Finite Group Databasebeta

← #11803911

Subgroups — #11803911

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10593837C212yesmaximal, complemented
3#10593812C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic
5#10593759C212yesmaximal, complemented
6#10593758C212yesmaximal, complemented
7#10593758C212yesmaximal, complemented
8#10593746C212yesmaximal
9C22⋊C4×#157C212yesmaximal
10C23×#157C2211yescharacteristic
11C23×#157C2211yescharacteristic
12C2×Q8×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C22⋊#157C2212yes—
15C2×C4⋊#157C2211yescharacteristic
16C2×C4⋊#157C2211yescharacteristic
17C2×C4⋊#157C2212yes—
18C2×C4⋊#157C2212yes—
19C2×C4×#157C2212yes—
20C2×C4×#157C2212yes—
21C32×C22⋊Q8C411yescharacteristic, complemented
22#64155C411yescharacteristic, complemented
23#64133C411yescharacteristic, complemented
24#64106C411yescharacteristic, complemented
25#64105C412yescomplemented
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2212yes—
28C22⋊C4×C3⋊D3C2212yes—
29#64087C412yescomplemented
30#63781C2212yes—
31#63781C2212yes—
32#63781C2212yes—
33#63781C2212yes—
34#63781C2212yes—
35#63781C2212yes—
36#63781C2212yes—
37D3×C22⋊Q8—62no—
38C23×C3⋊D3C2311yescharacteristic
39C22×#157—22no—
40C22×#157—41no—
41C22×#157—41no—
42C22×#157—41no—
43C22×#157—41no—
44C22×#157Q814yescomplemented
45C22×#157C2312yes—
46C22×#157C2312yes—
47C22×#157C2312yes—
48C22×#157C2312yes—
49C2×C32×Q8C2×C411yescharacteristic, complemented
50C22×C32×C4C2×C411yescharacteristic
51C22×C3⋊Dic3C2×C411yescharacteristic
52Q8×C3⋊D3—41no—
53Q8×C3⋊D3—41no—
54C2×C4×C3⋊D3—41no—
55C2×C4×C3⋊D3—41no—
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2312yes—
59C2×C4×C3⋊D3C2312yes—
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634C2×C412yescomplemented
63C2×#634C2×C411yescharacteristic, complemented
64C22⋊#157—24no—
65C4⋊#157—42no—
66C4⋊#157—41no—
67C4⋊#157—41no—
68C4⋊#157—42no—
69C4×#157—42no—
70C4×#157—42no—
71C32×C4⋊C4C2×C412yescomplemented
72C32×C4⋊C4C2×C411yescharacteristic, complemented
73C32×C22⋊C4C2×C412yes—
74#3757C2×C412yes—
75#3752C2×C412yes—
76#3752C2×C412yes—
77C4⋊(C3⋊Dic3)C2×C412yescomplemented
78C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
79#3750C2×C412yescomplemented
80#3750C2×C412yescomplemented
81#3750C2×C412yescomplemented
82#2329—91nomaximal, Sylow
83C2×D3×Q8—62no—
84C22×C4×D3—62no—
85C3×C22⋊Q8—22no—
86#946—62no—
87#924—62no—
88#897—62no—
89#896—64no—
90D3×C4⋊C4—62no—
91D3×C4⋊C4—64no—
92D3×C22⋊C4—64no—
93#878—64no—
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3C22×C411yescharacteristic
100C22×C3⋊D3C2×Q812yes—
101C22×C3⋊D3#4112yes—
102C22×C3⋊D3C2411yescharacteristic
103C2×#157—22no—
104C2×#157—22no—
105C2×#157—22no—
106C2×#157—22no—
107C2×#157—22no—
108C2×#157—22no—
109C2×#157—22no—
110C2×#157—22no—
111C2×#157—22no—
112C2×#157—22no—
113C2×#157—22no—
114C2×#157—44no—
115C2×#157—44no—
116C2×#157C2×Q814yes—
117C32×Q8—41no—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C412yes—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C411yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3⋊Dic3C22×C411yescharacteristic
