Finite Group Databasebeta

← #22586972

Subgroups — #22586972

Order 9088.

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

normal subgroups only

This group has 200 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#17986533C211yesmaximal, characteristic
2#17986056C211yesmaximal, characteristic, complemented
3#17985740C212yesmaximal, complemented
4#17985738C212yesmaximal, complemented
5#432×C71C211yesmaximal, characteristic, complemented
6#14556122—21no—
7#14556120C2211yescharacteristic
8#14556116C2211yescharacteristic
9#14556111—21no—
10#14556107C411yescharacteristic
11#14556102C411yescharacteristic
12C4×Dic142C411yescharacteristic
13C4×D284C411yescharacteristic
14C4×C22⋊D71—21no—
15#14556085—21no—
16C4⋊(C71⋊C8)—21no—
17C22⋊(C71⋊C8)—21no—
18#14556039C2212yes—
19C2×C42×C71C2211yescharacteristic
20C4⋊C8×C71—21no—
21C22⋊C8×C71—21no—
22#97×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×C71C2×C411yescharacteristic
41C22×C4×C71D411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C2×C8×C71—22no—
44C42×C71C2×C411yescharacteristic
45C42×C71D411yescharacteristic
46C42×C71D411yescharacteristic
47C42×C71C2311yescharacteristic
48C23×C71C22⋊C411yescharacteristic
49C22×D71—21no—
50C2×C4×C71—41no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71C22⋊C411yescharacteristic
54C2×C4×C71C22⋊C411yescharacteristic
55C2×C4×C71C22⋊C411yescharacteristic
56C2×C4×C71C22×C411yescharacteristic
57C2×C4×C71C2×D411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C22⋊D71—42no—
60C2×Dic71—21no—
61C2×Dic71—21no—
62C2×Dic71—21no—
63D284—41no—
64C4×D71—42no—
65Dic142—41no—
66C8×C71—42no—
67C71⋊C8—42no—
68C22×C71—21no—
69C22×C71—21no—
70C22×C71—21no—
71C22×C71C2×C22⋊C411yescharacteristic
72C2×D71—41no—
73C2×D71—41no—
74C2×D71—41no—
75C4×C71—21no—
76C4×C71—21no—
77C4×C71—21no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81Dic71—41no—
82Dic71—41no—
83Dic71—41no—
84C2×C71—41no—
85C2×C71#41311yescharacteristic
86C2×C71#42111yescharacteristic
87C2×C71#42111yescharacteristic
88D71—81no—
89#1535—711nomaximal, Sylow
90C71#153511yescharacteristic, complemented, Sylow
91#529—711no—
92#432—711no—
93#432D7111yescharacteristic, complemented
94#330—712no—
95#329—712no—
96#126—1421no—
97#125—711no—
98#124—711no—
99#123—1421no—
100C22⋊Q8—711no—
101#121—711no—
102C4×Q8—711no—
103C4×D4—711no—
104C4×D4—1421no—
105#117—1421no—
106C2×C42C2×D7111yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—1421no—
109C22⋊C8—21no—
110C22⋊C8—1421no—
111#97—712no—
112#97C2×D7112yes—
113C2×Q8—711no—
114C2×D4—711no—
115C2×D4—1421no—
116C22×C4—1421no—
117C22×C4C4×D7111yescharacteristic
118C22×C4D28411yescharacteristic
119C22×C4C22⋊D7111yescharacteristic
120C2×C8—22no—
121C2×C8—1422no—
122C4⋊C4—711no—
123C4⋊C4—711no—
124C4⋊C4—1421no—
125C4⋊C4—1421no—
126C4⋊C4—1421no—
127C4⋊C4—1421no—
128C22⋊C4—1421no—
129C22⋊C4—1421no—
130C22⋊C4—1421no—
131C22⋊C4—1421no—
132C22⋊C4—1421no—
133C42—1421no—
134C42C4×D7111yescharacteristic
135C42D28411yescharacteristic
136C42C22⋊D7111yescharacteristic
137C42C22×D7111yescharacteristic
138C23—1421no—
139C23(C2×D71)⋊C411yescharacteristic
140Q8—2841no—
141D4—2841no—
142D4—2842no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2842no—
147C2×C4—1421no—
148C2×C4—1421no—
149C2×C4—1421no—
150C2×C4(C2×D71)⋊C411yescharacteristic
151C2×C4(C2×D71)⋊C411yescharacteristic
152C2×C4(C2×D71)⋊C411yescharacteristic
153C2×C4C2×C4×D7111yescharacteristic
154C2×C4C2×C22⋊D7111yescharacteristic
155C2×C4C2×D28411yescharacteristic
156C8—42no—
157C8—2842no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—2841no—
162C22—2841no—
163C22—2841no—
164C22C2×(C2×D71)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—2841no—
172C4—2841no—
173C4—2841no—
174C2—41no—
175C2—5681no—
176C2#1798598111yescharacteristic
177C2#1798601511yescharacteristic
178C2#1798601711yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#432×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#432D71
hypocenterC71#1535
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #17986056C2semidirect
3. #17985740C2semidirect
4. #17985738C2semidirect
5. #432×C71C2semidirect
90. C71#1535semidirect
93. #432D71semidirect