Finite Group Databasebeta

← #22598162

Subgroups — #22598162

Order 9088.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556120C211yesmaximal, characteristic, complemented
2#17986306C214yesmaximal, complemented
3#17986299C214yesmaximal, complemented
4#17986042C212yesmaximal, complemented
5#17986023C211yesmaximal, characteristic, complemented
6#17986000C212yesmaximal
7C4×#41×C71C211yesmaximal, characteristic
8C2×#11765849C2212yes—
9#14556120—21no—
10#14556120—21no—
11#14556120C2214yes—
12C2×C4⋊Dic71C2212yes—
13C2×Dic71⋊C4—22no—
14#14556061C2214yes—
15#14556059C2214yes—
16C4⋊(C71⋊C8)C2214yes—
17#14556052C2214yes—
18#14556049C2214yes—
19C2×#41×C71C2211yescharacteristic
20C4×Q8×C71C2212yes—
21C4×D4×C71—22no—
22C4×D4×C71C2212yes—
23#117×C71—21no—
24#117×C71C2211yescharacteristic
25C2×C42×C71—21no—
26C2×C42×C71C2211yescharacteristic
27C22×Dic71—22no—
28#11765849—24no—
29C2×C71⋊C8C2314yes—
30C4⋊Dic71—22no—
31C4⋊Dic71C2314yes—
32Dic71⋊C4—24no—
33Dic71⋊C4—24no—
34#41×C71—22no—
35#41×C71Q814yes—
36C2×Q8×C71C2311yescharacteristic
37C2×D4×C71—21no—
38C2×D4×C71C2311yescharacteristic
39C22×C4×C71—21no—
40C22×C4×C71—22no—
41C22×C4×C71D412yes—
42C22×C4×C71C2311yescharacteristic
43C4⋊C4×C71—22no—
44C4⋊C4×C71C2312yes—
45C22⋊C4×C71—21no—
46C22⋊C4×C71—22no—
47C42×C71—21no—
48C42×C71—22no—
49C42×C71D411yescharacteristic
50C42×C71D411yescharacteristic
51C42×C71C2312yes—
52C23×C71—21no—
53C23×C71C2×D411yescharacteristic
54Q8×C71—21no—
55Q8×C71C2×Q812yes—
56D4×C71—24no—
57D4×C71—21no—
58D4×C71C2×Q812yes—
59C2×C4×C71—21no—
60C2×C4×C71—24no—
61C2×C4×C71—22no—
62C2×C4×C71—42no—
63C2×C4×C71—44no—
64C2×C4×C71C2×D412yes—
65C2×C4×C71C2×D412yes—
66C2×C4×C71C2×D411yescharacteristic
67C2×C4×C71C2×Q812yes—
68C2×C4×C71#4112yes—
69C2×C4×C71C2411yescharacteristic
70C2×Dic71—24no—
71C2×Dic71—44no—
72C71⋊C8—24no—
73C22×C71—22no—
74C22×C71—22no—
75C22×C71—42no—
76C22×C71C22⋊Q812yes—
77C22×C71C22×D411yescharacteristic
78C4×C71—22no—
79C4×C71—22no—
80C4×C71—22no—
81C4×C71—42no—
82C4×C71C22⋊Q812yes—
83C4×C71C22×Q811yescharacteristic
84C4×C71C2×#4111yescharacteristic
85Dic71—44no—
86C2×C71—22no—
87C2×C71—42no—
88C2×C71C2×C22⋊Q811yescharacteristic
89C2×C71#57512yes—
90#3080—711nomaximal, Sylow
91C71#308011yescharacteristic, complemented, Sylow
92C2×#125—711no—
93C4×#41D7111yescharacteristic
94#479—714no—
95#478—714no—
96#428—712no—
97#423—711no—
98#417—712no—
99C2×#41C2×D7111yescharacteristic
100C2×M16—712no—
101#125—714no—
102#125—1421no—
103#125—1421no—
104C4×Q8C2×D7112yes—
105C4×D4—22no—
106C4×D4C2×D7112yes—
107#117—21no—
108#117C2×D7111yescharacteristic
109C2×C4⋊C4—712no—
110C2×C4⋊C4—1422no—
111C2×C42—21no—
112C2×C42C2×D7111yescharacteristic
113#107—714no—
114#106—714no—
115C4⋊C8—714no—
116#103—714no—
117#102—714no—
118#41—22no—
119#41Dic14214yes—
120C2×Q8C22×D7111yescharacteristic
121C2×D4—21no—
122C2×D4C22×D7111yescharacteristic
123C22×C4—21no—
124C22×C4—22no—
125C22×C4—1422no—
126C22×C4C22⋊D7112yes—
127C22×C4C22×D7111yescharacteristic
128M16—1424no—
129C2×C8—714no—
130C4⋊C4—22no—
131C4⋊C4—714no—
132C4⋊C4—1424no—
133C4⋊C4—1424no—
134C4⋊C4—1422no—
135C4⋊C4C22×D7112yes—
136C22⋊C4—21no—
137C22⋊C4—22no—
138C42—21no—
139C42—22no—
140C42C22⋊D7111yescharacteristic
141C42C22⋊D7111yescharacteristic
142C42C22×D7112yes—
143C23—21no—
144C23C2×C22⋊D7111yescharacteristic
145Q8—21no—
146Q8C2×Dic14212yes—
147D4—24no—
148D4—21no—
149D4C2×Dic14212yes—
150C2×C4—21no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—44no—
155C2×C4—2844no—
156C2×C4—1424no—
157C2×C4C2×C22⋊D7112yes—
158C2×C4C2×C22⋊D7112yes—
159C2×C4C2×C22⋊D7111yescharacteristic
160C2×C4C2×Dic14212yes—
161C2×C4#1176586512yes—
162C2×C4C23×D7111yescharacteristic
163C8—1424no—
164C22—22no—
165C22—22no—
166C22—42no—
167C22#1455610712yes—
168C22C22×C22⋊D7111yescharacteristic
169C4—22no—
170C4—22no—
171C4—22no—
172C4—42no—
173C4—2844no—
174C4#1455610712yes—
175C4C22×Dic14211yescharacteristic
176C4C2×#1176586511yescharacteristic
177C2—22no—
178C2—42no—
179C2C2×#1455610711yescharacteristic
180C2#1798679712yes—
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC4×#41×C71C2
socleC22×C71C22×D4
hypercenterC4×#41D71
hypocenterC71#3080
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14556120C2semidirect
2. #17986306C2semidirect
3. #17986299C2semidirect
4. #17986042C2semidirect
5. #17986023C2semidirect
91. C71#3080semidirect