Finite Group Databasebeta

← #35971

Subgroups — #35971

Order 256.

752 conjugacy classes of subgroups.

The subgroup lattice has 247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2647C213yesmaximal
2#2571C213yesmaximal
3#2570C213yesmaximal
4#2509C213yesmaximal
5#2508C213yesmaximal
6#2508C213yesmaximal
7#2507C213yesmaximal
8#2402C213yesmaximal
9#2351C211yesmaximal, characteristic
10#2351C211yesmaximal, characteristic
11#2351C211yesmaximal, characteristic
12#2351C211yesmaximal, characteristic
13Q8×C4⋊C4C211yesmaximal, characteristic
14Q8×C4⋊C4C211yesmaximal, characteristic
15#2276C211yesmaximal, characteristic
16C2×C4×Q8C2211yescharacteristic
17C2×C4×Q8C2211yescharacteristic
18C2×C4×Q8C2211yescharacteristic
19C2×C4×Q8C2211yescharacteristic
20C2×C4×Q8C2211yescharacteristic
21C2×C4×Q8C2211yescharacteristic
22C2×C4×Q8C2211yescharacteristic
23#400C2216yes—
24#400C2213yes—
25#400C2216yes—
26#400C2211yescharacteristic
27#400C2213yes—
28#400C2213yes—
29#398C2213yes—
30#398C2213yes—
31#398C2216yes—
32#398C2213yes—
33#398C2213yes—
34#389C2213yes—
35#389C2213yes—
36#389C2213yes—
37#389C2213yes—
38#389C2216yes—
39#389C2213yes—
40#389C2213yes—
41#389C2213yes—
42#389C2213yes—
43#389C2213yes—
44#389C2213yes—
45#389C2213yes—
46#389C2213yes—
47#387C2216yes—
48#387C2216yes—
49#384C2213yes—
50#384C2213yes—
51#382C2213yes—
52#382C2213yes—
53#382C2213yes—
54#382C2213yes—
55#382C2216yes—
56C4×C4⋊C4C2213yes—
57C4×C4⋊C4C2213yes—
58C4×C4⋊C4C2213yes—
59C4×C4⋊C4C2213yes—
60C4×C4⋊C4C2213yes—
61C4×C4⋊C4C2213yes—
62C4×C4⋊C4C2213yes—
63C4×C4⋊C4C2213yes—
64C4×C4⋊C4C2213yes—
65#376C2213yes—
66C22×Q8C2311yescharacteristic
67C4×Q8—24no—
68C4×Q8—24no—
69C4×Q8—24no—
70C4×Q8—24no—
71C4×Q8—24no—
72C4×Q8—24no—
73C4×Q8Q818yes—
74C2×C4⋊C4C2313yes—
75C2×C4⋊C4C2313yes—
76C2×C4⋊C4C2313yes—
77C2×C4⋊C4C2313yes—
78C2×C4⋊C4C2313yes—
79C2×C4⋊C4C2313yes—
80C2×C4⋊C4C2311yescharacteristic
81C2×C4⋊C4C2311yescharacteristic
82C2×C4⋊C4C2313yes—
83C2×C4⋊C4C2313yes—
84C2×C4⋊C4C2313yes—
85C2×C4⋊C4C2313yes—
86C2×C4⋊C4C2313yes—
87C2×C4⋊C4C2313yes—
88C2×C4⋊C4C2313yes—
89C2×C4⋊C4C2313yes—
90C2×C4⋊C4C2313yes—
91C2×C4⋊C4C2313yes—
92C2×C4⋊C4C2316yes—
93C2×C4⋊C4C2316yes—
94C2×C4⋊C4C2313yes—
95C2×C42C2313yes—
96C2×C42C2313yes—
97C2×C42C2313yes—
98C2×C42C2313yes—
99C2×C42C2313yes—
100C2×C42C2313yes—
101C2×C42C2316yes—
102C2×C42C2313yes—
103#95C2311yescharacteristic
104#95C2313yes—
105#95C2313yes—
106#95C2313yes—
107#95C2311yescharacteristic
108#95C2311yescharacteristic
109#95C2311yescharacteristic
110#95C2311yescharacteristic
111#95C2313yes—
