Finite Group Databasebeta

← #22590028

Subgroups — #22590028

Order 9088.

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

normal subgroups only

This group has 230 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#17986574C211yesmaximal, characteristic
2#101×D71C212yesmaximal, complemented
3#17985798C211yesmaximal, characteristic, complemented
4#17985795C212yesmaximal, complemented
5#356×C71C211yesmaximal, characteristic, complemented
6C2×#11765866C411yescharacteristic
7C2×Q8×D71C2211yescharacteristic
8M16×D71—22no—
9#14556126C411yescharacteristic
10#14556117C2211yescharacteristic
11#14556116C411yescharacteristic
12#14556113—22no—
13#14556106—22no—
14#14556085C411yescharacteristic
15#14556047C2212yes—
16#14556046—22no—
17C4⋊Q8×C71C2211yescharacteristic
18#101×C71C2212yes—
19#11765866—42no—
20C2×Dic142C2×C411yescharacteristic
21C2×Dic142D412yes—
22Q8×D71—42no—
23C2×D284—21no—
24C2×D284C2×C411yescharacteristic
25C2×C4×D71—21no—
26C2×C4×D71C2×C411yescharacteristic
27C2×C4×D71D412yes—
28#11765849—22no—
29#11765848—42no—
30C8×D71—42no—
31Dic71⋊C4—21no—
32Dic71⋊C4—22no—
33(C2×D71)⋊C4—21no—
34(C2×D71)⋊C4—22no—
35(C2×D71)⋊C4—22no—
36C4×Dic71C2×C411yescharacteristic
37C2×Q8×C71C2×C411yescharacteristic
38C2×Q8×C71C2311yescharacteristic
39M16×C71—22no—
40C4⋊C4×C71—22no—
41C42×C71C2×C411yescharacteristic
42C22×D71—21no—
43C22×D71C22⋊C411yescharacteristic
44Q8×C71—41no—
45Q8×C71—41no—
46C2×C4×C71—21no—
47C2×C4×C71—21no—
48C2×C4×C71C22×C411yescharacteristic
49C2×C4×C71C2×D412yes—
50C2×Dic71—21no—
51C2×Dic71C22⋊C412yes—
52C2×Dic71C22⋊C411yescharacteristic
53D284—41no—
54D284—42no—
55C4×D71—22no—
56C4×D71—22no—
57C4×D71—22no—
58C4×D71—42no—
59Dic142—41no—
60Dic142—42no—
61C8×C71—42no—
62C71⋊C8—42no—
63C22×C71C2×C22⋊C411yescharacteristic
64C2×D71—41no—
65C2×D71—42no—
66C2×D71—41no—
67C2×D71#9912yes—
68C4×C71—22no—
69C4×C71—21no—
70C4×C71—41no—
71C4×C71—41no—
72Dic71—21no—
73Dic71—22no—
74Dic71—41no—
75C2×C71—21no—
76C2×C71C2×#9911yescharacteristic
77D71—22no—
78D71—81no—
79#2133—711nomaximal, Sylow
80C71#213311yescharacteristic, complemented, Sylow
81#536—711no—
82C2×#101—712no—
83#356—711no—
84#356D7111yescharacteristic, complemented
85#355—712no—
86C2×#41—711no—
87C22×Q8—711no—
88C2×M16—1422no—
89C4⋊Q8—711no—
90C4⋊Q8C2×D7111yescharacteristic
91#124—711no—
92#124—711no—
93#123—1422no—
94C22⋊Q8—1422no—
95#117—711no—
96#101—712no—
97#101—1422no—
98#101C2×D7112yes—
99#41—2842no—
100C2×Q8—2842no—
101C2×Q8—711no—
102C2×Q8—712no—
103C2×Q8C4×D7111yescharacteristic
104C2×Q8C22×D7111yescharacteristic
105C2×D4—711no—
106C2×D4—1421no—
107C22×C4—711no—
108C22×C4—712no—
109C22×C4—1421no—
110M16—22no—
111M16—2842no—
112M16—1422no—
113C2×C8—2842no—
114C4⋊C4—22no—
115C4⋊C4—1421no—
116C4⋊C4—1422no—
117C22⋊C4—1422no—
118C22⋊C4—1421no—
119C22⋊C4—1422no—
120C42—711no—
121C42C4×D7111yescharacteristic
122C23—711no—
123C23—1421no—
124Q8—41no—
125Q8—41no—
126Q8—2842no—
127Q8—2841no—
128D4—2841no—
129D4—2842no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2842no—
133C2×C4—712no—
134C2×C4—711no—
135C2×C4—1422no—
136C2×C4—1422no—
137C2×C4—1422no—
138C2×C4—1421no—
139C2×C4C2×C4×D7111yescharacteristic
140C2×C4D4×D7112yes—
141C8—42no—
142C8—2842no—
143C22—2842no—
144C22—2841no—
145C22—2841no—
146C22—712no—
147C22C22⋊C4×D7111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—2841no—
153C4—1421no—
154C4—1422no—
155C2—21no—
156C2—5681no—
157C2—1422no—
158C2#99×D7111yescharacteristic
subgroupG/H
centerC2#99×D71
commutatorC2×C4×C71C22×C4
FrattiniC2×Q8C22×D71
Fitting#356×C71C2
socleC2×C71C2×#99
hypercenter#356D71
hypocenterC71#2133
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D71C2semidirect
3. #17985798C2semidirect
4. #17985795C2semidirect
5. #356×C71C2semidirect
80. C71#2133semidirect
84. #356D71semidirect