Finite Group Databasebeta

← #44552029

Subgroups — #44552029

Order 32128.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#30632236C211yesmaximal, characteristic
2#30631659C212yesmaximal, complemented
3#30631482C211yesmaximal, characteristic, complemented
4#30631479C212yesmaximal, complemented
5#354×C251C211yesmaximal, characteristic, complemented
6C2×#16860811C411yescharacteristic, complemented
7C2×#16860809C2211yescharacteristic
8#22548713C411yescharacteristic, complemented
9#22548711C2211yescharacteristic
10#22548703C411yescharacteristic, complemented
11#22548688—22no—
12(C22⋊D251)⋊C4—22no—
13#22548671—22no—
14C42×D251C411yescharacteristic, complemented
15#22548630C2212yes—
16#22548629—22no—
17#124×C251C2211yescharacteristic
18#99×C251C2212yes—
19#16860811—41no—
20#16860811—41no—
21#16860809—41no—
22#16860809—41no—
23C2×Dic502C2×C411yescharacteristic
24C2×D1004—21no—
25C2×D1004C2×C411yescharacteristic
26C2×C22⋊D251—22no—
27C2×C22⋊D251D412yes—
28C22×Dic251D412yes—
29C2×C4×D251—21no—
30C2×C4×D251—21no—
31C2×C4×D251C2×C411yescharacteristic
32Dic251⋊C4—22no—
33Dic251⋊C4—42no—
34C22⋊Dic251—22no—
35(C2×D251)⋊C4—22no—
36C4×Dic251—21no—
37C4×Dic251—42no—
38C4×Dic251C2×C411yescharacteristic
39C2×Q8×C251C2×C411yescharacteristic
40C2×D4×C251C2311yescharacteristic
41C22⋊C4×C251—22no—
42C22⋊C4×C251—22no—
43C42×C251C2×C411yescharacteristic
44C22×D251—21no—
45C22×D251C22⋊C411yescharacteristic
46Dic502—41no—
47D1004—41no—
48D1004—42no—
49C22⋊D251—42no—
50C22⋊D251—44no—
51C2×Dic251—21no—
52C2×Dic251—22no—
53C2×Dic251—22no—
54C2×Dic251—42no—
55C2×Dic251C22⋊C412yes—
56C2×Dic251C22⋊C411yescharacteristic
57C4×D251—21no—
58C4×D251—21no—
59C4×D251—42no—
60C4×D251—41no—
61C4×D251—41no—
62C23×C251C2×D412yes—
63Q8×C251—41no—
64D4×C251—41no—
65C2×C4×C251—21no—
66C2×C4×C251—21no—
67C2×C4×C251—42no—
68C2×C4×C251C22×C411yescharacteristic
69C22×C251—22no—
70C22×C251—42no—
71C22×C251C2×C22⋊C411yescharacteristic
72C2×D251—21no—
73C2×D251—41no—
74C2×D251—42no—
75C2×D251—41no—
76C4×C251—21no—
77C4×C251—41no—
78C4×C251—41no—
79C4×C251—82no—
80Dic251—22no—
81Dic251—22no—
82Dic251—82no—
83Dic251#9911yescharacteristic
84Dic251#9911yescharacteristic
85C2×C251—21no—
86C2×C251—42no—
87C2×C251C2×#9911yescharacteristic
88D251—41no—
89D251—81no—
90C251#212611yescharacteristic, complemented, Sylow
91#2126—2511nomaximal, Sylow
92#532—2511no—
93#410—2512no—
94#354—2511no—
95#354D25111yescharacteristic, complemented
96#353—2512no—
97C2×#41—2511no—
98C2×#41—2511no—
99C4⋊Q8—2511no—
100#127—2511no—
101#124—2511no—
102#124C2×D25111yescharacteristic
103#121—5022no—
104C4×D4—5022no—
105#117—5022no—
106C2×C42—2511no—
107#99—5022no—
108#99—2512no—
109#99C2×D25112yes—
110#41—10041no—
111#41—10041no—
112#41—10041no—
113#41—10041no—
114C2×Q8—2511no—
115C2×Q8C4×D25111yescharacteristic
116C2×D4—5021no—
117C2×D4—5022no—
118C2×D4—2512no—
119C2×D4—2511no—
120C2×D4C22×D25111yescharacteristic
121C22×C4—5021no—
122C22×C4—5021no—
123C22×C4—2512no—
124C22×C4—2511no—
125C4⋊C4—10042no—
126C4⋊C4—5022no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—5022no—
130C22⋊C4—5022no—
131C42—10042no—
132C42—5021no—
133C42—2511no—
134C42C4×D25111yescharacteristic
135C23—5021no—
136C23—2511no—
137C23D4×D25112yes—
138Q8—41no—
139Q8—10041no—
140D4—41no—
141D4—10041no—
142D4—10042no—
143D4—10042no—
144D4—10044no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—10042no—
149C2×C4—10041no—
150C2×C4—10041no—
151C2×C4—10042no—
152C2×C4—5021no—
153C2×C4—5021no—
154C2×C4—5021no—
155C2×C4—5022no—
156C2×C4—5022no—
157C2×C4—2512no—
158C2×C4—2511no—
159C2×C4C2×C4×D25111yescharacteristic
160C22—22no—
161C22—42no—
162C22—10042no—
163C22—10041no—
164C22—10041no—
165C22—5021no—
166C22C22⋊C4×D25111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—20082no—
172C4—5022no—
173C4—5022no—
174C4—2511no—
175C4—2511no—
176C2—21no—
177C2—42no—
178C2—20081no—
179C2—10041no—
180C2#99×D25111yescharacteristic
subgroupG/H
centerC2#99×D251
commutatorC2×C4×C251C22×C4
FrattiniC2×D4C22×D251
Fitting#354×C251C2
socleC2×C251C2×#99
prime radical#30632236C2
cosocleC2×D4×C251C23
hypercenter#354D251
hypocenterC251#2126
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #30631659C2semidirect
3. #30631482C2semidirect
4. #30631479C2semidirect
5. #354×C251C2semidirect
6. C2×#16860811C4semidirect
8. #22548713C4semidirect
10. #22548703C4semidirect
14. C42×D251C4semidirect
90. C251#2126semidirect
95. #354D251semidirect

Maximal subgroups

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

subgroupindex
#306322362
#306316592
#306314822
#306314792
#354×C2512
#2126251