Finite Group Databasebeta

← C47×#34182 #26073880

Subgroups — C47×#34182 #26073880

Order 12032.

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×C47×#519C212yesmaximal
2C22×C4×Q8×C47C211yesmaximal, characteristic
3C47×#2351C218yesmaximal, complemented
4Q8×C4⋊C4×C47C218yesmaximal, complemented
5C47×#2316C216yesmaximal
6C47×#2285C216yesmaximal
7C23×Q8×C47C2211yescharacteristic
8C47×#519—216no—
9C2×C4×Q8×C47C4116yescomplemented
10C2×C4×Q8×C47C22116yes—
11C2×C4×Q8×C47C2214yes—
12C2×C4×Q8×C47C2214yes—
13C2×#117×C47C22112yes—
14C22×C4⋊C4×C47C2213yes—
15C22×C42×C47C2213yes—
16C47×#389C22148yes—
17C47×#384C22112yes—
18C47×#382C22112yes—
19C47×#380C2214yes—
20C47×#380C22112yes—
21C4×C4⋊C4×C47C22112yes—
22C4×C4⋊C4×C47C22112yes—
23C22×Q8×C47C2×C418yes—
24C22×Q8×C47D418yes—
25C22×Q8×C47Q818yes—
26C22×Q8×C47C2314yes—
27C23×C4×C47C2311yescharacteristic
28C23×C4×C47C2313yes—
29C23×C4×C47C2313yes—
30C4×Q8×C47—264no—
31C4×Q8×C47C2×C4132yes—
32C4×Q8×C47C2×C4132yes—
33#117×C47—248no—
34C2×C4⋊C4×C47C2×C4124yes—
35C2×C4⋊C4×C47C23124yes—
36C2×C4⋊C4×C47C2318yes—
37C2×C4⋊C4×C47C23124yes—
38C2×C4⋊C4×C47C23112yes—
39C2×C22⋊C4×C47C2318yes—
40C2×C42×C47C2×C4124yes—
41C2×C42×C47C23124yes—
42C2×C42×C47C2316yes—
43C2×C42×C47C2316yes—
44#95×C47C2318yes—
45#95×C47C23124yes—
46C24×C47C2411yescharacteristic
47C2×Q8×C47C4⋊C4164yescomplemented
48C2×Q8×C47C22×C4116yes—
49C2×Q8×C47C2×D4116yes—
50C2×Q8×C47C2×Q8116yes—
51C22×C4×C47—24no—
52C22×C4×C47—46no—
53C22×C4×C47C22×C414yes—
54C22×C4×C47C22×C4112yes—
55C22×C4×C47C22×C4112yes—
56C22×C4×C47C2×D4112yes—
57C22×C4×C47C2×Q8112yes—
58C22×C4×C47C24116yes—
59C22×C4×C47C2411yescharacteristic
60C22×C4×C47C2416yes—
61C22×C4×C47C2416yes—
62C22×C4×C47C2411yescharacteristic
63C4⋊C4×C47—248no—
64C4⋊C4×C47—216no—
65C4⋊C4×C47—424no—
66C4⋊C4×C47C22×C4148yes—
67C22⋊C4×C47—216no—
68C42×C47—248no—
69C42×C47C22×C4124yes—
70C42×C47C22×C4124yes—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47C23×C412yes—
74C23×C47C22×D412yes—
75C23×C47C22×Q812yes—
76C23×C47C2511yescharacteristic
77Q8×C47C2×C4⋊C4164yes—
78C2×C4×C47—22no—
79C2×C4×C47—212no—
80C2×C4×C47—28no—
81C2×C4×C47—216no—
82C2×C4×C47—216no—
83C2×C4×C47—216no—
84C2×C4×C47—412no—
85C2×C4×C47C2×C4⋊C4148yes—
86C2×C4×C47C23×C412yes—
87C2×C4×C47C23×C4112yes—
88C2×C4×C47C23×C4112yes—
89C2×C4×C47C23×C412yes—
90C2×C4×C47C22×D4112yes—
91C2×C4×C47C22×Q8112yes—
92C2×C4×C472−1+414yes—
93#34182C4711yesmaximal, characteristic, direct product factor, Sylow
94C22×C47—22no—
95C22×C47—22no—
96C22×C47—24no—
97C22×C47—24no—
98C22×C47C22×C4⋊C414yes—
99C22×C47C24×C411yescharacteristic
100C22×C47C23×D411yescharacteristic
101C22×C47C23×Q811yescharacteristic
102C22×C47C2×2−1+412yes—
103C22×C47#58512yes—
104C4×C47—22no—
105C4×C47—212no—
106C4×C47—416no—
107C4×C47C22×C4⋊C4124yes—
108C4×C47#51914yescomplemented
109C2×#519C2×C4712yes—
110C22×C4×Q8C2×C4711yescharacteristic
111#2351C2×C4718yescomplemented
112Q8×C4⋊C4C2×C4718yescomplemented
113#2316C2×C4716yes—
114#2285C2×C4716yes—
115C2×C47—24no—
116C2×C47C23×C4⋊C411yescharacteristic
117C2×C47C2×#51911yescharacteristic
118C2×C47#342811yescharacteristic
119C2×C47#349712yes—
