Finite Group Databasebeta

← #22586862

Subgroups — #22586862

Order 9088.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#17986530C211yesmaximal, characteristic
2#17986053C211yesmaximal, characteristic, complemented
3#17985850C211yesmaximal, characteristic, complemented
4#17985737C211yesmaximal, characteristic, complemented
5#17985735C211yesmaximal, characteristic, complemented
6#17985733C211yesmaximal, characteristic
7#327×C71C211yesmaximal, characteristic
8#14556121—21no—
9#14556119C411yescharacteristic, complemented
10#14556115C411yescharacteristic, complemented
11#14556109—21no—
12#14556107C2211yescharacteristic
13#14556093C411yescharacteristic, complemented
14D4×Dic71—21no—
15D4×Dic71C411yescharacteristic, complemented
16#14556084—21no—
17C2×Dic71⋊C4—21no—
18C2×C4×Dic71—21no—
19C2×C4×Dic71C2211yescharacteristic
20Dic71⋊C8—21no—
21C22⋊(C71⋊C8)C2211yescharacteristic
22#14556038—21no—
23C71⋊#95C2211yescharacteristic
24#121×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26#95×C71C2211yescharacteristic
27C2×Dic142C2×C411yescharacteristic
28C22×Dic71—21no—
29C22×Dic71—21no—
30C22×Dic71D411yescharacteristic
31C22×Dic71D411yescharacteristic
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71C2×C411yescharacteristic
35Dic71⋊C4—24no—
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38Dic71⋊C4—21no—
39C22⋊Dic71—21no—
40C22⋊Dic71—21no—
41C22⋊Dic71—21no—
42C22⋊Dic71—21no—
43C4×Dic71—21no—
44C4×Dic71—42no—
45C4×Dic71C2×C411yescharacteristic
46C4×Dic71C2×C411yescharacteristic
47C4×Dic71D411yescharacteristic
48C4×Dic71D411yescharacteristic
49C2×D4×C71—21no—
50C2×D4×C71C2×C411yescharacteristic
51C22×C4×C71—21no—
52C22×C4×C71C2311yescharacteristic
53C2×C8×C71—21no—
54C4⋊C4×C71C2×C411yescharacteristic
55C22⋊C4×C71—21no—
56C23×C71—21no—
57C23×C71C2×D411yescharacteristic
58D4×C71—41no—
59D4×C71—41no—
60D4×C71—41no—
61C2×C4×C71—22no—
62C2×C4×C71—21no—
63C2×C4×C71—41no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71C22×C411yescharacteristic
67C2×C4×C71C2×D411yescharacteristic
68C2×Dic71—21no—
69C2×Dic71—21no—
70C2×Dic71—22no—
71C2×Dic71—22no—
72C2×Dic71—21no—
73C2×Dic71—21no—
74C2×Dic71—41no—
75C2×Dic71—41no—
76C2×Dic71—42no—
77C2×Dic71C22⋊C411yescharacteristic
78C2×Dic71C22⋊C411yescharacteristic
79C2×Dic71C22⋊C411yescharacteristic
80C2×Dic71C22⋊C411yescharacteristic
81Dic142—41no—
82C8×C71—41no—
83C71⋊C8—41no—
84C22×C71—21no—
85C22×C71—21no—
86C22×C71—41no—
87C22×C71—41no—
88C22×C71—41no—
89C22×C71C2×C22⋊C411yescharacteristic
90C22×C71AGL(1,ℤ/8)11yescharacteristic
91C22×C71#13711yescharacteristic
92C4×C71—21no—
93C4×C71—21no—
94C4×C71—42no—
95C4×C71—41no—
96Dic71—21no—
97Dic71—21no—
98Dic71—21no—
99Dic71—42no—
100Dic71—41no—
101Dic71—41no—
102Dic71#10412yes—
103C2×C71—21no—
104C2×C71—21no—
105C2×C71—81no—
106C2×C71#41011yescharacteristic
107C2×C71#41711yescharacteristic
108C2×C71C2×#10411yescharacteristic
109#1509—711nomaximal, Sylow
110C71#150911yescharacteristic, complemented, Sylow
111#529—711no—
112#432—711no—
113C4×C4⋊C4—711no—
114#328—711no—
115#328—711no—
116#327—711no—
117#327D7111yescharacteristic
118#126—1421no—
119#125—711no—
120#124—711no—
121#123—1421no—
122C22⋊Q8—711no—
123#121C2×D7111yescharacteristic
124C4×Q8—711no—
125C4×D4—711no—
126C4×D4—1421no—
127#117—1421no—
128C2×C4⋊C4—1421no—
129C2×C42—711no—
130C2×C42—1421no—
131C4⋊C8—1421no—
132C22⋊C8—711no—
133C22⋊C8C2×D7111yescharacteristic
134#97—1421no—
135#95—711no—
136#95C2×D7111yescharacteristic
137C2×Q8—711no—
138C2×D4—21no—
139C2×D4C4×D7111yescharacteristic
140C22×C4—21no—
141C22×C4—711no—
142C22×C4—711no—
143C22×C4—1421no—
144C22×C4—1421no—
145C22×C4C22×D7111yescharacteristic
146C2×C8—21no—
147C2×C8—1421no—
148C4⋊C4—711no—
149C4⋊C4—1421no—
150C4⋊C4—1421no—
151C4⋊C4—1421no—
152C4⋊C4—1424no—
153C4⋊C4—1421no—
154C4⋊C4C4×D7111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—1421no—
157C22⋊C4—1421no—
158C22⋊C4—1421no—
159C22⋊C4—1421no—
160C42—2842no—
161C42—711no—
162C42—711no—
163C42—711no—
164C42—711no—
165C42—1421no—
166C23—21no—
167C23D4×D7111yescharacteristic
168Q8—2841no—
169D4—41no—
170D4—41no—
171D4—41no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2841no—
178C2×C4—2841no—
179C2×C4—2842no—
180C2×C4—711no—
181C2×C4—711no—
182C2×C4—711no—
183C2×C4—711no—
184C2×C4—1422no—
185C2×C4—1421no—
186C2×C4—1421no—
187C2×C4—1422no—
188C2×C4—1421no—
189C2×C4—1421no—
190C2×C4C2×C4×D7111yescharacteristic
191C2×C4D4×D7111yescharacteristic
192C8—41no—
193C8—2841no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22C22⋊C4×D7111yescharacteristic
200C22#1455615211yescharacteristic
201C22#1455615711yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—2842no—
207C4—2841no—
208C4—2841no—
209C4—712no—
210C4—1421no—
211C4—1421no—
212C4—1421no—
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1798597111yescharacteristic
217C2#1798599711yescharacteristic
218C2#104×D7111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#327×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#327D71
hypocenterC71#1509
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #17986053C2semidirect
3. #17985850C2semidirect
4. #17985737C2semidirect
5. #17985735C2semidirect
9. #14556119C4semidirect
10. #14556115C4semidirect
13. #14556093C4semidirect
15. D4×Dic71C4semidirect
110. C71#1509semidirect