Finite Group Databasebeta

← C107×#34182 #41060146

Subgroups — C107×#34182 #41060146

Order 27392.

2858 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#519×C107C212yesmaximal
2C22×C4×Q8×C107C211yesmaximal, characteristic
3C107×#2351C218yesmaximal, complemented
4Q8×C4⋊C4×C107C218yesmaximal, complemented
5C107×#2316C216yesmaximal
6C107×#2285C216yesmaximal
7C23×Q8×C107C2211yescharacteristic
8#519×C107—216no—
9C2×C4×Q8×C107C4116yescomplemented
10C2×C4×Q8×C107C22116yes—
11C2×C4×Q8×C107C2214yes—
12C2×C4×Q8×C107C2214yes—
13C2×#117×C107C22112yes—
14C22×C4⋊C4×C107C2213yes—
15C22×C42×C107C2213yes—
16#389×C107C22148yes—
17#384×C107C22112yes—
18#382×C107C22112yes—
19#380×C107C2214yes—
20#380×C107C22112yes—
21C4×C4⋊C4×C107C22112yes—
22C4×C4⋊C4×C107C22112yes—
23C22×Q8×C107C2×C418yes—
24C22×Q8×C107D418yes—
25C22×Q8×C107Q818yes—
26C22×Q8×C107C2314yes—
27C23×C4×C107C2311yescharacteristic
28C23×C4×C107C2313yes—
29C23×C4×C107C2313yes—
30C4×Q8×C107—264no—
31C4×Q8×C107C2×C4132yes—
32C4×Q8×C107C2×C4132yes—
33#117×C107—248no—
34C2×C4⋊C4×C107C2×C4124yes—
35C2×C4⋊C4×C107C2318yes—
36C2×C4⋊C4×C107C23124yes—
37C2×C4⋊C4×C107C23124yes—
38C2×C4⋊C4×C107C23112yes—
39C2×C22⋊C4×C107C2318yes—
40C2×C42×C107C2×C4124yes—
41C2×C42×C107C23124yes—
42C2×C42×C107C2316yes—
43C2×C42×C107C2316yes—
44#95×C107C2318yes—
45#95×C107C23124yes—
46C24×C107C2411yescharacteristic
47C2×Q8×C107C4⋊C4164yescomplemented
48C2×Q8×C107C22×C4116yes—
49C2×Q8×C107C2×D4116yes—
50C2×Q8×C107C2×Q8116yes—
51C22×C4×C107—24no—
52C22×C4×C107—46no—
53C22×C4×C107C22×C414yes—
54C22×C4×C107C22×C4112yes—
55C22×C4×C107C22×C4112yes—
56C22×C4×C107C2×D4112yes—
57C22×C4×C107C2×Q8112yes—
58C22×C4×C107C24116yes—
59C22×C4×C107C2411yescharacteristic
60C22×C4×C107C2416yes—
61C22×C4×C107C2416yes—
62C22×C4×C107C2411yescharacteristic
63C4⋊C4×C107—248no—
64C4⋊C4×C107—216no—
65C4⋊C4×C107—424no—
66C4⋊C4×C107C22×C4148yes—
67C22⋊C4×C107—216no—
68C42×C107—248no—
69C42×C107C22×C4124yes—
70C42×C107C22×C4124yes—
71C23×C107—22no—
72C23×C107—22no—
73C23×C107C23×C412yes—
74C23×C107C22×D412yes—
75C23×C107C22×Q812yes—
76C23×C107C2511yescharacteristic
77Q8×C107C2×C4⋊C4164yes—
78C2×C4×C107—22no—
79C2×C4×C107—212no—
80C2×C4×C107—28no—
81C2×C4×C107—216no—
82C2×C4×C107—216no—
83C2×C4×C107—216no—
84C2×C4×C107—412no—
85C2×C4×C107C2×C4⋊C4148yes—
86C2×C4×C107C23×C412yes—
87C2×C4×C107C23×C4112yes—
88C2×C4×C107C23×C4112yes—
89C2×C4×C107C23×C412yes—
90C2×C4×C107C22×D4112yes—
91C2×C4×C107C22×Q8112yes—
92C2×C4×C1072−1+414yes—
93C22×C107—22no—
94C22×C107—22no—
95C22×C107—24no—
96C22×C107—24no—
97C22×C107C22×C4⋊C414yes—
98C22×C107C24×C411yescharacteristic
99C22×C107C23×D411yescharacteristic
100C22×C107C23×Q811yescharacteristic
101C22×C107C2×2−1+412yes—
102C22×C107#58512yes—
103C4×C107—22no—
104C4×C107—212no—
105C4×C107—416no—
106C4×C107C22×C4⋊C4124yes—
107C4×C107#51914yescomplemented
108#34182C10711yesmaximal, characteristic, direct product factor, Sylow
109C2×C107—24no—
110C2×C107C23×C4⋊C411yescharacteristic
111C2×C107C2×#51911yescharacteristic
112C2×C107#342811yescharacteristic
113C2×C107#349712yes—
114C2×C107#350212yes—
115C2×#519C2×C10712yes—
116C22×C4×Q8C2×C10711yescharacteristic
117#2351C2×C10718yescomplemented
118Q8×C4⋊C4C2×C10718yescomplemented
119#2316C2×C10716yes—
120#2285C2×C10716yes—
