Finite Group Databasebeta

← #22586824

Subgroups — #22586824

Order 9088.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986533C211yesmaximal, characteristic
2#17986052C211yesmaximal, characteristic, complemented
3#17985735C212yesmaximal, complemented
4#17985732C212yesmaximal
5#376×C71C211yesmaximal, characteristic, complemented
6#14556122—21no—
7#14556120C411yescharacteristic, complemented
8#14556116C411yescharacteristic, complemented
9#14556111—21no—
10#14556107C2211yescharacteristic
11#14556102C2211yescharacteristic
12C4×Dic142C411yescharacteristic, complemented
13C4×D284C411yescharacteristic, complemented
14C4×C22⋊D71—21no—
15#14556085—21no—
16C4⋊(C71⋊C8)—21no—
17C22⋊(C71⋊C8)C2212yes—
18C4×C71⋊C8—21no—
19C2×C42×C71—21no—
20C2×C42×C71C2211yescharacteristic
21#95×C71—21no—
22#95×C71C2212yes—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27C2×C71⋊C8—22no—
28C4⋊Dic71C2×C411yescharacteristic
29C4⋊Dic71C2×C411yescharacteristic
30Dic71⋊C4—21no—
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34C22⋊Dic71—21no—
35(C2×D71)⋊C4—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39C4×Dic71—21no—
40C22×C4×C71—22no—
41C22×C4×C71D411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71C2311yescharacteristic
44C42×C71—24no—
45C42×C71C2×C411yescharacteristic
46C42×C71C2×C411yescharacteristic
47C42×C71D411yescharacteristic
48C42×C71D411yescharacteristic
49C23×C71C2×D411yescharacteristic
50C22×D71—21no—
51C2×C4×C71—22no—
52C2×C4×C71—22no—
53C2×C4×C71—24no—
54C2×C4×C71—41no—
55C2×C4×C71—42no—
56C2×C4×C71—42no—
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22⋊C411yescharacteristic
59C2×C4×C71C22⋊C411yescharacteristic
60C2×C4×C71C22⋊C411yescharacteristic
61C2×C4×C71C22×C411yescharacteristic
62C2×C4×C71C2×D411yescharacteristic
63C22⋊D71—42no—
64C2×Dic71—21no—
65C2×Dic71—21no—
66C2×Dic71—21no—
67D284—41no—
68C4×D71—42no—
69Dic142—41no—
70C71⋊C8—42no—
71C22×C71—21no—
72C22×C71—21no—
73C22×C71C2×C22⋊C411yescharacteristic
74C22×C71#13512yes—
75C2×D71—41no—
76C2×D71—41no—
77C2×D71—41no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—21no—
83C4×C71—44no—
84C4×C71#10412yes—
85Dic71—41no—
86Dic71—41no—
87Dic71—41no—
88C2×C71—22no—
89C2×C71#41011yescharacteristic
90C2×C71#41611yescharacteristic
91C2×C71C2×#10411yescharacteristic
92D71—81no—
93#1500—711nomaximal, Sylow
94C71#150011yescharacteristic, complemented, Sylow
95#529—711no—
96#431—711no—
97#376D7111yescharacteristic, complemented
98#328—712no—
99#327—712no—
100#126—1421no—
101#125—711no—
102#124—711no—
103#123—1421no—
104C22⋊Q8—711no—
105#121—711no—
106C4×Q8—711no—
107C4×D4—711no—
108C4×D4—1421no—
109#117—1421no—
110C2×C42—21no—
111C2×C42C2×D7111yescharacteristic
112C4⋊C8—1421no—
113C22⋊C8—712no—
114C4×C8—1421no—
115#95—21no—
116#95C2×D7112yes—
117C2×Q8—711no—
118C2×D4—711no—
119C2×D4—1421no—
120C22×C4—22no—
121C22×C4—1421no—
122C22×C4C22⋊D7111yescharacteristic
123C22×C4C22⋊D7111yescharacteristic
124C22×C4C22×D7111yescharacteristic
125C2×C8—1422no—
126C4⋊C4—711no—
127C4⋊C4—711no—
128C4⋊C4—1421no—
129C4⋊C4—1421no—
130C4⋊C4—1421no—
131C4⋊C4—1421no—
132C22⋊C4—1421no—
133C22⋊C4—1421no—
134C22⋊C4—1421no—
135C22⋊C4—1421no—
136C22⋊C4—1421no—
137C42—24no—
138C42—1421no—
139C42C4×D7111yescharacteristic
140C42C4×D7111yescharacteristic
141C42D28411yescharacteristic
142C42D28411yescharacteristic
143C23—1421no—
144C23C2×C22⋊D7111yescharacteristic
145Q8—2841no—
146D4—2841no—
147D4—2842no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—2842no—
155C2×C4—1421no—
156C2×C4—1421no—
157C2×C4—1421no—
158C2×C4(C2×D71)⋊C411yescharacteristic
159C2×C4(C2×D71)⋊C411yescharacteristic
160C2×C4(C2×D71)⋊C411yescharacteristic
161C2×C4(C2×D71)⋊C411yescharacteristic
162C2×C4C2×C4×D7111yescharacteristic
163C2×C4C2×D28411yescharacteristic
164C8—2842no—
165C22—21no—
166C22—21no—
167C22—2841no—
168C22—2841no—
169C22—2841no—
170C22C2×(C2×D71)⋊C411yescharacteristic
171C22#1455614812yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—44no—
178C4—2841no—
179C4—2841no—
180C4—2841no—
181C4#1455605612yes—
182C2—22no—
183C2—5681no—
184C2#1798597211yescharacteristic
185C2#1798599311yescharacteristic
186C2C2×#1455605611yescharacteristic
subgroupG/H
centerC2×C4(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#376×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#376D71
hypocenterC71#1500
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #17986052C2semidirect
3. #17985735C2semidirect
5. #376×C71C2semidirect
7. #14556120C4semidirect
8. #14556116C4semidirect
12. C4×Dic142C4semidirect
13. C4×D284C4semidirect
94. C71#1500semidirect
97. #376D71semidirect