Finite Group Databasebeta

← #44548995

Subgroups — #44548995

Order 32128.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#30632222C211yesmaximal, characteristic
2#30631742C211yesmaximal, characteristic, complemented
3#30631742C211yesmaximal, characteristic, complemented
4#30631429C211yesmaximal, characteristic, complemented
5#30631426C211yesmaximal, characteristic, complemented
6#30631426C211yesmaximal, characteristic, complemented
7#330×C251C211yesmaximal, characteristic, complemented
8#22548710—21no—
9#22548703C2211yescharacteristic
10#22548700—21no—
11#22548695C411yescharacteristic
12#22548690C411yescharacteristic
13#22548680C411yescharacteristic
14#22548677—21no—
15#22548677C411yescharacteristic
16#22548673—21no—
17C42×D251C2211yescharacteristic
18Dic251⋊C8—21no—
19Dic251⋊C8—21no—
20(C2×D251)⋊C8—21no—
21(C2×D251)⋊C8—21no—
22#22548626C2211yescharacteristic
23#22548626C2211yescharacteristic
24#125×C251C2211yescharacteristic
25#97×C251C2211yescharacteristic
26#97×C251C2211yescharacteristic
27C2×Dic502C2×C411yescharacteristic
28C2×D1004—21no—
29C2×D1004C2×C411yescharacteristic
30C2×C4×D251—21no—
31C2×C4×D251C2×C411yescharacteristic
32C2×C4×D251D411yescharacteristic
33C2×C4×D251D411yescharacteristic
34C2×C251⋊C8—21no—
35C2×C251⋊C8—21no—
36C4⋊Dic251—21no—
37Dic251⋊C4—21no—
38(C2×D251)⋊C4—21no—
39(C2×D251)⋊C4—21no—
40(C2×D251)⋊C4—21no—
41(C2×D251)⋊C4—21no—
42(C2×D251)⋊C4—21no—
43C4×Dic251—21no—
44C4×Dic251C2×C411yescharacteristic
45C4×Dic251D411yescharacteristic
46C4×Dic251D411yescharacteristic
47C2×C8×C251—21no—
48C2×C8×C251—21no—
49C4⋊C4×C251—21no—
50C4⋊C4×C251—21no—
51C4⋊C4×C251C2×C411yescharacteristic
52C4⋊C4×C251C2×C411yescharacteristic
53C42×C251C2311yescharacteristic
54C22×D251—21no—
55C22×D251C22⋊C411yescharacteristic
56Dic502—41no—
57D1004—41no—
58D1004—42no—
59C2×Dic251—21no—
60C2×Dic251C22⋊C411yescharacteristic
61C2×Dic251C22⋊C411yescharacteristic
62C2×Dic251C22⋊C411yescharacteristic
63C4×D251—41no—
64C4×D251—41no—
65C4×D251—41no—
66C4×D251—42no—
67C251⋊C8—41no—
68C251⋊C8—41no—
69C2×C4×C251—21no—
70C2×C4×C251—21no—
71C2×C4×C251C22×C411yescharacteristic
72C2×C4×C251C2×D411yescharacteristic
73C2×C4×C251C2×D411yescharacteristic
74C8×C251—41no—
75C8×C251—41no—
76C22×C251C2×C22⋊C411yescharacteristic
77C2×D251—21no—
78C2×D251—21no—
79C2×D251—21no—
80C2×D251—41no—
81C2×D251—41no—
82C2×D251—41no—
83C4×C251—21no—
84C4×C251—21no—
85C4×C251—21no—
86C4×C251—41no—
87C4×C251—41no—
88Dic251—21no—
89Dic251—21no—
90Dic251—21no—
91Dic251—41no—
92C2×C251#41311yescharacteristic
93C2×C251#42111yescharacteristic
94C2×C251#42111yescharacteristic
95D251—41no—
96D251—81no—
97C251#153511yescharacteristic, complemented, Sylow
98#1535—2511nomaximal, Sylow
99#529—2511no—
100#432—2511no—
101#432—2511no—
102#330—2511no—
103#330D25111yescharacteristic, complemented
104#329—2511no—
105#329—2511no—
106#126—5021no—
107#125C2×D25111yescharacteristic
108#124—2511no—
109#123—5021no—
110C22⋊Q8—2511no—
111#121—2511no—
112C4×Q8—2511no—
113C4×D4—5021no—
114C4×D4—2511no—
115#117—5021no—
116C2×C42—2511no—
117C4⋊C8—5021no—
118C4⋊C8—5021no—
119C22⋊C8—5021no—
120C22⋊C8—5021no—
121#97—2511no—
122#97—2511no—
123#97C2×D25111yescharacteristic
124#97C2×D25111yescharacteristic
125C2×Q8—2511no—
126C2×D4—5021no—
127C2×D4—2511no—
128C22×C4—5021no—
129C22×C4—2511no—
130C22×C4—2511no—
131C22×C4—2511no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—5021no—
135C2×C8—5021no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—5021no—
139C4⋊C4—5021no—
140C4⋊C4C4×D25111yescharacteristic
141C4⋊C4C4×D25111yescharacteristic
142C22⋊C4—5021no—
143C22⋊C4—5021no—
144C22⋊C4—5021no—
145C22⋊C4—5021no—
146C22⋊C4—5021no—
147C42—5021no—
148C42—2511no—
149C42—2511no—
150C42—2511no—
151C42C22×D25111yescharacteristic
152C23—5021no—
153C23—2511no—
154Q8—10041no—
155D4—10041no—
156D4—10042no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—10041no—
160C2×C4—10041no—
161C2×C4—10041no—
162C2×C4—10042no—
163C2×C4—5021no—
164C2×C4—2511no—
165C2×C4—2511no—
166C2×C4—2511no—
167C2×C4C2×C4×D25111yescharacteristic
168C2×C4D4×D25111yescharacteristic
169C2×C4D4×D25111yescharacteristic
170C8—41no—
171C8—41no—
172C8—10041no—
173C8—10041no—
174C22—10041no—
175C22—10041no—
176C22—10041no—
177C22—5021no—
178C22—5021no—
179C22—5021no—
180C22C22⋊C4×D25111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—10041no—
187C4—5021no—
188C4—5021no—
189C4—5021no—
190C2—20081no—
191C2—10041no—
192C2#3063167011yescharacteristic
193C2#3063170211yescharacteristic
194C2#3063170211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D251
commutatorC2×C4×C251C22×C4
FrattiniC42C22×D251
Fitting#330×C251C2
socleC22×C251C2×C22⋊C4
prime radical#22548690C4
cosocleC42×C251C23
hypercenter#330D251
hypocenterC251#1535
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #30631742C2semidirect
3. #30631742C2semidirect
4. #30631429C2semidirect
5. #30631426C2semidirect
6. #30631426C2semidirect
7. #330×C251C2semidirect
97. C251#1535semidirect
103. #330D251semidirect

Maximal subgroups

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

subgroupindex
#306322222
#306317422
#306314292
#306314262
#330×C2512
#1535251