Finite Group Databasebeta

← C107×#8527 #41034491

Subgroups — C107×#8527 #41034491

Order 27392.

656 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 142 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×#541×C107C211yesmaximal, characteristic
2C107×#1558C212yesmaximal, complemented
3C107×#1534C212yesmaximal, complemented
4C107×#1464C212yesmaximal
5#541×C107—24no—
6#541×C107—24no—
7C2×C4⋊Q8×C107C2211yescharacteristic
8C2×#126×C107—22no—
9C2×#125×C107—22no—
10C2×#125×C107C2211yescharacteristic
11C2×C22⋊Q8×C107C412yes—
12C2×C4×Q8×C107C412yes—
13C2×#117×C107C2211yescharacteristic
14#432×C107C2214yes—
15#333×C107—24no—
16#330×C107—24no—
17#324×C107—22no—
18#323×C107—22no—
19C22×Q8×C107C2×C412yes—
20C23×C4×C107C2×C411yescharacteristic
21C4⋊Q8×C107—22no—
22C4⋊Q8×C107D414yes—
23#126×C107—216no—
24#125×C107—216no—
25#125×C107—22no—
26#125×C107D414yes—
27C22⋊Q8×C107—24no—
28C22⋊Q8×C107—24no—
29C4×Q8×C107—24no—
30C4×Q8×C107—24no—
31#117×C107—22no—
32#117×C107—22no—
33C2×C4⋊C4×C107—22no—
34C2×C4⋊C4×C107—22no—
35C2×C4⋊C4×C107—22no—
36C2×C4⋊C4×C107—22no—
37C2×C4⋊C4×C107C2×C412yes—
38C2×C4⋊C4×C107D412yes—
39C2×C22⋊C4×C107—22no—
40C2×C22⋊C4×C107D412yes—
41C2×C42×C107—22no—
42C2×C42×C107C2×C411yescharacteristic
43C2×C42×C107C2311yescharacteristic
44C4⋊C8×C107—24no—
45C22⋊C8×C107—24no—
46#97×C107—24no—
47C24×C107C22⋊C411yescharacteristic
48C2×Q8×C107—22no—
49C2×Q8×C107—44no—
50C2×Q8×C107C22⋊C414yes—
51C22×C4×C107—22no—
52C22×C4×C107—22no—
53C22×C4×C107—21no—
54C22×C4×C107—21no—
55C22×C4×C107—42no—
56C22×C4×C107C22⋊C411yescharacteristic
57C22×C4×C107C22⋊C412yes—
58C22×C4×C107C22×C411yescharacteristic
59C22×C4×C107C2×D412yes—
60C2×C8×C107—44no—
61C4⋊C4×C107—28no—
62C4⋊C4×C107—28no—
63C4⋊C4×C107—22no—
64C4⋊C4×C107—28no—
65C4⋊C4×C107—28no—
66C4⋊C4×C107—24no—
67C4⋊C4×C107C22⋊C414yes—
68C22⋊C4×C107—28no—
69C22⋊C4×C107—24no—
70C42×C107—28no—
71C42×C107—21no—
72C42×C107—21no—
73C42×C107C2×D412yes—
74C42×C107C2×D412yes—
75C23×C107—21no—
76C23×C107—22no—
77C23×C107—42no—
78C23×C107C2×C22⋊C411yescharacteristic
79Q8×C107—44no—
80Q8×C107—44no—
81C2×C4×C107—22no—
82C2×C4×C107—22no—
83C2×C4×C107—24no—
84C2×C4×C107—24no—
85C2×C4×C107—21no—
86C2×C4×C107—22no—
87C2×C4×C107—42no—
88C2×C4×C107—42no—
89C2×C4×C107—42no—
90C2×C4×C107—44no—
91C2×C4×C107—44no—
92C2×C4×C107—42no—
93C2×C4×C107C2×C22⋊C411yescharacteristic
94C2×C4×C107C2×C22⋊C411yescharacteristic
95C2×C4×C107#12014yes—
96C8×C107—84no—
97C22×C107—22no—
98C22×C107—42no—
99C22×C107—41no—
100C22×C107—82no—
101C22×C107#37911yescharacteristic
102C22×C107#41312yes—
103C4×C107—24no—
104C4×C107—21no—
105C4×C107—21no—
106C4×C107—42no—
107C4×C107—44no—
108C4×C107—41no—
109C4×C107—44no—