112#95C2313yes—
113#95C2313yes—
114#95C2313yes—
115#95C2313yes—
116#95C2313yes—
117#95C2313yes—
118#95C2313yes—
119#95C2316yes—
120#95C2316yes—
121#95C2316yes—
122#95C2316yes—
123C2×Q8C2×Q814yes—
124C2×Q8#4114yes—
125C2×Q8#4114yes—
126C22×C4C2411yescharacteristic
127C22×C4C2411yescharacteristic
128C22×C4C2411yescharacteristic
129C22×C4C2413yes—
130C22×C4C2413yes—
131C22×C4C2411yescharacteristic
132C22×C4C2411yescharacteristic
133C22×C4C2413yes—
134C22×C4C2413yes—
135C22×C4C2413yes—
136C22×C4C2413yes—
137C22×C4C2411yescharacteristic
138C22×C4C2413yes—
139C22×C4C2411yescharacteristic
140C22×C4C2413yes—
141C4⋊C4—26no—
142C4⋊C4—26no—
143C4⋊C4—26no—
144C4⋊C4—26no—
145C4⋊C4—26no—
146C4⋊C4—26no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—26no—
150C4⋊C4—43no—
151C4⋊C4—43no—
152C4⋊C4—43no—
153C4⋊C4—43no—
154C4⋊C4—46no—
155C4⋊C4—43no—
156C4⋊C4—43no—
157C4⋊C4—43no—
158C4⋊C4—43no—
159C4⋊C4—43no—
160C4⋊C4—46no—
161C4⋊C4C2×Q8112yes—
162C42—26no—
163C42—26no—
164C42—26no—
165C42—26no—
166C42—26no—
167C42—26no—
168C42—46no—
169C42C2×Q8112yes—
170C23C2511yescharacteristic
171Q8#125116yes—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—23no—
175C2×C4—21no—
176C2×C4—23no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—23no—
184C2×C4—23no—
185C2×C4—23no—
186C2×C4—23no—
187C2×C4—23no—
188C2×C4—23no—
189C2×C4—21no—
190C2×C4—23no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—23no—
194C2×C4—23no—
195C2×C4—23no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—23no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—23no—
203C2×C4—23no—
204C2×C4—23no—
205C2×C4—23no—
206C2×C4—21no—
207C2×C4—23no—
208C2×C4—21no—
209C2×C4—23no—
210C2×C4—23no—
211C2×C4C22×Q812yes—
212C2×C4C22×Q816yes—
213C2×C4C22×Q816yes—
214C2×C4C2×#4116yes—
215C2×C4C2×#4116yes—
216C2×C42−1+412yes—
217C22C23×Q811yescharacteristic
218C22C22×#4111yescharacteristic
219C22C22×#4111yescharacteristic
220C22C2×2−1+411yescharacteristic
221C22#58511yescharacteristic
222C22#58511yescharacteristic
223C22#58511yescharacteristic
224C4—22no—
225C4—26no—
226C4—22no—
227C4—41no—
228C4—43no—
229C4—41no—
230C4—41no—
231C4—43no—
232C4—41no—
233C4—41no—
234C4—43no—
235C4—43no—
236C4—43no—
237C4—43no—
238C4C2×#125112yes—
239C2C22×#12511yescharacteristic
240C2#350211yescharacteristic
241C2#350411yescharacteristic
242C2#351611yescharacteristic
243C2#351811yescharacteristic
244C2#352411yescharacteristic
245C2#352411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#26472
#25712
#25702
#25092
#25082
#25072
#24022
#23512
Q8×C4⋊C42
#22762