Finite Group Databasebeta

← #22590013

Subgroups — #22590013

Order 9088.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#17986569C211yesmaximal, characteristic
2#17985971C212yesmaximal
3#17985794C211yesmaximal, characteristic, complemented
4#17985793C212yesmaximal, complemented
5#354×C71C211yesmaximal, characteristic, complemented
6C2×#11765864C2211yescharacteristic
7C2×Q8×D71C411yescharacteristic, complemented
8#14556128C411yescharacteristic, complemented
9#14556126C411yescharacteristic, complemented
10#14556115C2211yescharacteristic
11#14556110—22no—
12#14556105—22no—
13#14556085C411yescharacteristic, complemented
14#14556084—22no—
15#14556043C2212yes—
16#14556042—22no—
17#124×C71C2211yescharacteristic
18#99×C71C2212yes—
19#11765864—42no—
20C2×Dic142—21no—
21C2×Dic142C2×C411yescharacteristic
22C2×Dic142C2×C411yescharacteristic
23Q8×D71—42no—
24C2×C22⋊D71D412yes—
25C22×Dic71D412yes—
26C2×C4×D71—21no—
27C2×C4×D71C2×C411yescharacteristic
28C4⋊Dic71—22no—
29Dic71⋊C4—21no—
30Dic71⋊C4—22no—
31Dic71⋊C4—42no—
32C22⋊Dic71—22no—
33C22⋊Dic71—22no—
34(C2×D71)⋊C4—21no—
35C4×Dic71—42no—
36C4×Dic71C2×C411yescharacteristic
37C2×Q8×C71C2×C411yescharacteristic
38C2×D4×C71C2311yescharacteristic
39C22⋊C4×C71—22no—
40C22⋊C4×C71—22no—
41C42×C71C2×C411yescharacteristic
42C23×C71C2×D412yes—
43C22×D71C22⋊C411yescharacteristic
44Q8×C71—41no—
45D4×C71—41no—
46C2×C4×C71—21no—
47C2×C4×C71—21no—
48C2×C4×C71—42no—
49C2×C4×C71C22×C411yescharacteristic
50C22⋊D71—42no—
51C2×Dic71—22no—
52C2×Dic71—22no—
53C2×Dic71—21no—
54C2×Dic71—21no—
55C2×Dic71—42no—
56C2×Dic71C22⋊C412yes—
57C2×Dic71C22⋊C411yescharacteristic
58C4×D71—22no—
59C4×D71—42no—
60Dic142—41no—
61Dic142—42no—
62Dic142—41no—
63C22×C71—22no—
64C22×C71—42no—
65C22×C71C2×C22⋊C411yescharacteristic
66C2×D71—21no—
67C2×D71—41no—
68C4×C71—21no—
69C4×C71—41no—
70C4×C71—41no—
71C4×C71—82no—
72Dic71—22no—
73Dic71—41no—
74Dic71—41no—
75Dic71—82no—
76Dic71#9912yes—
77C2×C71—21no—
78C2×C71—42no—
79C2×C71C2×#9911yescharacteristic
80D71—41no—
81#2129—711nomaximal, Sylow
82C71#212911yescharacteristic, complemented, Sylow
83#536—711no—
84#410—712no—
85#354—711no—
86#354—712no—
87#354D7111yescharacteristic, complemented
88C2×#41—711no—
89C22×Q8—711no—
90C4⋊Q8—711no—
91C4⋊Q8—711no—
92#124—711no—
93#124C2×D7111yescharacteristic
94#123—1422no—
95C22⋊Q8—1422no—
96#117—711no—
97#117—1422no—
98#99—712no—
99#99—1422no—
100#99C2×D7112yes—
101#41—2842no—
102C2×Q8—2842no—
103C2×Q8—711no—
104C2×Q8—711no—
105C2×Q8—1421no—
106C2×Q8C4×D7111yescharacteristic
107C2×D4—712no—
108C2×D4C22×D7111yescharacteristic
109C22×C4—712no—
110C22×C4—711no—
111C22×C4—1421no—
112C4⋊C4—2842no—
113C4⋊C4—1421no—
114C4⋊C4—1422no—
115C4⋊C4—1422no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—1421no—
119C22⋊C4—1422no—
120C22⋊C4—1422no—
121C42—2842no—
122C42—711no—
123C42C4×D7111yescharacteristic
124C23—711no—
125C23D4×D7112yes—
126Q8—41no—
127Q8—2841no—
128Q8—2841no—
129Q8—2842no—
130D4—41no—
131D4—2842no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—2842no—
136C2×C4—2842no—
137C2×C4—711no—
138C2×C4—712no—
139C2×C4—1422no—
140C2×C4—1421no—
141C2×C4—1421no—
142C2×C4—1422no—
143C2×C4—1422no—
144C2×C4C2×C4×D7111yescharacteristic
145C22—22no—
146C22—42no—
147C22—2841no—
148C22—1421no—
149C22C22⋊C4×D7111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—2841no—
155C4—2841no—
156C4—5682no—
157C4—712no—
158C4—1422no—
159C2—21no—
160C2—42no—
161C2—2841no—
162C2#99×D7111yescharacteristic
subgroupG/H
centerC2#99×D71
commutatorC2×C4×C71C22×C4
FrattiniC2×D4C22×D71
Fitting#354×C71C2
socleC2×C71C2×#99
hypercenter#354D71
hypocenterC71#2129
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #17985794C2semidirect
4. #17985793C2semidirect
5. #354×C71C2semidirect
7. C2×Q8×D71C4semidirect
8. #14556128C4semidirect
9. #14556126C4semidirect
13. #14556085C4semidirect
82. C71#2129semidirect
87. #354D71semidirect