Finite Group Databasebeta

← C107×#7729 #41033693

Subgroups — C107×#7729 #41033693

Order 27392.

346 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
1C107×#2863C211yesmaximal, characteristic
2C107×#1839C211yesmaximal, characteristic
3C107×#1839C211yesmaximal, characteristic
4C107×#1272C212yesmaximal
5C107×#1271C212yesmaximal
6#391×C107C411yescharacteristic
7#391×C107C411yescharacteristic
8#391×C107C2211yescharacteristic
9#389×C107C411yescharacteristic
10#389×C107C411yescharacteristic
11#389×C107C2211yescharacteristic
12#387×C107—21no—
13#387×C107—21no—
14#387×C107—21no—
15#383×C107—21no—
16C43×C107C2211yescharacteristic
17#336×C107—21no—
18#336×C107—21no—
19#336×C107—21no—
20#336×C107—21no—
21#336×C107C2212yes—
22#336×C107C2212yes—
23C22×Q8×C107C2×C411yescharacteristic
24C22×C8×C107—22no—
25C22×C8×C107—22no—
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×C42×C107C2×C411yescharacteristic
33C2×C42×C107C2×C411yescharacteristic
34C2×C42×C107D411yescharacteristic
35C2×C42×C107D411yescharacteristic
36C2×C42×C107D411yescharacteristic
37C2×C42×C107D411yescharacteristic
38C2×C42×C107C2311yescharacteristic
39#95×C107—21no—
40#95×C107—21no—
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—
48C2×Q8×C107—22no—
49C2×Q8×C107—41no—
50C2×Q8×C107—41no—
51C22×C4×C107—21no—
52C22×C4×C107—21no—
53C22×C4×C107—21no—
54C22×C4×C107—21no—
55C22×C4×C107C22⋊C411yescharacteristic
56C22×C4×C107C22⋊C411yescharacteristic
57C22×C4×C107C22⋊C411yescharacteristic
58C22×C4×C107C22⋊C411yescharacteristic
59C22×C4×C107C22×C411yescharacteristic
60C22×C4×C107C2×D411yescharacteristic
61C22×C4×C107C2×D411yescharacteristic
62C2×C8×C107—42no—
63C2×C8×C107—42no—
64C2×C8×C107—42no—
65C2×C8×C107—42no—
66C2×C8×C107—42no—
67C2×C8×C107—42no—
68C4⋊C4×C107—22no—
69C4⋊C4×C107—41no—
70C4⋊C4×C107—41no—
71C4⋊C4×C107—42no—
72C4⋊C4×C107—42no—
73C4⋊C4×C107—42no—
74C42×C107—22no—
75C42×C107—22no—
76C42×C107—22no—
77C42×C107—41no—
78C42×C107—41no—
79C42×C107—41no—
80C42×C107—41no—
81C23×C107C2×C22⋊C411yescharacteristic
82Q8×C107—82no—
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—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
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—41no—
111C2×C4×C107—41no—
112C2×C4×C107—41no—
113C2×C4×C107#13112yes—
114C2×C4×C107#13512yes—
115C2×C4×C107#13712yes—
116C8×C107—82no—
117C8×C107—82no—
118C22×C107#40811yescharacteristic
119C22×C107#41011yescharacteristic
120C22×C107#41311yescharacteristic
121C22×C107#41611yescharacteristic
122C22×C107#41911yescharacteristic
123C22×C107#42111yescharacteristic
124C22×C107#42111yescharacteristic
125C4×C107—22no—
126C4×C107—22no—
127C4×C107—22no—
128C4×C107—41no—
129C4×C107—41no—
130C4×C107—41no—
131C4×C107—41no—
132C4×C107—81no—
133C4×C107—81no—
134C4×C107—81no—
135C4×C107—81no—
136#7729C10711yesmaximal, characteristic, direct product factor, Sylow
137C2×C107#147311yescharacteristic
138C2×C107#148211yescharacteristic
139C2×C107#149711yescharacteristic
140C2×C107#151511yescharacteristic
141C2×C107#152111yescharacteristic
142C2×C107#153511yescharacteristic
143C2×C107#155411yescharacteristic
144#2863C2×C10711yescharacteristic
145#1839C2×C10711yescharacteristic
146#1839C2×C10711yescharacteristic
147#1272C2×C10712yes—
148#1271C2×C10712yes—
149C107#772911yescharacteristic, direct product factor, Sylow
150#391C4×C10711yescharacteristic
151#391C4×C10711yescharacteristic
152#391C22×C10711yescharacteristic
153#389C4×C10711yescharacteristic
154#389C4×C10711yescharacteristic
155#389C22×C10711yescharacteristic
156#387—21no—
157#387—21no—
158#387—21no—
159#383—21no—
160C43C22×C10711yescharacteristic
161#336—21no—
162#336—21no—
163#336—21no—
164#336—21no—
165#336C22×C10712yes—
166#336C22×C10712yes—
167C22×Q8C2×C4×C10711yescharacteristic
168C22×C8—22no—
169C22×C8—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
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
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C2×Q8—22no—
193C2×Q8—41no—
194C2×Q8—41no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4C22⋊C4×C10711yescharacteristic
200C22×C4C22⋊C4×C10711yescharacteristic
201C22×C4C22⋊C4×C10711yescharacteristic
202C22×C4C22⋊C4×C10711yescharacteristic
203C22×C4C22×C4×C10711yescharacteristic
204C22×C4C2×D4×C10711yescharacteristic
205C22×C4C2×D4×C10711yescharacteristic
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C42—22no—
219C42—22no—
220C42—22no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42—41no—
225C23C2×C22⋊C4×C10711yescharacteristic
226Q8—82no—
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—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
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—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4#131×C10712yes—
258C2×C4#135×C10712yes—
259C2×C4#137×C10712yes—
260C8—82no—
261C8—82no—
262C22#408×C10711yescharacteristic
263C22#410×C10711yescharacteristic
264C22#413×C10711yescharacteristic
265C22#416×C10711yescharacteristic
266C22#419×C10711yescharacteristic
267C22#421×C10711yescharacteristic
268C22#421×C10711yescharacteristic
269C4—22no—
270C4—22no—
271C4—22no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—81no—
277C4—81no—
278C4—81no—
279C4—81no—
280C2C107×#147311yescharacteristic
281C2C107×#148211yescharacteristic
282C2C107×#149711yescharacteristic
283C2C107×#151511yescharacteristic
284C2C107×#152111yescharacteristic
285C2C107×#153511yescharacteristic
286C2C107×#155411yescharacteristic
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
136. #7729C107direct (N × H)
149. C107#7729direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#28632
C107×#18392
C107×#12722
C107×#12712
#7729107