Finite Group Databasebeta

← #46813628

Subgroups — #46813628

Order 34432.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575451C211yesmaximal, characteristic
2#31770512C211yesmaximal, characteristic
3#31770509C211yesmaximal, characteristic
4#31770509C211yesmaximal, characteristic
5#31770502C211yesmaximal, characteristic
6#31770500C211yesmaximal, characteristic
7#31770492C211yesmaximal, characteristic
8#31770489C211yesmaximal, characteristic
9#31770487C211yesmaximal, characteristic
10#31770486C211yesmaximal, characteristic
11#31770469C211yesmaximal, characteristic
12C4×#16864381C211yesmaximal, characteristic
13#31770456C211yesmaximal, characteristic
14#31770450C211yesmaximal, characteristic
15#391×C269C211yesmaximal, characteristic
16C22×Dic538C2211yescharacteristic
17#22575451C418yescomplemented
18C2×C4⋊Dic269C2211yescharacteristic
19C2×#16864381C2211yescharacteristic
20C2×#16864381C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×C4×Dic269C2211yescharacteristic
28C2×C4×Dic269C2211yescharacteristic
29C2×C4×Dic269C2211yescharacteristic
30C2×C4×Dic269C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
33#22575360C2211yescharacteristic
34#22575360C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C22×Q8×C269C2211yescharacteristic
46C2×C4⋊C4×C269C2211yescharacteristic
47C2×C42×C269C2211yescharacteristic
48#95×C269C2211yescharacteristic
49#95×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C2×Dic538—41no—
53C2×Dic538—41no—
54C2×Dic538C2×C414yes—
55C22×Dic269C2311yescharacteristic
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C4⋊Dic269—41no—
64#16864381—22no—
65#16864381—22no—
66#16864381—41no—
67#16864381—41no—
68#16864381C2×C414yes—
69#16864381C2×C414yes—
70#16864381C2×C414yes—
71#16864381C2×C414yes—
72C4×Dic269—22no—
73C4×Dic269—41no—
74C4×Dic269—41no—
75C4×Dic269—41no—
76C4×Dic269C2×C414yes—
77C4×Dic269Q814yescomplemented
78C2×Q8×C269—41no—
79C2×Q8×C269—41no—
80C2×Q8×C269C2×C414yes—
81C22×C4×C269C2311yescharacteristic
82C22×C4×C269C2311yescharacteristic
83C22×C4×C269C2311yescharacteristic
84C22×C4×C269C2311yescharacteristic
85C22×C4×C269C2311yescharacteristic
86C22×C4×C269C2311yescharacteristic
87C22×C4×C269C2311yescharacteristic
88C4⋊C4×C269—41no—
89C42×C269—41no—
90Dic538—44no—
91C2×Dic269—21no—
92C2×Dic269—21no—
93C2×Dic269—21no—
94C2×Dic269—21no—
95C2×Dic269—21no—
96C2×Dic269—21no—
97C2×Dic269—21no—
98C2×Dic269—21no—
99C2×Dic269—21no—
100C2×Dic269—21no—
101C2×Dic269—21no—
102C2×Dic269—21no—
103C2×Dic269—21no—
104C2×Dic269—21no—
105C2×Dic269—21no—
106C2×Dic269—21no—
107C2×Dic269—21no—
108C2×Dic269C22×C412yes—
109C2×Dic269C22×C412yes—
110C2×Dic269C22×C412yes—
111C2×Dic269C22×C412yes—
112C2×Dic269C2×Q812yes—
113C2×Dic269C2×Q812yes—
114C2×Dic269#4112yes—
115C23×C269C2411yescharacteristic
116Q8×C269—44no—
117C2×C4×C269—21no—
118C2×C4×C269—21no—
119C2×C4×C269—21no—
120C2×C4×C269—21no—
121C2×C4×C269—21no—
122C2×C4×C269—21no—
123C2×C4×C269—21no—
124C2×C4×C269—21no—
125C2×C4×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269C22×C412yes—
135C2×C4×C269C22×C412yes—
136C2×C4×C269C22×C412yes—
137C2×C4×C269C2×Q812yes—
138C22×C269C23×C411yescharacteristic
139C22×C269C22×Q811yescharacteristic
140C22×C269C2×#4111yescharacteristic
141C22×C269H(5,𝔽2)11yescharacteristic
142C22×C269H(5,𝔽2)11yescharacteristic
143C22×C2692−1+411yescharacteristic
144C22×C2692−1+411yescharacteristic
145C4×C269—22no—
146C4×C269—22no—
147C4×C269—22no—
148C4×C269—22no—
149C4×C269—41no—
150C4×C269—41no—
151C4×C269—41no—
152Dic269—22no—
153Dic269—22no—
154Dic269—22no—
155Dic269—22no—
156Dic269—41no—
157Dic269—41no—
158Dic269—41no—
159Dic269C4×Q814yes—
160C2×C269C2×C4×Q811yescharacteristic
