Finite Group Databasebeta

← #28393317

Subgroups — #28393317

Order 14464.

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×#16813620C211yesmaximal, characteristic
2#20298505C211yesmaximal, characteristic
3#20298502C211yesmaximal, characteristic
4#20298502C211yesmaximal, characteristic
5#20298495C211yesmaximal, characteristic
6#20298493C211yesmaximal, characteristic
7#20298485C211yesmaximal, characteristic
8#20298482C211yesmaximal, characteristic
9#20298480C211yesmaximal, characteristic
10#20298479C211yesmaximal, characteristic
11#20298462C211yesmaximal, characteristic
12C4×#14268626C211yesmaximal, characteristic
13#20298449C211yesmaximal, characteristic
14#20298443C211yesmaximal, characteristic
15#391×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17#16813620C418yescomplemented
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626C2211yescharacteristic
20C2×#14268626C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×C4×Dic113C2211yescharacteristic
28C2×C4×Dic113C2211yescharacteristic
29C2×C4×Dic113C2211yescharacteristic
30C2×C4×Dic113C2211yescharacteristic
31C2×C4×Dic113C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33#16813529C2211yescharacteristic
34#16813529C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45C22×Q8×C113C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C42×C113C2211yescharacteristic
48#95×C113C2211yescharacteristic
49#95×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C2×Dic226—41no—
53C2×Dic226—41no—
54C2×Dic226C2×C414yes—
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C4⋊Dic113—41no—
64#14268626—22no—
65#14268626—22no—
66#14268626—41no—
67#14268626—41no—
68#14268626C2×C414yes—
69#14268626C2×C414yes—
70#14268626C2×C414yes—
71#14268626C2×C414yes—
72C4×Dic113—22no—
73C4×Dic113—41no—
74C4×Dic113—41no—
75C4×Dic113—41no—
76C4×Dic113C2×C414yes—
77C4×Dic113Q814yescomplemented
78C2×Q8×C113—41no—
79C2×Q8×C113—41no—
80C2×Q8×C113C2×C414yes—
81C22×C4×C113C2311yescharacteristic
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C4⋊C4×C113—41no—
89C42×C113—41no—
90C23×C113C2411yescharacteristic
91Q8×C113—44no—
92C2×C4×C113—21no—
93C2×C4×C113—21no—
94C2×C4×C113—21no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113—21no—
99C2×C4×C113—21no—
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113C22×C412yes—
110C2×C4×C113C22×C412yes—
111C2×C4×C113C22×C412yes—
112C2×C4×C113C2×Q812yes—
113C2×Dic113—21no—
114C2×Dic113—21no—
115C2×Dic113—21no—
116C2×Dic113—21no—
117C2×Dic113—21no—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113C22×C412yes—
131C2×Dic113C22×C412yes—
132C2×Dic113C22×C412yes—
133C2×Dic113C22×C412yes—
134C2×Dic113C2×Q812yes—
135C2×Dic113C2×Q812yes—
136C2×Dic113#4112yes—
137Dic226—44no—
138C22×C113C23×C411yescharacteristic
139C22×C113C22×Q811yescharacteristic
140C22×C113C2×#4111yescharacteristic
141C22×C113H(5,𝔽2)11yescharacteristic
142C22×C113H(5,𝔽2)11yescharacteristic
143C22×C1132−1+411yescharacteristic
144C22×C1132−1+411yescharacteristic
145C4×C113—22no—
146C4×C113—22no—
147C4×C113—22no—
148C4×C113—22no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113—41no—
152Dic113—22no—
153Dic113—22no—
154Dic113—22no—
155Dic113—22no—
156Dic113—41no—
157Dic113—41no—
158Dic113—41no—
159Dic113C4×Q814yes—
160C2×C113C2×C4×Q811yescharacteristic
161C2×C113#51811yescharacteristic
162C2×C113#51911yescharacteristic
163C2×C113#54211yescharacteristic
164C2×C113#54211yescharacteristic
