Finite Group Databasebeta

← #28344427

Subgroups — #28344427

Order 13696.

408 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20292568C211yesmaximal, characteristic, complemented
2#20292567C211yesmaximal, characteristic, complemented
3#20292563C211yesmaximal, characteristic
4#20292563C211yesmaximal, characteristic
5#20292561C211yesmaximal, characteristic, complemented
6#20292558C211yesmaximal, characteristic, complemented
7#20292524C211yesmaximal, characteristic, complemented
8#20292523C211yesmaximal, characteristic, complemented
9#20292522C211yesmaximal, characteristic, complemented
10#20292522C211yesmaximal, characteristic, complemented
11#20292521C211yesmaximal, characteristic
12#20292515C211yesmaximal, characteristic
13#20292500C211yesmaximal, characteristic
14#20292500C211yesmaximal, characteristic
15#385×C107C211yesmaximal, characteristic
16C2×C4⋊Dic107C2211yescharacteristic
17C2×C4⋊Dic107C2211yescharacteristic
18C2×Dic107⋊C4C2211yescharacteristic
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×Dic107⋊C4C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C23×C4×C107C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C22⋊C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C22×Dic107C2311yescharacteristic
52C22×Dic107C2311yescharacteristic
53C22×Dic107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C4⋊Dic107—22no—
60C4⋊Dic107—41no—
61Dic107⋊C4—22no—
62Dic107⋊C4—22no—
63Dic107⋊C4—22no—
64Dic107⋊C4—41no—
65Dic107⋊C4—41no—
66Dic107⋊C4—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4—41no—
71C22⋊Dic107—22no—
72C22⋊Dic107—41no—
73C22⋊Dic107—41no—
74C22⋊Dic107Q814yes—
75C4×Dic107—41no—
76C4×Dic107—41no—
77C24×C107C2311yescharacteristic
78C22×C4×C107—41no—
79C22×C4×C107—41no—
80C22×C4×C107—41no—
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C4⋊C4×C107—41no—
88C4⋊C4×C107—41no—
89C22⋊C4×C107—22no—
90C22⋊C4×C107—41no—
91C23×C107—21no—
92C23×C107—21no—
93C23×C107—21no—
94C23×C107—21no—
95C23×C107—21no—
96C23×C107—21no—
97C23×C107C2×Q812yes—
98C23×C107C2411yescharacteristic
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×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—44no—
117C2×C4×C107#4112yes—
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×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107C2×Q812yes—
140C2×Dic107C2×Q812yes—
141C2×Dic107#4112yes—
142C22×C107—22no—
143C22×C107—22no—
144C22×C107—22no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107—41no—
148C22×C107—41no—
149C22×C107C22×Q811yescharacteristic
150C22×C107C2×#4111yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107H(5,𝔽2)11yescharacteristic
153C22×C107H(5,𝔽2)11yescharacteristic
154C22×C107H(5,𝔽2)11yescharacteristic
155C22×C1072−1+411yescharacteristic
156C4×C107—22no—
157C4×C107—41no—
158C4×C107—41no—
159C4×C107—41no—
160C4×C107—41no—
161C4×C107—41no—
162Dic107—22no—
163Dic107—22no—
164Dic107—22no—
165Dic107—41no—
166Dic107—41no—
167Dic107—41no—
168Dic107—41no—
169Dic107—41no—
170C2×C107—42no—
171C2×C107#53911yescharacteristic
172C2×C107#53911yescharacteristic
173C2×C107#54411yescharacteristic
174C2×C107#55411yescharacteristic
175C2×C107#55411yescharacteristic
176C2×C107#55911yescharacteristic
177C2×C107#56011yescharacteristic
178#2807—1071nomaximal, Sylow
179C107#280711yescharacteristic, complemented, Sylow
180#400—1071no—
181#400—1071no—
182#399—1071no—
183#399—1071no—
184#398—1071no—
185#398—1071no—
186#389—1071no—
187#389—1071no—
188#389—1071no—
189#389—1071no—
190#388—1071no—
191#388—1071no—
