Finite Group Databasebeta

← #44487291

Subgroups — #44487291

Order 30592.

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×#21439958C211yesmaximal, characteristic
2#29504679C211yesmaximal, characteristic
3#29504676C211yesmaximal, characteristic
4#29504676C211yesmaximal, characteristic
5#29504669C211yesmaximal, characteristic
6#29504667C211yesmaximal, characteristic
7#29504659C211yesmaximal, characteristic
8#29504656C211yesmaximal, characteristic
9#29504654C211yesmaximal, characteristic
10#29504653C211yesmaximal, characteristic
11#29504636C211yesmaximal, characteristic
12C4×Dic239⋊C4C211yesmaximal, characteristic
13#29504623C211yesmaximal, characteristic
14#29504617C211yesmaximal, characteristic
15#391×C239C211yesmaximal, characteristic
16C22×Dic478C2211yescharacteristic
17#21439958C418yescomplemented
18C2×C4⋊Dic239C2211yescharacteristic
19C2×Dic239⋊C4C2211yescharacteristic
20C2×Dic239⋊C4C2211yescharacteristic
21C2×Dic239⋊C4C2211yescharacteristic
22C2×Dic239⋊C4C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×Dic239⋊C4C2211yescharacteristic
27C2×C4×Dic239C2211yescharacteristic
28C2×C4×Dic239C2211yescharacteristic
29C2×C4×Dic239C2211yescharacteristic
30C2×C4×Dic239C2211yescharacteristic
31C2×C4×Dic239C2211yescharacteristic
32C2×C4×Dic239C2211yescharacteristic
33C239⋊#95C2211yescharacteristic
34C239⋊#95C2211yescharacteristic
35C239⋊#95C2211yescharacteristic
36C239⋊#95C2211yescharacteristic
37C239⋊#95C2211yescharacteristic
38C239⋊#95C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C22×Q8×C239C2211yescharacteristic
46C2×C4⋊C4×C239C2211yescharacteristic
47C2×C42×C239C2211yescharacteristic
48#95×C239C2211yescharacteristic
49#95×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52C2×Dic478—41no—
53C2×Dic478—41no—
54C2×Dic478C2×C414yes—
55C22×Dic239C2311yescharacteristic
56C22×Dic239C2311yescharacteristic
57C22×Dic239C2311yescharacteristic
58C22×Dic239C2311yescharacteristic
59C22×Dic239C2311yescharacteristic
60C22×Dic239C2311yescharacteristic
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C4⋊Dic239—41no—
64Dic239⋊C4—22no—
65Dic239⋊C4—22no—
66Dic239⋊C4—41no—
67Dic239⋊C4—41no—
68Dic239⋊C4C2×C414yes—
69Dic239⋊C4C2×C414yes—
70Dic239⋊C4C2×C414yes—
71Dic239⋊C4C2×C414yes—
72C4×Dic239—22no—
73C4×Dic239—41no—
74C4×Dic239—41no—
75C4×Dic239—41no—
76C4×Dic239C2×C414yes—
77C4×Dic239Q814yescomplemented
78C2×Q8×C239—41no—
79C2×Q8×C239—41no—
80C2×Q8×C239C2×C414yes—
81C22×C4×C239C2311yescharacteristic
82C22×C4×C239C2311yescharacteristic
83C22×C4×C239C2311yescharacteristic
84C22×C4×C239C2311yescharacteristic
85C22×C4×C239C2311yescharacteristic
86C22×C4×C239C2311yescharacteristic
87C22×C4×C239C2311yescharacteristic
88C4⋊C4×C239—41no—
89C42×C239—41no—
90Dic478—44no—
91C2×Dic239—21no—
92C2×Dic239—21no—
93C2×Dic239—21no—
94C2×Dic239—21no—
95C2×Dic239—21no—
96C2×Dic239—21no—
97C2×Dic239—21no—
98C2×Dic239—21no—
99C2×Dic239—21no—
100C2×Dic239—21no—
101C2×Dic239—21no—
102C2×Dic239—21no—
103C2×Dic239—21no—
104C2×Dic239—21no—
105C2×Dic239—21no—
106C2×Dic239—21no—
107C2×Dic239—21no—
108C2×Dic239C22×C412yes—
109C2×Dic239C22×C412yes—
110C2×Dic239C22×C412yes—
111C2×Dic239C22×C412yes—
112C2×Dic239C2×Q812yes—
113C2×Dic239C2×Q812yes—
114C2×Dic239#4112yes—
115C23×C239C2411yescharacteristic
116Q8×C239—44no—
117C2×C4×C239—21no—
118C2×C4×C239—21no—
119C2×C4×C239—21no—
120C2×C4×C239—21no—
121C2×C4×C239—21no—
122C2×C4×C239—21no—
123C2×C4×C239—21no—
124C2×C4×C239—21no—
125C2×C4×C239—21no—
126C2×C4×C239—21no—
127C2×C4×C239—21no—
128C2×C4×C239—21no—
129C2×C4×C239—21no—
130C2×C4×C239—21no—
131C2×C4×C239—21no—
132C2×C4×C239—21no—
133C2×C4×C239—21no—
134C2×C4×C239C22×C412yes—
135C2×C4×C239C22×C412yes—
136C2×C4×C239C22×C412yes—
137C2×C4×C239C2×Q812yes—
138C22×C239C23×C411yescharacteristic
139C22×C239C22×Q811yescharacteristic
140C22×C239C2×#4111yescharacteristic
141C22×C239H(5,𝔽2)11yescharacteristic
142C22×C239H(5,𝔽2)11yescharacteristic
143C22×C2392−1+411yescharacteristic
144C22×C2392−1+411yescharacteristic
145C4×C239—22no—
146C4×C239—22no—
147C4×C239—22no—
148C4×C239—22no—
