Finite Group Databasebeta

← #3241×C233 #44449273

Subgroups — #3241×C233 #44449273

Order 29824.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#544×C233C211yesmaximal, characteristic, complemented
2#540×C233C211yesmaximal, characteristic
3#501×C233C211yesmaximal, characteristic, complemented
4#499×C233C211yesmaximal, characteristic, complemented
5#490×C233C211yesmaximal, characteristic, complemented
6#486×C233C211yesmaximal, characteristic, complemented
7#482×C233C211yesmaximal, characteristic, complemented
8#482×C233C211yesmaximal, characteristic, complemented
9#481×C233C211yesmaximal, characteristic, complemented
10#480×C233C211yesmaximal, characteristic, complemented
11#478×C233C211yesmaximal, characteristic, complemented
12#478×C233C211yesmaximal, characteristic, complemented
13#476×C233C211yesmaximal, characteristic, complemented
14#474×C233C211yesmaximal, characteristic, complemented
15#433×C233C211yesmaximal, characteristic, complemented
16C4⋊Q8×C233—21no—
17C4⋊Q8×C233C2211yescharacteristic
18C4⋊Q8×C233C2211yescharacteristic
19#127×C233C2211yescharacteristic
20#125×C233—21no—
21#125×C233C2211yescharacteristic
22#125×C233C2211yescharacteristic
23#125×C233C2211yescharacteristic
24#123×C233—21no—
25#123×C233—21no—
26C22⋊Q8×C233—21no—
27C22⋊Q8×C233—21no—
28#121×C233—21no—
29#121×C233—21no—
30#121×C233C2211yescharacteristic
31#121×C233C2211yescharacteristic
32C4×D4×C233C2211yescharacteristic
33C4×D4×C233C2211yescharacteristic
34#117×C233C2211yescharacteristic
35#117×C233C2211yescharacteristic
36C2×C4⋊C4×C233C2211yescharacteristic
37#107×C233C2211yescharacteristic
38#107×C233C2211yescharacteristic
39#107×C233C2211yescharacteristic
40#107×C233C2211yescharacteristic
41#106×C233C2211yescharacteristic
42#106×C233C2211yescharacteristic
43#106×C233C2211yescharacteristic
44#106×C233C2211yescharacteristic
45C4⋊C8×C233C2211yescharacteristic
46C4⋊C8×C233C2211yescharacteristic
47#102×C233C2211yescharacteristic
48#102×C233C2211yescharacteristic
49#102×C233C2211yescharacteristic
50#102×C233C2211yescharacteristic
51#102×C233C2211yescharacteristic
52#102×C233C2211yescharacteristic
53#102×C233C2211yescharacteristic
54#102×C233C2211yescharacteristic
55C22⋊C8×C233C2211yescharacteristic
56C22⋊C8×C233C2211yescharacteristic
57#97×C233C2211yescharacteristic
58C4×C8×C233C2211yescharacteristic
59C2×Q8×C233—21no—
60C2×Q8×C233—21no—
61C2×D4×C233—21no—
62C2×D4×C233—21no—
63C2×D4×C233—21no—
64C2×D4×C233—21no—
65C2×D4×C233C2311yescharacteristic
66C2×D4×C233C2311yescharacteristic
67C22×C4×C233—21no—
68C22×C4×C233—21no—
69C22×C4×C233—21no—
70C22×C4×C233C2311yescharacteristic
71C2×C8×C233C2311yescharacteristic
72C2×C8×C233C2311yescharacteristic
73C2×C8×C233C2311yescharacteristic
74C2×C8×C233C2311yescharacteristic
75C4⋊C4×C233—21no—
76C4⋊C4×C233—21no—
77C4⋊C4×C233—21no—
78C4⋊C4×C233—21no—
79C4⋊C4×C233—21no—
80C4⋊C4×C233—21no—
81C4⋊C4×C233—21no—
82C4⋊C4×C233—21no—
83C4⋊C4×C233—21no—
84C4⋊C4×C233D411yescharacteristic
85C4⋊C4×C233D411yescharacteristic
86C4⋊C4×C233C2311yescharacteristic
87C4⋊C4×C233C2311yescharacteristic
88C4⋊C4×C233C2311yescharacteristic
89C4⋊C4×C233C2311yescharacteristic
90C4⋊C4×C233C2311yescharacteristic
91C4⋊C4×C233C2311yescharacteristic
92C22⋊C4×C233—21no—
93C22⋊C4×C233—21no—
94C22⋊C4×C233—21no—
95C22⋊C4×C233—21no—
96C22⋊C4×C233—21no—
97C22⋊C4×C233D411yescharacteristic
98C22⋊C4×C233D411yescharacteristic
99C42×C233—21no—
100C42×C233C2311yescharacteristic
101C42×C233C2311yescharacteristic
102C23×C233—21no—
103C23×C233—21no—
104C23×C233C2×D411yescharacteristic
105Q8×C233—81no—
106Q8×C233—81no—
107D4×C233—21no—
108D4×C233—21no—
109D4×C233—21no—
110D4×C233—21no—
111D4×C233—81no—
112D4×C233—81no—
113D4×C233—81no—
114D4×C233—81no—
115C2×C4×C233—21no—
116C2×C4×C233—21no—
117C2×C4×C233—21no—
118C2×C4×C233—21no—
119C2×C4×C233—21no—
120C2×C4×C233—21no—
121C2×C4×C233—21no—
122C2×C4×C233—21no—
123C2×C4×C233—81no—
124C2×C4×C233—81no—
125C2×C4×C233—81no—
126C2×C4×C233C2×D411yescharacteristic
127C2×C4×C233C2×D411yescharacteristic
128C2×C4×C233C2×D411yescharacteristic
129C2×C4×C233C2×D411yescharacteristic
130C2×C4×C233C2×D411yescharacteristic
131C2×C4×C233C2411yescharacteristic
132C8×C233—21no—
133C8×C233—21no—
134C8×C233—21no—
135C8×C233—21no—
136C22×C233—21no—
137C22×C233—21no—
138C22×C233—21no—
139C22×C233—41no—
