Finite Group Databasebeta

← #22588624

Subgroups — #22588624

Order 9088.

260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 79 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#17986765C211yesmaximal, characteristic
2#17986025C211yesmaximal, characteristic, complemented
3#17985972C211yesmaximal, characteristic
4#17985965C211yesmaximal, characteristic
5#17985770C211yesmaximal, characteristic, complemented
6#17985769C211yesmaximal, characteristic, complemented
7#424×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9#14556136—22no—
10#14556134—22no—
11C2×#11765849C2211yescharacteristic
12C2×#11765849C2211yescharacteristic
13M16×D71—22no—
14#14556087C2211yescharacteristic
15Dic71⋊C8—22no—
16#14556042C414yes—
17(C2×D71)⋊C8—22no—
18C2×M16×C71C2211yescharacteristic
19C22×C8×C71C2211yescharacteristic
20#117×C71C2211yescharacteristic
21C4⋊C8×C71—22no—
22#11765865—21no—
23#11765865—21no—
24#11765865—21no—
25#11765865—21no—
26C2×Dic142Q811yescharacteristic
27C2×D284Q811yescharacteristic
28C2×C22⋊D71C2×C412yes—
29C2×C4×D71D412yes—
30#11765849—21no—
31#11765849—21no—
32#11765849—21no—
33#11765849—21no—
34#11765848—24no—
35C2×C71⋊C8—21no—
36C2×C71⋊C8D412yes—
37C8×D71—24no—
38C4⋊Dic71—21no—
39C22⋊Dic71C2×C412yes—
40C4×Dic71—21no—
41C22×C4×C71C2311yescharacteristic
42M16×C71—21no—
43M16×C71—21no—
44C2×C8×C71—21no—
45C2×C8×C71—21no—
46C2×C8×C71—21no—
47C2×C8×C71D412yes—
48C4⋊C4×C71—21no—
49C22⋊C4×C71C2×C412yes—
50C42×C71—21no—
51C23×C71C22×C411yescharacteristic
52C22×D71C4⋊C412yes—
53C2×C4×C71—22no—
54C2×C4×C71C2×D411yescharacteristic
55C2×C4×C71C2×D411yescharacteristic
56C2×C4×C71C2×D411yescharacteristic
57C2×C4×C71C2×Q811yescharacteristic
58C2×C4×C71#4111yescharacteristic
59C2×C4×C71#4111yescharacteristic
60C22⋊D71—22no—
61C22⋊D71—22no—
62C2×Dic71—22no—
63C2×Dic71C4⋊C412yes—
64D284—21no—
65D284—21no—
66C4×D71—22no—
67C4×D71—22no—
68Dic142—21no—
69Dic142—21no—
70C8×C71—22no—
71C8×C71—41no—
72C71⋊C8—22no—
73C71⋊C8—41no—
74C22×C71—41no—
75C22×C71C2×C4⋊C411yescharacteristic
76C22×C71C4×D411yescharacteristic
77C22×C71C4×D411yescharacteristic
78C2×D71—22no—
79C2×D71—42no—
80C4×C71—42no—
81C4×C71#12011yescharacteristic
82C4×C71C22⋊Q811yescharacteristic
83C4×C71C22⋊Q811yescharacteristic
84C4×C71#12311yescharacteristic
85Dic71—22no—
86Dic71—42no—
87C2×C71—21no—
88C2×C71—21no—
89C2×C71—21no—
90C2×C71#38511yescharacteristic
91D71—42no—
92#1868—711nomaximal, Sylow
93C71#186811yescharacteristic, complemented, Sylow
94#568—711no—
95#424—711no—
96#424D7111yescharacteristic, complemented
97#410—711no—
98#408—711no—
99#344—711no—
100#344—711no—
101C2×#41—711no—
102#131—1422no—
103#131—1422no—
104C2×M16—711no—
105C2×M16—711no—
106C2×M16—1422no—
107C2×M16C2×D7111yescharacteristic
108C22×C8C2×D7111yescharacteristic
109#117—711no—
110#117C2×D7111yescharacteristic
111C4⋊C8—22no—
112C4⋊C8—1422no—
113#99—714no—
114C22⋊C8—1422no—
115#41—1421no—
116#41—1421no—
117#41—1421no—
118#41—1421no—
119C2×Q8—711no—
120C2×D4—712no—
121C2×D4—711no—
122C22×C4—712no—
123C22×C4C22×D7111yescharacteristic
124M16—21no—
125M16—21no—
126M16—1424no—
127M16—1421no—
128M16—1421no—
129M16—1421no—
130M16—1421no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—712no—
135C2×C8—1424no—
136C2×C8—1421no—
137C2×C8C22⋊D7112yes—
138C4⋊C4—21no—
139C4⋊C4—1421no—
140C22⋊C4—712no—
141C22⋊C4C4×D7112yes—
142C42—21no—
143C42—1421no—
144C23—712no—
145C23C2×C4×D7111yescharacteristic
146Q8—1421no—
147Q8—1421no—
148D4—1422no—
149D4—1422no—
150D4—1421no—
151D4—1421no—
152C2×C4—22no—
153C2×C4—712no—
154C2×C4—1422no—
155C2×C4—1422no—
156C2×C4—1422no—
157C2×C4D4×D7111yescharacteristic
158C2×C4D4×D7111yescharacteristic
159C2×C4C2×C22⋊D7111yescharacteristic
160C2×C4Q8×D7111yescharacteristic
161C2×C4#1176586511yescharacteristic
162C2×C4#1176586611yescharacteristic
163C8—22no—
164C8—41no—
165C8—2841no—
166C8—1422no—
167C22—41no—
168C22—2842no—
169C22—1422no—
170C22C4⋊C4×D7111yescharacteristic
171C22C4×C22⋊D7111yescharacteristic
172C22#1455609011yescharacteristic
173C4—42no—
174C4—2842no—
175C4—1422no—
176C4#1455609611yescharacteristic
177C4#1455610411yescharacteristic
178C4#1455610611yescharacteristic
179C4#1455611311yescharacteristic
180C2—21no—
181C2—21no—
182C2—21no—
183C2—2842no—
184C2#1798587011yescharacteristic
subgroupG/H
centerC4#14556096
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#424×C71C2
socleC2×C71#385
hypercenter#424D71
hypocenterC71#1868
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #17986025C2semidirect
5. #17985770C2semidirect
6. #17985769C2semidirect
7. #424×C71C2semidirect
93. C71#1868semidirect
96. #424D71semidirect