Finite Group Databasebeta

← C47×#36584 #26076282

Subgroups — C47×#36584 #26076282

Order 12032.

1590 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2859C213yesmaximal
2C47×#2571C216yesmaximal
3C47×#2509C2112yesmaximal
4C47×#2351C214yesmaximal
5Q8×C4⋊C4×C47C212yesmaximal
6C4×#125×C47C213yesmaximal
7C42×Q8×C47C211yesmaximal, characteristic
8C2×#125×C47C2213yes—
9C2×C4×Q8×C47C2212yes—
10C2×C4×Q8×C47C2214yes—
11C2×C4×Q8×C47C2211yescharacteristic
12C47×#400C22124yes—
13C47×#389C2216yes—
14C47×#389C22112yes—
15C47×#389C22112yes—
16C47×#389C22112yes—
17C47×#389C22112yes—
18C47×#387C22112yes—
19C47×#384C2216yes—
20C47×#382C2211yescharacteristic
21C47×#382C2216yes—
22C47×#382C22112yes—
23C4×C4⋊C4×C47C2213yes—
24C4×C4⋊C4×C47C2216yes—
25C4×C4⋊C4×C47C2216yes—
26C4×C4⋊C4×C47C22112yes—
27C43×C47C2213yes—
28C22×Q8×C47C2311yescharacteristic
29#125×C47—212no—
30C4×Q8×C47—28no—
31C4×Q8×C47—216no—
32C4×Q8×C47Q818yes—
33C2×C4⋊C4×C47C2316yes—
34C2×C4⋊C4×C47C23112yes—
35C2×C4⋊C4×C47C2316yes—
36C2×C4⋊C4×C47C23112yes—
37C2×C4⋊C4×C47C2312yes—
38C2×C4⋊C4×C47C23112yes—
39C2×C4⋊C4×C47C23112yes—
40C2×C4⋊C4×C47C2313yes—
41C2×C42×C47C2316yes—
42C2×C42×C47C23112yes—
43C2×C42×C47C2313yes—
44C2×C42×C47C2316yes—
45C2×C42×C47C2313yes—
46C2×C42×C47C2311yescharacteristic
47#95×C47C2314yes—
48#95×C47C2316yes—
49#95×C47C23112yes—
50#95×C47C23112yes—
51#95×C47C23124yes—
52C2×Q8×C47C2×Q814yes—
53C2×Q8×C47#4118yes—
54C22×C4×C47C2414yes—
55C22×C4×C47C2416yes—
56C22×C4×C47C24112yes—
57C22×C4×C47C2413yes—
58C22×C4×C47C2412yes—
59C22×C4×C47C2413yes—
60C22×C4×C47C2411yescharacteristic
61C4⋊C4×C47—212no—
62C4⋊C4×C47—224no—
63C4⋊C4×C47—224no—
64C4⋊C4×C47—212no—
65C4⋊C4×C47—24no—
66C4⋊C4×C47—412no—
67C4⋊C4×C47—412no—
68C4⋊C4×C47C2×Q8112yes—
69C42×C47—212no—
70C42×C47—224no—
71C42×C47—26no—
72C42×C47—46no—
73C42×C47C2×Q8112yes—
74C42×C47#4114yes—
75C23×C47C2511yescharacteristic
76Q8×C47#125116yescomplemented
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—26no—
80C2×C4×C47—24no—
81C2×C4×C47—212no—
82C2×C4×C47—26no—
83C2×C4×C47—212no—
84C2×C4×C47—26no—
85C2×C4×C47—24no—
86C2×C4×C47—26no—
87C2×C4×C47—212no—
88C2×C4×C47—24no—
89C2×C4×C47C22×Q816yes—
90C2×C4×C47C22×Q816yes—
91C2×C4×C47C22×Q812yes—
92C2×C4×C47C2×#4114yes—
93C2×C4×C47C2×#41112yes—
94C2×C4×C47C2×#4112yes—
95C2×C4×C472−1+412yes—
96#36584C4711yesmaximal, characteristic, direct product factor, Sylow
97C22×C47C23×Q811yescharacteristic
98C22×C47C22×#4112yes—
99C22×C47C22×#4111yescharacteristic
100C22×C47C2×2−1+411yescharacteristic
101C22×C47#58512yes—
102C4×C47—24no—
103C4×C47—26no—
104C4×C47—412no—
105C4×C47—44no—
106C4×C47—46no—
107C4×C47C2×#125112yes—
108C4×C47#55714yes—
109#2859C2×C4713yes—
110#2571C2×C4716yes—
111#2509C2×C47112yes—
112#2351C2×C4714yes—
113Q8×C4⋊C4C2×C4712yes—
114C4×#125C2×C4713yes—
115C42×Q8C2×C4711yescharacteristic
116C2×C47C22×#12511yescharacteristic
117C2×C47C2×#55711yescharacteristic