161C2×C269#51811yescharacteristic
162C2×C269#51911yescharacteristic
163C2×C269#54211yescharacteristic
164C2×C269#54211yescharacteristic
165C2×C269#54411yescharacteristic
166C2×C269#54411yescharacteristic
167C269#233111yescharacteristic, complemented, Sylow
168#2331—2691nomaximal, Sylow
169C2×C4⋊Q8—2691no—
170#391—2691no—
171#391—2691no—
172#391—2691no—
173#391D26911yescharacteristic
174#389—2691no—
175#389—2691no—
176#387—2691no—
177#387—2691no—
178#387—2691no—
179#387—2691no—
180#382—2691no—
181C4×C4⋊C4—2691no—
182C4×C4⋊C4—2691no—
183#376—2691no—
184C22×Q8—2691no—
185C22×Q8C2×D26911yescharacteristic
186C4⋊Q8—2698no—
187C2×C4⋊C4—2691no—
188C2×C4⋊C4—2691no—
189C2×C4⋊C4—2691no—
190C2×C4⋊C4—2691no—
191C2×C4⋊C4—2691no—
192C2×C4⋊C4—2691no—
193C2×C4⋊C4—2691no—
194C2×C4⋊C4—2691no—
195C2×C4⋊C4—2691no—
196C2×C4⋊C4C2×D26911yescharacteristic
197C2×C42—2691no—
198C2×C42—2691no—
199C2×C42—2691no—
200C2×C42—2691no—
201C2×C42—2691no—
202C2×C42—2691no—
203C2×C42C2×D26911yescharacteristic
204#95—2691no—
205#95—2691no—
206#95—2691no—
207#95—2691no—
208#95—2691no—
209#95—2691no—
210#95—2691no—
211#95—2691no—
212#95—2691no—
213#95—2691no—
214#95—2691no—
215#95—2691no—
216#95C2×D26911yescharacteristic
217#95C2×D26911yescharacteristic
218#95C2×D26911yescharacteristic
219#95C2×D26911yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—2694no—
223C2×Q8—10761no—
224C2×Q8—10761no—
225C2×Q8C4×D26914yes—
226C22×C4—2691no—
227C22×C4—2691no—
228C22×C4—2691no—
229C22×C4—2691no—
230C22×C4—2691no—
231C22×C4—2691no—
232C22×C4—2691no—
233C22×C4—2691no—
234C22×C4C22×D26911yescharacteristic
235C22×C4C22×D26911yescharacteristic
236C22×C4C22×D26911yescharacteristic
237C22×C4C22×D26911yescharacteristic
238C22×C4C22×D26911yescharacteristic
239C22×C4C22×D26911yescharacteristic
240C22×C4C22×D26911yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—2694no—
243C4⋊C4—2694no—
244C4⋊C4—2694no—
245C4⋊C4—2694no—
246C4⋊C4—5382no—
247C4⋊C4—5382no—
248C4⋊C4—10761no—
249C4⋊C4—10761no—
250C4⋊C4—10761no—
251C42—41no—
252C42—2694no—
253C42—2694no—
254C42—5382no—
255C42—10761no—
256C42—10761no—
257C42—10761no—
258C23C23×D26911yescharacteristic
259Q8—44no—
260Q8—10764no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2692no—
279C2×C4—2692no—
280C2×C4—2692no—
281C2×C4—2692no—
282C2×C4—2692no—
283C2×C4—2692no—
284C2×C4—2692no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—5381no—
288C2×C4—5381no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4C2×C4×D26912yes—
303C2×C4C2×C4×D26912yes—
304C2×C4C2×C4×D26912yes—
305C2×C4Q8×D26912yes—
306C22C22×C4×D26911yescharacteristic
307C22C2×Q8×D26911yescharacteristic
308C22#41×D26911yescharacteristic
309C22#2257549811yescharacteristic
310C22#2257549811yescharacteristic
311C22#2257550011yescharacteristic
312C22#2257550111yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2694no—
321C4—5382no—
322C4—5382no—
323C4—5382no—
324C4—5382no—
325C4—10761no—
326C4—10761no—
327C4—10761no—
328C2C4×Q8×D26911yescharacteristic
329C2#3177107811yescharacteristic
330C2#3177108111yescharacteristic
331C2#3177121911yescharacteristic
332C2#3177122511yescharacteristic
333C2#3177123211yescharacteristic
334C2#3177123411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#391×C269C2
socle, prime radical, cosocleC23×C269C24
hypercenter#391D269
hypocenterC269#2331
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #22575451C4semidirect
77. C4×Dic269Q8semidirect
167. C269#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#225754512
#317705122
#317705092
#317705022
#317705002
#317704922
#317704892
#317704872
#317704862
#317704692
C4×#168643812
#317704562
#317704502
#391×C2692
#2331269