140C22×C233—41no—
141C22×C233—41no—
142C22×C233—41no—
143C22×C233—41no—
144C22×C233—41no—
145C22×C233C22×D411yescharacteristic
146C4×C233—21no—
147C4×C233—21no—
148C4×C233—21no—
149C4×C233—21no—
150C4×C233—21no—
151C4×C233—41no—
152C4×C233—41no—
153C4×C233—41no—
154C4×C233—41no—
155C4×C233—41no—
156C4×C233—41no—
157C4×C2332−1+411yescharacteristic
158C4×C2332−1+411yescharacteristic
159C2×C233—41no—
160C2×C233—81no—
161C2×C233—81no—
162C2×C233#53611yescharacteristic
163C2×C233#57611yescharacteristic
164C2×C233#57711yescharacteristic
165C233#324111yescharacteristic, direct product factor, Sylow
166#3241C23311yesmaximal, characteristic, direct product factor, Sylow
167#544C2×C23311yescharacteristic, complemented
168#540C2×C23311yescharacteristic
169#501C2×C23311yescharacteristic, complemented
170#499C2×C23311yescharacteristic, complemented
171#490C2×C23311yescharacteristic, complemented
172#486C2×C23311yescharacteristic, complemented
173#482C2×C23311yescharacteristic, complemented
174#482C2×C23311yescharacteristic, complemented
175#481C2×C23311yescharacteristic, complemented
176#480C2×C23311yescharacteristic, complemented
177#478C2×C23311yescharacteristic, complemented
178#478C2×C23311yescharacteristic, complemented
179#476C2×C23311yescharacteristic, complemented
180#474C2×C23311yescharacteristic, complemented
181#433C2×C23311yescharacteristic, complemented
182C4⋊Q8—21no—
183C4⋊Q8C22×C23311yescharacteristic
184C4⋊Q8C22×C23311yescharacteristic
185#127C22×C23311yescharacteristic
186#125—21no—
187#125C22×C23311yescharacteristic
188#125C22×C23311yescharacteristic
189#125C22×C23311yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#121—21no—
195#121—21no—
196#121C22×C23311yescharacteristic
197#121C22×C23311yescharacteristic
198C4×D4C22×C23311yescharacteristic
199C4×D4C22×C23311yescharacteristic
200#117C22×C23311yescharacteristic
201#117C22×C23311yescharacteristic
202C2×C4⋊C4C22×C23311yescharacteristic
203#107C22×C23311yescharacteristic
204#107C22×C23311yescharacteristic
205#107C22×C23311yescharacteristic
206#107C22×C23311yescharacteristic
207#106C22×C23311yescharacteristic
208#106C22×C23311yescharacteristic
209#106C22×C23311yescharacteristic
210#106C22×C23311yescharacteristic
211C4⋊C8C22×C23311yescharacteristic
212C4⋊C8C22×C23311yescharacteristic
213#102C22×C23311yescharacteristic
214#102C22×C23311yescharacteristic
215#102C22×C23311yescharacteristic
216#102C22×C23311yescharacteristic
217#102C22×C23311yescharacteristic
218#102C22×C23311yescharacteristic
219#102C22×C23311yescharacteristic
220#102C22×C23311yescharacteristic
221C22⋊C8C22×C23311yescharacteristic
222C22⋊C8C22×C23311yescharacteristic
223#97C22×C23311yescharacteristic
224C4×C8C22×C23311yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C23×C23311yescharacteristic
232C2×D4C23×C23311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C23×C23311yescharacteristic
237C2×C8C23×C23311yescharacteristic
238C2×C8C23×C23311yescharacteristic
239C2×C8C23×C23311yescharacteristic
240C2×C8C23×C23311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C23311yescharacteristic
251C4⋊C4D4×C23311yescharacteristic
252C4⋊C4C23×C23311yescharacteristic
253C4⋊C4C23×C23311yescharacteristic
254C4⋊C4C23×C23311yescharacteristic
255C4⋊C4C23×C23311yescharacteristic
256C4⋊C4C23×C23311yescharacteristic
257C4⋊C4C23×C23311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C23311yescharacteristic
264C22⋊C4D4×C23311yescharacteristic
265C42—21no—
266C42C23×C23311yescharacteristic
267C42C23×C23311yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×D4×C23311yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C23311yescharacteristic
293C2×C4C2×D4×C23311yescharacteristic
294C2×C4C2×D4×C23311yescharacteristic
295C2×C4C2×D4×C23311yescharacteristic
296C2×C4C2×D4×C23311yescharacteristic
297C2×C4C24×C23311yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C23311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C42−1+4×C23311yescharacteristic
324C42−1+4×C23311yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#536×C23311yescharacteristic
329C2#576×C23311yescharacteristic
330C2#577×C23311yescharacteristic
subgroupG/H
center, socleC22×C233C22×D4
commutator, Frattini, cosocleC2×C4C24×C233
prime radical#540×C233C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C233 ◁ #117×C233 ◁ G