118C2×C47#348012yes—
119C2×C47#350411yescharacteristic
120C2×C47#351812yes—
121C2×#125C22×C4713yes—
122C2×C4×Q8C22×C4714yes—
123C2×C4×Q8C22×C4712yes—
124C2×C4×Q8C22×C4711yescharacteristic
125#400C22×C47124yes—
126#389C22×C4716yes—
127#389C22×C47112yes—
128#389C22×C47112yes—
129#389C22×C47112yes—
130#389C22×C47112yes—
131#387C22×C47112yes—
132#384C22×C4716yes—
133#382C22×C4711yescharacteristic
134#382C22×C4716yes—
135#382C22×C47112yes—
136C4×C4⋊C4C22×C4716yes—
137C4×C4⋊C4C22×C47112yes—
138C4×C4⋊C4C22×C4713yes—
139C4×C4⋊C4C22×C4716yes—
140C43C22×C4713yes—
141C47#3658411yescharacteristic, direct product factor, Sylow
142C22×Q8C23×C4711yescharacteristic
143#125—212no—
144C4×Q8—216no—
145C4×Q8—28no—
146C4×Q8Q8×C4718yes—
147C2×C4⋊C4C23×C4716yes—
148C2×C4⋊C4C23×C47112yes—
149C2×C4⋊C4C23×C4716yes—
150C2×C4⋊C4C23×C47112yes—
151C2×C4⋊C4C23×C4712yes—
152C2×C4⋊C4C23×C47112yes—
153C2×C4⋊C4C23×C47112yes—
154C2×C4⋊C4C23×C4713yes—
155C2×C42C23×C4716yes—
156C2×C42C23×C47112yes—
157C2×C42C23×C4713yes—
158C2×C42C23×C4716yes—
159C2×C42C23×C4713yes—
160C2×C42C23×C4711yescharacteristic
161#95C23×C4714yes—
162#95C23×C4716yes—
163#95C23×C47112yes—
164#95C23×C47112yes—
165#95C23×C47124yes—
166C2×Q8C2×Q8×C4714yes—
167C2×Q8#41×C4718yes—
168C22×C4C24×C4714yes—
169C22×C4C24×C4716yes—
170C22×C4C24×C47112yes—
171C22×C4C24×C4713yes—
172C22×C4C24×C4712yes—
173C22×C4C24×C4713yes—
174C22×C4C24×C4711yescharacteristic
175C4⋊C4—212no—
176C4⋊C4—224no—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—24no—
180C4⋊C4—412no—
181C4⋊C4—412no—
182C4⋊C4C2×Q8×C47112yes—
183C42—212no—
184C42—224no—
185C42—26no—
186C42—46no—
187C42C2×Q8×C47112yes—
188C42#41×C4714yes—
189C23C25×C4711yescharacteristic
190Q8#125×C47116yescomplemented
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—26no—
194C2×C4—24no—
195C2×C4—212no—
196C2×C4—26no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—24no—
200C2×C4—26no—
201C2×C4—212no—
202C2×C4—24no—
203C2×C4C22×Q8×C4716yes—
204C2×C4C22×Q8×C4716yes—
205C2×C4C22×Q8×C4712yes—
206C2×C4C2×#41×C4714yes—
207C2×C4C2×#41×C47112yes—
208C2×C4C2×#41×C4712yes—
209C2×C42−1+4×C4712yes—
210C22C23×Q8×C4711yescharacteristic
211C22C22×#41×C4712yes—
212C22C22×#41×C4711yescharacteristic
213C22C2×2−1+4×C4711yescharacteristic
214C22C47×#58512yes—
215C4—24no—
216C4—26no—
217C4—412no—
218C4—44no—
219C4—46no—
220C4C2×#125×C47112yes—
221C4C47×#55714yes—
222C2C22×#125×C4711yescharacteristic
223C2C2×C47×#55711yescharacteristic
224C2C47×#348012yes—
225C2C47×#350411yescharacteristic
226C2C47×#351812yes—
subgroupG/H
center, socle, prime radicalC23×C47C25
commutator, Frattini, cosocleC23C25×C47
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
76. Q8×C47#125semidirect
96. #36584C47direct (N × H)
141. C47#36584direct (N × H)
190. Q8#125×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#28592
C47×#25712
C47×#25092
C47×#23512
Q8×C4⋊C4×C472
C4×#125×C472
C42×Q8×C472
#3658447