120C2×C47#350212yes—
121C23×Q8C22×C4711yescharacteristic
122#519—216no—
123C2×C4×Q8C4×C47116yescomplemented
124C2×C4×Q8C22×C47116yes—
125C2×C4×Q8C22×C4714yes—
126C2×C4×Q8C22×C4714yes—
127C2×#117C22×C47112yes—
128C22×C4⋊C4C22×C4713yes—
129C22×C42C22×C4713yes—
130#389C22×C47148yes—
131#384C22×C47112yes—
132#382C22×C47112yes—
133#380C22×C47112yes—
134#380C22×C4714yes—
135C4×C4⋊C4C22×C47112yes—
136C4×C4⋊C4C22×C47112yes—
137C47#3418211yescharacteristic, direct product factor, Sylow
138C22×Q8C2×C4×C4718yes—
139C22×Q8D4×C4718yes—
140C22×Q8Q8×C4718yes—
141C22×Q8C23×C4714yes—
142C23×C4C23×C4711yescharacteristic
143C23×C4C23×C4713yes—
144C23×C4C23×C4713yes—
145C4×Q8—264no—
146C4×Q8C2×C4×C47132yes—
147C4×Q8C2×C4×C47132yes—
148#117—248no—
149C2×C4⋊C4C2×C4×C47124yes—
150C2×C4⋊C4C23×C47124yes—
151C2×C4⋊C4C23×C4718yes—
152C2×C4⋊C4C23×C47124yes—
153C2×C4⋊C4C23×C47112yes—
154C2×C22⋊C4C23×C4718yes—
155C2×C42C2×C4×C47124yes—
156C2×C42C23×C47124yes—
157C2×C42C23×C4716yes—
158C2×C42C23×C4716yes—
159#95C23×C4718yes—
160#95C23×C47124yes—
161C24C24×C4711yescharacteristic
162C2×Q8C4⋊C4×C47164yescomplemented
163C2×Q8C22×C4×C47116yes—
164C2×Q8C2×D4×C47116yes—
165C2×Q8C2×Q8×C47116yes—
166C22×C4—24no—
167C22×C4—46no—
168C22×C4C22×C4×C4714yes—
169C22×C4C22×C4×C47112yes—
170C22×C4C22×C4×C47112yes—
171C22×C4C2×D4×C47112yes—
172C22×C4C2×Q8×C47112yes—
173C22×C4C24×C47116yes—
174C22×C4C24×C4711yescharacteristic
175C22×C4C24×C4716yes—
176C22×C4C24×C4716yes—
177C22×C4C24×C4711yescharacteristic
178C4⋊C4—248no—
179C4⋊C4—216no—
180C4⋊C4—424no—
181C4⋊C4C22×C4×C47148yes—
182C22⋊C4—216no—
183C42—248no—
184C42C22×C4×C47124yes—
185C42C22×C4×C47124yes—
186C23—22no—
187C23—22no—
188C23C23×C4×C4712yes—
189C23C22×D4×C4712yes—
190C23C22×Q8×C4712yes—
191C23C25×C4711yescharacteristic
192Q8C2×C4⋊C4×C47164yes—
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×C47148yes—
201C2×C4C23×C4×C4712yes—
202C2×C4C23×C4×C47112yes—
203C2×C4C23×C4×C47112yes—
204C2×C4C23×C4×C4712yes—
205C2×C4C22×D4×C47112yes—
206C2×C4C22×Q8×C47112yes—
207C2×C42−1+4×C4714yes—
208C22—22no—
209C22—22no—
210C22—24no—
211C22—24no—
212C22C22×C4⋊C4×C4714yes—
213C22C24×C4×C4711yescharacteristic
214C22C23×D4×C4711yescharacteristic
215C22C23×Q8×C4711yescharacteristic
216C22C2×2−1+4×C4712yes—
217C22C47×#58512yes—
218C4—22no—
219C4—212no—
220C4—416no—
221C4C22×C4⋊C4×C47124yes—
222C4C47×#51914yescomplemented
223C2—24no—
224C2C23×C4⋊C4×C4711yescharacteristic
225C2C2×C47×#51911yescharacteristic
226C2C47×#342811yescharacteristic
227C2C47×#349712yes—
228C2C47×#350212yes—
subgroupG/H
center, socleC23×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC24×C47C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2351C2semidirect
4. Q8×C4⋊C4×C47C2semidirect
9. C2×C4×Q8×C47C4semidirect
47. C2×Q8×C47C4⋊C4semidirect
93. #34182C47direct (N × H)
108. C4×C47#519semidirect
111. #2351C2×C47semidirect
112. Q8×C4⋊C4C2×C47semidirect
123. C2×C4×Q8C4×C47semidirect
137. C47#34182direct (N × H)
162. C2×Q8C4⋊C4×C47semidirect
222. C4C47×#519semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5192
C22×C4×Q8×C472
C47×#23512
Q8×C4⋊C4×C472
C47×#23162
C47×#22852
#3418247