Finite Group Databasebeta

← #11897652

Subgroups — #11897652

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596010C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×#5018C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic
5#10591495C211yesmaximal, characteristic
6#10591494C211yesmaximal, characteristic
7#10591446C211yesmaximal, characteristic
8#10591445C211yesmaximal, characteristic
9#10590563C211yesmaximal, characteristic, complemented
10#10590496C211yesmaximal, characteristic, complemented
11#10590494C211yesmaximal, characteristic, complemented
12#10590415C211yesmaximal, characteristic, complemented
13#10590305C211yesmaximal, characteristic, complemented
14#10590302C211yesmaximal, characteristic, complemented
15#10590255C211yesmaximal, characteristic, complemented
16#80960—31nomaximal
17#79759—31nomaximal
18C32×C4×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64133—21no—
22C2×#3750—21no—
23#64099C2211yescharacteristic
24#64097C2211yescharacteristic
25#64087—21no—
26#64087—21no—
27#64079C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63919C2211yescharacteristic
33#63919C2211yescharacteristic
34#63918—21no—
35#63844—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63839—21no—
39#63839—21no—
40C3×#832C2211yescharacteristic
41C3×#832C2211yescharacteristic
42C3×#832C2211yescharacteristic
43C3×#810C2211yescharacteristic
44C3×#807C2211yescharacteristic
45C3×#807C2211yescharacteristic
46C3×#807C2211yescharacteristic
47C3×C4⋊(C3⋊C8)C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63572C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5722—31no—
62Q8×Dic6—31no—
63#5539—31no—
64#5539—31no—
65#5539—61no—
66C3×#474—31no—
67C3×#440—31no—
68#5164—31no—
69Dic3×SD16—31no—
70#5081—31no—
71#5022—31no—
72#5018D311yescharacteristic
73#5007D311yescharacteristic
74#4877—31no—
75#4876—31no—
76#4876—31no—
77#4875—31no—
78#4874—31no—
79#4874—31no—
80#4829—31no—
81#4828—31no—
82#4799—31no—
83#4793—31no—
84#4761—31no—
85#4761—31no—
86#4759—31no—
87#4759—31no—
88#4758—31no—
89#4757—31no—
90#4702—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C22×C3⋊Dic3—21no—
95C22×C3⋊Dic3—21no—
96C2×#634—21no—
97C2×#634D411yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104C32×C42C2311yescharacteristic
105#3757—21no—
106#3757—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)D411yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750D411yescharacteristic
116#3750D411yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#214Q814yescomplemented
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3385—91noSylow
137C2×C3×SD16—31no—
138C3×C4⋊Q8—31no—
139C3×C4×Q8—31no—
140C3×C4×D4—21no—
141C3×C4×D4C2×D311yescharacteristic
142C3×C4×D4C2×D311yescharacteristic
143Q8×Dic3—31no—
144Q8×Dic3—31no—
145#944—61no—
146#944—61no—
147D4×Dic3—31no—
148D4×Dic3—31no—
149D4×Dic3—31no—
150D4×Dic3—31no—
151D4×Dic3—61no—
152D4×Dic3—61no—
153C2×#214C2×D311yescharacteristic
154#924—61no—
155#924—61no—
156#924—62no—
157C2×Dic3⋊C4—61no—
158C2×Dic3⋊C4—61no—
159C2×Dic3⋊C4—62no—
160#890—31no—
161#890—31no—
162#890—61no—
163#888—31no—
164#888—31no—
165#888—31no—
166#888—31no—
167#888—31no—
168#888—31no—
169#888—61no—
170#888—61no—
171#888—61no—
172#888—61no—
173#887—31no—
174#887—31no—
175#887—61no—
176#878—61no—
177#878—61no—
178#878—61no—
179#878—61no—
180#878—62no—
181#878—62no—
182#870—31no—
183#870—31no—
184#870—61no—
185#869—61no—
186#869C2×D311yescharacteristic
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C4×Dic6C2×D311yescharacteristic
192C3×#107—31no—
193C3×#107—31no—
194C3×#107—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#97—31no—
201#835—31no—
202#835—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#818—31no—
207#818—31no—
208#818—31no—
209#817—31no—
210#817—31no—
211#817—31no—
212#816—31no—
213#816—31no—
214#815—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231#807C2×D311yescharacteristic
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803C2×D311yescharacteristic
234C23×C32—21no—
235C32×D4—21no—
236C32×D4C2×Q812yes—
237C2×C32×C4—21no—
238C2×C32×C4—81no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—42no—
245C2×C3⋊Dic3—81no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250#634—22no—
251#634—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
258C3×Dic6C2×Q812yes—
259#627—81no—
260#627—81no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yes—
265Q82—91no—
266#554—91no—
267#501—91no—
268#501—91no—
269#500—91no—
270#479—91no—
271#479—91no—
272#477—91no—
273#476—91no—
274#474—31no—
275#474—91no—
276#446—91no—
277#440—31no—
278#440—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—21no—
283C2×C3×D4C22×D311yescharacteristic
284C2×C3×D4C22×D311yescharacteristic
285C22×C3×C4—22no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—62no—
293C22×Dic3—62no—
294C2×Dic6—21no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—62no—
305C2×Dic6C22×D311yescharacteristic
306C3×SD16—34no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C22⋊C4—22no—
320C3×C22⋊C4—21no—
321C3×C22⋊C4—21no—
322C3×C42—21no—
323C3×C42—61no—
324C3×C42C22×D311yescharacteristic
325C3×C42C22×D311yescharacteristic
326#217—61no—
327#217—61no—
328#217—61no—
329#217—61no—
330#217—62no—
331#217—62no—
