Finite Group Databasebeta

← #44548901

Subgroups — #44548901

Order 32128.

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

normal subgroups only

This group has 222 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#30631744C211yesmaximal, characteristic, complemented
3#30631423C212yesmaximal, complemented
4#30631420C212yesmaximal
5#382×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—
18#22548626—21no—
19C2×C4⋊C4×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
44C4⋊C4×C251—42no—
45C42×C251C2×C411yescharacteristic
46C42×C251C2×C411yescharacteristic
47C42×C251D411yescharacteristic
48C42×C251D411yescharacteristic
49C22×D251—21no—
50Dic502—41no—
51D1004—41no—
52C22⋊D251—41no—
53C22⋊D251—41no—
54C2×Dic251—21no—
55C2×Dic251—21no—
56C2×Dic251—21no—
57C4×D251—42no—
58C251⋊C8—42no—
59C23×C251C2×D411yescharacteristic
60C2×C4×C251—21no—
61C2×C4×C251—21no—
62C2×C4×C251—41no—
63C2×C4×C251—41no—
64C2×C4×C251—42no—
65C2×C4×C251—42no—
66C2×C4×C251—42no—
67C2×C4×C251C22⋊C411yescharacteristic
68C2×C4×C251C22⋊C411yescharacteristic
69C2×C4×C251C22⋊C411yescharacteristic
70C2×C4×C251C22⋊C411yescharacteristic
71C2×C4×C251C22×C411yescharacteristic
72C2×C4×C251C2×D411yescharacteristic
73C22×C251—21no—
74C22×C251—21no—
75C22×C251C2×C22⋊C411yescharacteristic
76C22×C251AGL(1,ℤ/8)11yescharacteristic
77C22×C251#13711yescharacteristic
78C2×D251—41no—
79C2×D251—41no—
80C2×D251—41no—
81C4×C251—21no—
82C4×C251—21no—
83C4×C251—21no—
84C4×C251—21no—
85C4×C251—21no—
86C4×C251—21no—
87C4×C251—82no—
88Dic251—41no—
89Dic251—41no—
90Dic251—41no—
91C2×C251—21no—
92C2×C251—21no—
93C2×C251#41011yescharacteristic
94C2×C251#41711yescharacteristic
95C2×C251#42111yescharacteristic
96D251—81no—
97C251#151211yescharacteristic, complemented, Sylow
98#1512—2511nomaximal, Sylow
99#529—2511no—
100#432—2511no—
101#382D25111yescharacteristic, complemented
102#328—2512no—
103#327—2512no—
104#126—5021no—
105#125—2511no—
106#124—2511no—
107#123—5021no—
108C22⋊Q8—2511no—
109#121—2511no—
110C4×Q8—2511no—
111C4×D4—5021no—
112C4×D4—2511no—
113#117—5021no—
114C2×C4⋊C4—21no—
115C2×C42C2×D25111yescharacteristic
116C4⋊C8—5021no—
117C22⋊C8—2512no—
118#97—5021no—
119#95—21no—
120#95C2×D25112yes—
121C2×Q8—2511no—
122C2×D4—5021no—
123C2×D4—2511no—
124C22×C4—22no—
125C22×C4—5021no—
126C22×C4C22⋊D25111yescharacteristic
127C22×C4C22⋊D25111yescharacteristic
128C22×C4C22×D25111yescharacteristic
129C2×C8—5022no—
130C4⋊C4—42no—
131C4⋊C4—5021no—
132C4⋊C4—5021no—
133C4⋊C4—5021no—
134C4⋊C4—5021no—
135C4⋊C4—2511no—
136C4⋊C4—2511no—
137C22⋊C4—5021no—
138C22⋊C4—5021no—
139C22⋊C4—5021no—
140C22⋊C4—5021no—
141C22⋊C4—5021no—
142C42—5021no—
143C42C4×D25111yescharacteristic
144C42C4×D25111yescharacteristic
145C42D100411yescharacteristic
146C42D100411yescharacteristic
147C23—5021no—
148C23C2×C22⋊D25111yescharacteristic
149Q8—10041no—
150D4—10041no—
151D4—10041no—
152D4—10041no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—10042no—
161C2×C4—5021no—
162C2×C4—5021no—
163C2×C4—5021no—
164C2×C4(C2×D251)⋊C411yescharacteristic
165C2×C4(C2×D251)⋊C411yescharacteristic
166C2×C4(C2×D251)⋊C411yescharacteristic
167C2×C4(C2×D251)⋊C411yescharacteristic
168C2×C4C2×C4×D25111yescharacteristic
169C2×C4C2×D100411yescharacteristic
170C8—10042no—
171C22—21no—
172C22—21no—
173C22—10041no—
174C22—10041no—
175C22—10041no—
176C22C2×(C2×D251)⋊C411yescharacteristic
177C22#2254874111yescharacteristic
178C22#2254874611yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—10041no—
187C4—10041no—
188C4—10041no—
189C2—21no—
190C2—21no—
191C2—20081no—
192C2#3063166011yescharacteristic
193C2#3063168611yescharacteristic
194C2#3063170511yescharacteristic
subgroupG/H
centerC22C2×(C2×D251)⋊C4
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting#382×C251C2
socleC22×C251C2×C22⋊C4
prime radical#22548689C22
cosocleC22×C4×C251C23
hypercenter#382D251
hypocenterC251#1512
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #30631744C2semidirect
3. #30631423C2semidirect
5. #382×C251C2semidirect
7. #22548707C4semidirect
8. #22548703C4semidirect
12. C4×Dic502C4semidirect
13. C4×D1004C4semidirect
97. C251#1512semidirect
101. #382D251semidirect

Maximal subgroups

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

subgroupindex
#306322212
#306317442
#306314232
#306314202
#382×C2512
#1512251