Finite Group Databasebeta

← C22×C47×#423 #26099793

Subgroups — C22×C47×#423 #26099793

Order 12032.

3438 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C47C212yesmaximal
2C23×C42×C47C211yesmaximal, characteristic
3C2×C47×#423C2124yesmaximal, direct product factor
4C22×C4⋊C8×C47C214yesmaximal, complemented
5C24×C4×C47C412yes—
6C24×C4×C47C2211yescharacteristic
7C22×M16×C47—216no—
8C22×M16×C47C22124yes—
9C23×C8×C47C2214yes—
10C22×C42×C47C411yescharacteristic
11C22×C42×C47C4112yes—
12C22×C42×C47C411yescharacteristic
13C22×C42×C47C22112yes—
14C22×C42×C47C2212yes—
15C47×#423C22164yesdirect product factor
16C2×C4⋊C8×C47C22148yescomplemented
17C25×C47C2×C411yescharacteristic
18C23×C4×C47—216no—
19C23×C4×C47C2×C412yes—
20C23×C4×C47C2×C4124yes—
21C23×C4×C47C2×C411yescharacteristic
22C23×C4×C47C2×C416yes—
23C23×C4×C47C2×C412yes—
24C23×C4×C47D418yes—
25C23×C4×C47Q818yes—
26C23×C4×C47C2316yes—
27C23×C4×C47C2311yescharacteristic
28C2×M16×C47—296no—
29C2×M16×C47C23132yes—
30C22×C8×C47—216no—
31C22×C8×C47C23124yes—
32C2×C42×C47C2×C4112yes—
33C2×C42×C47C2×C4148yes—
34C2×C42×C47C2×C4112yes—
35C2×C42×C47C2×C4112yes—
36C2×C42×C47C23112yes—
37C2×C42×C47C23116yes—
38C4⋊C8×C47C23164yescomplemented
39C24×C47—28no—
40C24×C47C4⋊C418yes—
41C24×C47C22×C416yes—
42C24×C47C22×C411yescharacteristic
43C22×C4×C47—28no—
44C22×C4×C47—296no—
45C22×C4×C47C4⋊C4148yes—
46C22×C4×C47C4⋊C418yes—
47C22×C4×C47M16116yescomplemented
48C22×C4×C47C22×C4112yes—
49C22×C4×C47C22×C4132yes—
50C22×C4×C47C22×C4112yes—
51C22×C4×C47C22×C416yes—
52C22×C4×C47C22×C413yes—
53C22×C4×C47C22×C4112yes—
54C22×C4×C47C2×D414yes—
55C22×C4×C47C2×D4124yes—
56C22×C4×C47C2×Q8124yes—
57C22×C4×C47C2×Q814yes—
58C22×C4×C47C2413yes—
59C22×C4×C47C2414yes—
60M16×C47—264no—
61C2×C8×C47—248no—
62C2×C8×C47C24116yes—
63C42×C47C22×C4116yes—
64C42×C47C22×C4124yes—
65C42×C47C22×C4116yes—
66C42×C47C2418yes—
67C23×C47—224no—
68C23×C47—232no—
69C23×C47C2×C4⋊C4124yes—
70C23×C47C2×C4⋊C414yes—
71C23×C47C2×M1618yes—
72C23×C47C23×C414yes—
73C23×C47C23×C413yes—
74C2×C4×C47—224no—
75C2×C4×C47—264no—
76C2×C4×C47C2×C4⋊C4148yes—
77C2×C4×C47C2×C4⋊C4124yes—
78C2×C4×C47C2×C4⋊C4112yes—
79C2×C4×C47C2×M16148yescomplemented
80C2×C4×C47C23×C418yes—
81C2×C4×C47C23×C414yes—
82C2×C4×C47C23×C413yes—
83C2×C4×C47C23×C418yes—
84C2×C4×C47C22×D416yes—
85C2×C4×C47C22×D418yes—
86C2×C4×C47C22×Q818yes—
87C2×C4×C47C22×Q816yes—
88C2×C4×C47C2511yescharacteristic
89C8×C47—216no—
90C22×#423C4711yesmaximal, characteristic, direct product factor, Sylow
91C22×C47—248no—
92C22×C47—28no—
93C22×C47#423116yesdirect product factor
94C22×C47C22×C4⋊C418yes—
95C22×C47C22×C4⋊C416yes—
96C22×C47C22×M16112yes—
97C22×C47C24×C411yescharacteristic
98C4×C47—28no—
99C4×C47C22×C4⋊C416yes—
100C4×C47C22×C4⋊C418yes—
101C4×C47C22×M16116yescomplemented
102C4×C47C23×D411yescharacteristic
103C4×C47C23×Q811yescharacteristic
104C23×M16C2×C4712yes—
105C23×C42C2×C4711yescharacteristic
106C2×#423C2×C47124yesdirect product factor
107C22×C4⋊C8C2×C4714yescomplemented
108C2×C47—28no—
109C2×C47C2×#423112yesdirect product factor
110C2×C47C23×C4⋊C411yescharacteristic
111C2×C47C23×M1612yes—
112C24×C4C4×C4712yes—
113C24×C4C22×C4711yescharacteristic
114C22×M16—216no—
115C22×M16C22×C47124yes—
116C23×C8C22×C4714yes—
117C22×C42C4×C4711yescharacteristic
118C22×C42C4×C47112yes—
119C22×C42C4×C4711yescharacteristic
120C22×C42C22×C4712yes—