332#214Dic614yescomplemented
333C4⋊Dic3—21no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—62no—
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376C4×Dic3—21no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C22×C32—22no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32C22×D411yescharacteristic
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—41no—
398C32×C4C22×Q811yescharacteristic
399C32×C42−1+411yescharacteristic
400C3⋊Dic3—21no—
401C3⋊Dic3—21no—
402C3⋊Dic3—21no—
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
405C3⋊Dic3#13712yes—
406C3×Dic3—22no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C2×SD16—31no—
411C4⋊Q8—31no—
412C4⋊Q8—91no—
413C4⋊Q8—91no—
414C4⋊Q8—91no—
415C4⋊Q8—181no—
416C4⋊Q8—181no—
417C4⋊Q8—181no—
418#125—91no—
419#125—91no—
420C22⋊Q8—181no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—181no—
428C4×D4—91no—
429C4×D4—91no—
430C4×D4D3211yescharacteristic
431C2×C4⋊C4—181no—
432#107—31no—
433#107—31no—
434#107—31no—
435#107—91no—
436#107—91no—
437#107—91no—
438#106—91no—
439#106—91no—
440#106—91no—
441C4⋊C8—31no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444#103—31no—
445#103—91no—
446#103—91no—
447#102—31no—
448#102—31no—
449#102—31no—
450#97—31no—
451#97—91no—
452C4×C8—91no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C3×Q8—32no—
457C3×Q8—61no—
458C3×Q8—241no—
459C3×D4—22no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—22no—
463C3×D4C2×Dic612yes—
464C3×D4D3×Q812yes—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—81no—
476C2×C3×C4—81no—
477C2×C3×C4—82no—
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4D3×D411yescharacteristic
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—122no—
507C2×Dic3—122no—
508C2×Dic3—124no—
509C2×Dic3—241no—
510C2×Dic3—241no—
511C2×Dic3—242no—
512Dic6—21no—
513Dic6—62no—
514Dic6—62no—
515Dic6—81no—
516Dic6—122no—
517Dic6—241no—
518Dic6—241no—
519Dic6—241no—
520Dic6—241no—
521Dic6—241no—
522Dic6—241no—
523Dic6—242no—
524Dic6C2×Dic612yes—
525C3×C8—32no—
526C3×C8—61no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C3⋊C8—21no—
532C3⋊C8C2×Dic612yes—
533C2×C32—42no—
534C2×C32D4×Q811yescharacteristic
535C2×C32C2×#13711yescharacteristic
536C2×C32#57611yescharacteristic
537C2×Q8—31no—
538C2×Q8—61no—
539C2×Q8—91no—
540C2×Q8—181no—
541C2×Q8—181no—
542C2×Q8—181no—
543C2×D4C2×D3211yescharacteristic
544C22×C4—21no—
545C22×C4—181no—
546C22×C4—181no—
547SD16—34no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4C2×D3211yescharacteristic
572C22⋊C4—21no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C42—61no—
576C42—91no—
577C42—91no—
578C42—181no—
579C42—181no—
580C42C2×D3211yescharacteristic
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3C2×D3×D411yescharacteristic
592C22×C3C2×D3×D411yescharacteristic
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—62no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C22×Dic611yescharacteristic
609C3×C4C2×D3×Q811yescharacteristic
610C3×C4#101011yescharacteristic
611C3×C4#101011yescharacteristic
612Dic3—22no—
613Dic3—32no—
614Dic3—32no—
615Dic3—41no—
616Dic3—41no—
617Dic3—41no—
618Dic3—62no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—61no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—122no—
629Dic3—122no—
630Dic3—121no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634C32#338511yescharacteristic, complemented, Sylow
635C23—21no—
636Q8—32no—
637Q8—61no—
638Q8—182no—
639Q8—241no—
640Q8—721no—
641Q8—721no—
642Q8—721no—
643D4—21no—
644D4D3×Dic612yes—
645C2×C4—21no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—81no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—362no—
658C2×C4—721no—
659C2×C4#381111yescharacteristic
660C2×C4#381111yescharacteristic
661C2×C4C22×D3211yescharacteristic
662C8—32no—
663C8—61no—
664C8—61no—
665C8—61no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—44no—
670C2×C3—42no—
671C2×C3—42no—
672C2×C3D4×Dic611yescharacteristic
673C2×C3#563211yescharacteristic
674C2×C3#575711yescharacteristic
675C2×C3#577411yescharacteristic
676C2×C3D3×#13711yescharacteristic
677C2×C3D3×#13711yescharacteristic
678C22—22no—
679C22—41no—
680C22—41no—
681C22C2×#381111yescharacteristic
682C4—21no—
683C4—21no—
684C4—41no—
685C4—62no—
686C4—92no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—181no—
691C4—181no—
692C4—181no—
693C4—361no—
694C4—361no—
695C4C2×D3×Dic611yescharacteristic
696C4#6429811yescharacteristic
697C3—21no—
698C3#7975911yescharacteristic, complemented
699C3#8096011yescharacteristic, complemented
700C2—42no—
701C2#1059491511yescharacteristic
702C2#1059510211yescharacteristic
703C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
9. #10590563C2semidirect
10. #10590496C2semidirect
11. #10590494C2semidirect
12. #10590415C2semidirect
13. #10590305C2semidirect
14. #10590302C2semidirect
15. #10590255C2semidirect
119. C3×#214Q8semidirect
332. #214Dic6semidirect
634. C32#3385semidirect
698. C3#79759semidirect
699. C3#80960semidirect

Maximal subgroups

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

subgroupindex
#105960102
#105938562
C3×#50182
C3×#50072
#105914952
#105914942
#105914462
#105914452
#105905632
#105904962
#105904942
#105904152
#105903052
#105903022
#105902552
#809603
#797593