Finite Group Databasebeta

← #22586970

Subgroups — #22586970

Order 9088.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#17986054C211yesmaximal, characteristic, complemented
4#17985741C211yesmaximal, characteristic, complemented
5#17985738C211yesmaximal, characteristic, complemented
6#17985738C211yesmaximal, characteristic, complemented
7#330×C71C211yesmaximal, characteristic, complemented
8#14556123—21no—
9#14556116C2211yescharacteristic
10#14556113—21no—
11#14556108C411yescharacteristic
12#14556103C411yescharacteristic
13#14556093C411yescharacteristic
14#14556090—21no—
15#14556090C411yescharacteristic
16#14556086—21no—
17C42×D71C2211yescharacteristic
18Dic71⋊C8—21no—
19Dic71⋊C8—21no—
20(C2×D71)⋊C8—21no—
21(C2×D71)⋊C8—21no—
22#14556039C2211yescharacteristic
23#14556039C2211yescharacteristic
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—
36C4⋊Dic71—21no—
37Dic71⋊C4—21no—
38(C2×D71)⋊C4—21no—
39(C2×D71)⋊C4—21no—
40(C2×D71)⋊C4—21no—
41(C2×D71)⋊C4—21no—
42(C2×D71)⋊C4—21no—
43C4×Dic71—21no—
44C4×Dic71C2×C411yescharacteristic
45C4×Dic71D411yescharacteristic
46C4×Dic71D411yescharacteristic
47C2×C8×C71—21no—
48C2×C8×C71—21no—
49C4⋊C4×C71—21no—
50C4⋊C4×C71—21no—
51C4⋊C4×C71C2×C411yescharacteristic
52C4⋊C4×C71C2×C411yescharacteristic
53C42×C71C2311yescharacteristic
54C22×D71—21no—
55C22×D71C22⋊C411yescharacteristic
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71C22×C411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×Dic71—21no—
62C2×Dic71C22⋊C411yescharacteristic
63C2×Dic71C22⋊C411yescharacteristic
64C2×Dic71C22⋊C411yescharacteristic
65D284—41no—
66D284—42no—
67C4×D71—41no—
68C4×D71—41no—
69C4×D71—41no—
70C4×D71—42no—
71Dic142—41no—
72C8×C71—41no—
73C8×C71—41no—
74C71⋊C8—41no—
75C71⋊C8—41no—
76C22×C71C2×C22⋊C411yescharacteristic
77C2×D71—21no—
78C2×D71—21no—
79C2×D71—21no—
80C2×D71—41no—
81C2×D71—41no—
82C2×D71—41no—
83C4×C71—21no—
84C4×C71—21no—
85C4×C71—21no—
86C4×C71—41no—
87C4×C71—41no—
88Dic71—21no—
89Dic71—21no—
90Dic71—21no—
91Dic71—41no—
92C2×C71#41311yescharacteristic
93C2×C71#42111yescharacteristic
94C2×C71#42111yescharacteristic
95D71—41no—
96D71—81no—
97#1535—711nomaximal, Sylow
98C71#153511yescharacteristic, complemented, Sylow
99#529—711no—
100#432—711no—
101#432—711no—
102#330—711no—
103#330D7111yescharacteristic, complemented
104#329—711no—
105#329—711no—
106#126—1421no—
107#125C2×D7111yescharacteristic
108#124—711no—
109#123—1421no—
110C22⋊Q8—711no—
111#121—711no—
112C4×Q8—711no—
113C4×D4—711no—
114C4×D4—1421no—
115#117—1421no—
116C2×C42—711no—
117C4⋊C8—1421no—
118C4⋊C8—1421no—
119C22⋊C8—1421no—
120C22⋊C8—1421no—
121#97—711no—
122#97—711no—
123#97C2×D7111yescharacteristic
124#97C2×D7111yescharacteristic
125C2×Q8—711no—
126C2×D4—711no—
127C2×D4—1421no—
128C22×C4—711no—
129C22×C4—711no—
130C22×C4—711no—
131C22×C4—1421no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—1421no—
135C2×C8—1421no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1421no—
139C4⋊C4—1421no—
140C4⋊C4C4×D7111yescharacteristic
141C4⋊C4C4×D7111yescharacteristic
142C22⋊C4—1421no—
143C22⋊C4—1421no—
144C22⋊C4—1421no—
145C22⋊C4—1421no—
146C22⋊C4—1421no—
147C42—711no—
148C42—711no—
149C42—711no—
150C42—1421no—
151C42C22×D7111yescharacteristic
152C23—711no—
153C23—1421no—
154Q8—2841no—
155D4—2841no—
156D4—2842no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2841no—
160C2×C4—2841no—
161C2×C4—2841no—
162C2×C4—2842no—
163C2×C4—711no—
164C2×C4—711no—
165C2×C4—711no—
166C2×C4—1421no—
167C2×C4C2×C4×D7111yescharacteristic
168C2×C4D4×D7111yescharacteristic
169C2×C4D4×D7111yescharacteristic
170C8—41no—
171C8—41no—
172C8—2841no—
173C8—2841no—
174C22—2841no—
175C22—2841no—
176C22—2841no—
177C22—1421no—
178C22—1421no—
179C22—1421no—
180C22C22⋊C4×D7111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2841no—
187C4—1421no—
188C4—1421no—
189C4—1421no—
190C2—2841no—
191C2—5681no—
192C2#1798598211yescharacteristic
193C2#1798601411yescharacteristic
194C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#330×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#330D71
hypocenterC71#1535
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. #17986054C2semidirect
4. #17985741C2semidirect
5. #17985738C2semidirect
6. #17985738C2semidirect
7. #330×C71C2semidirect
98. C71#1535semidirect
103. #330D71semidirect