149C4×C239—41no—
150C4×C239—41no—
151C4×C239—41no—
152Dic239—22no—
153Dic239—22no—
154Dic239—22no—
155Dic239—22no—
156Dic239—41no—
157Dic239—41no—
158Dic239—41no—
159Dic239C4×Q814yes—
160C2×C239C2×C4×Q811yescharacteristic
161C2×C239#51811yescharacteristic
162C2×C239#51911yescharacteristic
163C2×C239#54211yescharacteristic
164C2×C239#54211yescharacteristic
165C2×C239#54411yescharacteristic
166C2×C239#54411yescharacteristic
167C239#233111yescharacteristic, complemented, Sylow
168#2331—2391nomaximal, Sylow
169C2×C4⋊Q8—2391no—
170#391—2391no—
171#391—2391no—
172#391—2391no—
173#391D23911yescharacteristic
174#389—2391no—
175#389—2391no—
176#387—2391no—
177#387—2391no—
178#387—2391no—
179#387—2391no—
180#382—2391no—
181C4×C4⋊C4—2391no—
182C4×C4⋊C4—2391no—
183#376—2391no—
184C22×Q8—2391no—
185C22×Q8C2×D23911yescharacteristic
186C4⋊Q8—2398no—
187C2×C4⋊C4—2391no—
188C2×C4⋊C4—2391no—
189C2×C4⋊C4—2391no—
190C2×C4⋊C4—2391no—
191C2×C4⋊C4—2391no—
192C2×C4⋊C4—2391no—
193C2×C4⋊C4—2391no—
194C2×C4⋊C4—2391no—
195C2×C4⋊C4—2391no—
196C2×C4⋊C4C2×D23911yescharacteristic
197C2×C42—2391no—
198C2×C42—2391no—
199C2×C42—2391no—
200C2×C42—2391no—
201C2×C42—2391no—
202C2×C42—2391no—
203C2×C42C2×D23911yescharacteristic
204#95—2391no—
205#95—2391no—
206#95—2391no—
207#95—2391no—
208#95—2391no—
209#95—2391no—
210#95—2391no—
211#95—2391no—
212#95—2391no—
213#95—2391no—
214#95—2391no—
215#95—2391no—
216#95C2×D23911yescharacteristic
217#95C2×D23911yescharacteristic
218#95C2×D23911yescharacteristic
219#95C2×D23911yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—9561no—
223C2×Q8—9561no—
224C2×Q8—2394no—
225C2×Q8C4×D23914yes—
226C22×C4—2391no—
227C22×C4—2391no—
228C22×C4—2391no—
229C22×C4—2391no—
230C22×C4—2391no—
231C22×C4—2391no—
232C22×C4—2391no—
233C22×C4—2391no—
234C22×C4C22×D23911yescharacteristic
235C22×C4C22×D23911yescharacteristic
236C22×C4C22×D23911yescharacteristic
237C22×C4C22×D23911yescharacteristic
238C22×C4C22×D23911yescharacteristic
239C22×C4C22×D23911yescharacteristic
240C22×C4C22×D23911yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—9561no—
243C4⋊C4—9561no—
244C4⋊C4—9561no—
245C4⋊C4—4782no—
246C4⋊C4—4782no—
247C4⋊C4—2394no—
248C4⋊C4—2394no—
249C4⋊C4—2394no—
250C4⋊C4—2394no—
251C42—41no—
252C42—9561no—
253C42—9561no—
254C42—9561no—
255C42—4782no—
256C42—2394no—
257C42—2394no—
258C23C23×D23911yescharacteristic
259Q8—44no—
260Q8—9564no—
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—4781no—
279C2×C4—4781no—
280C2×C4—4781no—
281C2×C4—4781no—
282C2×C4—4781no—
283C2×C4—4781no—
284C2×C4—4781no—
285C2×C4—4781no—
286C2×C4—4781no—
287C2×C4—4781no—
288C2×C4—4781no—
289C2×C4—4781no—
290C2×C4—4781no—
291C2×C4—4781no—
292C2×C4—4781no—
293C2×C4—4781no—
294C2×C4—4781no—
295C2×C4—2392no—
296C2×C4—2392no—
297C2×C4—2392no—
298C2×C4—2392no—
299C2×C4—2392no—
300C2×C4—2392no—
301C2×C4—2392no—
302C2×C4C2×C4×D23912yes—
303C2×C4C2×C4×D23912yes—
304C2×C4C2×C4×D23912yes—
305C2×C4Q8×D23912yes—
306C22C22×C4×D23911yescharacteristic
307C22C2×Q8×D23911yescharacteristic
308C22#41×D23911yescharacteristic
309C22#2144000511yescharacteristic
310C22#2144000511yescharacteristic
311C22#2144000711yescharacteristic
312C22#2144000811yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—9561no—
321C4—9561no—
322C4—9561no—
323C4—4782no—
324C4—4782no—
325C4—4782no—
326C4—4782no—
327C4—2394no—
328C2C4×Q8×D23911yescharacteristic
329C2#2950524511yescharacteristic
330C2#2950524811yescharacteristic
331C2#2950538611yescharacteristic
332C2#2950539211yescharacteristic
333C2#2950539911yescharacteristic
334C2#2950540111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#391×C239C2
socle, prime radical, cosocleC23×C239C24
hypercenter#391D239
hypocenterC239#2331
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #21439958C4semidirect
77. C4×Dic239Q8semidirect
167. C239#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#214399582
#295046792
#295046762
#295046692
#295046672
#295046592
#295046562
#295046542
#295046532
#295046362
C4×Dic239⋊C42
#295046232
#295046172
#391×C2392
#2331239