Finite Group Databasebeta

← #44398367

Subgroups — #44398367

Order 29056.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#28409581C211yesmaximal, characteristic
2#28409087C212yesmaximal, complemented
3#28408772C211yesmaximal, characteristic, complemented
4#28408771C212yesmaximal, complemented
5#329×C227C211yesmaximal, characteristic, complemented
6C2×#16813885C411yescharacteristic
7C2×#16813883C411yescharacteristic
8#20300286C411yescharacteristic
9#20300284C411yescharacteristic
10#20300276C2211yescharacteristic
11#20300261—22no—
12(C22⋊D227)⋊C4—22no—
13C42×D227C2211yescharacteristic
14Dic227⋊C8—22no—
15(C2×D227)⋊C8—22no—
16#20300199C2212yes—
17#124×C227C2211yescharacteristic
18#97×C227C2212yes—
19#16813885—42no—
20#16813883—42no—
21C2×Dic454C2×C411yescharacteristic
22C2×D908—21no—
23C2×D908C2×C411yescharacteristic
24C2×C22⋊D227—21no—
25C2×C22⋊D227—22no—
26C22×Dic227—21no—
27C2×C4×D227—21no—
28C2×C4×D227C2×C411yescharacteristic
29C2×C4×D227D412yes—
30C2×C227⋊C8—22no—
31Dic227⋊C4—22no—
32(C2×D227)⋊C4—22no—
33C4×Dic227C2×C411yescharacteristic
34C4×Dic227D412yes—
35C2×Q8×C227C2×C411yescharacteristic
36C2×D4×C227C2×C411yescharacteristic
37C2×C8×C227—22no—
38C22⋊C4×C227—22no—
39C42×C227C2311yescharacteristic
40C22×D227—21no—
41C22×D227C22⋊C411yescharacteristic
42Dic454—41no—
43D908—41no—
44D908—42no—
45C22⋊D227—44no—
46C22⋊D227—42no—
47C2×Dic227—21no—
48C2×Dic227—42no—
49C2×Dic227C22⋊C412yes—
50C2×Dic227C22⋊C411yescharacteristic
51C4×D227—22no—
52C4×D227—42no—
53C4×D227—42no—
54C227⋊C8—42no—
55C23×C227—21no—
56Q8×C227—41no—
57D4×C227—41no—
58C2×C4×C227—21no—
59C2×C4×C227C22×C411yescharacteristic
60C2×C4×C227C2×D412yes—
61C8×C227—42no—
62C22×C227—41no—
63C22×C227—42no—
64C22×C227C2×C22⋊C411yescharacteristic
65C2×D227—21no—
66C2×D227—22no—
67C2×D227—41no—
68C2×D227—42no—
69C4×C227—21no—
70C4×C227—22no—
71C4×C227—41no—
72Dic227—22no—
73Dic227—41no—
74Dic227#10012yes—
75C2×C227—81no—
76C2×C227C2×#10011yescharacteristic
77C2×C227#42112yes—
78D227—41no—
79D227—81no—
80C227#153611yescharacteristic, complemented, Sylow
81#1536—2271nomaximal, Sylow
82#532—2271no—
83#432—2272no—
84#329—2271no—
85#329—2272no—
86#329D22711yescharacteristic, complemented
87C2×#41—2271no—
88C2×#41—2271no—
89C4⋊Q8—2271no—
90#127—2271no—
91#124—2271no—
92#124C2×D22711yescharacteristic
93#121—4542no—
94C4×D4—4542no—
95C2×C42—2271no—
96C4⋊C8—4542no—
97C22⋊C8—4542no—
98#97—2272no—
99#97C2×D22712yes—
100#41—9082no—
101#41—9082no—
102C2×Q8—2271no—
103C2×Q8C4×D22711yescharacteristic
104C2×D4—4541no—
105C2×D4—4541no—
106C2×D4—4542no—
107C2×D4—2271no—
108C2×D4C4×D22711yescharacteristic
109C22×C4—4541no—
110C22×C4—4541no—
111C22×C4—2272no—
112C22×C4—2271no—
113C2×C8—22no—
114C2×C8—4542no—
115C4⋊C4—4542no—
116C22⋊C4—22no—
117C22⋊C4—4542no—
118C42—2271no—
119C42—2272no—
120C42C22×D22711yescharacteristic
121C23—21no—
122C23—4541no—
123C23—2271no—
124Q8—41no—
125Q8—9081no—
126D4—41no—
127D4—9081no—
128D4—9082no—
129D4—9082no—
130D4—9084no—
131C2×C4—21no—
132C2×C4—9082no—
133C2×C4—9082no—
134C2×C4—9082no—
135C2×C4—4542no—
136C2×C4—4541no—
137C2×C4—2272no—
138C2×C4—2271no—
139C2×C4C2×C4×D22711yescharacteristic
140C2×C4D4×D22712yes—
141C8—42no—
142C8—9082no—
143C22—41no—
144C22—42no—
145C22—9081no—
146C22—9082no—
147C22—4541no—
148C22—4542no—
149C22C22⋊C4×D22711yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—9081no—
154C4—4542no—
155C4—2272no—
156C2—81no—
157C2—18161no—
158C2—9081no—
159C2#100×D22711yescharacteristic
160C2#2840904712yes—
subgroupG/H
centerC22C22⋊C4×D227
commutatorC2×C4×C227C22×C4
FrattiniC42C22×D227
Fitting#329×C227C2
socleC22×C227C2×C22⋊C4
prime radical#28409581C2
cosocleC42×C227C23
hypercenter#329D227
hypocenterC227#1536
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #28409087C2semidirect
3. #28408772C2semidirect
4. #28408771C2semidirect
5. #329×C227C2semidirect
80. C227#1536semidirect
86. #329D227semidirect

Maximal subgroups

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

subgroupindex
#284095812
#284090872
#284087722
#284087712
#329×C2272
#1536227