Finite Group Databasebeta

← #28344697

Subgroups — #28344697

Order 13696.

366 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107⋊#401C211yesmaximal, characteristic, complemented
2#20292569C211yesmaximal, characteristic, complemented
3#20292562C211yesmaximal, characteristic
4#20292557C211yesmaximal, characteristic, complemented
5#20292556C211yesmaximal, characteristic
6#20292556C211yesmaximal, characteristic
7#20292554C211yesmaximal, characteristic
8#20292549C211yesmaximal, characteristic
9#20292548C211yesmaximal, characteristic, complemented
10#20292547C211yesmaximal, characteristic, complemented
11#20292540C211yesmaximal, characteristic
12#20292524C211yesmaximal, characteristic, complemented
13#20292519C211yesmaximal, characteristic
14#20292510C211yesmaximal, characteristic, complemented
15#400×C107C211yesmaximal, characteristic, complemented
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×(C2×D107)⋊C4C2211yescharacteristic
26C2×(C2×D107)⋊C4C2211yescharacteristic
27C2×(C2×D107)⋊C4C2211yescharacteristic
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
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
44C2×C4⋊C4×C107C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46#95×C107C2211yescharacteristic
47#95×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C23×D107C2311yescharacteristic
52C2×Dic214—41no—
53C2×Dic214—41no—
54C2×Dic214—41no—
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C4⋊Dic107—22no—
63C4⋊Dic107—41no—
64C4⋊Dic107—41no—
65Dic107⋊C4—22no—
66Dic107⋊C4—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70(C2×D107)⋊C4—22no—
71(C2×D107)⋊C4—41no—
72(C2×D107)⋊C4—41no—
73(C2×D107)⋊C4—41no—
74(C2×D107)⋊C4—41no—
75(C2×D107)⋊C4—41no—
76(C2×D107)⋊C4—41no—
77C4×Dic107—41no—
78C22×C4×C107C2311yescharacteristic
79C22×C4×C107C2311yescharacteristic
80C22×C4×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C4⋊C4×C107—41no—
86C4⋊C4×C107—41no—
87C23×C107C2411yescharacteristic
88C22×D107—21no—
89C22×D107—21no—
90C22×D107—21no—
91C22×D107—21no—
92C22×D107—21no—
93C22×D107—21no—
94C22×D107—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×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×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×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107#4112yes—
137Dic214—44no—
138C22×C107C2×#4111yescharacteristic
139C22×C107H(5,𝔽2)11yescharacteristic
140C22×C107H(5,𝔽2)11yescharacteristic
141C22×C107H(5,𝔽2)11yescharacteristic
142C22×C1072−1+411yescharacteristic
143C22×C1072−1+411yescharacteristic
144C22×C1072−1+411yescharacteristic
145C2×D107—41no—
146C2×D107—41no—
147C2×D107—41no—
148C2×D107—41no—
149C2×D107—41no—
150C2×D107—41no—
151C2×D107—41no—
152C4×C107—41no—
153C4×C107—41no—
154C4×C107—41no—
155C4×C107—41no—
156C4×C107—41no—
157C4×C107—41no—
158C4×C107—41no—
159Dic107—22no—
160Dic107—41no—
161Dic107—41no—
162Dic107—41no—
163Dic107—41no—
164Dic107—41no—
165Dic107—41no—
166C2×C107#53911yescharacteristic
167C2×C107#54211yescharacteristic
168C2×C107#54211yescharacteristic
169C2×C107#56011yescharacteristic
170C2×C107#56311yescharacteristic
171C2×C107#56311yescharacteristic
172C2×C107#56311yescharacteristic
173D107—81no—
174#2838—1071nomaximal, Sylow
175C107#283811yescharacteristic, complemented, Sylow
176#401—1071no—
177#400—1071no—
178#400D10711yescharacteristic, complemented
179#399—1071no—
180#398—1071no—
181#397—1071no—