126C2×C3⋊Dic3C22×C411yescharacteristic
127C2×C3⋊Dic3C22×C412yes—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—21no—
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—21no—
133C4×C3⋊D3—21no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—41no—
137C4×C3⋊D3—41no—
138#634—42no—
139#634—41no—
140C2×C22⋊Q8—91no—
141#391—92no—
142#389—92no—
143#387—92no—
144#387—92no—
145#385—92no—
146#380—91no—
147C4×C22⋊C4—92no—
148C2×#95—91no—
149C23×D3—62no—
150C2×C3×Q8—22no—
151C22×C3×C4—22no—
152C22×Dic3—62no—
153D3×Q8—124no—
154D3×Q8—124no—
155C2×C4×D3—62no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C2×Dic6—64no—
164C2×Dic6—62no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—22no—
167C3×C22⋊C4—24no—
168#217—64no—
169(C2×D3)⋊C4—64no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—64no—
172C4⋊Dic3—62no—
173Dic3⋊C4—64no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32C4×Q812yes—
179C22×C32C23×C411yescharacteristic
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—22no—
186C2×C3⋊D3C4×Q812yes—
187C2×C3⋊D3C22×Q811yescharacteristic
188C2×C3⋊D3C2×#4111yescharacteristic
189C2×C3⋊D3H(5,𝔽2)11yescharacteristic
190C2×C3⋊D3H(5,𝔽2)11yescharacteristic
191C2×C3⋊D3H(5,𝔽2)11yescharacteristic
192C2×C3⋊D32−1+411yescharacteristic
193#157—24no—
194#157—42no—
195#157—42no—
196#157—42no—
197C32×C4—21no—
198C32×C4—22no—
199C32×C4—21no—
200C32×C4—22no—
201C3⋊Dic3—21no—
202C3⋊Dic3—22no—
203C3⋊Dic3—21no—
204C3⋊Dic3—22no—
205C22×Q8—91no—
206C23×C4—91no—
207C23×C4—91no—
208C23×C4—91no—
209C22⋊Q8—91no—
210C22⋊Q8—91no—
211C22⋊Q8—92no—
212C22⋊Q8—91no—
213C22⋊Q8—92no—
214C22⋊Q8#15711yescharacteristic, complemented
215C2×C4⋊C4—91no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—92no—
221C2×C22⋊C4—92no—
222C2×C22⋊C4—92no—
223C2×C42—92no—
224C2×C42—92no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95—92no—
229#95—92no—
230#95—92no—
231#95—92no—
232C23×C3—22no—
233C22×D3—62no—
234C22×D3—62no—
235C22×D3—64no—
236C22×D3—64no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—122no—
241C3×Q8—44no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—44no—
247C2×Dic3—62no—
248C2×Dic3—64no—
249C2×Dic3—62no—
250C2×Dic3—64no—
251C2×Dic3—124no—
252C4×D3—64no—
253C4×D3—64no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—122no—
257C4×D3—122no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—124no—
262Dic6—128no—
263Dic6—124no—
264C2×C32—22no—
265C2×C32C2×C4×Q811yescharacteristic
266C2×C32#51811yescharacteristic
267C2×C32#52011yescharacteristic
268C3⋊D3—22no—
269C3⋊D3#53811yescharacteristic
270C3⋊D3#53911yescharacteristic
271C3⋊D3#54311yescharacteristic
272C3⋊D3#54411yescharacteristic
273C24—91no—
274C2×Q8—91no—
275C2×Q8—92no—
276C2×Q8—361no—
277C2×Q8—361no—
278C2×Q8C2×#15711yescharacteristic, complemented
279C22×C4—92no—
280C22×C4—94no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4—92no—
284C22×C4—92no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—92no—
289C22×C4—92no—
