Finite Group Databasebeta

← #44558318

Subgroups — #44558318

Order 32128.

368 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30631626C212yesmaximal
2#30631626C212yesmaximal
3#30631608C212yesmaximal
4#30631593C211yesmaximal, characteristic
5#30631586C212yesmaximal
6#30631585C211yesmaximal, characteristic
7#30631574C212yesmaximal
8#30631573C212yesmaximal
9#389×C251C211yesmaximal, characteristic
10C22×Dic502C2211yescharacteristic
11C2×C4⋊Dic251C2211yescharacteristic
12C2×C4⋊Dic251C2212yes—
13C2×C4⋊Dic251C2211yescharacteristic
14C2×C4⋊Dic251C2211yescharacteristic
15C2×C4⋊Dic251C2212yes—
16C2×Dic251⋊C4C2212yes—
17C2×C4×Dic251C2212yes—
18C251⋊#95C2212yes—
19C251⋊#95C2212yes—
20C251⋊#95C2212yes—
21C251⋊#95C2212yes—
22C251⋊#95C2212yes—
23C251⋊#95C2212yes—
24C251⋊#95C2212yes—
25C251⋊#95C2212yes—
26C2×C4⋊C4×C251C2212yes—
27C2×C4⋊C4×C251C2211yescharacteristic
28C2×C4⋊C4×C251C2211yescharacteristic
29C2×C42×C251C2211yescharacteristic
30#95×C251C2212yes—
31C2×Dic502—22no—
32C2×Dic502—41no—
33C2×Dic502—41no—
34C22×Dic251C2312yes—
35C22×Dic251C2312yes—
36C22×Dic251C2312yes—
37C22×Dic251C2312yes—
38C4⋊Dic251—22no—
39C4⋊Dic251—41no—
40C4⋊Dic251—42no—
41C4⋊Dic251—41no—
42C4⋊Dic251—42no—
43Dic251⋊C4—24no—
44C4×Dic251—42no—
45C22×C4×C251C2312yes—
46C22×C4×C251C2312yes—
47C22×C4×C251C2311yescharacteristic
48C22×C4×C251C2311yescharacteristic
49C22×C4×C251C2311yescharacteristic
50C4⋊C4×C251—24no—
51C4⋊C4×C251—41no—
52C4⋊C4×C251Q814yescomplemented
53C42×C251—41no—
54Dic502—44no—
55C2×Dic251—22no—
56C2×Dic251—22no—
57C2×Dic251—22no—
58C2×Dic251—22no—
59C2×Dic251—22no—
60C2×Dic251—22no—
61C2×Dic251—22no—
62C2×Dic251—22no—
63C2×Dic251—22no—
64C2×Dic251—22no—
65C2×Dic251—22no—
66C2×Dic251—22no—
67C23×C251C2411yescharacteristic
68C2×C4×C251—22no—
69C2×C4×C251—21no—
70C2×C4×C251—21no—
71C2×C4×C251—21no—
72C2×C4×C251—22no—
73C2×C4×C251—21no—
74C2×C4×C251—21no—
75C2×C4×C251—21no—
76C2×C4×C251—22no—
77C2×C4×C251—22no—
78C2×C4×C251—22no—
79C2×C4×C251C2×Q812yes—
80C2×C4×C251C2×Q814yes—
81C2×C4×C251#4112yes—
82C2×C4×C251#4112yes—
83C22×C251C22×Q811yescharacteristic
84C22×C251C2×#4111yescharacteristic
85C22×C251C2×#4111yescharacteristic
86C22×C251H(5,𝔽2)11yescharacteristic
87C22×C251H(5,𝔽2)11yescharacteristic
88C22×C2512−1+411yescharacteristic
89C22×C2512−1+411yescharacteristic
90C4×C251—22no—
91C4×C251—22no—
92C4×C251—22no—
93C4×C251—24no—
94C4×C251—42no—
95Dic251—42no—
96Dic251—42no—
97Dic251—42no—
98Dic251—42no—
99C2×C251#53811yescharacteristic
100C2×C251#53911yescharacteristic
101C2×C251#54411yescharacteristic
102C2×C251#55411yescharacteristic
103C2×C251#55611yescharacteristic
104C2×C251#55711yescharacteristic
105C2×C251#56311yescharacteristic
