Finite Group Databasebeta

← #19152196

Subgroups — #19152196

Order 5696.

218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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#15668007C211yesmaximal, characteristic, complemented
2#15668006C211yesmaximal, characteristic, complemented
3#15668002C211yesmaximal, characteristic, complemented
4#15667997C211yesmaximal, characteristic, complemented
5#15667997C211yesmaximal, characteristic, complemented
6#15667997C211yesmaximal, characteristic, complemented
7#15667997C211yesmaximal, characteristic, complemented
8#15667992C211yesmaximal, characteristic, complemented
9#15667990C211yesmaximal, characteristic, complemented
10#15667990C211yesmaximal, characteristic, complemented
11#15667987C211yesmaximal, characteristic
12C4×D356C211yesmaximal, characteristic, complemented
13#15667974C211yesmaximal, characteristic, complemented
14C4⋊C4×D89C211yesmaximal, characteristic, complemented
15#125×C89C211yesmaximal, characteristic, complemented
16C2×Dic178C2211yescharacteristic
17C2×D356C2211yescharacteristic
18C2×D356C2211yescharacteristic
19C2×D356C2211yescharacteristic
20C2×C4×D89C2211yescharacteristic
21C2×C4×D89C2211yescharacteristic
22C2×C4×D89C2211yescharacteristic
23C2×C4×D89C2211yescharacteristic
24C2×C4×D89C2211yescharacteristic
25C4⋊Dic89C2211yescharacteristic
26C4⋊Dic89C2211yescharacteristic
27#13083553C2211yescharacteristic
28#13083553C2211yescharacteristic
29#13083553C2211yescharacteristic
30#13083553C2211yescharacteristic
31#13083553C2211yescharacteristic
32#13083553C2211yescharacteristic
33#13083551C2211yescharacteristic
34#13083551C2211yescharacteristic
35#13083551C2211yescharacteristic
36#13083551C2211yescharacteristic
37#13083551C2211yescharacteristic
38#13083551C2211yescharacteristic
39#13083551C2211yescharacteristic
40#13083551C2211yescharacteristic
41#13083551C2211yescharacteristic
42#13083551C2211yescharacteristic
43C4×Dic89C2211yescharacteristic
44C4⋊C4×C89C2211yescharacteristic
45C4⋊C4×C89C2211yescharacteristic
46C4⋊C4×C89C2211yescharacteristic
47C4⋊C4×C89C2211yescharacteristic
48C4⋊C4×C89C2211yescharacteristic
49C4⋊C4×C89C2211yescharacteristic
50C42×C89C2211yescharacteristic
51C22×D89C2311yescharacteristic
52C22×D89C2311yescharacteristic
53C22×D89C2311yescharacteristic
54C2×C4×C89C2311yescharacteristic
55C2×C4×C89C2311yescharacteristic
56C2×C4×C89C2311yescharacteristic
57C2×C4×C89C2311yescharacteristic
58C2×C4×C89C2311yescharacteristic
59C2×C4×C89C2311yescharacteristic
60C2×C4×C89C2311yescharacteristic
61C2×Dic89C2311yescharacteristic
62C2×Dic89C2311yescharacteristic
63C2×Dic89C2311yescharacteristic
64C2×Dic89C2311yescharacteristic
65C2×Dic89C2311yescharacteristic
66D356—22no—
67D356—22no—
68D356—41no—
69C4×D89—22no—
70C4×D89—41no—
71C4×D89—41no—
72C4×D89—41no—
73C4×D89—41no—
74Dic178—41no—
75C22×C89C2411yescharacteristic
76C2×D89—21no—
77C2×D89—21no—
78C2×D89—21no—
79C2×D89—21no—
80C2×D89—21no—