165C2×C113#54411yescharacteristic
166C2×C113#54411yescharacteristic
167#2331—1131nomaximal, Sylow
168C113#233111yescharacteristic, complemented, Sylow
169C2×C4⋊Q8—1131no—
170#391—1131no—
171#391—1131no—
172#391—1131no—
173#391D11311yescharacteristic
174#389—1131no—
175#389—1131no—
176#387—1131no—
177#387—1131no—
178#387—1131no—
179#387—1131no—
180#382—1131no—
181C4×C4⋊C4—1131no—
182C4×C4⋊C4—1131no—
183#376—1131no—
184C22×Q8—1131no—
185C22×Q8C2×D11311yescharacteristic
186C4⋊Q8—1138no—
187C2×C4⋊C4—1131no—
188C2×C4⋊C4—1131no—
189C2×C4⋊C4—1131no—
190C2×C4⋊C4—1131no—
191C2×C4⋊C4—1131no—
192C2×C4⋊C4—1131no—
193C2×C4⋊C4—1131no—
194C2×C4⋊C4—1131no—
195C2×C4⋊C4—1131no—
196C2×C4⋊C4C2×D11311yescharacteristic
197C2×C42—1131no—
198C2×C42—1131no—
199C2×C42—1131no—
200C2×C42—1131no—
201C2×C42—1131no—
202C2×C42—1131no—
203C2×C42C2×D11311yescharacteristic
204#95—1131no—
205#95—1131no—
206#95—1131no—
207#95—1131no—
208#95—1131no—
209#95—1131no—
210#95—1131no—
211#95—1131no—
212#95—1131no—
213#95—1131no—
214#95—1131no—
215#95—1131no—
216#95C2×D11311yescharacteristic
217#95C2×D11311yescharacteristic
218#95C2×D11311yescharacteristic
219#95C2×D11311yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—1134no—
223C2×Q8—4521no—
224C2×Q8—4521no—
225C2×Q8C4×D11314yes—
226C22×C4—1131no—
227C22×C4—1131no—
228C22×C4—1131no—
229C22×C4—1131no—
230C22×C4—1131no—
231C22×C4—1131no—
232C22×C4—1131no—
233C22×C4—1131no—
234C22×C4C22×D11311yescharacteristic
235C22×C4C22×D11311yescharacteristic
236C22×C4C22×D11311yescharacteristic
237C22×C4C22×D11311yescharacteristic
238C22×C4C22×D11311yescharacteristic
239C22×C4C22×D11311yescharacteristic
240C22×C4C22×D11311yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—1134no—
243C4⋊C4—1134no—
244C4⋊C4—1134no—
245C4⋊C4—1134no—
246C4⋊C4—4521no—
247C4⋊C4—4521no—
248C4⋊C4—4521no—
249C4⋊C4—2262no—
250C4⋊C4—2262no—
251C42—41no—
252C42—1134no—
253C42—1134no—
254C42—4521no—
255C42—4521no—
256C42—4521no—
257C42—2262no—
258C23C23×D11311yescharacteristic
259Q8—44no—
260Q8—4524no—
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—1132no—
279C2×C4—1132no—
280C2×C4—1132no—
281C2×C4—1132no—
282C2×C4—1132no—
283C2×C4—1132no—
284C2×C4—1132no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4C2×C4×D11312yes—
303C2×C4C2×C4×D11312yes—
304C2×C4C2×C4×D11312yes—
305C2×C4Q8×D11312yes—
306C22C22×C4×D11311yescharacteristic
307C22C2×Q8×D11311yescharacteristic
308C22#41×D11311yescharacteristic
309C22#1681366711yescharacteristic
310C22#1681366711yescharacteristic
311C22#1681366911yescharacteristic
312C22#1681367011yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1134no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—2262no—
325C4—2262no—
326C4—2262no—
327C4—2262no—
328C2C4×Q8×D11311yescharacteristic
329C2#2029907111yescharacteristic
330C2#2029907411yescharacteristic
331C2#2029921211yescharacteristic
332C2#2029921811yescharacteristic
333C2#2029922511yescharacteristic
334C2#2029922711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#391×C113C2
socle, prime radical, cosocleC23×C113C24
hypercenter#391D113
hypocenterC113#2331
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #16813620C4semidirect
77. C4×Dic113Q8semidirect
168. C113#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#168136202
#202985052
#202985022
#202984952
#202984932
#202984852
#202984822
#202984802
#202984792
#202984622
C4×#142686262
#202984492
#202984432
#391×C1132
#2331113