Finite Group Databasebeta

← C107×#3553 #28334236

Subgroups — C107×#3553 #28334236

Order 13696.

932 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#564×C107C211yesmaximal, characteristic, complemented
2#563×C107C212yesmaximal, complemented
3#562×C107C211yesmaximal, characteristic, complemented
4#554×C107C214yesmaximal, complemented
5#553×C107C214yesmaximal, complemented
6#552×C107C214yesmaximal, complemented
7#541×C107C214yesmaximal, complemented
8#539×C107C214yesmaximal, complemented
9#539×C107C214yesmaximal, complemented
10#529×C107C212yesmaximal, complemented
11C2×#125×C107C211yesmaximal, characteristic, complemented
12C4⋊Q8×C107C2214yes—
13#126×C107C2214yes—
14#126×C107C2214yes—
15#126×C107C2214yes—
16#126×C107C2214yes—
17#126×C107C2214yes—
18#125×C107C2214yes—
19#125×C107C2212yes—
20#125×C107C2211yescharacteristic
21#125×C107C2211yescharacteristic
22#125×C107C2212yes—
23#125×C107C2214yes—
24#125×C107C2214yes—
25#125×C107C2214yes—
26#125×C107C2214yes—
27#125×C107C2214yes—
28#124×C107C2212yes—
29#123×C107C2214yes—
30#123×C107C2214yes—
31#123×C107C2214yes—
32#123×C107C2214yes—
33#123×C107C2214yes—
34C22⋊Q8×C107C2212yes—
35C22⋊Q8×C107C2214yes—
36C22⋊Q8×C107C2214yes—
37C22⋊Q8×C107C2214yes—
38C22⋊Q8×C107C2214yes—
39C22⋊Q8×C107C2214yes—
40C22⋊Q8×C107C2214yes—
41#121×C107C2212yes—
42#121×C107C2214yes—
43#121×C107C2214yes—
44C4×Q8×C107C2212yes—
45C4×Q8×C107C2214yes—
46C4×D4×C107C2212yes—
47C4×D4×C107C2214yes—
48C4×D4×C107C2214yes—
49C4×D4×C107C2214yes—
50C4×D4×C107C2214yes—
51#117×C107C2214yes—
52#117×C107C2214yes—
53C2×C4⋊C4×C107C2212yes—
54C2×C4⋊C4×C107C2214yes—
55C2×C4⋊C4×C107C2214yes—
56C2×C42×C107C2211yescharacteristic
57C2×Q8×C107C2314yes—
58C2×Q8×C107C2312yes—
59C2×D4×C107C2314yes—
60C2×D4×C107C2314yes—
61C2×D4×C107C2312yes—
62C22×C4×C107C2311yescharacteristic
63C22×C4×C107C2312yes—
64C22×C4×C107C2314yes—
65C22×C4×C107C2314yes—
66C22×C4×C107C2314yes—
67C22×C4×C107C2314yes—
68C4⋊C4×C107C2314yes—
69C4⋊C4×C107C2314yes—
70C4⋊C4×C107C2314yes—
71C4⋊C4×C107C2314yes—
72C4⋊C4×C107C2314yes—
73C4⋊C4×C107C2312yes—
74C4⋊C4×C107C2314yes—
75C4⋊C4×C107C2314yes—
76C4⋊C4×C107C2314yes—
77C4⋊C4×C107C2312yes—
78C4⋊C4×C107C2314yes—
79C4⋊C4×C107C2314yes—
80C4⋊C4×C107C2312yes—
81C4⋊C4×C107C2314yes—
82C4⋊C4×C107C2314yes—
83C4⋊C4×C107C2314yes—
84C4⋊C4×C107C2312yes—
85C4⋊C4×C107C2314yes—
86C4⋊C4×C107C2314yes—
87C22⋊C4×C107C2314yes—
88C22⋊C4×C107C2314yes—
89C22⋊C4×C107C2314yes—
90C22⋊C4×C107C2314yes—
91C22⋊C4×C107C2314yes—
92C22⋊C4×C107C2314yes—
93C22⋊C4×C107C2314yes—
94C22⋊C4×C107C2314yes—
95C22⋊C4×C107C2314yes—
96C42×C107C2311yescharacteristic
97C42×C107C2312yes—
98C42×C107C2311yescharacteristic
99C42×C107C2314yes—