290C22×C4—92no—
291C22×C4—182no—
292C22×C4—361no—
293C22×C4—361no—
294C22×C4—361no—
295C22×C4—361no—
296C22×C4—361no—
297C22×C4—361no—
298C22×C4C2×#15711yescharacteristic
299C4⋊C4—92no—
300C4⋊C4—92no—
301C4⋊C4—92no—
302C4⋊C4—91no—
303C4⋊C4—92no—
304C4⋊C4—362no—
305C4⋊C4—361no—
306C4⋊C4—361no—
307C4⋊C4—362no—
308C4⋊C4C2×#15711yescharacteristic, complemented
309C4⋊C4C2×#15712yescomplemented
310C22⋊C4—92no—
311C22⋊C4—92no—
312C22⋊C4—92no—
313C22⋊C4—184no—
314C22⋊C4C2×#15712yes—
315C42—362no—
316C42—362no—
317C22×C3—24no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—64no—
328C2×D3—124no—
329C2×D3—124no—
330C2×D3—124no—
331C2×D3—124no—
332C2×D3—122no—
333C2×D3—122no—
334C3×C4—24no—
335C3×C4—44no—
336C3×C4—42no—
337C3×C4—44no—
338Dic3—64no—
339Dic3—124no—
340Dic3—122no—
341Dic3—124no—
342C32#232911yescharacteristic, complemented, Sylow
343C23—91no—
344C23—92no—
345C23—92no—
346C23—91no—
347C23—181no—
348C23—181no—
349C23—181no—
350C23—181no—
351C23C22×#15711yescharacteristic
352Q8—41no—
353Q8—361no—
354Q8—362no—
355C2×C4—41no—
356C2×C4—94no—
357C2×C4—92no—
358C2×C4—92no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—361no—
381C2×C4—361no—
382C2×C4—361no—
383C2×C4—364no—
384C2×C4—364no—
385C2×C4C22×#15712yes—
386C2×C4C22×#15712yes—
387C2×C4C22×#15711yescharacteristic
388C2×C4C22×#15711yescharacteristic
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—22no—
392C2×C3—44no—
393D3—62no—
394D3—62no—
395D3—62no—
396D3—62no—
397D3—124no—
398C22—21no—
399C22—21no—
400C22—91no—
401C22—91no—
402C22—91no—
403C22—91no—
404C22—91no—
405C22—91no—
406C22—92no—
407C22—182no—
408C22—182no—
409C22—182no—
410C22—182no—
411C22—181no—
412C22—181no—
413C22Q8×#15712yes—
414C22C23×#15711yescharacteristic
415C4—21no—
416C4—21no—
417C4—22no—
418C4—22no—
419C4—184no—
420C4—181no—
421C4—181no—
422C4—182no—
423C4—182no—
424C4—362no—
425C4—362no—
426C4—362no—
427C3—22no—
428C2—22no—
429C2—91no—
430C2—91no—
431C2—91no—
432C2—91no—
433C2—182no—
434C2#1059664211yescharacteristic
435C2C2×Q8×#15711yescharacteristic
436C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C22⋊Q8C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC22⋊Q8#157
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593837C2semidirect
5. #10593759C2semidirect
6. #10593758C2semidirect
7. #10593758C2semidirect
21. C32×C22⋊Q8C4semidirect
22. #64155C4semidirect
23. #64133C4semidirect
24. #64106C4semidirect
25. #64105C4semidirect
29. #64087C4semidirect
44. C22×#157Q8semidirect
49. C2×C32×Q8C2×C4semidirect
62. C2×#634C2×C4semidirect
63. C2×#634C2×C4semidirect
71. C32×C4⋊C4C2×C4semidirect
72. C32×C4⋊C4C2×C4semidirect
77. C4⋊(C3⋊Dic3)C2×C4semidirect
78. C4⋊(C3⋊Dic3)C2×C4semidirect
79. #3750C2×C4semidirect
80. #3750C2×C4semidirect
81. #3750C2×C4semidirect
214. C22⋊Q8#157semidirect
278. C2×Q8C2×#157semidirect
308. C4⋊C4C2×#157semidirect
309. C4⋊C4C2×#157semidirect
342. C32#2329semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105938372
#105938122
C2×#637812
#105937592
#105937582
#105937462
C22⋊C4×#1572
#23299