81C2×D89—21no—
82C2×D89—21no—
83C2×D89—21no—
84C2×D89#4112yes—
85C4×C89—21no—
86C4×C89—21no—
87C4×C89—21no—
88C4×C89—21no—
89C4×C89—21no—
90C4×C89—21no—
91C4×C89—21no—
92Dic89—21no—
93Dic89—21no—
94Dic89—21no—
95Dic89—21no—
96Dic89—21no—
97C2×C89C2×#4111yescharacteristic
98C2×C89H(5,𝔽2)11yescharacteristic
99C2×C892−1+411yescharacteristic
100D89—22no—
101D89—41no—
102D89—41no—
103C89#53911yescharacteristic, complemented, Sylow
104#539—891nomaximal, Sylow
105#126—891no—
106#126—891no—
107#125—891no—
108#125D8911yescharacteristic, complemented
109#123—891no—
110#123—891no—
111#123—891no—
112#123—891no—
113C22⋊Q8—891no—
114C22⋊Q8—891no—
115C22⋊Q8—891no—
116#121—891no—
117C4×D4—891no—
118C4×D4—891no—
119C2×C4⋊C4—891no—
120C2×Q8—891no—
121C2×D4—891no—
122C2×D4—891no—
123C2×D4—891no—
124C22×C4—891no—
125C22×C4—891no—
126C22×C4—891no—
127C22×C4—891no—
128C22×C4—891no—
129C4⋊C4—891no—
130C4⋊C4—891no—
131C4⋊C4—891no—
132C4⋊C4—891no—
133C4⋊C4—891no—
134C4⋊C4—891no—
135C4⋊C4—891no—
136C4⋊C4—891no—
137C4⋊C4C2×D8911yescharacteristic
138C4⋊C4C2×D8911yescharacteristic
139C4⋊C4C2×D8911yescharacteristic
140C4⋊C4C2×D8911yescharacteristic
141C4⋊C4C2×D8911yescharacteristic
142C4⋊C4C2×D8911yescharacteristic
143C22⋊C4—891no—
144C22⋊C4—891no—
145C22⋊C4—891no—
146C22⋊C4—891no—
147C22⋊C4—891no—
148C22⋊C4—891no—
149C22⋊C4—891no—
150C22⋊C4—891no—
151C22⋊C4—891no—
152C22⋊C4—891no—
153C42—891no—
154C42C2×D8911yescharacteristic
155C23—891no—
156C23—891no—
157C23—891no—
158Q8—3561no—
159D4—3561no—
160D4—1782no—
161D4—1782no—
162C2×C4—891no—
163C2×C4—891no—
164C2×C4—891no—
165C2×C4—891no—
166C2×C4—891no—
167C2×C4—3561no—
168C2×C4—3561no—
169C2×C4—3561no—
170C2×C4—3561no—
171C2×C4—1782no—
172C2×C4C22×D8911yescharacteristic
173C2×C4C22×D8911yescharacteristic
174C2×C4C22×D8911yescharacteristic
175C2×C4C22×D8911yescharacteristic
176C2×C4C22×D8911yescharacteristic
177C2×C4C22×D8911yescharacteristic
178C2×C4C22×D8911yescharacteristic
179C22—892no—
180C22—1781no—
181C22—1781no—
182C22—1781no—
183C22—1781no—
184C22—1781no—
185C22—1781no—
186C22—1781no—
187C22—1781no—
188C22C23×D8911yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—1781no—
197C4—1781no—
198C4—1781no—
199C4—1781no—
200C4—1781no—
201C2—3561no—
202C2—3561no—
203C2—1782no—
204C2#41×D8911yescharacteristic
205C2#1566805811yescharacteristic
206C2#1566806011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D89
commutator, socleC22×C89C24
Fitting#125×C89C2
hypercenter#125D89
hypocenterC89#539
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #15668007C2semidirect
2. #15668006C2semidirect
3. #15668002C2semidirect
4. #15667997C2semidirect
5. #15667997C2semidirect
6. #15667997C2semidirect
7. #15667997C2semidirect
8. #15667992C2semidirect
9. #15667990C2semidirect
10. #15667990C2semidirect
12. C4×D356C2semidirect
13. #15667974C2semidirect
14. C4⋊C4×D89C2semidirect
15. #125×C89C2semidirect
103. C89#539semidirect
108. #125D89semidirect