Finite Group Databasebeta

← #28339204

Subgroups — #28339204

Order 13696.

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×#16812107C211yesmaximal, characteristic
2#20292534C211yesmaximal, characteristic
3#20292531C211yesmaximal, characteristic
4#20292531C211yesmaximal, characteristic
5#20292524C211yesmaximal, characteristic
6#20292522C211yesmaximal, characteristic
7#20292514C211yesmaximal, characteristic
8#20292511C211yesmaximal, characteristic
9#20292509C211yesmaximal, characteristic
10#20292508C211yesmaximal, characteristic
11#20292491C211yesmaximal, characteristic
12C4×Dic107⋊C4C211yesmaximal, characteristic
13#20292478C211yesmaximal, characteristic
14#20292472C211yesmaximal, characteristic
15#391×C107C211yesmaximal, characteristic
16C22×Dic214C2211yescharacteristic
17#16812107C418yescomplemented
18C2×C4⋊Dic107C2211yescharacteristic
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×C4×Dic107C2211yescharacteristic
28C2×C4×Dic107C2211yescharacteristic
29C2×C4×Dic107C2211yescharacteristic
30C2×C4×Dic107C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C107⋊#95C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C22×Q8×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C42×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52C2×Dic214—41no—
53C2×Dic214—41no—
54C2×Dic214C2×C414yes—
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C4⋊Dic107—41no—
64Dic107⋊C4—22no—
65Dic107⋊C4—22no—
66Dic107⋊C4—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4C2×C414yes—
69Dic107⋊C4C2×C414yes—
70Dic107⋊C4C2×C414yes—
71Dic107⋊C4C2×C414yes—
72C4×Dic107—22no—
73C4×Dic107—41no—
74C4×Dic107—41no—
75C4×Dic107—41no—
76C4×Dic107C2×C414yes—
77C4×Dic107Q814yescomplemented
78C2×Q8×C107—41no—
79C2×Q8×C107—41no—
80C2×Q8×C107C2×C414yes—
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C4⋊C4×C107—41no—
89C42×C107—41no—
90C23×C107C2411yescharacteristic
91Q8×C107—44no—
92C2×C4×C107—21no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—21no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107C22×C412yes—
110C2×C4×C107C22×C412yes—
111C2×C4×C107C22×C412yes—
112C2×C4×C107C2×Q812yes—
113C2×Dic107—21no—
114C2×Dic107—21no—
115C2×Dic107—21no—
116C2×Dic107—21no—
117C2×Dic107—21no—
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107C22×C412yes—
131C2×Dic107C22×C412yes—
132C2×Dic107C22×C412yes—
133C2×Dic107C22×C412yes—
134C2×Dic107C2×Q812yes—
135C2×Dic107C2×Q812yes—
136C2×Dic107#4112yes—
137Dic214—44no—
138C22×C107C23×C411yescharacteristic
139C22×C107C22×Q811yescharacteristic
140C22×C107C2×#4111yescharacteristic
141C22×C107H(5,𝔽2)11yescharacteristic
142C22×C107H(5,𝔽2)11yescharacteristic
143C22×C1072−1+411yescharacteristic
144C22×C1072−1+411yescharacteristic
145C4×C107—22no—
146C4×C107—22no—
147C4×C107—22no—
148C4×C107—22no—
149C4×C107—41no—
150C4×C107—41no—
151C4×C107—41no—
152Dic107—22no—
153Dic107—22no—
154Dic107—22no—
155Dic107—22no—
156Dic107—41no—
157Dic107—41no—
158Dic107—41no—
159Dic107C4×Q814yes—
160C2×C107C2×C4×Q811yescharacteristic
161C2×C107#51811yescharacteristic
162C2×C107#51911yescharacteristic
163C2×C107#54211yescharacteristic
164C2×C107#54211yescharacteristic
165C2×C107#54411yescharacteristic
166C2×C107#54411yescharacteristic
167#2331—1071nomaximal, Sylow
168C107#233111yescharacteristic, complemented, Sylow
169C2×C4⋊Q8—1071no—
170#391—1071no—
171#391—1071no—
172#391—1071no—
173#391D10711yescharacteristic
174#389—1071no—
