Finite Group Databasebeta

← C107×#7646 #41033610

Subgroups — C107×#7646 #41033610

Order 27392.

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

normal subgroups only

This group has 490 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
1C107×#2296C211yesmaximal, characteristic
2C107×#1817C212yesmaximal
3C107×#1271C214yesmaximal, complemented
4C2×#117×C107C411yescharacteristic
5C2×#117×C107C411yescharacteristic
6C22×C42×C107C2211yescharacteristic
7C2×C22⋊C8×C107—22no—
8#389×C107C412yes—
9#389×C107C2212yes—
10#385×C107—22no—
11C4×C4⋊C4×C107—22no—
12#336×C107—22no—
13#336×C107C2214yes—
14C23×C4×C107C2×C411yescharacteristic
15C23×C4×C107D412yes—
16C22×C8×C107—24no—
17#117×C107—24no—
18#117×C107—42no—
19C2×C4⋊C4×C107—22no—
20C2×C4⋊C4×C107—22no—
21C2×C4⋊C4×C107C2×C412yes—
22C2×C4⋊C4×C107C2×C412yes—
23C2×C22⋊C4×C107—21no—
24C2×C22⋊C4×C107—21no—
25C2×C42×C107—21no—
26C2×C42×C107—21no—
27C2×C42×C107—42no—
28C2×C42×C107C2×C411yescharacteristic
29C2×C42×C107D412yes—
30C2×C42×C107C2311yescharacteristic
31C22⋊C8×C107—44no—
32#95×C107—22no—
33#95×C107—22no—
34C24×C107C22⋊C411yescharacteristic
35C22×C4×C107—22no—
36C22×C4×C107—22no—
37C22×C4×C107—22no—
38C22×C4×C107—24no—
39C22×C4×C107—22no—
40C22×C4×C107—24no—
41C22×C4×C107—22no—
42C22×C4×C107—42no—
43C22×C4×C107C22⋊C412yes—
44C22×C4×C107C22⋊C411yescharacteristic
45C22×C4×C107C22×C411yescharacteristic
46C22×C4×C107C2×D412yes—
47C2×C8×C107—44no—
48C2×C8×C107—44no—
49C2×C8×C107—44no—
50C4⋊C4×C107—22no—
51C4⋊C4×C107—42no—
52C4⋊C4×C107—44no—
53C4⋊C4×C107—44no—
54C4⋊C4×C107M1614yes—
55C22⋊C4×C107—24no—
56C22⋊C4×C107—42no—
57C42×C107—24no—
58C42×C107—41no—
59C42×C107—42no—
60C42×C107—41no—
61C42×C107—42no—
62C23×C107—21no—
63C23×C107—21no—
64C23×C107—22no—
65C23×C107—22no—
66C23×C107#9912yes—
67C23×C107C2×C22⋊C411yescharacteristic
68C2×C4×C107—28no—
69C2×C4×C107—21no—
70C2×C4×C107—21no—
71C2×C4×C107—21no—
72C2×C4×C107—22no—
73C2×C4×C107—21no—
74C2×C4×C107—22no—
75C2×C4×C107—24no—
76C2×C4×C107—22no—
77C2×C4×C107—22no—
78C2×C4×C107—22no—
79C2×C4×C107—48no—
80C2×C4×C107—42no—
81C2×C4×C107—42no—
82C2×C4×C107—42no—
83C2×C4×C107—42no—
84C2×C4×C107—42no—
85C2×C4×C107#10112yes—
86C2×C4×C107C2×M1612yes—
87C2×C4×C107#13514yes—
88C8×C107—84no—
89C22×C107—22no—
90C22×C107—24no—
91C22×C107—41no—
92C22×C107—41no—
93C22×C107—42no—
94C22×C107#40711yescharacteristic
95C22×C107C2×#9911yescharacteristic
96C22×C107C2×#10111yescharacteristic
97C22×C107#41612yes—
98C22×C107#42112yes—
99C4×C107—22no—
100C4×C107—22no—
101C4×C107—24no—
102C4×C107—44no—
103C4×C107—42no—
104C4×C107—82no—
105#7646C10711yesmaximal, characteristic, direct product factor, Sylow
106C2×C107—42no—
107C2×C107#146311yescharacteristic
108C2×C107#148812yes—
109C2×C107#151612yes—
110C2×C107#153711yescharacteristic
111C2×C107#154411yescharacteristic
112#2296C2×C10711yescharacteristic
113#1817C2×C10712yes—
114#1271C2×C10714yescomplemented
115C107#764611yescharacteristic, direct product factor, Sylow
116C2×#117C4×C10711yescharacteristic
117C2×#117C4×C10711yescharacteristic
118C22×C42C22×C10711yescharacteristic
119C2×C22⋊C8—22no—
120#389C4×C10712yes—
121#389C22×C10712yes—
122#385—22no—
123C4×C4⋊C4—22no—
124#336—22no—
125#336C22×C10714yes—
126C23×C4C2×C4×C10711yescharacteristic
127C23×C4D4×C10712yes—
128C22×C8—24no—
129#117—24no—
130#117—42no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4C2×C4×C10712yes—
134C2×C4⋊C4C2×C4×C10712yes—
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—42no—
140C2×C42C2×C4×C10711yescharacteristic
141C2×C42D4×C10712yes—
142C2×C42C23×C10711yescharacteristic
143C22⋊C8—44no—
144#95—22no—
145#95—22no—
146C24C22⋊C4×C10711yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4C22⋊C4×C10712yes—
156C22×C4C22⋊C4×C10711yescharacteristic
157C22×C4C22×C4×C10711yescharacteristic
158C22×C4C2×D4×C10712yes—
159C2×C8—44no—
160C2×C8—44no—
161C2×C8—44no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—44no—
166C4⋊C4M16×C10714yes—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C42—24no—
170C42—41no—
171C42—42no—
172C42—41no—
173C42—42no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#99×C10712yes—
179C23C2×C22⋊C4×C10711yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—48no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4#101×C10712yes—
198C2×C4C2×M16×C10712yes—
199C2×C4#135×C10714yes—
200C8—84no—
201C22—22no—
202C22—24no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22#407×C10711yescharacteristic
207C22C2×#99×C10711yescharacteristic
208C22C2×#101×C10711yescharacteristic
209C22#416×C10712yes—
210C22#421×C10712yes—
211C4—22no—
212C4—22no—
213C4—24no—
214C4—44no—
215C4—42no—
216C4—82no—
217C2—42no—
218C2C107×#146311yescharacteristic
219C2C107×#148812yes—
220C2C107×#151612yes—
221C2C107×#153711yescharacteristic
222C2C107×#154411yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC24×C107C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1271C2semidirect
105. #7646C107direct (N × H)
114. #1271C2×C107semidirect
115. C107#7646direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#22962
C107×#18172
C107×#12712
#7646107