Complements

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

NH ≅ G/Ntype
1. #544×C233C2semidirect
3. #501×C233C2semidirect
4. #499×C233C2semidirect
5. #490×C233C2semidirect
6. #486×C233C2semidirect
7. #482×C233C2semidirect
8. #482×C233C2semidirect
9. #481×C233C2semidirect
10. #480×C233C2semidirect
11. #478×C233C2semidirect
12. #478×C233C2semidirect
13. #476×C233C2semidirect
14. #474×C233C2semidirect
15. #433×C233C2semidirect
165. C233#3241direct (N × H)
166. #3241C233direct (N × H)
167. #544C2×C233semidirect
169. #501C2×C233semidirect
170. #499C2×C233semidirect
171. #490C2×C233semidirect
172. #486C2×C233semidirect
173. #482C2×C233semidirect
174. #482C2×C233semidirect
175. #481C2×C233semidirect
176. #480C2×C233semidirect
177. #478C2×C233semidirect
178. #478C2×C233semidirect
179. #476C2×C233semidirect
180. #474C2×C233semidirect
181. #433C2×C233semidirect

Maximal subgroups

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

subgroupindex
#544×C2332
#540×C2332
#501×C2332
#499×C2332
#490×C2332
#486×C2332
#482×C2332
#481×C2332
#480×C2332
#478×C2332
#476×C2332
#474×C2332
#433×C2332
#3241233