106C251#280511yescharacteristic, complemented, Sylow
107#2805—2511nomaximal, Sylow
108#400—2512no—
109#400—2512no—
110#395—2512no—
111#391—2511no—
112#389—2512no—
113#389—2511no—
114#389D25111yescharacteristic
115#387—2512no—
116#387—2512no—
117C22×Q8—2511no—
118C2×C4⋊C4—2511no—
119C2×C4⋊C4—2512no—
120C2×C4⋊C4—2511no—
121C2×C4⋊C4—2512no—
122C2×C4⋊C4—2512no—
123C2×C4⋊C4—2511no—
124C2×C4⋊C4C2×D25112yes—
125C2×C4⋊C4C2×D25111yescharacteristic
126C2×C4⋊C4C2×D25111yescharacteristic
127C2×C42—2512no—
128C2×C42C2×D25111yescharacteristic
129#95—2512no—
130#95—2512no—
131#95—2512no—
132#95—2512no—
133#95—2512no—
134#95—2512no—
135#95—2512no—
136#95—2512no—
137#95C2×D25112yes—
138C2×Q8—10041no—
139C2×Q8—10041no—
140C2×Q8—5022no—
141C22×C4—2512no—
142C22×C4—2512no—
143C22×C4—2512no—
144C22×C4—2512no—
145C22×C4C22×D25112yes—
146C22×C4C22×D25111yescharacteristic
147C22×C4C22×D25112yes—
148C22×C4C22×D25111yescharacteristic
149C22×C4C22×D25111yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—10041no—
153C4⋊C4—10042no—
154C4⋊C4—10041no—
155C4⋊C4—10042no—
156C4⋊C4—5022no—
157C4⋊C4—5024no—
158C4⋊C4Dic50214yescomplemented
159C42—41no—
160C42—10042no—
161C23C23×D25111yescharacteristic
162Q8—10044no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—5022no—
175C2×C4—5022no—
176C2×C4—5022no—
177C2×C4—5022no—
178C2×C4—5022no—
179C2×C4—5022no—
180C2×C4—5022no—
181C2×C4—5022no—
182C2×C4—5022no—
183C2×C4—5022no—
184C2×C4—5022no—
185C2×C4—5022no—
186C2×C4C2×Dic50212yes—
187C2×C4C2×Dic50214yes—
188C2×C4#1686080912yes—
189C2×C4#1686081112yes—
190C22C22×Dic50211yescharacteristic
191C22C2×#1686080911yescharacteristic
192C22C2×#1686081111yescharacteristic
193C22#2254876011yescharacteristic
194C22#2254876111yescharacteristic
195C22#2254876211yescharacteristic
196C22#2254876311yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—24no—
201C4—42no—
202C4—10042no—
203C4—10042no—
204C4—10042no—
205C4—10042no—
206C2#3063227711yescharacteristic
207C2#3063228211yescharacteristic
208C2#3063231811yescharacteristic
209C2#3063239411yescharacteristic
210C2#3063241111yescharacteristic
211C2#3063241611yescharacteristic
212C2#3063244111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D251
commutator, socle, prime radical, cosocleC23×C251C24
Fitting#389×C251C2
hypercenter#389D251
hypocenterC251#2805
LCSG ▷ C23×C251 ▷ C251
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
52. C4⋊C4×C251Q8semidirect
106. C251#2805semidirect
158. C4⋊C4Dic502semidirect

Maximal subgroups

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

subgroupindex
#306316262
#306316082
#306315932
#306315862
#306315852
#306315742
#306315732
#389×C2512
#2805251