Finite Group Databasebeta

← #22586959

Subgroups — #22586959

Order 9088.

218 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 59 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#17986534C211yesmaximal, characteristic
2#17986054C211yesmaximal, characteristic, complemented
3#97×D71C211yesmaximal, characteristic, complemented
4#17985741C211yesmaximal, characteristic, complemented
5#17985738C211yesmaximal, characteristic, complemented
6#17985738C211yesmaximal, characteristic, complemented
7#330×C71C211yesmaximal, characteristic, complemented
8C2×C8×D71—21no—
9#14556123—21no—
10#14556116C2211yescharacteristic
11#14556113—21no—
12#14556108C411yescharacteristic
13#14556103C411yescharacteristic
14#14556093C411yescharacteristic
15#14556090—21no—
16#14556090C411yescharacteristic
17#14556086—21no—
18C42×D71C2211yescharacteristic
19Dic71⋊C8—21no—
20(C2×D71)⋊C8—21no—
21#14556039C2211yescharacteristic
22#14556039C2211yescharacteristic
23#14556038—21no—
24#125×C71C2211yescharacteristic
25#97×C71C2211yescharacteristic
26#97×C71C2211yescharacteristic
27C2×Dic142C2×C411yescharacteristic
28C2×D284—21no—
29C2×D284C2×C411yescharacteristic
30C2×C4×D71—21no—
31C2×C4×D71C2×C411yescharacteristic
32C2×C4×D71D411yescharacteristic
33C2×C4×D71D411yescharacteristic
34C2×C71⋊C8—21no—
35C2×C71⋊C8—21no—
36C8×D71—24no—
37C4⋊Dic71—21no—
38Dic71⋊C4—21no—
39(C2×D71)⋊C4—21no—
40(C2×D71)⋊C4—21no—
41(C2×D71)⋊C4—21no—
42(C2×D71)⋊C4—21no—
43(C2×D71)⋊C4—21no—
44C4×Dic71—21no—
45C4×Dic71C2×C411yescharacteristic
46C4×Dic71D411yescharacteristic
47C4×Dic71D411yescharacteristic
48C2×C8×C71—21no—
49C2×C8×C71—21no—
50C4⋊C4×C71—21no—
51C4⋊C4×C71—21no—
52C4⋊C4×C71C2×C411yescharacteristic
53C4⋊C4×C71C2×C411yescharacteristic
54C42×C71C2311yescharacteristic
55C22×D71—21no—
56C22×D71C22⋊C411yescharacteristic
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71C22×C411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C2×Dic71—21no—
63C2×Dic71C22⋊C411yescharacteristic
64C2×Dic71C22⋊C411yescharacteristic
65C2×Dic71C22⋊C411yescharacteristic
66D284—41no—
67D284—42no—
68C4×D71—22no—
69C4×D71—41no—
70C4×D71—41no—
71C4×D71—42no—
72Dic142—41no—
73C8×C71—22no—
74C8×C71—41no—
75C71⋊C8—22no—
76C71⋊C8—41no—
77C22×C71C2×C22⋊C411yescharacteristic
78C2×D71—21no—
79C2×D71—21no—
80C2×D71—41no—
81C2×D71—41no—
82C2×D71—41no—
83C2×D71#10412yes—
84C4×C71—21no—
85C4×C71—21no—
86C4×C71—21no—
87C4×C71—41no—
88C4×C71—41no—
89Dic71—21no—
90Dic71—21no—
91Dic71—21no—
92Dic71—41no—
93C2×C71#41311yescharacteristic
94C2×C71C2×#10411yescharacteristic
95C2×C71#42111yescharacteristic
96D71—22no—
97D71—81no—
98#1532—711nomaximal, Sylow
99C71#153211yescharacteristic, complemented, Sylow
100#529—711no—
101#432—711no—
102C2×#97—711no—
103#330—711no—
104#330D7111yescharacteristic, complemented
105#329—711no—
106#329—711no—
107C22×C8—1421no—
108#126—1421no—
109#125C2×D7111yescharacteristic
110#124—711no—
111#123—1421no—
112C22⋊Q8—711no—
113#121—711no—
114C4×Q8—711no—
115C4×D4—711no—
116C4×D4—1421no—
117#117—1421no—
118C2×C42—711no—
119C4⋊C8—1421no—
120C22⋊C8—1421no—
121#97—711no—
122#97—711no—
123#97—1421no—
124#97C2×D7111yescharacteristic
125#97C2×D7111yescharacteristic
126C2×Q8—711no—
127C2×D4—711no—
128C2×D4—1421no—
129C22×C4—711no—
130C22×C4—711no—
131C22×C4—711no—
132C22×C4—1421no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1424no—
136C2×C8—1421no—
137C2×C8—1421no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1421no—
141C4⋊C4—1421no—
142C4⋊C4C4×D7111yescharacteristic
143C4⋊C4C4×D7111yescharacteristic
144C22⋊C4—1421no—
145C22⋊C4—1421no—
146C22⋊C4—1421no—
147C22⋊C4—1421no—
148C22⋊C4—1421no—
149C42—711no—
150C42—711no—
151C42—711no—
152C42—1421no—
153C42C22×D7111yescharacteristic
154C23—711no—
155C23—1421no—
156Q8—2841no—
157D4—2841no—
158D4—2842no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—2841no—
162C2×C4—2841no—
163C2×C4—2842no—
164C2×C4—711no—
165C2×C4—711no—
166C2×C4—711no—
167C2×C4—1422no—
168C2×C4—1421no—
169C2×C4C2×C4×D7111yescharacteristic
170C2×C4D4×D7111yescharacteristic
171C2×C4D4×D7111yescharacteristic
172C8—22no—
173C8—41no—
174C8—2841no—
175C8—1422no—
176C22—2841no—
177C22—2841no—
178C22—2841no—
179C22—712no—
180C22—1421no—
181C22—1421no—
182C22C22⋊C4×D7111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—2841no—
189C4—1421no—
190C4—1421no—
191C4—1421no—
192C2—5681no—
193C2—1422no—
194C2#1798598211yescharacteristic
195C2#104×D7111yescharacteristic
196C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#330×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#330D71
hypocenterC71#1532
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #17986054C2semidirect
3. #97×D71C2semidirect
4. #17985741C2semidirect
5. #17985738C2semidirect
6. #17985738C2semidirect
7. #330×C71C2semidirect
99. C71#1532semidirect
104. #330D71semidirect