Finite Group Databasebeta

← C107×#7657 #41033621

Subgroups — C107×#7657 #41033621

Order 27392.

370 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2864C211yesmaximal, characteristic
2C107×#1839C211yesmaximal, characteristic
3C107×#1744C211yesmaximal, characteristic
4C107×#1271C212yesmaximal
5C107×#1271C212yesmaximal
6C2×C4×C8×C107—21no—
7#389×C107C411yescharacteristic
8#389×C107C411yescharacteristic
9#389×C107C2211yescharacteristic
10#389×C107C2211yescharacteristic
11#387×C107—21no—
12#387×C107—21no—
13#387×C107—21no—
14#387×C107—21no—
15#382×C107C411yescharacteristic
16#382×C107C411yescharacteristic
17C43×C107C2211yescharacteristic
18#336×C107—21no—
19#336×C107—21no—
20#336×C107—21no—
21#336×C107C2212yes—
22#336×C107C2212yes—
23C22×C8×C107—22no—
24C22×C8×C107—22no—
25C2×C4⋊C4×C107—21no—
26C2×C4⋊C4×C107—21no—
27C2×C4⋊C4×C107—21no—
28C2×C4⋊C4×C107—21no—
29C2×C4⋊C4×C107C2×C411yescharacteristic
30C2×C4⋊C4×C107C2×C411yescharacteristic
31C2×C4⋊C4×C107C2×C411yescharacteristic
32C2×C4⋊C4×C107C2×C411yescharacteristic
33C2×C42×C107C2×C411yescharacteristic
34C2×C42×C107C2×C411yescharacteristic
35C2×C42×C107D411yescharacteristic
36C2×C42×C107D411yescharacteristic
37C2×C42×C107D411yescharacteristic
38C2×C42×C107D411yescharacteristic
39C2×C42×C107C2311yescharacteristic
40C4×C8×C107—24no—
41#95×C107—21no—
42#95×C107—21no—
43#95×C107—21no—
44#95×C107—21no—
45#95×C107—21no—
46#95×C107—21no—
47#95×C107—21no—
48#95×C107—21no—
49C22×C4×C107—21no—
50C22×C4×C107—21no—
51C22×C4×C107—21no—
52C22×C4×C107—21no—
53C22×C4×C107C22⋊C411yescharacteristic
54C22×C4×C107C22⋊C411yescharacteristic
55C22×C4×C107C22⋊C411yescharacteristic
56C22×C4×C107C22⋊C411yescharacteristic
57C22×C4×C107C22×C411yescharacteristic
58C22×C4×C107C2×D411yescharacteristic
59C22×C4×C107C2×D411yescharacteristic
60C2×C8×C107—24no—
61C2×C8×C107—42no—
62C2×C8×C107—42no—
63C2×C8×C107—42no—
64C2×C8×C107—42no—
65C2×C8×C107—42no—
66C4⋊C4×C107—22no—
67C4⋊C4×C107—22no—
68C4⋊C4×C107—41no—
69C4⋊C4×C107—41no—
70C4⋊C4×C107—42no—
71C4⋊C4×C107—42no—
72C4⋊C4×C107—42no—
73C4⋊C4×C107—42no—
74C42×C107—22no—
75C42×C107—22no—
76C42×C107—22no—
77C42×C107—22no—
78C42×C107—22no—
79C42×C107—41no—
80C42×C107—41no—
81C23×C107C2×C22⋊C411yescharacteristic
82C2×C4×C107—21no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—21no—
87C2×C4×C107—21no—
88C2×C4×C107—21no—
89C2×C4×C107—21no—
90C2×C4×C107—21no—
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—41no—
99C2×C4×C107—41no—
100C2×C4×C107—41no—
101C2×C4×C107—41no—
102C2×C4×C107—41no—
103C2×C4×C107—41no—
104C2×C4×C107—41no—
105C2×C4×C107—41no—
106C2×C4×C107—41no—
107C2×C4×C107—41no—
108C2×C4×C107—41no—
109C2×C4×C107—41no—
110C2×C4×C107#10112yes—
111C2×C4×C107#10412yes—
112C2×C4×C107#13112yes—
113C2×C4×C107#13512yes—
114C2×C4×C107#13512yes—
115C8×C107—44no—
116C8×C107—82no—
117C22×C107#40811yescharacteristic
118C22×C107#41011yescharacteristic
119C22×C107C2×#10111yescharacteristic
120C22×C107#41611yescharacteristic
121C22×C107#41611yescharacteristic
122C22×C107C2×#10411yescharacteristic
123C22×C107#42111yescharacteristic
124C4×C107—22no—
