Finite Group Databasebeta

← #44560743

Subgroups — #44560743

Order 32128.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#30632240C211yesmaximal, characteristic
2C2×#22548713C211yesmaximal, characteristic
3#30632054C214yesmaximal, complemented
4#30632036C214yesmaximal, complemented
5#30631697C211yesmaximal, characteristic
6#30631696C211yesmaximal, characteristic
7#30631695C211yesmaximal, characteristic
8M16×Dic251C211yesmaximal, characteristic
9#419×C251C211yesmaximal, characteristic
10C22×Dic502C2211yescharacteristic
11C2×#16860794C2211yescharacteristic
12#22548714C2212yes—
13#22548713—22no—
14#22548713C2212yes—
15#22548713C2212yes—
16#22548706C2212yes—
17#22548692—22no—
18C4×Dic502—22no—
19#22548674C2211yescharacteristic
20C2×Dic251⋊C4—22no—
21C2×C4×Dic251C2211yescharacteristic
22#22548640C2214yes—
23#22548639C2214yes—
24#22548638C2214yes—
25#22548625C2212yes—
26C8×Dic251C2212yes—
27C22×Q8×C251C2211yescharacteristic
28C2×M16×C251C2211yescharacteristic
29#117×C251C2211yescharacteristic
30#103×C251C2214yes—
31C2×Dic502—22no—
32C2×Dic502—21no—
33C2×Dic502—22no—
34C2×Dic502—22no—
35C2×Dic502C2312yes—
36C22×Dic251—21no—
37C22×Dic251D412yes—
38#16860794—22no—
39C2×C251⋊C8C2312yes—
40C4⋊Dic251—22no—
41C4⋊Dic251C2312yes—
42Dic251⋊C4—24no—
43Dic251⋊C4—24no—
44Dic251⋊C4—22no—
45Dic251⋊C4—22no—
46C22⋊Dic251—21no—
47C4×Dic251—21no—
48C4×Dic251D412yes—
49C4×Dic251C2311yescharacteristic
50C4×Dic251C2311yescharacteristic
51C2×Q8×C251—21no—
52C2×Q8×C251—22no—
53C2×Q8×C251—22no—
54C2×Q8×C251C2312yes—
55C22×C4×C251—21no—
56C22×C4×C251C2311yescharacteristic
57M16×C251—22no—
58C2×C8×C251C2312yes—
59C4⋊C4×C251C2312yes—
60C22⋊C4×C251—21no—
61C42×C251—21no—
62Dic502—22no—
63Dic502—22no—
64Dic502—42no—
65Dic502—44no—
66C2×Dic251—24no—
67C2×Dic251—22no—
68C2×Dic251—22no—
69C2×Dic251—42no—
70C2×Dic251C2×D412yes—
71C2×Dic251C2×D412yes—
72C251⋊C8—22no—
73C23×C251C2×D411yescharacteristic
74Q8×C251—22no—
75Q8×C251—22no—
76Q8×C251—42no—
77C2×C4×C251—22no—
78C2×C4×C251—22no—
79C2×C4×C251—42no—
80C2×C4×C251C2×D411yescharacteristic
81C2×C4×C251#4112yes—
82C2×C4×C251#4112yes—
83C2×C4×C251C2411yescharacteristic
84C8×C251—22no—
85C22×C251—22no—
86C22×C251#12412yes—
87C22×C251C22×D411yescharacteristic
88C4×C251—42no—
89C4×C251—42no—
90C4×C251#12412yes—
91C4×C251C2×#4111yescharacteristic
92C4×C251C2×#4111yescharacteristic
93Dic251—22no—
94Dic251—42no—
95Dic251—42no—
96Dic251#13714yes—
97C2×C251—22no—
98C2×C251C2×#12411yescharacteristic
99C2×C251C2×#13712yes—
100C251#313911yescharacteristic, complemented, Sylow
101#3139—2511nomaximal, Sylow
102#533—2511no—
103C2×C4⋊Q8—2511no—
104#491—2514no—
105#487—2514no—
106#419—2511no—
107#419—2511no—
108#419—2511no—
109#419D25111yescharacteristic
110C4×M16—2511no—
111C22×Q8—2511no—
112C22×Q8C2×D25111yescharacteristic
113C2×M16—2511no—
114C2×M16C2×D25111yescharacteristic
115C4⋊Q8—5022no—
116C4⋊Q8—2512no—
117C4⋊Q8—2512no—
118C4⋊Q8—2512no—
119#125—2512no—
120C22⋊Q8—5022no—
121C4×Q8—5022no—
122#117—2511no—
123#117C2×D25111yescharacteristic
124C2×C4⋊C4—5022no—
125C2×C42—2511no—
126#103—2514no—
127#103—2514no—
128#103—2514no—
129#103C2×D25114yes—
130#97—2512no—
131C4×C8—2512no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—5022no—
136C2×Q8—5022no—
137C2×Q8—5022no—
138C2×Q8—5021no—
139C2×Q8—2512no—
140C2×Q8C22×D25112yes—
141C22×C4—21no—
142C22×C4—5021no—
143C22×C4—2512no—
144C22×C4C22×D25111yescharacteristic
145M16—22no—
146M16—5022no—
147C2×C8—2512no—
148C2×C8C22×D25112yes—
149C4⋊C4—5024no—
150C4⋊C4—5024no—
151C4⋊C4—5022no—
152C4⋊C4—5022no—
153C4⋊C4—5022no—
154C4⋊C4—2512no—
155C4⋊C4C22×D25112yes—
156C22⋊C4—21no—
157C22⋊C4—5021no—
158C42—21no—
159C42—5021no—
160C42—2512no—
161C42—2511no—
162C42—2511no—
163C23D4×D25111yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—10044no—
168Q8—10042no—
169Q8—5022no—
170Q8—5022no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—10042no—
175C2×C4—5022no—
176C2×C4—5022no—
177C2×C4—5024no—
178C2×C4—2512no—
179C2×C4—2512no—
180C2×C4D4×D25111yescharacteristic
181C2×C4#1686080912yes—
182C2×C4#1686081012yes—
183C2×C4C23×D25111yescharacteristic
184C8—22no—
185C8—5022no—
186C22—22no—
187C22#2254870112yes—
188C22C2×D4×D25111yescharacteristic
189C4—42no—
190C4—42no—
191C4—10042no—
192C4—10042no—
193C4—5022no—
194C4—2514no—
195C4#2254870112yes—
196C4C2×#1686080911yescharacteristic
197C4C2×#1686081011yescharacteristic
198C2—22no—
199C2C2×#2254870111yescharacteristic
200C2#137×D25112yes—
subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#419×C251C2
socleC22×C251C22×D4
prime radicalC23×C251C2×D4
hypercenter#419D251
hypocenterC251#3139
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #30632054C2semidirect
4. #30632036C2semidirect
100. C251#3139semidirect

Maximal subgroups

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

subgroupindex
#306322402
C2×#225487132
#306320542
#306320362
#306316972
#306316962
#306316952
M16×Dic2512
#419×C2512
#3139251