192#385—1071no—
193#385—1071no—
194#385D10711yescharacteristic
195C23×C4C2×D10711yescharacteristic
196C2×C4⋊C4—1071no—
197C2×C4⋊C4—1071no—
198C2×C4⋊C4—1071no—
199C2×C4⋊C4—1071no—
200C2×C4⋊C4—1071no—
201C2×C4⋊C4—1071no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4—1071no—
204C2×C4⋊C4—1071no—
205C2×C4⋊C4—1071no—
206C2×C4⋊C4—1071no—
207C2×C4⋊C4—1071no—
208C2×C4⋊C4C2×D10711yescharacteristic
209C2×C4⋊C4C2×D10711yescharacteristic
210C2×C22⋊C4—1071no—
211C2×C22⋊C4—1071no—
212C2×C22⋊C4—1071no—
213C2×C22⋊C4—1071no—
214C2×C22⋊C4C2×D10711yescharacteristic
215C2×C22⋊C4C2×D10711yescharacteristic
216C2×C42—1071no—
217C2×C42—1071no—
218#95—1071no—
219#95—1071no—
220#95—1071no—
221#95—1071no—
222#95—1071no—
223#95—1071no—
224#95—1071no—
225#95—1071no—
226#95—1071no—
227#95—1071no—
228#95C2×D10711yescharacteristic
229#95C2×D10711yescharacteristic
230C24C22×D10711yescharacteristic
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—1071no—
235C22×C4—1071no—
236C22×C4—1071no—
237C22×C4—1071no—
238C22×C4—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4C22×D10711yescharacteristic
243C22×C4C22×D10711yescharacteristic
244C22×C4C22×D10711yescharacteristic
245C22×C4C22×D10711yescharacteristic
246C22×C4C22×D10711yescharacteristic
247C22×C4C22×D10711yescharacteristic
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—4281no—
251C4⋊C4—4281no—
252C4⋊C4—4281no—
253C4⋊C4—4281no—
254C4⋊C4—4281no—
255C4⋊C4—4281no—
256C4⋊C4—4281no—
257C4⋊C4—4281no—
258C4⋊C4—2142no—
259C4⋊C4—2142no—
260C4⋊C4—2142no—
261C4⋊C4—2142no—
262C22⋊C4—22no—
263C22⋊C4—41no—
264C22⋊C4—1074no—
265C22⋊C4—4281no—
266C22⋊C4—4281no—
267C22⋊C4—2142no—
268C42—4281no—
269C42—4281no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23Q8×D10712yes—
277C23C23×D10711yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—44no—
296C2×C4—1072no—
297C2×C4—1072no—
298C2×C4—1072no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4—2141no—
302C2×C4—2141no—
303C2×C4—2141no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4—2141no—
310C2×C4—2141no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4—2141no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4#1313381812yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C2×Q8×D10711yescharacteristic
329C22#41×D10711yescharacteristic
330C22C2×#1313381811yescharacteristic
331C22#1681215411yescharacteristic
332C22#1681215411yescharacteristic
333C22#1681215411yescharacteristic
334C22#1681215611yescharacteristic
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—4281no—
342C4—4281no—
343C4—4281no—
344C4—4281no—
345C4—4281no—
346C4—2142no—
347C4—2142no—
348C4—2142no—
349C2—42no—
350C2#2029321911yescharacteristic
351C2#2029322011yescharacteristic
352C2#2029325611yescharacteristic
353C2#2029333111yescharacteristic
354C2#2029333211yescharacteristic
355C2#2029336011yescharacteristic
356C2#2029336611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#385×C107C2
prime radicalC24×C107C23
hypercenter#385D107
hypocenterC107#2807
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #20292568C2semidirect
2. #20292567C2semidirect
5. #20292561C2semidirect
6. #20292558C2semidirect
7. #20292524C2semidirect
8. #20292523C2semidirect
9. #20292522C2semidirect
10. #20292522C2semidirect
179. C107#2807semidirect

Maximal subgroups

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

subgroupindex
#202925682
#202925672
#202925632
#202925612
#202925582
#202925242
#202925232
#202925222
#202925212
#202925152
#202925002
#385×C1072
#2807107