110#8527C10711yesmaximal, characteristic, direct product factor, Sylow
111C2×C107—22no—
112C2×C107—81no—
113C2×C107#178511yescharacteristic
114C2×C107#179612yes—
115C2×#541C2×C10711yescharacteristic
116#1558C2×C10712yescomplemented
117#1534C2×C10712yescomplemented
118#1464C2×C10712yes—
119C107#852711yescharacteristic, direct product factor, Sylow
120#541—24no—
121#541—24no—
122C2×C4⋊Q8C22×C10711yescharacteristic
123C2×#126—22no—
124C2×#125—22no—
125C2×#125C22×C10711yescharacteristic
126C2×C22⋊Q8C4×C10712yes—
127C2×C4×Q8C4×C10712yes—
128C2×#117C22×C10711yescharacteristic
129#432C22×C10714yes—
130#333—24no—
131#330—24no—
132#324—22no—
133#323—22no—
134C22×Q8C2×C4×C10712yes—
135C23×C4C2×C4×C10711yescharacteristic
136C4⋊Q8—22no—
137C4⋊Q8D4×C10714yes—
138#126—216no—
139#125—216no—
140#125—22no—
141#125D4×C10714yes—
142C22⋊Q8—24no—
143C22⋊Q8—24no—
144C4×Q8—24no—
145C4×Q8—24no—
146#117—22no—
147#117—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4C2×C4×C10712yes—
153C2×C4⋊C4D4×C10712yes—
154C2×C22⋊C4—22no—
155C2×C22⋊C4D4×C10712yes—
156C2×C42—22no—
157C2×C42C2×C4×C10711yescharacteristic
158C2×C42C23×C10711yescharacteristic
159C4⋊C8—24no—
160C22⋊C8—24no—
161#97—24no—
162C24C22⋊C4×C10711yescharacteristic
163C2×Q8—22no—
164C2×Q8—44no—
165C2×Q8C22⋊C4×C10714yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4C22⋊C4×C10711yescharacteristic
172C22×C4C22⋊C4×C10712yes—
173C22×C4C22×C4×C10711yescharacteristic
174C22×C4C2×D4×C10712yes—
175C2×C8—44no—
176C4⋊C4—28no—
177C4⋊C4—28no—
178C4⋊C4—22no—
179C4⋊C4—28no—
180C4⋊C4—28no—
181C4⋊C4—24no—
182C4⋊C4C22⋊C4×C10714yes—
183C22⋊C4—28no—
184C22⋊C4—24no—
185C42—28no—
186C42—21no—
187C42—21no—
188C42C2×D4×C10712yes—
189C42C2×D4×C10712yes—
190C23—21no—
191C23—22no—
192C23—42no—
193C23C2×C22⋊C4×C10711yescharacteristic
194Q8—44no—
195Q8—44no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4C2×C22⋊C4×C10711yescharacteristic
209C2×C4C2×C22⋊C4×C10711yescharacteristic
210C2×C4#120×C10714yes—
211C8—84no—
212C22—22no—
213C22—41no—
214C22—42no—
215C22—82no—
216C22#379×C10711yescharacteristic
217C22#413×C10712yes—
218C4—21no—
219C4—21no—
220C4—24no—
221C4—41no—
222C4—44no—
223C4—44no—
224C4—42no—
225C2—22no—
226C2—81no—
227C2C107×#178511yescharacteristic
228C2C107×#179612yes—
subgroupG/H
center, socleC22×C107#379
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC24×C107C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1558C2semidirect
3. C107×#1534C2semidirect
110. #8527C107direct (N × H)
116. #1558C2×C107semidirect
117. #1534C2×C107semidirect
119. C107#8527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#541×C1072
C107×#15582
C107×#15342
C107×#14642
#8527107