Finite Group Databasebeta

← #28344424

Subgroups — #28344424

Order 13696.

392 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20292561C211yesmaximal, characteristic
2#20292560C211yesmaximal, characteristic
3#20292558C211yesmaximal, characteristic
4#20292557C211yesmaximal, characteristic
5#20292546C211yesmaximal, characteristic
6#20292534C211yesmaximal, characteristic
7#20292532C211yesmaximal, characteristic
8#20292531C211yesmaximal, characteristic
9#20292531C211yesmaximal, characteristic
10#20292526C211yesmaximal, characteristic
11#20292524C211yesmaximal, characteristic
12#20292522C211yesmaximal, characteristic
13#20292514C211yesmaximal, characteristic
14#20292509C211yesmaximal, characteristic
15#395×C107C211yesmaximal, characteristic
16C22×Dic214C2211yescharacteristic
17C2×C4⋊Dic107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×C4×Dic107C2211yescharacteristic
29C2×C4×Dic107C2211yescharacteristic
30C2×C4×Dic107C2211yescharacteristic
31C107⋊#95C2211yescharacteristic
32C107⋊#95C2211yescharacteristic
33C107⋊#95C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C22×Q8×C107C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C2×Dic214—41no—
52C2×Dic214—41no—
53C2×Dic214Q814yescomplemented
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C4⋊Dic107—41no—
63C4⋊Dic107—41no—
64C4⋊Dic107—41no—
65Dic107⋊C4—22no—
66Dic107⋊C4—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4—41no—
71Dic107⋊C4—41no—
72Dic107⋊C4Q814yescomplemented
73C4×Dic107—41no—
74C4×Dic107—41no—
75C4×Dic107—41no—
76C2×Q8×C107—22no—
77C2×Q8×C107—41no—
78C2×Q8×C107—41no—
79C22×C4×C107C2311yescharacteristic
80C22×C4×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C4⋊C4×C107—22no—
87C4⋊C4×C107—41no—
88C4⋊C4×C107—41no—
89C23×C107C2411yescharacteristic
90Q8×C107—44no—
91C2×C4×C107—21no—
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×C107C2×Q812yes—
110C2×C4×C107C2×Q812yes—
111C2×C4×C107#4112yes—
112C2×Dic107—21no—
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×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107C2×Q812yes—
133C2×Dic107C2×Q812yes—
134C2×Dic107C2×Q812yes—
135C2×Dic107C2×Q812yes—
136Dic214—44no—
137C22×C107C22×Q811yescharacteristic
138C22×C107C22×Q811yescharacteristic
139C22×C107C2×#4111yescharacteristic
140C22×C107H(5,𝔽2)11yescharacteristic
141C22×C107H(5,𝔽2)11yescharacteristic
142C22×C107H(5,𝔽2)11yescharacteristic
143C22×C1072−1+411yescharacteristic
144C4×C107—22no—
145C4×C107—22no—
146C4×C107—22no—
147C4×C107—41no—
148C4×C107—41no—
149C4×C107—41no—
150C4×C107—41no—
151Dic107—22no—
152Dic107—22no—
153Dic107—22no—
154Dic107—22no—
155Dic107—41no—
156Dic107—41no—
157Dic107—41no—
158Dic107—41no—
159C2×C107#53811yescharacteristic
160C2×C107#54311yescharacteristic
161C2×C107#54411yescharacteristic
162C2×C107#55411yescharacteristic
163C2×C107#55711yescharacteristic
164C2×C107Q8211yescharacteristic
165C2×C107#56211yescharacteristic
166#2806—1071nomaximal, Sylow
167C107#280611yescharacteristic, complemented, Sylow
168#398—1071no—
169#398—1071no—
170#398—1071no—
171#398—1071no—
172#395—1071no—
173#395D10711yescharacteristic
174#391—1071no—
175#391—1071no—
176#391—1071no—
177#391—1071no—
178#389—1071no—
179#389—1071no—
180#389—1071no—
181#387—1071no—
182#387—1071no—
183C22×Q8—1071no—
184C22×Q8C2×D10711yescharacteristic
185C2×C4⋊C4—1071no—
186C2×C4⋊C4—1071no—
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×C4⋊C4C2×D10711yescharacteristic
198C2×C4⋊C4C2×D10711yescharacteristic
199C2×C42—1071no—
200C2×C42—1071no—
201C2×C42—1071no—
202#95—1071no—
203#95—1071no—
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#95C2×D10711yescharacteristic
216#95C2×D10711yescharacteristic
217#95C2×D10711yescharacteristic
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—1074no—
222C2×Q8—4281no—
223C2×Q8—4281no—
224C22×C4—1071no—
225C22×C4—1071no—
226C22×C4—1071no—
227C22×C4—1071no—
228C22×C4—1071no—
229C22×C4—1071no—
230C22×C4—1071no—
231C22×C4—1071no—
232C22×C4C22×D10711yescharacteristic
233C22×C4C22×D10711yescharacteristic
234C22×C4C22×D10711yescharacteristic
235C22×C4C22×D10711yescharacteristic
236C22×C4C22×D10711yescharacteristic
237C22×C4C22×D10711yescharacteristic
238C22×C4C22×D10711yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1074no—
243C4⋊C4—4281no—
244C4⋊C4—4281no—
245C4⋊C4—4281no—
246C4⋊C4—4281no—
247C4⋊C4—4281no—
248C4⋊C4—4281no—
249C4⋊C4—4281no—
250C4⋊C4—4281no—
251C4⋊C4—4281no—
252C4⋊C4—2142no—
253C42—4281no—
254C42—4281no—
255C42—4281no—
256C23C23×D10711yescharacteristic
257Q8—44no—
258Q8—4284no—
259C2×C4—21no—
260C2×C4—21no—
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—1072no—
278C2×C4—1072no—
279C2×C4—1072no—
280C2×C4—1072no—
281C2×C4—2141no—
282C2×C4—2141no—
283C2×C4—2141no—
284C2×C4—2141no—
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×C4Q8×D10712yes—
302C2×C4Q8×D10712yes—
303C2×C4#1313381712yes—
304C22C2×Q8×D10711yescharacteristic
305C22C2×Q8×D10711yescharacteristic
306C22C2×#1313381711yescharacteristic
307C22#1681215411yescharacteristic
308C22#1681215411yescharacteristic
309C22#1681215511yescharacteristic
310C22#1681215711yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—4281no—
319C4—4281no—
320C4—4281no—
321C4—4281no—
322C4—2142no—
323C4—2142no—
324C4—2142no—
325C4—2142no—
326C2#2029321211yescharacteristic
327C2#2029325211yescharacteristic
328C2#2029325411yescharacteristic
329C2#2029333511yescharacteristic
330C2#2029335211yescharacteristic
331C2#2029335711yescharacteristic
332C2#2029337311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#395×C107C2
hypercenter#395D107
hypocenterC107#2806
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
53. C2×Dic214Q8semidirect
72. Dic107⋊C4Q8semidirect
167. C107#2806semidirect

Maximal subgroups

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

subgroupindex
#202925612
#202925602
#202925582
#202925572
#202925462
#202925342
#202925322
#202925312
#202925262
#202925242
#202925222
#202925142
#202925092
#395×C1072
#2806107