Finite Group Databasebeta

← #22586889

Subgroups — #22586889

Order 9088.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#17986551C211yesmaximal, characteristic
2#17986053C211yesmaximal, characteristic
3#17985866C211yesmaximal, characteristic
4#17985737C211yesmaximal, characteristic
5#17985736C211yesmaximal, characteristic
6#17985735C211yesmaximal, characteristic
7#328×C71C211yesmaximal, characteristic
8#14556127C411yescharacteristic, complemented
9#14556126C411yescharacteristic, complemented
10#14556118—21no—
11#14556107C2211yescharacteristic
12#14556105—21no—
13Q8×Dic71C411yescharacteristic, complemented
14#14556093—21no—
15#14556093C411yescharacteristic, complemented
16#14556084—21no—
17C2×C4×Dic71C2211yescharacteristic
18Dic71⋊C8—21no—
19C22⋊(C71⋊C8)C2211yescharacteristic
20#14556038—21no—
21C71⋊#95—21no—
22C71⋊#95—21no—
23C71⋊#95C2211yescharacteristic
24C22⋊Q8×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26#95×C71C2211yescharacteristic
27C2×Dic142—21no—
28C2×Dic142C2×C411yescharacteristic
29C22×Dic71—21no—
30C22×Dic71D411yescharacteristic
31C22×Dic71D411yescharacteristic
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71C2×C411yescharacteristic
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38Dic71⋊C4—21no—
39Dic71⋊C4—21no—
40C22⋊Dic71—21no—
41C4×Dic71—21no—
42C4×Dic71—21no—
43C4×Dic71C2×C411yescharacteristic
44C4×Dic71C2×C411yescharacteristic
45C4×Dic71D411yescharacteristic
46C4×Dic71D411yescharacteristic
47C2×Q8×C71C2×C411yescharacteristic
48C22×C4×C71—21no—
49C22×C4×C71C2311yescharacteristic
50C2×C8×C71—21no—
51C4⋊C4×C71—21no—
52C4⋊C4×C71C2×C411yescharacteristic
53C22⋊C4×C71—21no—
54C23×C71C2×D411yescharacteristic
55Q8×C71—41no—
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71—41no—
59C2×C4×C71—41no—
60C2×C4×C71—41no—
61C2×C4×C71—41no—
62C2×C4×C71C22×C411yescharacteristic
63C2×C4×C71C2×D411yescharacteristic
64C2×Dic71—21no—
65C2×Dic71—21no—
66C2×Dic71—21no—
67C2×Dic71—21no—
68C2×Dic71—41no—
69C2×Dic71—41no—
70C2×Dic71—41no—
71C2×Dic71—41no—
72C2×Dic71C22⋊C411yescharacteristic
73C2×Dic71C22⋊C411yescharacteristic
74C2×Dic71C22⋊C411yescharacteristic
75C2×Dic71C22⋊C411yescharacteristic
76Dic142—42no—
77Dic142—41no—
78C8×C71—41no—
79C71⋊C8—41no—
80C22×C71—21no—
81C22×C71—21no—
82C22×C71C2×C22⋊C411yescharacteristic
83C22×C71#13711yescharacteristic
84C22×C71#13711yescharacteristic
85C4×C71—21no—
86C4×C71—21no—
87C4×C71—41no—
88C4×C71—41no—
89C4×C71—81no—
90Dic71—21no—
91Dic71—21no—
92Dic71—21no—
93Dic71—21no—
94Dic71—41no—
95Dic71—41no—
96Dic71—81no—
97C2×C71—21no—
98C2×C71—21no—
99C2×C71#41011yescharacteristic
100C2×C71#41911yescharacteristic
101C2×C71#42111yescharacteristic
102#1515—711nomaximal, Sylow
103C71#151511yescharacteristic, complemented, Sylow
104#533—711no—
105#432—711no—
106#383—711no—
107#328—711no—
108#328—711no—
109#328—711no—
110#328D7111yescharacteristic
111C4⋊Q8—711no—
112C4⋊Q8—711no—
113#125—1421no—
114C22⋊Q8—711no—
115C22⋊Q8—1421no—
116C22⋊Q8C2×D7111yescharacteristic
117C4×Q8—711no—
118C4×Q8—711no—
119C4×Q8—1421no—
120#117—1421no—
121C2×C42—711no—
122C4⋊C8—1421no—
123C22⋊C8—711no—
124C22⋊C8C2×D7111yescharacteristic
125#97—1421no—
126#95—711no—
127#95—1421no—
128#95—1421no—
129#95C2×D7111yescharacteristic
130C2×Q8—711no—
131C2×Q8—1421no—
132C2×Q8C4×D7111yescharacteristic
133C22×C4—21no—
134C22×C4—711no—
135C22×C4—711no—
136C22×C4—1421no—
137C22×C4C22×D7111yescharacteristic
138C2×C8—21no—
139C2×C8—1421no—
140C4⋊C4—21no—
141C4⋊C4—711no—
142C4⋊C4—1421no—
143C4⋊C4—1421no—
144C4⋊C4—1421no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C4⋊C4—1421no—
148C4⋊C4C4×D7111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—1421no—
151C42—711no—
152C42—711no—
153C42—711no—
154C42—711no—
155C42—1421no—
156C42—1421no—
157C23D4×D7111yescharacteristic
158Q8—41no—
159Q8—2841no—
160Q8—2842no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—2841no—
168C2×C4—2841no—
169C2×C4—2841no—
170C2×C4—2841no—
171C2×C4—711no—
172C2×C4—711no—
173C2×C4—711no—
174C2×C4—711no—
175C2×C4—1421no—
176C2×C4—1421no—
177C2×C4—1421no—
178C2×C4—1421no—
179C2×C4C2×C4×D7111yescharacteristic
180C2×C4D4×D7111yescharacteristic
181C8—41no—
182C8—2841no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D7111yescharacteristic
186C22#1455615711yescharacteristic
187C22#1455616011yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—2841no—
194C4—2841no—
195C4—5681no—
196C4—1421no—
197C4—1421no—
198C4—1421no—
199C4—1421no—
200C2—21no—
201C2—21no—
202C2#1798597111yescharacteristic
203C2#1798600611yescharacteristic
204C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#328×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#328D71
hypocenterC71#1515
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14556127C4semidirect
9. #14556126C4semidirect
13. Q8×Dic71C4semidirect
15. #14556093C4semidirect
103. C71#1515semidirect