125C4×C107—22no—
126C4×C107—22no—
127C4×C107—22no—
128C4×C107—22no—
129C4×C107—41no—
130C4×C107—41no—
131C4×C107—81no—
132C4×C107—81no—
133C4×C107—81no—
134C4×C107—81no—
135#7657C10711yesmaximal, characteristic, direct product factor, Sylow
136C2×C107#147011yescharacteristic
137C2×C107#148211yescharacteristic
138C2×C107#149411yescharacteristic
139C2×C107#150011yescharacteristic
140C2×C107#152111yescharacteristic
141C2×C107#153111yescharacteristic
142C2×C107#154411yescharacteristic
143#2864C2×C10711yescharacteristic
144#1839C2×C10711yescharacteristic
145#1744C2×C10711yescharacteristic
146#1271C2×C10712yes—
147#1271C2×C10712yes—
148C107#765711yescharacteristic, direct product factor, Sylow
149C2×C4×C8—21no—
150#389C4×C10711yescharacteristic
151#389C4×C10711yescharacteristic
152#389C22×C10711yescharacteristic
153#389C22×C10711yescharacteristic
154#387—21no—
155#387—21no—
156#387—21no—
157#387—21no—
158#382C4×C10711yescharacteristic
159#382C4×C10711yescharacteristic
160C43C22×C10711yescharacteristic
161#336—21no—
162#336—21no—
163#336—21no—
164#336C22×C10712yes—
165#336C22×C10712yes—
166C22×C8—22no—
167C22×C8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C2×C4×C10711yescharacteristic
173C2×C4⋊C4C2×C4×C10711yescharacteristic
174C2×C4⋊C4C2×C4×C10711yescharacteristic
175C2×C4⋊C4C2×C4×C10711yescharacteristic
176C2×C42C2×C4×C10711yescharacteristic
177C2×C42C2×C4×C10711yescharacteristic
178C2×C42D4×C10711yescharacteristic
179C2×C42D4×C10711yescharacteristic
180C2×C42D4×C10711yescharacteristic
181C2×C42D4×C10711yescharacteristic
182C2×C42C23×C10711yescharacteristic
183C4×C8—24no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4C22⋊C4×C10711yescharacteristic
197C22×C4C22⋊C4×C10711yescharacteristic
198C22×C4C22⋊C4×C10711yescharacteristic
199C22×C4C22⋊C4×C10711yescharacteristic
200C22×C4C22×C4×C10711yescharacteristic
201C22×C4C2×D4×C10711yescharacteristic
202C22×C4C2×D4×C10711yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C42—22no—
218C42—22no—
219C42—22no—
220C42—22no—
221C42—22no—
222C42—41no—
223C42—41no—
224C23C2×C22⋊C4×C10711yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4#101×C10712yes—
254C2×C4#104×C10712yes—
255C2×C4#131×C10712yes—
256C2×C4#135×C10712yes—
257C2×C4#135×C10712yes—
258C8—44no—
259C8—82no—
260C22#408×C10711yescharacteristic
261C22#410×C10711yescharacteristic
262C22C2×#101×C10711yescharacteristic
263C22#416×C10711yescharacteristic
264C22#416×C10711yescharacteristic
265C22C2×#104×C10711yescharacteristic
266C22#421×C10711yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—22no—
271C4—22no—
272C4—41no—
273C4—41no—
274C4—81no—
275C4—81no—
276C4—81no—
277C4—81no—
278C2C107×#147011yescharacteristic
279C2C107×#148211yescharacteristic
280C2C107×#149411yescharacteristic
281C2C107×#150011yescharacteristic
282C2C107×#152111yescharacteristic
283C2C107×#153111yescharacteristic
284C2C107×#154411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
135. #7657C107direct (N × H)
148. C107#7657direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#28642
C107×#18392
C107×#17442
C107×#12712
#7657107