100C42×C107C2314yes—
101C42×C107C2314yes—
102C23×C107C2414yes—
103C23×C107C2411yescharacteristic
104Q8×C107—44no—
105Q8×C107—42no—
106D4×C107—28no—
107D4×C107—44no—
108D4×C107—42no—
109C2×C4×C107—22no—
110C2×C4×C107—44no—
111C2×C4×C107—42no—
112C2×C4×C107—44no—
113C2×C4×C107—44no—
114C2×C4×C107—44no—
115C2×C4×C107C2412yes—
116C2×C4×C107C2414yes—
117C2×C4×C107C2411yescharacteristic
118C2×C4×C107C2411yescharacteristic
119C2×C4×C107C2414yes—
120C2×C4×C107C2412yes—
121C2×C4×C107C2414yes—
122C2×C4×C107C2414yes—
123C2×C4×C107C2414yes—
124C22×C107—22no—
125C22×C107—24no—
126C22×C107—24no—
127C22×C107—24no—
128C22×C1072−1+412yes—
129C22×C107C2511yescharacteristic
130C4×C107—21no—
131C4×C107—21no—
132C4×C107—24no—
133C4×C107—22no—
134C4×C107—24no—
135C4×C107—24no—
136C4×C107—24no—
137C4×C107—22no—
138C4×C107—24no—
139C2×C107—22no—
140C2×C107—44no—
141C2×C107C2×2−1+411yescharacteristic
142C2×C107#58512yes—
143#3553C10711yesmaximal, characteristic, direct product factor, Sylow
144C107#355311yescharacteristic, direct product factor, Sylow
145#564C2×C10711yescharacteristic, complemented
146#563C2×C10712yescomplemented
147#562C2×C10711yescharacteristic, complemented
148#554C2×C10714yescomplemented
149#553C2×C10714yescomplemented
150#552C2×C10714yescomplemented
151#541C2×C10714yescomplemented
152#539C2×C10714yescomplemented
153#539C2×C10714yescomplemented
154#529C2×C10712yescomplemented
155C2×#125C2×C10711yescharacteristic, complemented
156C4⋊Q8C22×C10714yes—
157#126C22×C10714yes—
158#126C22×C10714yes—
159#126C22×C10714yes—
160#126C22×C10714yes—
161#126C22×C10714yes—
162#125C22×C10714yes—
163#125C22×C10712yes—
164#125C22×C10711yescharacteristic
165#125C22×C10711yescharacteristic
166#125C22×C10712yes—
167#125C22×C10714yes—
168#125C22×C10714yes—
169#125C22×C10714yes—
170#125C22×C10714yes—
171#125C22×C10714yes—
172#124C22×C10712yes—
173#123C22×C10714yes—
174#123C22×C10714yes—
175#123C22×C10714yes—
176#123C22×C10714yes—
177#123C22×C10714yes—
178C22⋊Q8C22×C10712yes—
179C22⋊Q8C22×C10714yes—
180C22⋊Q8C22×C10714yes—
181C22⋊Q8C22×C10714yes—
182C22⋊Q8C22×C10714yes—
183C22⋊Q8C22×C10714yes—
184C22⋊Q8C22×C10714yes—
185#121C22×C10712yes—
186#121C22×C10714yes—
187#121C22×C10714yes—
188C4×Q8C22×C10712yes—
189C4×Q8C22×C10714yes—
190C4×D4C22×C10712yes—
191C4×D4C22×C10714yes—
192C4×D4C22×C10714yes—
193C4×D4C22×C10714yes—
194C4×D4C22×C10714yes—
195#117C22×C10714yes—
196#117C22×C10714yes—
197C2×C4⋊C4C22×C10712yes—
198C2×C4⋊C4C22×C10714yes—
199C2×C4⋊C4C22×C10714yes—
200C2×C42C22×C10711yescharacteristic
201C2×Q8C23×C10714yes—
202C2×Q8C23×C10712yes—
203C2×D4C23×C10714yes—
204C2×D4C23×C10714yes—
205C2×D4C23×C10712yes—
