Finite Group Databasebeta

← #28339197

Subgroups — #28339197

Order 13696.

444 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812099C211yesmaximal, characteristic
2#20292526C211yesmaximal, characteristic
3#20292525C211yesmaximal, characteristic
4#20292524C211yesmaximal, characteristic
5#20292524C211yesmaximal, characteristic
6#20292524C211yesmaximal, characteristic
7#20292522C211yesmaximal, characteristic
8#20292514C211yesmaximal, characteristic
9#20292512C211yesmaximal, characteristic
10#20292509C211yesmaximal, characteristic
11#20292496C211yesmaximal, characteristic
12C4×Dic107⋊C4C211yesmaximal, characteristic
13#20292478C211yesmaximal, characteristic
14#20292472C211yesmaximal, characteristic
15#387×C107C211yesmaximal, characteristic
16#16812099C418yescomplemented
17C2×C4⋊Dic107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×C4⋊Dic107C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×Dic107⋊C4C2211yescharacteristic
29C2×Dic107⋊C4C2211yescharacteristic
30C2×Dic107⋊C4C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C2×C4×Dic107C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C42×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52C22×Dic107C2311yescharacteristic
53C22×Dic107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C4⋊Dic107—41no—
61C4⋊Dic107—41no—
62C4⋊Dic107—41no—
63C4⋊Dic107C2×C414yes—
64Dic107⋊C4—22no—
65Dic107⋊C4—22no—
66Dic107⋊C4—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4C2×C414yes—
71Dic107⋊C4C2×C414yes—
72Dic107⋊C4C2×C414yes—
73Dic107⋊C4C2×C414yes—
74C4×Dic107—22no—
75C4×Dic107—41no—
76C4×Dic107—41no—
77C4×Dic107—41no—
78C4×Dic107C2×C414yes—
79C4×Dic107Q814yes—
80C22×C4×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C4⋊C4×C107—41no—
88C4⋊C4×C107C2×C414yes—
89C42×C107—41no—
90C23×C107C2411yescharacteristic
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×C107C22×C412yes—
109C2×C4×C107C22×C412yes—
110C2×C4×C107C22×C412yes—
111C2×C4×C107C2×Q812yes—
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×Dic107C22×C412yes—
130C2×Dic107C22×C412yes—
131C2×Dic107C22×C412yes—
132C2×Dic107C22×C412yes—
133C2×Dic107C2×Q812yes—
134C2×Dic107C2×Q812yes—
135C2×Dic107#4112yes—
136C22×C107C23×C411yescharacteristic
137C22×C107C22×Q811yescharacteristic
138C22×C107C2×#4111yescharacteristic
139C22×C107H(5,𝔽2)11yescharacteristic
140C22×C107H(5,𝔽2)11yescharacteristic
141C22×C1072−1+411yescharacteristic
142C22×C1072−1+411yescharacteristic
143C4×C107—22no—
144C4×C107—22no—
145C4×C107—22no—
146C4×C107—22no—
147C4×C107—41no—
148C4×C107—41no—
149C4×C107—41no—
150Dic107—22no—
151Dic107—22no—
152Dic107—22no—
153Dic107—22no—
154Dic107—41no—
155Dic107—41no—
156Dic107—41no—
157Dic107C4×Q814yes—
158C2×C107C2×C4×Q811yescharacteristic
159C2×C107#52011yescharacteristic
160C2×C107#52011yescharacteristic
161C2×C107#54011yescharacteristic
162C2×C107#54111yescharacteristic
163C2×C107#54411yescharacteristic
164C2×C107#54411yescharacteristic
165#2330—1071nomaximal, Sylow
166C107#233011yescharacteristic, complemented, Sylow
167C2×#125—1071no—
168#389—1071no—
169#389—1071no—
170#389—1071no—
171#389—1071no—
172#389—1071no—
173#389—1071no—
174#387—1071no—
175#387—1071no—
176#387—1071no—
177#387D10711yescharacteristic
178#384—1071no—
179C4×C4⋊C4—1071no—
180C4×C4⋊C4—1071no—
181#376—1071no—
182#125—1078no—
183C2×C4⋊C4—1071no—
184C2×C4⋊C4—1071no—
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⋊C4—1071no—
197C2×C4⋊C4C2×D10711yescharacteristic
198C2×C4⋊C4C2×D10711yescharacteristic
199C2×C42—1071no—
200C2×C42—1071no—
201C2×C42—1071no—
202C2×C42—1071no—
203C2×C42—1071no—
204C2×C42—1071no—
205C2×C42C2×D10711yescharacteristic
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#95C2×D10711yescharacteristic
215#95C2×D10711yescharacteristic
216#95C2×D10711yescharacteristic
217#95C2×D10711yescharacteristic
218C22×C4—1071no—
219C22×C4—1071no—
220C22×C4—1071no—
221C22×C4—1071no—
222C22×C4—1071no—
223C22×C4—1071no—
224C22×C4—1071no—
225C22×C4—1071no—
226C22×C4C22×D10711yescharacteristic
227C22×C4C22×D10711yescharacteristic
228C22×C4C22×D10711yescharacteristic
229C22×C4C22×D10711yescharacteristic
230C22×C4C22×D10711yescharacteristic
231C22×C4C22×D10711yescharacteristic
232C22×C4C22×D10711yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—1074no—
235C4⋊C4—1074no—
236C4⋊C4—1074no—
237C4⋊C4—1074no—
238C4⋊C4—1074no—
239C4⋊C4—4281no—
240C4⋊C4—4281no—
241C4⋊C4—4281no—
242C4⋊C4—4281no—
243C4⋊C4—4281no—
244C4⋊C4—4281no—
245C4⋊C4—4281no—
246C4⋊C4—2142no—
247C4⋊C4—2142no—
248C4⋊C4C4×D10714yes—
249C42—41no—
250C42—1074no—
251C42—1074no—
252C42—4281no—
253C42—4281no—
254C42—4281no—
255C42—2142no—
256C23C23×D10711yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
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—1072no—
275C2×C4—1072no—
276C2×C4—1072no—
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×C4C2×C4×D10712yes—
299C2×C4C2×C4×D10712yes—
300C2×C4C2×C4×D10712yes—
301C2×C4Q8×D10712yes—
302C22C22×C4×D10711yescharacteristic
303C22C2×Q8×D10711yescharacteristic
304C22#41×D10711yescharacteristic
305C22#1681215411yescharacteristic
306C22#1681215511yescharacteristic
307C22#1681215611yescharacteristic
308C22#1681215611yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—1074no—
317C4—4281no—
318C4—4281no—
319C4—4281no—
320C4—2142no—
321C4—2142no—
322C4—2142no—
323C4—2142no—
324C2C4×Q8×D10711yescharacteristic
325C2#2029310611yescharacteristic
326C2#2029310711yescharacteristic
327C2#2029322911yescharacteristic
328C2#2029323411yescharacteristic
329C2#2029325611yescharacteristic
330C2#2029325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#387×C107C2
socle, prime radical, cosocleC23×C107C24
hypercenter#387D107
hypocenterC107#2330
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #16812099C4semidirect
166. C107#2330semidirect

Maximal subgroups

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

subgroupindex
C2×#168120992
#202925262
#202925252
#202925242
#202925222
#202925142
#202925122
#202925092
#202924962
C4×Dic107⋊C42
#202924782
#202924722
#387×C1072
#2330107