Finite Group Databasebeta

← #11896047

Subgroups — #11896047

Order 1152.

724 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#10593932C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4845C211yesmaximal, characteristic
5C3×#4828C211yesmaximal, characteristic, complemented
6#10590895C211yesmaximal, characteristic
7#10590890C211yesmaximal, characteristic, complemented
8#10590859C211yesmaximal, characteristic
9#10590812C211yesmaximal, characteristic, complemented
10#10590803C211yesmaximal, characteristic, complemented
11#10590800C211yesmaximal, characteristic, complemented
12#10590757C211yesmaximal, characteristic
13Dic3×#204C211yesmaximal, characteristic
14#10590383C211yesmaximal, characteristic, complemented
15#10590276C211yesmaximal, characteristic
16#80582—31nomaximal
17#79981—31nomaximal
18#64078C2211yescharacteristic
19C4×#634C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×#875C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2211yescharacteristic
27#63918C2211yescharacteristic
28Dic3×D12C2211yescharacteristic
29#63887—21no—
30#63878—21no—
31#63866C2211yescharacteristic
32#63862—21no—
33#63860C2211yescharacteristic
34#63858—21no—
35Dic3×Dic6—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63840—21no—
40#63840—21no—
41C2×#3719C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43#63644C2211yescharacteristic
44#63644C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5671—31no—
62#5584—31no—
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#464—31no—
66C3×#446—31no—
67#5184—31no—
68#5182—31no—
69#5166—31no—
70Dic3×SD16—31no—
71#5055—31no—
72#5030—31no—
73#4851—31no—
74#4851—31no—
75#4851—31no—
76#4851—61no—
77#4849—31no—
78#4845—31no—
79#4845D311yescharacteristic
80#4842—31no—
81#4828D311yescharacteristic, complemented
82#4792—31no—
83#4791—31no—
84#4765—31no—
85#4761—31no—
86#4716—31no—
87#4716—31no—
88#4714—31no—
89#4714—31no—
90C4×#204—31no—
91#4681—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6D411yescharacteristic
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)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C3×(C2×D3)⋊C4—21no—
111C3×(C2×D3)⋊C4—21no—
112C3×C4⋊Dic3D411yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4D411yescharacteristic
116C3×Dic3⋊C4D411yescharacteristic
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C3×Dic12—22no—
123C3×#204—22no—
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—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#3719—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143C3×C4×Q8—31no—
144#946—61no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—61no—
149#944—31no—
150C2×#216—31no—
151#936—31no—
152D4×Dic3—31no—
153C2×Dic12—31no—
154C2×Dic12C2×D311yescharacteristic
155C2×#204C2×D311yescharacteristic
156#898—61no—
157#898—61no—
158#892—61no—
159#888—31no—
160#888—31no—
161#888—61no—
162#888—61no—
163#888—61no—
164#888—61no—
165#888—61no—
166#879—61no—
167#879—61no—
168#878—61no—
169#877—61no—
170#875—31no—
171#875C2×D311yescharacteristic
172C4×D12—31no—
173#869—31no—
174#869—31no—
175#869—31no—
176#869—31no—
177#869—31no—
178#869—61no—
179#869—61no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×C4⋊C8—21no—
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8C2×D311yescharacteristic
193C3×C4⋊C8C2×D311yescharacteristic
194C3×#103—31no—
195C3×#102—31no—
196C3×#97—31no—
197C3×#97—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#821—31no—
205#821—31no—
206#821C2×D311yescharacteristic
207#817—31no—
208#817—31no—
209#817—31no—
210#817—31no—
211#817—31no—
212#817—61no—
213#817—61no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#816—61no—
224#816C2×D311yescharacteristic
225#815C2×D311yescharacteristic
226Dic3⋊C8C2×D311yescharacteristic
227Dic3⋊C8C2×D311yescharacteristic
228C8×Dic3C2×D311yescharacteristic
229#810—31no—
230#808—31no—
231#803C2×D311yescharacteristic
232C22×C3×D3—21no—
233C2×C32×C4C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240#634—21no—
241#634—21no—
242#634—81no—
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×D12—21no—
252C3×Dic6—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
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—91no—
271#475—91no—
272#464—31no—
273#464—91no—
274#462—91no—
275#446—31no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C22×Dic3—61no—
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—61no—
286C2×Dic6—31no—
287C2×Dic6—31no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—121no—
296C2×Dic6D1211yescharacteristic
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C3×Q16—62no—
300C3×SD16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C22⋊C4—61no—
316C3×C42—21no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42C22×D311yescharacteristic
321C3×C42C22×D311yescharacteristic
322#217—61no—
323#217—61no—
324#217—61no—
325#216—62no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—121no—
