Finite Group Databasebeta

← #44548943

Subgroups — #44548943

Order 32128.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#30632221C211yesmaximal, characteristic
2#30631555C211yesmaximal, characteristic, complemented
3#30631425C212yesmaximal, complemented
4#30631422C212yesmaximal
5#431×C251C211yesmaximal, characteristic, complemented
6#22548709—21no—
7#22548707C411yescharacteristic, complemented
8#22548703C411yescharacteristic, complemented
9#22548698—21no—
10#22548694C2211yescharacteristic
11#22548689C2211yescharacteristic
12C4×Dic502C411yescharacteristic, complemented
13C4×D1004C411yescharacteristic, complemented
14C4×C22⋊D251—21no—
15#22548672—21no—
16C251⋊#95—21no—
17C251⋊#95—21no—
18C251⋊#95C2212yes—
19C2×C42×C251C2211yescharacteristic
20C4⋊C8×C251—21no—
21C22⋊C8×C251C2212yes—
22C4×C8×C251—21no—
23C2×Dic502C2×C411yescharacteristic
24C2×D1004C2×C411yescharacteristic
25C2×C22⋊D251—21no—
26C22×Dic251—22no—
27C2×C4×D251—21no—
28C4⋊Dic251C2×C411yescharacteristic
29C4⋊Dic251C2×C411yescharacteristic
30Dic251⋊C4—21no—
31Dic251⋊C4—21no—
32Dic251⋊C4—21no—
33Dic251⋊C4—21no—
34C22⋊Dic251—21no—
35(C2×D251)⋊C4—21no—
36(C2×D251)⋊C4—21no—
37(C2×D251)⋊C4—21no—
38(C2×D251)⋊C4—21no—
39C4×Dic251—21no—
40C22×C4×C251D411yescharacteristic
41C22×C4×C251D411yescharacteristic
42C22×C4×C251C2311yescharacteristic
43C2×C8×C251—22no—
44C42×C251C2×C411yescharacteristic
45C42×C251C2×C411yescharacteristic
46C42×C251D411yescharacteristic
47C42×C251D411yescharacteristic
48C22×D251—21no—
49Dic502—41no—
50D1004—41no—
51C22⋊D251—42no—
52C2×Dic251—21no—
53C2×Dic251—21no—
54C2×Dic251—21no—
55C2×Dic251—42no—
56C2×Dic251—42no—
57C2×Dic251—42no—
58C4×D251—42no—
59C23×C251C2×D411yescharacteristic
60C2×C4×C251—22no—
61C2×C4×C251—41no—
62C2×C4×C251—41no—
63C2×C4×C251C22⋊C411yescharacteristic
64C2×C4×C251C22⋊C411yescharacteristic
65C2×C4×C251C22⋊C411yescharacteristic
66C2×C4×C251C22⋊C411yescharacteristic
67C2×C4×C251C22×C411yescharacteristic
68C2×C4×C251C2×D411yescharacteristic
69C8×C251—42no—
70C22×C251—21no—
71C22×C251—21no—
72C22×C251C2×C22⋊C411yescharacteristic
73C22×C251#13512yes—
74C2×D251—41no—
75C2×D251—41no—
76C2×D251—41no—
77C4×C251—21no—
78C4×C251—21no—
79C4×C251—21no—
80C4×C251—21no—
81C4×C251—21no—
82C4×C251—21no—
83Dic251—41no—
84Dic251—41no—
85Dic251—41no—
86Dic251—82no—
87C2×C251—22no—
88C2×C251#41011yescharacteristic
89C2×C251#41611yescharacteristic
90C2×C251#42111yescharacteristic
91D251—81no—
92C251#152111yescharacteristic, complemented, Sylow
93#1521—2511nomaximal, Sylow
94#529—2511no—
95#431D25111yescharacteristic, complemented
96#383—2511no—
97#328—2512no—
98#327—2512no—
99#126—5021no—
100#125—2511no—
101#124—2511no—
102#123—5021no—
103C22⋊Q8—2511no—
104#121—2511no—
105C4×Q8—2511no—
106C4×D4—5021no—
107C4×D4—2511no—
108#117—5021no—
109C2×C42C2×D25111yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D25112yes—
112C4×C8—21no—
113#95—5021no—
114#95—5021no—
115#95—2512no—
116C2×Q8—2511no—
117C2×D4—5021no—
118C2×D4—2511no—
119C22×C4—5022no—
120C22×C4—5021no—
121C22×C4D100411yescharacteristic
122C22×C4D100411yescharacteristic
123C22×C4C22×D25111yescharacteristic
124C2×C8—22no—
125C4⋊C4—5021no—
126C4⋊C4—5021no—
127C4⋊C4—5021no—
128C4⋊C4—5021no—
129C4⋊C4—2511no—
130C4⋊C4—2511no—
131C22⋊C4—5021no—
132C22⋊C4—5021no—
133C22⋊C4—5021no—
134C22⋊C4—5021no—
135C22⋊C4—5021no—
136C42—5021no—
137C42C4×D25111yescharacteristic
138C42C4×D25111yescharacteristic
139C42C22⋊D25111yescharacteristic
140C42C22⋊D25111yescharacteristic
141C23—5021no—
142C23C2×D100411yescharacteristic
143Q8—10041no—
144D4—10041no—
145D4—10042no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—10042no—
150C2×C4—10042no—
151C2×C4—10042no—
152C2×C4—10042no—
153C2×C4—5021no—
154C2×C4—5021no—
155C2×C4—5021no—
156C2×C4(C2×D251)⋊C411yescharacteristic
157C2×C4(C2×D251)⋊C411yescharacteristic
158C2×C4(C2×D251)⋊C411yescharacteristic
159C2×C4(C2×D251)⋊C411yescharacteristic
160C2×C4C2×C4×D25111yescharacteristic
161C2×C4C2×C22⋊D25111yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—10041no—
166C22—10041no—
167C22—10041no—
168C22C2×(C2×D251)⋊C411yescharacteristic
169C22#2254873712yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—20082no—
177C4—10041no—
178C4—10041no—
179C4—10041no—
180C2—22no—
181C2—20081no—
182C2#3063166011yescharacteristic
183C2#3063168411yescharacteristic
184C2#3063170311yescharacteristic
subgroupG/H
centerC22C2×(C2×D251)⋊C4
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting#431×C251C2
socleC22×C251C2×C22⋊C4
prime radical#22548689C22
cosocleC22×C4×C251C23
hypercenter#431D251
hypocenterC251#1521
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #30631555C2semidirect
3. #30631425C2semidirect
5. #431×C251C2semidirect
7. #22548707C4semidirect
8. #22548703C4semidirect
12. C4×Dic502C4semidirect
13. C4×D1004C4semidirect
92. C251#1521semidirect
95. #431D251semidirect

Maximal subgroups

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

subgroupindex
#306322212
#306315552
#306314252
#306314222
#431×C2512
#1521251