206C22×C4C23×C10711yescharacteristic
207C22×C4C23×C10712yes—
208C22×C4C23×C10714yes—
209C22×C4C23×C10714yes—
210C22×C4C23×C10714yes—
211C22×C4C23×C10714yes—
212C4⋊C4C23×C10714yes—
213C4⋊C4C23×C10714yes—
214C4⋊C4C23×C10714yes—
215C4⋊C4C23×C10714yes—
216C4⋊C4C23×C10714yes—
217C4⋊C4C23×C10712yes—
218C4⋊C4C23×C10714yes—
219C4⋊C4C23×C10714yes—
220C4⋊C4C23×C10714yes—
221C4⋊C4C23×C10712yes—
222C4⋊C4C23×C10714yes—
223C4⋊C4C23×C10714yes—
224C4⋊C4C23×C10712yes—
225C4⋊C4C23×C10714yes—
226C4⋊C4C23×C10714yes—
227C4⋊C4C23×C10714yes—
228C4⋊C4C23×C10712yes—
229C4⋊C4C23×C10714yes—
230C4⋊C4C23×C10714yes—
231C22⋊C4C23×C10714yes—
232C22⋊C4C23×C10714yes—
233C22⋊C4C23×C10714yes—
234C22⋊C4C23×C10714yes—
235C22⋊C4C23×C10714yes—
236C22⋊C4C23×C10714yes—
237C22⋊C4C23×C10714yes—
238C22⋊C4C23×C10714yes—
239C22⋊C4C23×C10714yes—
240C42C23×C10711yescharacteristic
241C42C23×C10712yes—
242C42C23×C10711yescharacteristic
243C42C23×C10714yes—
244C42C23×C10714yes—
245C42C23×C10714yes—
246C23C24×C10714yes—
247C23C24×C10711yescharacteristic
248Q8—44no—
249Q8—42no—
250D4—28no—
251D4—44no—
252D4—42no—
253C2×C4—22no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4C24×C10712yes—
260C2×C4C24×C10714yes—
261C2×C4C24×C10711yescharacteristic
262C2×C4C24×C10711yescharacteristic
263C2×C4C24×C10714yes—
264C2×C4C24×C10712yes—
265C2×C4C24×C10714yes—
266C2×C4C24×C10714yes—
267C2×C4C24×C10714yes—
268C22—22no—
269C22—24no—
270C22—24no—
271C22—24no—
272C222−1+4×C10712yes—
273C22C25×C10711yescharacteristic
274C4—21no—
275C4—21no—
276C4—24no—
277C4—22no—
278C4—24no—
279C4—24no—
280C4—24no—
281C4—22no—
282C4—24no—
283C2—22no—
284C2—44no—
285C2C2×2−1+4×C10711yescharacteristic
286C2#585×C10712yes—
subgroupG/H
center, socleC22×C107C25
commutator, Frattini, cosocleC22C25×C107
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. #564×C107C2semidirect
2. #563×C107C2semidirect
3. #562×C107C2semidirect
4. #554×C107C2semidirect
5. #553×C107C2semidirect
6. #552×C107C2semidirect
7. #541×C107C2semidirect
8. #539×C107C2semidirect
9. #539×C107C2semidirect
10. #529×C107C2semidirect
11. C2×#125×C107C2semidirect
143. #3553C107direct (N × H)
144. C107#3553direct (N × H)
145. #564C2×C107semidirect
146. #563C2×C107semidirect
147. #562C2×C107semidirect
148. #554C2×C107semidirect
149. #553C2×C107semidirect
150. #552C2×C107semidirect
151. #541C2×C107semidirect
152. #539C2×C107semidirect
153. #539C2×C107semidirect
154. #529C2×C107semidirect
155. C2×#125C2×C107semidirect

Maximal subgroups

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

subgroupindex
#564×C1072
#563×C1072
#562×C1072
#554×C1072
#553×C1072
#552×C1072
#541×C1072
#539×C1072
#529×C1072
C2×#125×C1072
#3553107