121C107#3418211yescharacteristic, direct product factor, Sylow
122C23×Q8C22×C10711yescharacteristic
123#519—216no—
124C2×C4×Q8C4×C107116yescomplemented
125C2×C4×Q8C22×C107116yes—
126C2×C4×Q8C22×C10714yes—
127C2×C4×Q8C22×C10714yes—
128C2×#117C22×C107112yes—
129C22×C4⋊C4C22×C10713yes—
130C22×C42C22×C10713yes—
131#389C22×C107148yes—
132#384C22×C107112yes—
133#382C22×C107112yes—
134#380C22×C107112yes—
135#380C22×C10714yes—
136C4×C4⋊C4C22×C107112yes—
137C4×C4⋊C4C22×C107112yes—
138C22×Q8C2×C4×C10718yes—
139C22×Q8D4×C10718yes—
140C22×Q8Q8×C10718yes—
141C22×Q8C23×C10714yes—
142C23×C4C23×C10711yescharacteristic
143C23×C4C23×C10713yes—
144C23×C4C23×C10713yes—
145C4×Q8—264no—
146C4×Q8C2×C4×C107132yes—
147C4×Q8C2×C4×C107132yes—
148#117—248no—
149C2×C4⋊C4C2×C4×C107124yes—
150C2×C4⋊C4C23×C107124yes—
151C2×C4⋊C4C23×C10718yes—
152C2×C4⋊C4C23×C107124yes—
153C2×C4⋊C4C23×C107112yes—
154C2×C22⋊C4C23×C10718yes—
155C2×C42C2×C4×C107124yes—
156C2×C42C23×C107124yes—
157C2×C42C23×C10716yes—
158C2×C42C23×C10716yes—
159#95C23×C10718yes—
160#95C23×C107124yes—
161C24C24×C10711yescharacteristic
162C2×Q8C4⋊C4×C107164yescomplemented
163C2×Q8C22×C4×C107116yes—
164C2×Q8C2×D4×C107116yes—
165C2×Q8C2×Q8×C107116yes—
166C22×C4—24no—
167C22×C4—46no—
168C22×C4C22×C4×C10714yes—
169C22×C4C22×C4×C107112yes—
170C22×C4C22×C4×C107112yes—
171C22×C4C2×D4×C107112yes—
172C22×C4C2×Q8×C107112yes—
173C22×C4C24×C107116yes—
174C22×C4C24×C10711yescharacteristic
175C22×C4C24×C10716yes—
176C22×C4C24×C10716yes—
177C22×C4C24×C10711yescharacteristic
178C4⋊C4—248no—
179C4⋊C4—216no—
180C4⋊C4—424no—
181C4⋊C4C22×C4×C107148yes—
182C22⋊C4—216no—
183C42—248no—
184C42C22×C4×C107124yes—
185C42C22×C4×C107124yes—
186C23—22no—
187C23—22no—
188C23C23×C4×C10712yes—
189C23C22×D4×C10712yes—
190C23C22×Q8×C10712yes—
191C23C25×C10711yescharacteristic
192Q8C2×C4⋊C4×C107164yes—
193C2×C4—22no—
194C2×C4—212no—
195C2×C4—28no—
196C2×C4—216no—
197C2×C4—216no—
198C2×C4—216no—
199C2×C4—412no—
200C2×C4C2×C4⋊C4×C107148yes—
201C2×C4C23×C4×C10712yes—
202C2×C4C23×C4×C107112yes—
203C2×C4C23×C4×C107112yes—
204C2×C4C23×C4×C10712yes—
205C2×C4C22×D4×C107112yes—
206C2×C4C22×Q8×C107112yes—
207C2×C42−1+4×C10714yes—
208C22—22no—
209C22—22no—
210C22—24no—
211C22—24no—
212C22C22×C4⋊C4×C10714yes—
213C22C24×C4×C10711yescharacteristic
214C22C23×D4×C10711yescharacteristic
215C22C23×Q8×C10711yescharacteristic
216C22C2×2−1+4×C10712yes—
217C22#585×C10712yes—
218C4—22no—
219C4—212no—
220C4—416no—
221C4C22×C4⋊C4×C107124yes—
222C4#519×C10714yescomplemented
223C2—24no—
224C2C23×C4⋊C4×C10711yescharacteristic
225C2C2×#519×C10711yescharacteristic
226C2C107×#342811yescharacteristic
227C2C107×#349712yes—
228C2C107×#350212yes—
subgroupG/H
center, socleC23×C107C25
commutatorC22C24×C4×C107
Frattini, cosocleC23C25×C107
prime radicalC24×C107C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#2351C2semidirect
4. Q8×C4⋊C4×C107C2semidirect
9. C2×C4×Q8×C107C4semidirect
47. C2×Q8×C107C4⋊C4semidirect
107. C4×C107#519semidirect
108. #34182C107direct (N × H)
117. #2351C2×C107semidirect
118. Q8×C4⋊C4C2×C107semidirect
121. C107#34182direct (N × H)
124. C2×C4×Q8C4×C107semidirect
162. C2×Q8C4⋊C4×C107semidirect
222. C4#519×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#519×C1072
C22×C4×Q8×C1072
C107×#23512
Q8×C4⋊C4×C1072
C107×#23162
C107×#22852
#34182107