350C4⋊Dic3D1211yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363Dic3⋊C4D1211yescharacteristic
364Dic3⋊C4D1211yescharacteristic
365C4×Dic3—21no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—121no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378C2×C3⋊C8C22×D311yescharacteristic
379Dic12—22no—
380Dic12—62no—
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—41no—
391C3⋊Dic3—41no—
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3×Dic3—22no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—31no—
404C4⋊Q8—91no—
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—91no—
426#106—91no—
427#106—91no—
428C4⋊C8—31no—
429C4⋊C8—31no—
430C4⋊C8D3211yescharacteristic
431#103—31no—
432#103—91no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#97—31no—
442#97—31no—
443C4×C8—31no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—32no—
447C3×Q8—62no—
448C3×Q8—61no—
449C3×Q8—61no—
450C3×Q8—61no—
451C3×D4—61no—
452C3×D4—61no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4C2×D1211yescharacteristic
464C2×C3×C4C2×D1211yescharacteristic
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4C23×D311yescharacteristic
468C2×C3×C4C23×D311yescharacteristic
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—122no—
485C2×Dic3C2×D1211yescharacteristic
486C2×Dic3C2×D1211yescharacteristic
487C2×Dic3C2×D1211yescharacteristic
488C2×Dic3C2×D1211yescharacteristic
489D12—21no—
490D12—21no—
491C4×D3—122no—
492Dic6—21no—
493Dic6—22no—
494Dic6—21no—
495Dic6—21no—
496Dic6—62no—
497Dic6—61no—
498Dic6—61no—
499Dic6—61no—
500Dic6—61no—
501Dic6—121no—
502Dic6—241no—
503Dic6—241no—
504Dic6—241no—
505Dic6—241no—
506Dic6—241no—
507Dic6—241no—
508Dic6—242no—
509Dic6#23712yes—
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—21no—
513C3×C8—21no—
514C3×C8—41no—
515C3×C8—41no—
516C3×C8—61no—
517C3×C8—61no—
518C3⋊C8—21no—
519C3⋊C8—21no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57711yescharacteristic
523C3×D3—81no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8—91no—
528C2×Q8—181no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×D4—31no—
532C22×C4—181no—
533Q16—62no—
534Q16—182no—
535SD16—62no—
536C2×C8—31no—
537C2×C8—31no—
538C2×C8C2×D3211yescharacteristic
539C2×C8C2×D3211yescharacteristic
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—181no—
549C4⋊C4—181no—
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—31no—
563C42—31no—
564C42—61no—
565C42—181no—
566C42—181no—
567C42—181no—
568C42—181no—
569C42C2×D3211yescharacteristic
570C22×C3—21no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3C22×D1211yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—22no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—62no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×#23711yescharacteristic
595C3×C4#100711yescharacteristic
596C3×C4D3×#4111yescharacteristic
597C3×C4#101011yescharacteristic
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—22no—
602Dic3—41no—
603Dic3—41no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—241no—
614Dic3—241no—
615Dic3—241no—
616Dic3#90912yes—
617C32#336911yescharacteristic, complemented, Sylow
618C23—61no—
619Q8—32no—
620Q8—62no—
621Q8—61no—
622Q8—61no—
623Q8—61no—
624Q8—181no—
625Q8—181no—
626Q8—721no—
627Q8—721no—
628Q8—721no—
629D4—61no—
630D4—61no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—362no—
643C2×C4D3×D1211yescharacteristic
644C2×C4D3×D1211yescharacteristic
645C2×C4C22×D3211yescharacteristic
646C8—21no—
647C8—21no—
648C8—61no—
649C8—61no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—241no—
654C2×C3#557611yescharacteristic
655C2×C3#559811yescharacteristic
656C2×C3C2×#90911yescharacteristic
657C2×C3#575111yescharacteristic
658C2×C3#577011yescharacteristic
659C2×C3D3×#13711yescharacteristic
660D3—81no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22C2×D3×D1211yescharacteristic
665C4—21no—
666C4—21no—
667C4—32no—
668C4—62no—
669C4—61no—
670C4—61no—
671C4—61no—
672C4—121no—
673C4—121no—
674C4—361no—
675C4—361no—
676C4—361no—
677C4—361no—
678C4D3×#23711yescharacteristic
679C4#6431511yescharacteristic
680C3—21no—
681C3#7998111yescharacteristic, complemented
682C3#8058211yescharacteristic, complemented
683C2—241no—
684C2#1059438211yescharacteristic
685C2#1059467911yescharacteristic
686C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. Dic62C2semidirect
3. #10592550C2semidirect
5. C3×#4828C2semidirect
7. #10590890C2semidirect
9. #10590812C2semidirect
10. #10590803C2semidirect
11. #10590800C2semidirect
14. #10590383C2semidirect
81. #4828D3semidirect
617. C32#3369semidirect
681. C3#79981semidirect
682. C3#80582semidirect

Maximal subgroups

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

subgroupindex
#105939322
Dic622
#105925502
C3×#48452
C3×#48282
#105908952
#105908902
#105908592
#105908122
#105908032
#105908002
#105907572
Dic3×#2042
#105903832
#105902762
#805823
#799813