175#389—1071no—
176#387—1071no—
177#387—1071no—
178#387—1071no—
179#387—1071no—
180#382—1071no—
181C4×C4⋊C4—1071no—
182C4×C4⋊C4—1071no—
183#376—1071no—
184C22×Q8—1071no—
185C22×Q8C2×D10711yescharacteristic
186C4⋊Q8—1078no—
187C2×C4⋊C4—1071no—
188C2×C4⋊C4—1071no—
189C2×C4⋊C4—1071no—
190C2×C4⋊C4—1071no—
191C2×C4⋊C4—1071no—
192C2×C4⋊C4—1071no—
193C2×C4⋊C4—1071no—
194C2×C4⋊C4—1071no—
195C2×C4⋊C4—1071no—
196C2×C4⋊C4C2×D10711yescharacteristic
197C2×C42—1071no—
198C2×C42—1071no—
199C2×C42—1071no—
200C2×C42—1071no—
201C2×C42—1071no—
202C2×C42—1071no—
203C2×C42C2×D10711yescharacteristic
204#95—1071no—
205#95—1071no—
206#95—1071no—
207#95—1071no—
208#95—1071no—
209#95—1071no—
210#95—1071no—
211#95—1071no—
212#95—1071no—
213#95—1071no—
214#95—1071no—
215#95—1071no—
216#95C2×D10711yescharacteristic
217#95C2×D10711yescharacteristic
218#95C2×D10711yescharacteristic
219#95C2×D10711yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—1074no—
223C2×Q8—4281no—
224C2×Q8—4281no—
225C2×Q8C4×D10714yes—
226C22×C4—1071no—
227C22×C4—1071no—
228C22×C4—1071no—
229C22×C4—1071no—
230C22×C4—1071no—
231C22×C4—1071no—
232C22×C4—1071no—
233C22×C4—1071no—
234C22×C4C22×D10711yescharacteristic
235C22×C4C22×D10711yescharacteristic
236C22×C4C22×D10711yescharacteristic
237C22×C4C22×D10711yescharacteristic
238C22×C4C22×D10711yescharacteristic
239C22×C4C22×D10711yescharacteristic
240C22×C4C22×D10711yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—1074no—
243C4⋊C4—1074no—
244C4⋊C4—1074no—
245C4⋊C4—1074no—
246C4⋊C4—4281no—
247C4⋊C4—4281no—
248C4⋊C4—4281no—
249C4⋊C4—2142no—
250C4⋊C4—2142no—
251C42—41no—
252C42—1074no—
253C42—1074no—
254C42—4281no—
255C42—4281no—
256C42—4281no—
257C42—2142no—
258C23C23×D10711yescharacteristic
259Q8—44no—
260Q8—4284no—
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—1072no—
279C2×C4—1072no—
280C2×C4—1072no—
281C2×C4—1072no—
282C2×C4—1072no—
283C2×C4—1072no—
284C2×C4—1072no—
285C2×C4—2141no—
286C2×C4—2141no—
287C2×C4—2141no—
288C2×C4—2141no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4—2141no—
292C2×C4—2141no—
293C2×C4—2141no—
294C2×C4—2141no—
295C2×C4—2141no—
296C2×C4—2141no—
297C2×C4—2141no—
298C2×C4—2141no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4—2141no—
302C2×C4C2×C4×D10712yes—
303C2×C4C2×C4×D10712yes—
304C2×C4C2×C4×D10712yes—
305C2×C4Q8×D10712yes—
306C22C22×C4×D10711yescharacteristic
307C22C2×Q8×D10711yescharacteristic
308C22#41×D10711yescharacteristic
309C22#1681215411yescharacteristic
310C22#1681215411yescharacteristic
311C22#1681215611yescharacteristic
312C22#1681215711yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1074no—
321C4—4281no—
322C4—4281no—
323C4—4281no—
324C4—2142no—
325C4—2142no—
326C4—2142no—
327C4—2142no—
328C2C4×Q8×D10711yescharacteristic
329C2#2029310011yescharacteristic
330C2#2029310311yescharacteristic
331C2#2029324111yescharacteristic
332C2#2029324711yescharacteristic
333C2#2029325411yescharacteristic
334C2#2029325611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#391×C107C2
socle, prime radical, cosocleC23×C107C24
hypercenter#391D107
hypocenterC107#2331
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #16812107C4semidirect
77. C4×Dic107Q8semidirect
168. C107#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#168121072
#202925342
#202925312
#202925242
#202925222
#202925142
#202925112
#202925092
#202925082
#202924912
C4×Dic107⋊C42
#202924782
#202924722
#391×C1072
#2331107