Finite Group Databasebeta

← #49132708

Subgroups — #49132708

Order 36224.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827077C211yesmaximal, characteristic, complemented
2#31827070C211yesmaximal, characteristic
3#31826773C212yesmaximal, complemented
4#31826766C212yesmaximal, complemented
5#31826711C212yesmaximal, complemented
6#31826694C212yesmaximal, complemented
7#31826671C212yesmaximal, complemented
8#31826666C212yesmaximal, complemented
9#424×C283C211yesmaximal, characteristic, complemented
10C2×#17985381C2212yes—
11C2×#17985381C2212yes—
12#22583610C2211yescharacteristic
13#22583607C2211yescharacteristic
14#22583603—22no—
15#22583602C2211yescharacteristic
16#22583602C2211yescharacteristic
17#22583600—22no—
18#22583595—22no—
19#22583589C2212yes—
20#22583584C2212yes—
21#22583583—22no—
22C4×Dic566C2212yes—
23C4×D1132C2212yes—
24#22583544C2212yes—
25#22583542C2212yes—
26#22583535C2212yes—
27#22583535C2212yes—
28#22583532C2212yes—
29#22583532C2212yes—
30C2×M16×C283C2211yescharacteristic
31C22×C8×C283C2211yescharacteristic
32#117×C283C2211yescharacteristic
33C4⋊C8×C283C2212yes—
34C4⋊C8×C283C2212yes—
35C2×Dic566C2312yes—
36C2×D1132—22no—
37C2×D1132C2312yes—
38C2×C22⋊D283—22no—
39C2×C4×D283—22no—
40#17985381—42no—
41#17985381—42no—
42C4⋊Dic283—22no—
43C4⋊Dic283C2312yes—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47Dic283⋊C4—22no—
48Dic283⋊C4—22no—
49C22⋊Dic283—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52C4×Dic283—22no—
53C22×C4×C283C2311yescharacteristic
54M16×C283—41no—
55C2×C8×C283—41no—
56C2×C8×C283C2312yes—
57C2×C8×C283C2312yes—
58C4⋊C4×C283D412yes—
59C22⋊C4×C283D412yes—
60C42×C283C2311yescharacteristic
61C42×C283C2311yescharacteristic
62C22×D283—22no—
63Dic566—22no—
64Dic566—22no—
65D1132—22no—
66D1132—22no—
67D1132—82no—
68C22⋊D283—82no—
69C2×Dic283—22no—
70C2×Dic283—22no—
71C2×Dic283—22no—
72C4×D283—82no—
73C23×C283C2×D411yescharacteristic
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283C2×D412yes—
77C2×C4×C283C2×D412yes—
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2411yescharacteristic
80C8×C283—22no—
81C8×C283—22no—
82C22×C283—21no—
83C22×C283—22no—
84C22×C283C22×D411yescharacteristic
85C2×D283—42no—
86C2×D283—42no—
87C2×D283—42no—
88C4×C283—21no—
89C4×C283—22no—
90C4×C283—22no—
91C4×C283H(5,𝔽2)11yescharacteristic
92C4×C2832−1+411yescharacteristic
93Dic283—42no—
94Dic283—42no—
95Dic283—42no—
96C2×C283—41no—
97C2×C283#53711yescharacteristic
98C2×C283#57712yes—
99D283—82no—
100C283#326011yescharacteristic, complemented, Sylow
101#3260—2831nomaximal, Sylow
102#541—2831no—
103#540—2831no—
104#479—2832no—
105#478—2832no—
106#468—2832no—
107#465—2832no—
108#461—2832no—
109#460—2832no—
110#424D28311yescharacteristic, complemented
111C2×SD16—2832no—
112C2×SD16—2832no—
113C2×M16C2×D28311yescharacteristic
114C22×C8C2×D28311yescharacteristic
115C4⋊Q8—2831no—
116#127—2831no—
117#126—5662no—
118#125—2831no—
119#125—2831no—
120#125—5662no—
121#123—5662no—
122C22⋊Q8—2832no—
123#121—2832no—
124#121—5662no—
125C4×Q8—2832no—
126C4×D4—2832no—
127#117C2×D28311yescharacteristic
128#107—2832no—
129#106—2832no—
130C4⋊C8C2×D28312yes—
131C4⋊C8C2×D28312yes—
132#103—2832no—
133#103—2832no—
134#102—2832no—
135#102—2832no—
136C2×Q8—2832no—
137C2×D4—2832no—
138C2×D4—5662no—
139C2×D4—5662no—
140C22×C4—5662no—
141C22×C4C22×D28311yescharacteristic
142SD16—11322no—
143SD16—11322no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D28312yes—
147C2×C8C22×D28312yes—
148C4⋊C4—2832no—
149C4⋊C4—2832no—
150C4⋊C4—5662no—
151C4⋊C4—5662no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4D113212yes—
156C22⋊C4—5662no—
157C22⋊C4—5662no—
158C22⋊C4—5662no—
159C22⋊C4D113212yes—
160C42—5662no—
161C42C22×D28311yescharacteristic
162C42C22×D28311yescharacteristic
163C23—5662no—
164C23C2×D113211yescharacteristic
165Q8—5662no—
166Q8—5662no—
167D4—5662no—
168D4—5662no—
169D4—22642no—
170D4—22642no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—22642no—
177C2×C4C2×D113212yes—
178C2×C4C2×D113212yes—
179C2×C4C2×D113211yescharacteristic
180C2×C4C23×D28311yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—11322no—
186C22—11322no—
187C22—11322no—
188C22C22×D113211yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—11322no—
193C4—11322no—
194C4—11322no—
195C4#2258365511yescharacteristic
196C4#2258365811yescharacteristic
197C2—41no—
198C2—22642no—
199C2#3182704611yescharacteristic
200C2#3182727712yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#424×C283C2
socleC22×C283C22×D4
prime radical#31827070C2
hypercenter#424D283
hypocenterC283#3260
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #31827077C2semidirect
3. #31826773C2semidirect
4. #31826766C2semidirect
5. #31826711C2semidirect
6. #31826694C2semidirect
7. #31826671C2semidirect
8. #31826666C2semidirect
9. #424×C283C2semidirect
100. C283#3260semidirect
110. #424D283semidirect

Maximal subgroups

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

subgroupindex
#318270772
#318270702
#318267732
#318267662
#318267112
#318266942
#318266712
#318266662
#424×C2832
#3260283