Finite Group Databasebeta

← C107×#8718 #41034682

Subgroups — C107×#8718 #41034682

Order 27392.

554 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 150 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×#382×C107C211yesmaximal, characteristic
2C107×#1749C212yesmaximal
3C107×#1295C214yesmaximal, complemented
4C22×C4⋊C4×C107C411yescharacteristic
5C22×C4⋊C4×C107C411yescharacteristic
6C22×C42×C107C2211yescharacteristic
7C2×C22⋊C8×C107—22no—
8C2×#97×C107C2214yes—
9#382×C107—22no—
10#382×C107C412yes—
11#382×C107C2212yes—
12C2×#95×C107—22no—
13#336×C107—22no—
14C23×C4×C107—21no—
15C23×C4×C107—21no—
16C23×C4×C107C2×C411yescharacteristic
17C23×C4×C107D412yes—
18C22×C8×C107—24no—
19C2×C4⋊C4×C107—21no—
20C2×C4⋊C4×C107—21no—
21C2×C4⋊C4×C107—42no—
22C2×C4⋊C4×C107—42no—
23C2×C4⋊C4×C107C2×C412yes—
24C2×C4⋊C4×C107C2×C412yes—
25C2×C42×C107—24no—
26C2×C42×C107C2×C411yescharacteristic
27C2×C42×C107D412yes—
28C2×C42×C107C2311yescharacteristic
29C22⋊C8×C107—28no—
30#97×C107—28no—
31#95×C107—24no—
32#95×C107—24no—
33C24×C107C22⋊C411yescharacteristic
34C22×C4×C107—22no—
35C22×C4×C107—22no—
36C22×C4×C107—22no—
37C22×C4×C107—24no—
38C22×C4×C107—24no—
39C22×C4×C107—22no—
40C22×C4×C107—22no—
41C22×C4×C107—42no—
42C22×C4×C107—44no—
43C22×C4×C107—42no—
44C22×C4×C107—42no—
45C22×C4×C107—44no—
46C22×C4×C107C22⋊C412yes—
47C22×C4×C107C22⋊C411yescharacteristic
48C22×C4×C107C22×C411yescharacteristic
49C22×C4×C107C2×D412yes—
50C2×C8×C107—28no—
51C2×C8×C107—44no—
52C2×C8×C107—44no—
53C4⋊C4×C107—42no—
54C4⋊C4×C107—42no—
55C4⋊C4×C107—42no—
56C4⋊C4×C107—42no—
57C42×C107—22no—
58C42×C107—24no—
59C42×C107#4114yes—
60C23×C107—21no—
61C23×C107—21no—
62C23×C107—22no—
63C23×C107#10012yes—
64C23×C107#10414yes—
65C23×C107C2×C22⋊C411yescharacteristic
66C2×C4×C107—28no—
67C2×C4×C107—21no—
68C2×C4×C107—21no—
69C2×C4×C107—21no—
70C2×C4×C107—21no—
71C2×C4×C107—22no—
72C2×C4×C107—22no—
73C2×C4×C107—22no—
74C2×C4×C107—22no—
75C2×C4×C107—22no—
76C2×C4×C107—48no—
77C2×C4×C107—42no—
78C2×C4×C107—42no—
79C2×C4×C107—44no—
80C2×C4×C107—44no—
81C2×C4×C107—84no—
82C2×C4×C107—84no—
83C2×C4×C107#10112yes—
84C2×C4×C107#11712yes—
85C2×C4×C107#12314yes—
86C8×C107—48no—
87C22×C107—22no—
88C22×C107—24no—
89C22×C107—24no—
90C22×C107—22no—
91C22×C107#32914yes—
92C22×C107#38111yescharacteristic
93C22×C107C2×#10011yescharacteristic
94C22×C107C2×#10111yescharacteristic
95C22×C107C2×#10412yes—
96C22×C107#42112yes—
97C4×C107—22no—
98C4×C107—22no—
99C4×C107—24no—
100C4×C107—42no—
101C4×C107—82no—
102C4×C107—82no—
103#8718C10711yesmaximal, characteristic, direct product factor, Sylow
104C2×C107—24no—
105C2×C107C2×#32911yescharacteristic
106C2×C107#152812yes—
107C2×C107#153311yescharacteristic
108C2×C107#182111yescharacteristic
109C2×C107#182612yes—
110C2×#382C2×C10711yescharacteristic
111#1749C2×C10712yes—
112#1295C2×C10714yescomplemented
113C107#871811yescharacteristic, direct product factor, Sylow
114C22×C4⋊C4C4×C10711yescharacteristic
115C22×C4⋊C4C4×C10711yescharacteristic
116C22×C42C22×C10711yescharacteristic
117C2×C22⋊C8—22no—
118C2×#97C22×C10714yes—
119#382—22no—
120#382C4×C10712yes—
121#382C22×C10712yes—
122C2×#95—22no—
123#336—22no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4C2×C4×C10711yescharacteristic
127C23×C4D4×C10712yes—
128C22×C8—24no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4C2×C4×C10712yes—
134C2×C4⋊C4C2×C4×C10712yes—
135C2×C42—24no—
136C2×C42C2×C4×C10711yescharacteristic
137C2×C42D4×C10712yes—
138C2×C42C23×C10711yescharacteristic
139C22⋊C8—28no—
140#97—28no—
141#95—24no—
142#95—24no—
143C24C22⋊C4×C10711yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—24no—
148C22×C4—24no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—44no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—44no—
156C22×C4C22⋊C4×C10712yes—
157C22×C4C22⋊C4×C10711yescharacteristic
158C22×C4C22×C4×C10711yescharacteristic
159C22×C4C2×D4×C10712yes—
160C2×C8—28no—
161C2×C8—44no—
162C2×C8—44no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C42—22no—
168C42—24no—
169C42#41×C10714yes—
170C23—21no—
171C23—21no—
172C23—22no—
173C23#100×C10712yes—
174C23#104×C10714yes—
175C23C2×C22⋊C4×C10711yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—84no—
192C2×C4—84no—
193C2×C4#101×C10712yes—
194C2×C4#117×C10712yes—
195C2×C4#123×C10714yes—
196C8—48no—
197C22—24no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22#329×C10714yes—
202C22#381×C10711yescharacteristic
203C22C2×#100×C10711yescharacteristic
204C22C2×#101×C10711yescharacteristic
205C22C2×#104×C10712yes—
206C22#421×C10712yes—
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—24no—
214C2C2×#329×C10711yescharacteristic
215C2C107×#152812yes—
216C2C107×#153311yescharacteristic
217C2C107×#182111yescharacteristic
218C2C107×#182612yes—
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×#1295C2semidirect
103. #8718C107direct (N × H)
112. #1295C2×C107semidirect
113. C107#8718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#382×C1072
C107×#17492
C107×#12952
#8718107