Finite Group Databasebeta

← C107×#9004 #41034968

Subgroups — C107×#9004 #41034968

Order 27392.

458 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#491×C107C211yesmaximal, characteristic
2C107×#2382C211yesmaximal, characteristic
3C107×#1993C212yesmaximal
4C2×#330×C107C211yesmaximal, characteristic
5C107×#1295C212yesmaximal
6C2×C4⋊Q8×C107C2211yescharacteristic
7C2×#125×C107C2211yescharacteristic
8#491×C107—22no—
9#491×C107C414yescomplemented
10C2×#103×C107—22no—
11C2×#97×C107C2212yes—
12C2×#97×C107C2211yescharacteristic
13#389×C107—22no—
14#387×C107—22no—
15#387×C107—22no—
16#382×C107C2212yes—
17#340×C107—22no—
18#340×C107—22no—
19#330×C107—22no—
20C22×Q8×C107—21no—
21C22×C8×C107—22no—
22C22×C8×C107—21no—
23C4⋊Q8×C107—21no—
24C4⋊Q8×C107—22no—
25C4⋊Q8×C107C2×C412yes—
26#125×C107—22no—
27#125×C107C2×C412yes—
28#125×C107D412yes—
29C2×C4⋊C4×C107—22no—
30C2×C4⋊C4×C107—22no—
31C2×C4⋊C4×C107—22no—
32C2×C4⋊C4×C107D412yes—
33C2×C4⋊C4×C107D412yes—
34C2×C4⋊C4×C107D412yes—
35C2×C42×C107—22no—
36C2×C42×C107C2311yescharacteristic
37#103×C107—28no—
38#97×C107—21no—
39#97×C107—22no—
40#97×C107—22no—
41#97×C107C2×C412yes—
42#95×C107—22no—
43#95×C107—22no—
44#95×C107—22no—
45#95×C107—22no—
46C2×Q8×C107—22no—
47C2×Q8×C107—42no—
48C2×Q8×C107—42no—
49C2×Q8×C107—41no—
50C22×C4×C107—22no—
51C22×C4×C107—22no—
52C22×C4×C107—22no—
53C22×C4×C107—41no—
54C22×C4×C107C2×D411yescharacteristic
55C22×C4×C107C2×D412yes—
56C2×C8×C107—24no—
57C2×C8×C107—22no—
58C2×C8×C107—41no—
59C2×C8×C107—41no—
60C2×C8×C107—42no—
61C2×C8×C107—42no—
62C4⋊C4×C107—24no—
63C4⋊C4×C107—24no—
64C4⋊C4×C107—22no—
65C4⋊C4×C107—24no—
66C4⋊C4×C107—42no—
67C4⋊C4×C107—42no—
68C4⋊C4×C107—42no—
69C4⋊C4×C107—82no—
70C4⋊C4×C107C22⋊C414yes—
71C42×C107—82no—
72C42×C107C22×C411yescharacteristic
73C42×C107C2×D411yescharacteristic
74C42×C107#4112yes—
75C23×C107#12011yescharacteristic
76Q8×C107—44no—
77Q8×C107—82no—
78C2×C4×C107—21no—
79C2×C4×C107—21no—
80C2×C4×C107—22no—
81C2×C4×C107—22no—
82C2×C4×C107—24no—
83C2×C4×C107—42no—
84C2×C4×C107—42no—
85C2×C4×C107—42no—
86C2×C4×C107—42no—
87C2×C4×C107—42no—
88C2×C4×C107—42no—
89C2×C4×C107—42no—
90C2×C4×C107—42no—
91C2×C4×C107—42no—
92C2×C4×C107—81no—
93C2×C4×C107—81no—
94C2×C4×C107C2×C22⋊C411yescharacteristic
95C2×C4×C107C4×D412yes—
96C2×C4×C107#12112yes—
97C2×C4×C107#12311yescharacteristic
98C8×C107—44no—
99C8×C107—42no—
100C22×C107#38611yescharacteristic
101C22×C107#45411yescharacteristic
102C22×C107#45411yescharacteristic
103C22×C107#45512yes—
104C22×C107#45612yes—
105C4×C107—22no—
106C4×C107—22no—
107C4×C107—21no—
108C4×C107—21no—
109C4×C107—44no—
110C4×C107—82no—
111C4×C107—82no—
112C4×C107—82no—
113#9004C10711yesmaximal, characteristic, direct product factor, Sylow
114C2×C107#166211yescharacteristic
115C2×C107#166311yescharacteristic
116C2×C107#166412yes—
117C2×C107#188212yes—
118C2×C107#188811yescharacteristic
119C2×#491C2×C10711yescharacteristic
120#2382C2×C10711yescharacteristic
121#1993C2×C10712yes—
122C2×#330C2×C10711yescharacteristic
123#1295C2×C10712yes—
124C107#900411yescharacteristic, direct product factor, Sylow
125C2×C4⋊Q8C22×C10711yescharacteristic
126C2×#125C22×C10711yescharacteristic
127#491—22no—
128#491C4×C10714yescomplemented
129C2×#103—22no—
130C2×#97C22×C10712yes—
131C2×#97C22×C10711yescharacteristic
132#389—22no—
133#387—22no—
134#387—22no—
135#382C22×C10712yes—
136#340—22no—
137#340—22no—
138#330—22no—
139C22×Q8—21no—
140C22×C8—22no—
141C22×C8—21no—
142C4⋊Q8—21no—
143C4⋊Q8—22no—
144C4⋊Q8C2×C4×C10712yes—
145#125—22no—
146#125C2×C4×C10712yes—
147#125D4×C10712yes—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4D4×C10712yes—
152C2×C4⋊C4D4×C10712yes—
153C2×C4⋊C4D4×C10712yes—
154C2×C42—22no—
155C2×C42C23×C10711yescharacteristic
156#103—28no—
157#97—21no—
158#97—22no—
159#97—22no—
160#97C2×C4×C10712yes—
161#95—22no—
162#95—22no—
163#95—22no—
164#95—22no—
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—41no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4C2×D4×C10711yescharacteristic
174C22×C4C2×D4×C10712yes—
175C2×C8—24no—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—82no—
189C4⋊C4C22⋊C4×C10714yes—
190C42—82no—
191C42C22×C4×C10711yescharacteristic
192C42C2×D4×C10711yescharacteristic
193C42#41×C10712yes—
194C23#120×C10711yescharacteristic
195Q8—44no—
196Q8—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4C2×C22⋊C4×C10711yescharacteristic
214C2×C4C4×D4×C10712yes—
215C2×C4#121×C10712yes—
216C2×C4#123×C10711yescharacteristic
217C8—44no—
218C8—42no—
219C22#386×C10711yescharacteristic
220C22#454×C10711yescharacteristic
221C22#454×C10711yescharacteristic
222C22#455×C10712yes—
223C22#456×C10712yes—
224C4—22no—
225C4—22no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—82no—
230C4—82no—
231C4—82no—
232C2C107×#166211yescharacteristic
233C2C107×#166311yescharacteristic
234C2C107×#166412yes—
235C2C107×#188212yes—
236C2C107×#188811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
9. #491×C107C4semidirect
113. #9004C107direct (N × H)
124. C107#9004direct (N × H)
128. #491C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#491×C1072
C107×#23822
C107×#19932
C2×#330×C1072
C107×#12952
#9004107