121C22×C42C22×C47112yes—
122#423C22×C47164yesdirect product factor
123C2×C4⋊C8C22×C47148yescomplemented
124C47C22×#42311yescharacteristic, direct product factor, Sylow
125C25C2×C4×C4711yescharacteristic
126C23×C4—216no—
127C23×C4C2×C4×C4712yes—
128C23×C4C2×C4×C47124yes—
129C23×C4C2×C4×C4716yes—
130C23×C4C2×C4×C4711yescharacteristic
131C23×C4C2×C4×C4712yes—
132C23×C4D4×C4718yes—
133C23×C4Q8×C4718yes—
134C23×C4C23×C4716yes—
135C23×C4C23×C4711yescharacteristic
136C2×M16—296no—
137C2×M16C23×C47132yes—
138C22×C8—216no—
139C22×C8C23×C47124yes—
140C2×C42C2×C4×C47112yes—
141C2×C42C2×C4×C47148yes—
142C2×C42C2×C4×C47112yes—
143C2×C42C2×C4×C47112yes—
144C2×C42C23×C47112yes—
145C2×C42C23×C47116yes—
146C4⋊C8C23×C47164yescomplemented
147C24—28no—
148C24C4⋊C4×C4718yes—
149C24C22×C4×C4716yes—
150C24C22×C4×C4711yescharacteristic
151C22×C4—28no—
152C22×C4—296no—
153C22×C4C4⋊C4×C47148yes—
154C22×C4C4⋊C4×C4718yes—
155C22×C4M16×C47116yescomplemented
156C22×C4C22×C4×C47112yes—
157C22×C4C22×C4×C47132yes—
158C22×C4C22×C4×C47112yes—
159C22×C4C22×C4×C4716yes—
160C22×C4C22×C4×C4713yes—
161C22×C4C22×C4×C47112yes—
162C22×C4C2×D4×C4714yes—
163C22×C4C2×D4×C47124yes—
164C22×C4C2×Q8×C47124yes—
165C22×C4C2×Q8×C4714yes—
166C22×C4C24×C4713yes—
167C22×C4C24×C4714yes—
168M16—264no—
169C2×C8—248no—
170C2×C8C24×C47116yes—
171C42C22×C4×C47116yes—
172C42C22×C4×C47124yes—
173C42C22×C4×C47116yes—
174C42C24×C4718yes—
175C23—224no—
176C23—232no—
177C23C2×C4⋊C4×C47124yes—
178C23C2×C4⋊C4×C4714yes—
179C23C2×M16×C4718yes—
180C23C23×C4×C4714yes—
181C23C23×C4×C4713yes—
182C2×C4—224no—
183C2×C4—264no—
184C2×C4C2×C4⋊C4×C47148yes—
185C2×C4C2×C4⋊C4×C47112yes—
186C2×C4C2×C4⋊C4×C47124yes—
187C2×C4C2×M16×C47148yescomplemented
188C2×C4C23×C4×C4718yes—
189C2×C4C23×C4×C4713yes—
190C2×C4C23×C4×C4714yes—
191C2×C4C23×C4×C4718yes—
192C2×C4C22×D4×C4716yes—
193C2×C4C22×D4×C4718yes—
194C2×C4C22×Q8×C4718yes—
195C2×C4C22×Q8×C4716yes—
196C2×C4C25×C4711yescharacteristic
197C8—216no—
198C22—28no—
199C22—248no—
200C22C47×#423116yesdirect product factor
201C22C22×C4⋊C4×C4718yes—
202C22C22×C4⋊C4×C4716yes—
203C22C22×M16×C47112yes—
204C22C24×C4×C4711yescharacteristic
205C4—28no—
206C4C22×C4⋊C4×C4716yes—
207C4C22×C4⋊C4×C4718yes—
208C4C22×M16×C47116yescomplemented
209C4C23×D4×C4711yescharacteristic
210C4C23×Q8×C4711yescharacteristic
211C2—28no—
212C2C2×C47×#423112yesdirect product factor
213C2C23×C4⋊C4×C4711yescharacteristic
214C2C23×M16×C4712yes—
subgroupG/H
centerC23×C4×C47C23
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC24×C47C22×C4
prime radicalC25×C47C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#423C2direct (N × H)
4. C22×C4⋊C8×C47C2semidirect
15. C47×#423C22direct (N × H)
16. C2×C4⋊C8×C47C22semidirect
38. C4⋊C8×C47C23semidirect
47. C22×C4×C47M16semidirect
79. C2×C4×C47C2×M16semidirect
90. C22×#423C47direct (N × H)
93. C22×C47#423direct (N × H)
101. C4×C47C22×M16semidirect
106. C2×#423C2×C47direct (N × H)
107. C22×C4⋊C8C2×C47semidirect
109. C2×C47C2×#423direct (N × H)
122. #423C22×C47direct (N × H)
123. C2×C4⋊C8C22×C47semidirect
124. C47C22×#423direct (N × H)
146. C4⋊C8C23×C47semidirect
155. C22×C4M16×C47semidirect
187. C2×C4C2×M16×C47semidirect
200. C22C47×#423direct (N × H)
208. C4C22×M16×C47semidirect
212. C2C2×C47×#423direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C472
C23×C42×C472
C2×C47×#4232
C22×C4⋊C8×C472
C22×#42347