Finite Group Databasebeta

← #44398743

Subgroups — #44398743

Order 29056.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#28409661C211yesmaximal, characteristic
2#28409363C211yesmaximal, characteristic
3#28409360C211yesmaximal, characteristic
4#28408964C211yesmaximal, characteristic
5#28408768C211yesmaximal, characteristic
6#28408757C211yesmaximal, characteristic
7#328×C227C211yesmaximal, characteristic
8#20300287—21no—
9#20300286—21no—
10#20300278—21no—
11#20300278—21no—
12#20300267C2211yescharacteristic
13#20300265—21no—
14#20300244—21no—
15C2×C4⋊Dic227—21no—
16C2×C4⋊Dic227C2211yescharacteristic
17C2×Dic227⋊C4C2211yescharacteristic
18#20300220—21no—
19#20300219—21no—
20#20300213—21no—
21#20300212—21no—
22C22⋊(C227⋊C8)C2211yescharacteristic
23C227⋊#95—21no—
24C22⋊Q8×C227C2211yescharacteristic
25C22⋊C8×C227C2211yescharacteristic
26#95×C227C2211yescharacteristic
27C2×Dic454—21no—
28C2×Dic454D411yescharacteristic
29C22×Dic227—21no—
30C22×Dic227D411yescharacteristic
31C22×Dic227D411yescharacteristic
32C2×C227⋊C8—21no—
33C4⋊Dic227—21no—
34C4⋊Dic227—21no—
35C4⋊Dic227—21no—
36C4⋊Dic227—42no—
37C4⋊Dic227D411yescharacteristic
38Dic227⋊C4—21no—
39Dic227⋊C4—21no—
40Dic227⋊C4—21no—
41Dic227⋊C4—21no—
42Dic227⋊C4—21no—
43Dic227⋊C4—21no—
44Dic227⋊C4—21no—
45C22⋊Dic227—21no—
46C4×Dic227—21no—
47C4×Dic227—21no—
48C2×Q8×C227D411yescharacteristic
49C22×C4×C227—21no—
50C22×C4×C227C2311yescharacteristic
51C2×C8×C227—21no—
52C4⋊C4×C227—21no—
53C4⋊C4×C227D411yescharacteristic
54C22⋊C4×C227—21no—
55Dic454—41no—
56Dic454—81no—
57C2×Dic227—21no—
58C2×Dic227—21no—
59C2×Dic227—21no—
60C2×Dic227—21no—
61C2×Dic227—21no—
62C2×Dic227—41no—
63C2×Dic227—41no—
64C2×Dic227—41no—
65C2×Dic227—41no—
66C2×Dic227SD1612yes—
67C227⋊C8—41no—
68C23×C227C2×D411yescharacteristic
69Q8×C227—41no—
70C2×C4×C227—22no—
71C2×C4×C227—21no—
72C2×C4×C227—21no—
73C2×C4×C227—41no—
74C2×C4×C227—41no—
75C2×C4×C227—41no—
76C2×C4×C227C2×D411yescharacteristic
77C2×C4×C227C2×D411yescharacteristic
78C8×C227—41no—
79C22×C227—21no—
80C22×C227—21no—
81C22×C227#12011yescharacteristic
82C22×C227C2×SD1611yescharacteristic
83C22×C227#13711yescharacteristic
84C4×C227—21no—
85C4×C227—21no—
86C4×C227—42no—
87C4×C227—41no—
88C4×C227—41no—
89Dic227—22no—
90Dic227—41no—
91Dic227—41no—
92Dic227—41no—
93Dic227—81no—
94C2×C227—21no—
95C2×C227—21no—
96C2×C227#44811yescharacteristic
97C2×C227#45611yescharacteristic
98C2×C227#45811yescharacteristic
99C227#161111yescharacteristic, complemented, Sylow
100#1611—2271nomaximal, Sylow
101#544—2271no—
102#483—2271no—
103#483—2271no—
104#398—2271no—
105#328—2271no—
106#328D22711yescharacteristic
107#324—2271no—
108C4⋊Q8—4541no—
109C4⋊Q8—4541no—
110#125—4541no—
111#125—4541no—
112C22⋊Q8—4541no—
113C22⋊Q8—2271no—
114C22⋊Q8C2×D22711yescharacteristic
115#117—4541no—
116C2×C4⋊C4—4541no—
117C2×C4⋊C4—2271no—
118C2×C4⋊C4—2271no—
119#106—4541no—
120#106—4541no—
121#103—4541no—
122#103—4541no—
123C22⋊C8—2271no—
124C22⋊C8C2×D22711yescharacteristic
125#95—4541no—
126#95C2×D22711yescharacteristic
127C2×Q8—4541no—
128C2×Q8—2271no—
129C2×Q8D90811yescharacteristic
130C22×C4—21no—
131C22×C4—4541no—
132C22×C4—2271no—
133C22×C4—2271no—
134C22×C4C22×D22711yescharacteristic
135C2×C8—21no—
136C2×C8—4541no—
137C4⋊C4—21no—
138C4⋊C4—9082no—
139C4⋊C4—4541no—
140C4⋊C4—4541no—
141C4⋊C4—4541no—
142C4⋊C4—4541no—
143C4⋊C4—4541no—
144C4⋊C4—4541no—
145C4⋊C4—4541no—
146C4⋊C4—4541no—
147C4⋊C4—4541no—
148C4⋊C4—4541no—
149C4⋊C4—2271no—
150C4⋊C4D90811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—4541no—
153C42—4541no—
154C42—4541no—
155C23D4×D22711yescharacteristic
156Q8—41no—
157Q8—18161no—
158Q8—9081no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—9081no—
166C2×C4—9081no—
167C2×C4—9081no—
168C2×C4—9081no—
169C2×C4—4541no—
170C2×C4—4541no—
171C2×C4—4541no—
172C2×C4—4541no—
173C2×C4—4541no—
174C2×C4—2272no—
175C2×C4D4×D22711yescharacteristic
176C2×C4C2×D90811yescharacteristic
177C8—41no—
178C8—9081no—
179C22—21no—
180C22—21no—
181C22#2030025811yescharacteristic
182C22SD16×D22711yescharacteristic
183C22#2030032011yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—18161no—
190C4—9081no—
191C4—9081no—
192C4—9081no—
193C4—4542no—
194C2—21no—
195C2—21no—
196C2#2840917211yescharacteristic
197C2#2840921611yescharacteristic
198C2#2840922311yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
Fitting#328×C227C2
socleC22×C227#120
prime radicalC23×C227C2×D4
hypercenter#328D227
hypocenterC227#1611
LCSG ▷ C22×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C227#1611semidirect

Maximal subgroups

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

subgroupindex
#284096612
#284093632
#284093602
#284089642
#284087682
#284087572
#328×C2272
#1611227