Finite Group Databasebeta

← #11895261

Subgroups — #11895261

Order 1152.

767 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590811C212yesmaximal, complemented
8#10590792C212yesmaximal, complemented
9#10590770C212yesmaximal
10#10590379C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81621—31nomaximal
13#79926—31nomaximal
14C2×#3745C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63900—21no—
21#63894C2212yes—
22#63888—22no—
23#63871—21no—
24#63871—21no—
25#63869C2212yes—
26#63864C2212yes—
27#63849—21no—
28#63848—22no—
29Dic3×Dic6C2212yes—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63648C2211yescharacteristic
34#63645C2211yescharacteristic
35C3×#816C2212yes—
36C3×#816C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#5732—31no—
44#5730—31no—
45#5584—31no—
46#5579—31no—
47C3×#487—31no—
48C3×C8×Q8—31no—
49#5084—31no—
50#5083—31no—
51#4844—32no—
52#4842—31no—
53#4841—31no—
54#4829—32no—
55#4819—32no—
56#4800—32no—
57#4796—32no—
58#4788—32no—
59#4697—32no—
60C4×D24—31no—
61C4×D24—31no—
62C4×D24—61no—
63C4×#204—32no—
64#4681D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#624—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3752—21no—
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3745—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96Dic32—22no—
97#3717—24no—
98#3360—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—31no—
102#947—32no—
103#946—61no—
104#946—61no—
105#946—62no—
106Q8×Dic3—32no—
107C2×#215—32no—
108C2×D24—31no—
109C2×D24—31no—
110C2×D24—61no—
111C2×#204—32no—
112#898—62no—
113#898—62no—
114#897—61no—
115#897—61no—
116#896—62no—
117#893—32no—
118#892—61no—
119#892—61no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—61no—
122#890—32no—
123#875—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—31no—
127C4×D12—31no—
128C4×D12—32no—
129C4×D12—61no—
130C4×D12—61no—
131#870—32no—
132#869C2×D311yescharacteristic
133#869C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#103—32no—
139C3×#103—32no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—31no—
146#821—31no—
147#821—31no—
148#821—31no—
149#821—32no—
150#821—61no—
151#821—61no—
152#818—31no—
153#818—31no—
154#818—61no—
155#817—32no—
156#816—32no—
157#816C2×D312yes—
158#816C2×D312yes—
159Dic3⋊C8C2×D312yes—
160C8×Dic3C2×D312yes—
161#809—32no—
162#808—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)#4112yes—
175C4×C3⋊D3—42no—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—81no—
185#624—82no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#556—91no—
190#554—91no—
191#488—92no—
192#487—31no—
193#479—92no—
194#476—91no—
195#463—92no—
196#461—91no—
197C8×Q8—31no—
198C4×SD16—92no—
199C4×D8—91no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—121no—
216C2×C4×D3—121no—
217C2×Dic6—21no—
218C2×Dic6D1211yescharacteristic
219C2×Dic6C22×D312yes—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C42—21no—
234C3×C42—32no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#215—64no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—61no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—61no—
244(C2×D3)⋊C4—61no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—121no—
249(C2×D3)⋊C4—121no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3D1211yescharacteristic
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4D1212yes—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8C22×D312yes—
272D24—62no—
273D24—62no—
274D24—64no—
275#204—64no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4#13512yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×SD16—92no—
294C2×D8—91no—
295C4⋊Q8—31no—
296C4⋊Q8—31no—
297#126—182no—
298#125—92no—
299#124—92no—
300C22⋊Q8—182no—
301C22⋊Q8—181no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—92no—
305C4×D4—92no—
306C4×D4—91no—
307C4×D4—91no—
308#117—181no—
309C2×C4⋊C4—181no—
310#107—91no—
311#106—92no—
312C4⋊C8—32no—
313C4⋊C8—31no—
314#103—32no—
315#103—32no—
316#103—92no—
317#102—92no—
318#102—91no—
319#102—91no—
320C4×C8—32no—
321C4×C8D3211yescharacteristic
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—121no—
327C22×D3—121no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—241no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3C2×D1212yes—
354C2×Dic3C2×D1212yes—
355D12—32no—
356D12—32no—
357D12—62no—
358D12—62no—
359D12—61no—
360D12—61no—
361D12—61no—
362D12—61no—
363D12—61no—
364D12—61no—
365D12—121no—
366D12—121no—
367C4×D3—122no—
368C4×D3—122no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—242no—
372C4×D3—242no—
373C4×D3—242no—
374C4×D3—242no—
375Dic6—22no—
376Dic6—22no—
377Dic6—22no—
378Dic6—81no—
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—41no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32#57711yescharacteristic
390C3⋊D3—42no—
391C3⋊D3—81no—
392C2×Q8—31no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×D4—91no—
396C2×D4—91no—
397C22×C4—182no—
398C22×C4—181no—
399C22×C4—181no—
400SD16—184no—
401D8—182no—
402C2×C8—32no—
403C2×C8C2×D3211yescharacteristic
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—32no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C42—32no—
422C42—182no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3C22×D1211yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—122no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—122no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—241no—
444C2×D3—241no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—62no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4#90412yes—
456C3×C4#91912yes—
457C3×C4#100711yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4#101011yescharacteristic
461Dic3—22no—
462Dic3—22no—
463Dic3—42no—
464Dic3—42no—
465Dic3—121no—
466Dic3—121no—
467Dic3—121no—
468Dic3—121no—
469Dic3—241no—
470Dic3—241no—
471C32#336011yescharacteristic, complemented, Sylow
472C23—181no—
473C23—181no—
474Q8—62no—
475Q8—62no—
476Q8—62no—
477Q8—241no—
478D4—92no—
479D4—181no—
480D4—181no—
481D4—181no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—722no—
491C2×C4D3×D1211yescharacteristic
492C2×C4D3×D1211yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—21no—
495C8—21no—
496C8—62no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3#557611yescharacteristic
501C2×C3#567711yescharacteristic
502C2×C3C2×#90411yescharacteristic
503C2×C3#575111yescharacteristic
504C2×C3#576211yescharacteristic
505C2×C3C2×#91911yescharacteristic
506D3—122no—
507D3—122no—
508D3—242no—
509D3—242no—
510D3—241no—
511D3—241no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22C2×D3×D1211yescharacteristic
519C4—21no—
520C4—62no—
521C4—62no—
522C4—122no—
523C4—122no—
524C4—361no—
525C4—361no—
526C4#6380812yes—
527C4#6429711yescharacteristic
528C4#6430611yescharacteristic
529C3—21no—
530C3#7992611yescharacteristic, complemented
531C3#8162111yescharacteristic, complemented
532C2—362no—
533C2—721no—
534C2#1059390111yescharacteristic
535C2#1059467711yescharacteristic
536C2C2×#6380811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×C8D32
hypocenterC32#3360
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
1. #10593958C2semidirect
2. #10593865C2semidirect
4. C3×#4681C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590872C2semidirect
7. #10590811C2semidirect
8. #10590792C2semidirect
10. #10590379C2semidirect
11. #10590300C2semidirect
64. #4681D3semidirect
65. C8×Dic6D3semidirect
471. C32#3360semidirect
530. C3#79926semidirect
531. C3#81621semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105938652
C4×#37452
C3×#46812
C3×C8×Dic62
#105908722
#105908112
#105907922
#105907702
#105903792
#105903002
#816213
#799263