182#397—1071no—
183#397—1071no—
184#396—1071no—
185#395—1071no—
186#395—1071no—
187#393—1071no—
188#389—1071no—
189#388—1071no—
190#387—1071no—
191C22×Q8—1071no—
192C2×C4⋊C4—1071no—
193C2×C4⋊C4—1071no—
194C2×C4⋊C4—1071no—
195C2×C4⋊C4—1071no—
196C2×C4⋊C4—1071no—
197C2×C4⋊C4—1071no—
198C2×C4⋊C4—1071no—
199C2×C4⋊C4—1071no—
200C2×C4⋊C4C2×D10711yescharacteristic
201C2×C4⋊C4C2×D10711yescharacteristic
202C2×C22⋊C4—1071no—
203C2×C22⋊C4—1071no—
204C2×C22⋊C4—1071no—
205C2×C22⋊C4—1071no—
206C2×C22⋊C4—1071no—
207C2×C22⋊C4—1071no—
208C2×C22⋊C4—1071no—
209C2×C42—1071no—
210#95—1071no—
211#95—1071no—
212#95—1071no—
213#95—1071no—
214#95—1071no—
215#95—1071no—
216#95—1071no—
217#95—1071no—
218#95—1071no—
219#95—1071no—
220#95—1071no—
221#95C2×D10711yescharacteristic
222#95C2×D10711yescharacteristic
223#95C2×D10711yescharacteristic
224#95C2×D10711yescharacteristic
225#95C2×D10711yescharacteristic
226C24—1071no—
227C2×Q8—4281no—
228C2×Q8—4281no—
229C2×Q8—4281no—
230C22×C4—1071no—
231C22×C4—1071no—
232C22×C4—1071no—
233C22×C4—1071no—
234C22×C4—1071no—
235C22×C4—1071no—
236C22×C4—1071no—
237C22×C4C22×D10711yescharacteristic
238C22×C4C22×D10711yescharacteristic
239C22×C4C22×D10711yescharacteristic
240C22×C4C22×D10711yescharacteristic
241C22×C4C22×D10711yescharacteristic
242C22×C4C22×D10711yescharacteristic
243C22×C4C22×D10711yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—4281no—
247C4⋊C4—4281no—
248C4⋊C4—4281no—
249C4⋊C4—4281no—
250C4⋊C4—4281no—
251C4⋊C4—4281no—
252C4⋊C4—2142no—
253C4⋊C4—2142no—
254C22⋊C4—4281no—
255C22⋊C4—4281no—
256C22⋊C4—4281no—
257C22⋊C4—4281no—
258C22⋊C4—4281no—
259C22⋊C4—4281no—
260C22⋊C4—2142no—
261C42—4281no—
262C23—2141no—
263C23—2141no—
264C23—2141no—
265C23—2141no—
266C23—2141no—
267C23—2141no—
268C23—2141no—
269C23C23×D10711yescharacteristic
270Q8—4284no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—1072no—
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×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—
313C22—4281no—
314C22—4281no—
315C22—4281no—
316C22—4281no—
317C22—4281no—
318C22—4281no—
319C22—4281no—
320C22#41×D10711yescharacteristic
321C22#1681215411yescharacteristic
322C22#1681215511yescharacteristic
323C22#1681215511yescharacteristic
324C22#1681215611yescharacteristic
325C22#1681215611yescharacteristic
326C22#1681215711yescharacteristic
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—4281no—
335C4—4281no—
336C4—4281no—
337C4—4281no—
338C4—4281no—
339C4—4281no—
340C4—2142no—
341C2—8561no—
342C2#2029322511yescharacteristic
343C2#2029324111yescharacteristic
344C2#2029324311yescharacteristic
345C2#2029336711yescharacteristic
346C2#2029337811yescharacteristic
347C2#2029337911yescharacteristic
348C2#2029338111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#400×C107C2
prime radicalC23×D107C23
hypercenter#400D107
hypocenterC107#2838
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C107⋊#401C2semidirect
2. #20292569C2semidirect
4. #20292557C2semidirect
9. #20292548C2semidirect
10. #20292547C2semidirect
12. #20292524C2semidirect
14. #20292510C2semidirect
15. #400×C107C2semidirect
175. C107#2838semidirect
178. #400D107semidirect

Maximal subgroups

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

subgroupindex
C107⋊#4012
#202925692
#202925622
#202925572
#202925562
#202925542
#202925492
#202925482
#202925472
#202925402
#202925242
#202925192
#202925102
#400×C1072
#2838107