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

subgroupindex
#105939422
#105938562
#105925272
C3×#48512
C3×#48452
#105909012
#105908662
#105908192
#105908162
#105907982
#105907962
#105907762
#105907752
#105903812
#105902802
#810043
#805823