Finite Group Databasebeta

← #22589114

Subgroups — #22589114

Order 9088.

200 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14556064C211yesmaximal, characteristic
2C2×#14556063C211yesmaximal, characteristic
3#17986022C211yesmaximal, characteristic
4C2×Dic71⋊C8C211yesmaximal, characteristic
5M16×Dic71C211yesmaximal, characteristic
6#17985763C211yesmaximal, characteristic
7#341×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C22×C71⋊C8C2211yescharacteristic
11C2×C4×Dic71C2211yescharacteristic
12#14556064—22no—
13#14556063—22no—
14Dic71⋊C8—21no—
15Dic71⋊C8—21no—
16Dic71⋊C8C412yes—
17Dic71⋊C8C412yes—
18#14556038—21no—
19C8×Dic71—21no—
20C2×M16×C71C2211yescharacteristic
21C2×M16×C71C2211yescharacteristic
22C22×C8×C71C2211yescharacteristic
23C22×Dic71Q811yescharacteristic
24C22×Dic71Q811yescharacteristic
25#11765849—21no—
26#11765849—21no—
27#11765849—21no—
28#11765849D412yes—
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C2×C71⋊C8C2×C412yes—
34C4×Dic71C2×C411yescharacteristic
35C4×Dic71C2×C411yescharacteristic
36C4×Dic71D411yescharacteristic
37C4×Dic71D411yescharacteristic
38C22×C4×C71C2311yescharacteristic
39M16×C71—21no—
40M16×C71—21no—
41M16×C71—21no—
42M16×C71Q812yes—
43C2×C8×C71—21no—
44C2×C8×C71—21no—
45C2×C8×C71—21no—
46C2×C8×C71—21no—
47C2×C8×C71C2×C412yes—
48C23×C71C2×Q811yescharacteristic
49C2×C4×C71C22×C411yescharacteristic
50C2×C4×C71C2×D411yescharacteristic
51C2×C4×C71C2×D411yescharacteristic
52C2×C4×C71C2×Q811yescharacteristic
53C2×C4×C71#4111yescharacteristic
54C2×C4×C71#4111yescharacteristic
55C2×Dic71—22no—
56C2×Dic71—41no—
57C2×Dic71C4⋊C411yescharacteristic
58C2×Dic71C4⋊C411yescharacteristic
59C2×Dic71C4⋊C411yescharacteristic
60C2×Dic71C4⋊C411yescharacteristic
61C8×C71—22no—
62C8×C71—22no—
63C8×C71—41no—
64C71⋊C8—22no—
65C71⋊C8—22no—
66C71⋊C8—41no—
67C22×C71—21no—
68C22×C71—21no—
69C22×C71C2×C4⋊C411yescharacteristic
70C22×C71#12511yescharacteristic
71C22×C71C4⋊Q811yescharacteristic
72C4×C71C4×D411yescharacteristic
73C4×C71C4×Q811yescharacteristic
74C4×C71#12111yescharacteristic
75C4×C71C22⋊Q811yescharacteristic
76Dic71—21no—
77Dic71—21no—
78Dic71—21no—
79Dic71#10812yescomplemented
80C2×C71—21no—
81C2×C71—21no—
82C2×C71#38911yescharacteristic
83C2×C71C2×#10811yescharacteristic
84C2×C71#43011yescharacteristic
85#1950—711nomaximal, Sylow
86C71#195011yescharacteristic, complemented, Sylow
87C2×#108—711no—
88C2×#108—711no—
89#423—711no—
90C2×C4⋊C8—711no—
91C4×M16—711no—
92#341—711no—
93#341D7111yescharacteristic
94C2×M16—711no—
95C2×M16—711no—
96C2×M16C2×D7111yescharacteristic
97C2×M16C2×D7111yescharacteristic
98C22×C8—711no—
99C22×C8C2×D7111yescharacteristic
100C2×C42—711no—
101#108—1422no—
102#108—1422no—
103C4⋊C8—712no—
104C4⋊C8—712no—
105C4⋊C8—1421no—
106C4⋊C8—1421no—
107#97—1421no—
108C4×C8—1421no—
109C22×C4—711no—
110C22×C4—711no—
111C22×C4C22×D7111yescharacteristic
112M16—21no—
113M16—21no—
114M16—21no—
115M16—712no—
116M16—1421no—
117M16—1421no—
118M16—1421no—
119M16Dic14212yes—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—712no—
125C2×C8—1421no—
126C2×C8—1421no—
127C2×C8—1421no—
128C2×C8—1421no—
129C2×C8C4×D7112yes—
130C42—711no—
131C42—711no—
132C42—711no—
133C42—711no—
134C23Q8×D7111yescharacteristic
135C2×C4—2841no—
136C2×C4—711no—
137C2×C4—711no—
138C2×C4—711no—
139C2×C4—711no—
140C2×C4—1422no—
141C2×C4C2×C4×D7111yescharacteristic
142C2×C4D4×D7111yescharacteristic
143C2×C4D4×D7111yescharacteristic
144C2×C4C2×Dic14211yescharacteristic
145C2×C4#1176586411yescharacteristic
146C2×C4#1176586511yescharacteristic
147C8—22no—
148C8—22no—
149C8—41no—
150C8—2841no—
151C8—1422no—
152C8—1422no—
153C22—21no—
154C22—21no—
155C22C4⋊C4×D7111yescharacteristic
156C22#1455611811yescharacteristic
157C22#1455612711yescharacteristic
158C4—712no—
159C4—1421no—
160C4—1421no—
161C4—1421no—
162C4(C22⋊D71)⋊C411yescharacteristic
163C4C4×Dic14211yescharacteristic
164C4#1455610111yescharacteristic
165C4#1455610511yescharacteristic
166C2—21no—
167C2—21no—
168C2#1798589611yescharacteristic
169C2#108×D7111yescharacteristic
170C2#1798604611yescharacteristic
subgroupG/H
centerC2×C4D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#341×C71C2
socleC22×C71C2×C4⋊C4
hypercenter#341D71
hypocenterC71#1950
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
79. Dic71#108semidirect
86. C71#1950semidirect