Finite Group Databasebeta

← #22589995

Subgroups — #22589995

Order 9088.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#17986570C211yesmaximal, characteristic
2#17985973C211yesmaximal, characteristic
3#17985790C214yesmaximal, complemented
4#413×C71C211yesmaximal, characteristic
5C22×Dic142C411yescharacteristic, complemented
6#14556126—21no—
7#14556115—21no—
8#14556109C412yescomplemented
9#14556109C2212yes—
10#14556107—21no—
11#14556107—21no—
12#14556087—21no—
13#14556087C411yescharacteristic, complemented
14#14556043—21no—
15#14556043C2212yes—
16C2×#41×C71C2211yescharacteristic
17C2×M16×C71—21no—
18#101×C71—21no—
19#100×C71C2212yes—
20C2×Dic142—21no—
21C2×Dic142—21no—
22C2×Dic142—41no—
23C2×Dic142—41no—
24C22×Dic71C2×C412yes—
25C4⋊Dic71—21no—
26C4⋊Dic71—41no—
27Dic71⋊C4—22no—
28Dic71⋊C4—22no—
29C22⋊Dic71—22no—
30C22⋊Dic71—22no—
31C22⋊Dic71—22no—
32C22⋊Dic71C2×C412yes—
33C4×Dic71—21no—
34C4×Dic71—41no—
35#41×C71—41no—
36#41×C71—41no—
37C2×Q8×C71D411yescharacteristic
38C2×D4×C71C2×C411yescharacteristic
39C2×D4×C71D411yescharacteristic
40C2×D4×C71C2311yescharacteristic
41C22×C4×C71C2×C411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71D411yescharacteristic
44M16×C71—22no—
45M16×C71—41no—
46C2×C8×C71—41no—
47C23×C71C22⋊C411yescharacteristic
48C23×C71C22×C411yescharacteristic
49C23×C71C2×D411yescharacteristic
50Q8×C71—41no—
51D4×C71—41no—
52D4×C71—41no—
53D4×C71—41no—
54C2×C4×C71—21no—
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71C22⋊C411yescharacteristic
61C2×C4×C71C22⋊C411yescharacteristic
62C2×C4×C71C22⋊C411yescharacteristic
63C2×C4×C71C2×D411yescharacteristic
64C2×Dic71—22no—
65C2×Dic71—22no—
66C2×Dic71—42no—
67C2×Dic71—42no—
68Dic142—42no—
69Dic142—41no—
70Dic142—41no—
71C8×C71—42no—
72C22×C71—21no—
73C22×C71—21no—
74C22×C71—21no—
75C22×C71—41no—
76C22×C71—41no—
77C22×C71—41no—
78C22×C71C2×C22⋊C411yescharacteristic
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71#9911yescharacteristic
83C4×C71#9911yescharacteristic
84Dic71—42no—
85Dic71—42no—
86Dic71—82no—
87C2×C71—21no—
88C2×C71—41no—
89C2×C71—41no—
90C2×C71—41no—
91C2×C71C2×#9911yescharacteristic
92#2123—711nomaximal, Sylow
93C71#212311yescharacteristic, complemented, Sylow
94#536—711no—
95#413D7111yescharacteristic
96#410—711no—
97#352—714no—
98C2×#41C2×D7111yescharacteristic
99C22×Q8—711no—
100C2×M16—21no—
101C4⋊Q8—1421no—
102#124—1421no—
103#123—712no—
104#123—712no—
105C22⋊Q8—1421no—
106C22⋊Q8—1421no—
107#117—711no—
108#117—1421no—
109#101—21no—
110#100C2×D7112yes—
111#99—712no—
112#99—1421no—
113#41—41no—
114#41—41no—
115C2×Q8—2841no—
116C2×Q8—2841no—
117C2×Q8—1421no—
118C2×Q8—1421no—
119C2×Q8C22⋊D7111yescharacteristic
120C2×D4C4×D7111yescharacteristic
121C2×D4D28411yescharacteristic
122C2×D4C22×D7111yescharacteristic
123C22×C4—712no—
124C22×C4C4×D7111yescharacteristic
125C22×C4D28411yescharacteristic
126C22×C4C22⋊D7111yescharacteristic
127M16—22no—
128M16—41no—
129C2×C8—41no—
130C4⋊C4—2841no—
131C4⋊C4—1422no—
132C4⋊C4—1421no—
133C4⋊C4—1422no—
134C22⋊C4—712no—
135C22⋊C4—1422no—
136C22⋊C4—1422no—
137C22⋊C4—1422no—
138C42—2841no—
139C42—1421no—
140C23(C2×D71)⋊C411yescharacteristic
141C23C2×C4×D7111yescharacteristic
142C23C2×D28411yescharacteristic
143Q8—41no—
144Q8—2842no—
145Q8—2841no—
146Q8—2841no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—2842no—
157C2×C4—2842no—
158C2×C4—1422no—
159C2×C4—1422no—
160C2×C4(C2×D71)⋊C411yescharacteristic
161C2×C4(C2×D71)⋊C411yescharacteristic
162C2×C4(C2×D71)⋊C411yescharacteristic
163C2×C4C2×C22⋊D7111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D71)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—2842no—
176C4—2842no—
177C4—5682no—
178C4#1455604211yescharacteristic
179C4#1455604211yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1455604211yescharacteristic
subgroupG/H
centerC2C2×#14556042
commutatorC23×C71C22×C4
FrattiniC2×D4C22×D71
Fitting#413×C71C2
socleC2×C71C2×#99
hypercenter#413D71
hypocenterC71#2123
LCSG ▷ C23×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #17985790C2semidirect
5. C22×Dic142C4semidirect
8. #14556109C4semidirect
13. #14556087C4semidirect
93. C71#2123semidirect