Finite Group Databasebeta

← #44548849

Subgroups — #44548849

Order 32128.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#30631740C211yesmaximal, characteristic, complemented
3#30631423C212yesmaximal, complemented
4#30631420C212yesmaximal
5#376×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—
16C4⋊(C251⋊C8)—21no—
17C22⋊(C251⋊C8)C2212yes—
18C4×C251⋊C8—21no—
19C2×C42×C251—21no—
20C2×C42×C251C2211yescharacteristic
21#95×C251—21no—
22#95×C251C2212yes—
23C2×Dic502C2×C411yescharacteristic
24C2×D1004C2×C411yescharacteristic
25C2×C22⋊D251—21no—
26C2×C4×D251—21no—
27C2×C251⋊C8—22no—
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×C251—22no—
41C22×C4×C251D411yescharacteristic
42C22×C4×C251D411yescharacteristic
43C22×C4×C251C2311yescharacteristic
44C42×C251—24no—
45C42×C251C2×C411yescharacteristic
46C42×C251C2×C411yescharacteristic
47C42×C251D411yescharacteristic
48C42×C251D411yescharacteristic
49C22×D251—21no—
50Dic502—41no—
51D1004—41no—
52C22⋊D251—42no—
53C2×Dic251—21no—
54C2×Dic251—21no—
55C2×Dic251—21no—
56C4×D251—42no—
57C251⋊C8—42no—
58C23×C251C2×D411yescharacteristic
59C2×C4×C251—22no—
60C2×C4×C251—22no—
61C2×C4×C251—24no—
62C2×C4×C251—41no—
63C2×C4×C251—42no—
64C2×C4×C251—42no—
65C2×C4×C251C22⋊C411yescharacteristic
66C2×C4×C251C22⋊C411yescharacteristic
67C2×C4×C251C22⋊C411yescharacteristic
68C2×C4×C251C22⋊C411yescharacteristic
69C2×C4×C251C22×C411yescharacteristic
70C2×C4×C251C2×D411yescharacteristic
71C22×C251—21no—
72C22×C251—21no—
73C22×C251C2×C22⋊C411yescharacteristic
74C22×C251#13512yes—
75C2×D251—41no—
76C2×D251—41no—
77C2×D251—41no—
78C4×C251—21no—
79C4×C251—21no—
80C4×C251—21no—
81C4×C251—21no—
82C4×C251—21no—
83C4×C251—44no—
84C4×C251#10412yes—
85Dic251—41no—
86Dic251—41no—
87Dic251—41no—
88C2×C251—22no—
89C2×C251#41011yescharacteristic
90C2×C251#41611yescharacteristic
91C2×C251C2×#10411yescharacteristic
92D251—81no—
93C251#150011yescharacteristic, complemented, Sylow
94#1500—2511nomaximal, Sylow
95#529—2511no—
96#431—2511no—
97#376D25111yescharacteristic, complemented
98#328—2512no—
99#327—2512no—
100#126—5021no—
101#125—2511no—
102#124—2511no—
103#123—5021no—
104C22⋊Q8—2511no—
105#121—2511no—
106C4×Q8—2511no—
107C4×D4—5021no—
108C4×D4—2511no—
109#117—5021no—
110C2×C42—21no—
111C2×C42C2×D25111yescharacteristic
112C4⋊C8—5021no—
113C22⋊C8—2512no—
114C4×C8—5021no—
115#95—21no—
116#95C2×D25112yes—
117C2×Q8—2511no—
118C2×D4—5021no—
119C2×D4—2511no—
120C22×C4—22no—
121C22×C4—5021no—
122C22×C4C22⋊D25111yescharacteristic
123C22×C4C22⋊D25111yescharacteristic
124C22×C4C22×D25111yescharacteristic
125C2×C8—5022no—
126C4⋊C4—5021no—
127C4⋊C4—5021no—
128C4⋊C4—5021no—
129C4⋊C4—5021no—
130C4⋊C4—2511no—
131C4⋊C4—2511no—
132C22⋊C4—5021no—
133C22⋊C4—5021no—
134C22⋊C4—5021no—
135C22⋊C4—5021no—
136C22⋊C4—5021no—
137C42—24no—
138C42—5021no—
139C42C4×D25111yescharacteristic
140C42C4×D25111yescharacteristic
141C42D100411yescharacteristic
142C42D100411yescharacteristic
143C23—5021no—
144C23C2×C22⋊D25111yescharacteristic
145Q8—10041no—
146D4—10041no—
147D4—10042no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—10042no—
155C2×C4—5021no—
156C2×C4—5021no—
157C2×C4—5021no—
158C2×C4(C2×D251)⋊C411yescharacteristic
159C2×C4(C2×D251)⋊C411yescharacteristic
160C2×C4(C2×D251)⋊C411yescharacteristic
161C2×C4(C2×D251)⋊C411yescharacteristic
162C2×C4C2×C4×D25111yescharacteristic
163C2×C4C2×D100411yescharacteristic
164C8—10042no—
165C22—21no—
166C22—21no—
167C22—10041no—
168C22—10041no—
169C22—10041no—
170C22C2×(C2×D251)⋊C411yescharacteristic
171C22#2254873512yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—44no—
178C4—10041no—
179C4—10041no—
180C4—10041no—
181C4#2254864312yes—
182C2—22no—
183C2—20081no—
184C2#3063166011yescharacteristic
185C2#3063168111yescharacteristic
186C2C2×#2254864311yescharacteristic
subgroupG/H
centerC2×C4(C2×D251)⋊C4
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting#376×C251C2
socleC22×C251C2×C22⋊C4
prime radical#22548689C22
cosocleC22×C4×C251C23
hypercenter#376D251
hypocenterC251#1500
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #30631740C2semidirect
3. #30631423C2semidirect
5. #376×C251C2semidirect
7. #22548707C4semidirect
8. #22548703C4semidirect
12. C4×Dic502C4semidirect
13. C4×D1004C4semidirect
93. C251#1500semidirect
97. #376D251semidirect

Maximal subgroups

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

subgroupindex
#306322212
#306317402
#306314232
#306314202
#376×C2512
#1500251