Finite Group Databasebeta

← #44401418

Subgroups — #44401418

Order 29056.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#28409583C211yesmaximal, characteristic
2#28409015C212yesmaximal, complemented
3#28408831C211yesmaximal, characteristic, complemented
4#28408828C212yesmaximal, complemented
5#356×C227C211yesmaximal, characteristic, complemented
6C2×#16813885C411yescharacteristic
7C2×#16813885C2211yescharacteristic
8M16×D227—22no—
9#20300285C411yescharacteristic
10#20300277C411yescharacteristic
11#20300277C2211yescharacteristic
12#20300263—22no—
13#20300250—22no—
14C42×D227C411yescharacteristic
15#20300207C2212yes—
16#20300204—22no—
17C4⋊Q8×C227C2211yescharacteristic
18#101×C227C2212yes—
19#16813885—41no—
20#16813885—41no—
21#16813885—41no—
22#16813885—41no—
23C2×D908—21no—
24C2×D908—22no—
25C2×D908C2×C411yescharacteristic
26C2×D908C2×C411yescharacteristic
27C2×D908D412yes—
28C2×C4×D227—21no—
29C2×C4×D227—21no—
30C2×C4×D227C2×C411yescharacteristic
31C2×C4×D227D412yes—
32#16813868—22no—
33#16813867—42no—
34C8×D227—42no—
35(C2×D227)⋊C4—22no—
36(C2×D227)⋊C4—22no—
37C4×Dic227—21no—
38C4×Dic227C2×C411yescharacteristic
39C2×Q8×C227C2×C411yescharacteristic
40C2×Q8×C227C2311yescharacteristic
41M16×C227—22no—
42C4⋊C4×C227—22no—
43C42×C227C2×C411yescharacteristic
44C22×D227—21no—
45C22×D227C22⋊C412yes—
46C22×D227C22⋊C411yescharacteristic
47D908—41no—
48D908—42no—
49D908—44no—
50D908—41no—
51D908—42no—
52C2×Dic227—21no—
53C2×Dic227C22⋊C411yescharacteristic
54C4×D227—22no—
55C4×D227—22no—
56C4×D227—21no—
57C4×D227—21no—
58C4×D227—42no—
59C4×D227—41no—
60C4×D227—41no—
61C227⋊C8—42no—
62Q8×C227—41no—
63Q8×C227—41no—
64C2×C4×C227—21no—
65C2×C4×C227—21no—
66C2×C4×C227C22×C411yescharacteristic
67C2×C4×C227C2×D412yes—
68C8×C227—42no—
69C22×C227C2×C22⋊C411yescharacteristic
70C2×D227—21no—
71C2×D227—22no—
72C2×D227—41no—
73C2×D227—42no—
74C2×D227—42no—
75C2×D227—41no—
76C4×C227—22no—
77C4×C227—22no—
78C4×C227—21no—
79C4×C227—41no—
80Dic227—41no—
81Dic227#9911yescharacteristic
82Dic227#9911yescharacteristic
83C2×C227—21no—
84C2×C227C2×#9911yescharacteristic
85D227—41no—
86D227—42no—
87D227—81no—
88C227#213211yescharacteristic, complemented, Sylow
89#2132—2271nomaximal, Sylow
90#532—2271no—
91#413—2272no—
92#356—2271no—
93#356D22711yescharacteristic, complemented
94#355—2272no—
95C2×#41—2271no—
96C2×#41—2271no—
97C2×M16—4542no—
98C4⋊Q8C2×D22711yescharacteristic
99#127—2271no—
100#124—2271no—
101#124—2271no—
102#121—4542no—
103C4×D4—4542no—
104C2×C42—2271no—
105#101—2272no—
106#101C2×D22712yes—
107#100—4542no—
108#41—9081no—
109#41—9081no—
110#41—9081no—
111#41—9081no—
112C2×Q8C4×D22711yescharacteristic
113C2×Q8C22×D22711yescharacteristic
114C2×D4—4542no—
115C2×D4—4541no—
116C2×D4—2271no—
117C2×D4—2271no—
118C2×D4—2272no—
119C22×C4—4541no—
120C22×C4—4541no—
121C22×C4—2271no—
122C22×C4—2272no—
123M16—22no—
124M16—9082no—
125M16—4542no—
126C2×C8—9082no—
127C4⋊C4—22no—
128C22⋊C4—4542no—
129C22⋊C4—4542no—
130C42—4541no—
131C42—2271no—
132C42C4×D22711yescharacteristic
133C23—4541no—
134C23—2272no—
135C23—2271no—
136Q8—41no—
137Q8—41no—
138D4—9081no—
139D4—9084no—
140D4—9082no—
141D4—9081no—
142D4—9082no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—9082no—
146C2×C4—9081no—
147C2×C4—9081no—
148C2×C4—4542no—
149C2×C4—4542no—
150C2×C4—4541no—
151C2×C4—4541no—
152C2×C4—4541no—
153C2×C4—2271no—
154C2×C4C2×C4×D22711yescharacteristic
155C2×C4D4×D22712yes—
156C8—42no—
157C8—9082no—
158C22—9082no—
159C22—9081no—
160C22—9082no—
161C22—9081no—
162C22—4541no—
163C22—4542no—
164C22C22⋊C4×D22711yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—9081no—
170C4—2271no—
171C4—2271no—
172C2—21no—
173C2—18161no—
174C2—9081no—
175C2—9082no—
176C2#99×D22711yescharacteristic
subgroupG/H
centerC2#99×D227
commutatorC2×C4×C227C22×C4
FrattiniC2×Q8C22×D227
Fitting#356×C227C2
socleC2×C227C2×#99
prime radical#28409583C2
cosocleC2×Q8×C227C23
hypercenter#356D227
hypocenterC227#2132
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #28409015C2semidirect
3. #28408831C2semidirect
4. #28408828C2semidirect
5. #356×C227C2semidirect
88. C227#2132semidirect
93. #356D227semidirect

Maximal subgroups

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

subgroupindex
#284095832
#284090152
#284088312
#284088282
#356×C2272
#2132227