Finite Group Databasebeta

← #22589331

Subgroups — #22589331

Order 9088.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556119C211yesmaximal, characteristic
2#17986022C211yesmaximal, characteristic
3M16×Dic71C211yesmaximal, characteristic
4#17985768C211yesmaximal, characteristic
5#17985767C211yesmaximal, characteristic
6#17985767C211yesmaximal, characteristic
7#343×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10#14556119—21no—
11#14556119—21no—
12#14556119—21no—
13#14556119—21no—
14C2×C4⋊Dic71C412yes—
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4C412yes—
17C2×C4×Dic71C2211yescharacteristic
18Dic71⋊C8—21no—
19Dic71⋊C8—21no—
20#14556038—21no—
21C8×Dic71—21no—
22C2×M16×C71C2211yescharacteristic
23C2×M16×C71C2211yescharacteristic
24C2×C4⋊C4×C71C2211yescharacteristic
25C22×Dic71C2×C412yes—
26C22×Dic71C2×C411yescharacteristic
27C22×Dic71C2×C411yescharacteristic
28#11765849—21no—
29#11765849—21no—
30#11765849—21no—
31#11765849Q812yes—
32C2×C71⋊C8—21no—
33C2×C71⋊C8—21no—
34C4⋊Dic71—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—22no—
37C4⋊Dic71—22no—
38Dic71⋊C4—22no—
39Dic71⋊C4—22no—
40C4×Dic71D411yescharacteristic
41C4×Dic71D411yescharacteristic
42C4×Dic71D411yescharacteristic
43C4×Dic71D411yescharacteristic
44C22×C4×C71C2×C412yes—
45C22×C4×C71C2311yescharacteristic
46M16×C71—21no—
47M16×C71—21no—
48M16×C71—21no—
49M16×C71Q812yes—
50C2×C8×C71—21no—
51C2×C8×C71—21no—
52C4⋊C4×C71—21no—
53C4⋊C4×C71—21no—
54C23×C71C22×C411yescharacteristic
55C2×C4×C71—22no—
56C2×C4×C71—42no—
57C2×C4×C71C2×D411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×Q811yescharacteristic
60C2×C4×C71C2×Q811yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×C4×C71#4111yescharacteristic
63C2×Dic71—22no—
64C2×Dic71—41no—
65C2×Dic71—41no—
66C2×Dic71—42no—
67C2×Dic71C22⋊C411yescharacteristic
68C2×Dic71C22⋊C411yescharacteristic
69C2×Dic71C22⋊C411yescharacteristic
70C2×Dic71C22⋊C411yescharacteristic
71C8×C71—22no—
72C8×C71—41no—
73C71⋊C8—22no—
74C71⋊C8—41no—
75C22×C71—21no—
76C22×C71—21no—
77C22×C71C2×C22⋊C411yescharacteristic
78C22×C71C4×Q811yescharacteristic
79C22×C71C4×Q811yescharacteristic
80C4×C71—42no—
81C4×C71C22⋊Q811yescharacteristic
82C4×C71C22⋊Q811yescharacteristic
83C4×C71#12411yescharacteristic
84C4×C71C4⋊Q811yescharacteristic
85Dic71—21no—
86Dic71—21no—
87Dic71—21no—
88Dic71—21no—
89Dic71—42no—
90C2×C71—21no—
91C2×C71—21no—
92C2×C71#39111yescharacteristic
93C2×C71#41311yescharacteristic
94C2×C71#41311yescharacteristic
95#1998—711nomaximal, Sylow
96C71#199811yescharacteristic, complemented, Sylow
97C2×#125—711no—
98#423—711no—
99C4×M16—711no—
100#343—711no—
101#343—711no—
102#343—711no—
103#343D7111yescharacteristic
104C2×M16—711no—
105C2×M16—711no—
106C2×M16C2×D7111yescharacteristic
107C2×M16C2×D7111yescharacteristic
108#125—1421no—
109#125—1421no—
110#125—1421no—
111#125—1421no—
112C2×C4⋊C4—712no—
113C2×C4⋊C4—712no—
114C2×C4⋊C4—711no—
115C2×C4⋊C4C2×D7111yescharacteristic
116C2×C42—711no—
117C4⋊C8—1421no—
118C4⋊C8—1421no—
119#97—1421no—
120C4×C8—1421no—
121C22×C4—711no—
122C22×C4—711no—
123C22×C4—712no—
124C22×C4C4×D7112yes—
125C22×C4C22×D7111yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—712no—
130M16—1421no—
131M16—1421no—
132M16—1421no—
133M16Dic14212yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1421no—
137C2×C8—1421no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1422no—
141C4⋊C4—1422no—
142C4⋊C4—1422no—
143C4⋊C4—1422no—
144C4⋊C4—1421no—
145C4⋊C4—1421no—
146C42—711no—
147C42—711no—
148C42—711no—
149C42—711no—
150C23C2×C4×D7111yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—2842no—
154C2×C4—2841no—
155C2×C4—2841no—
156C2×C4—711no—
157C2×C4—711no—
158C2×C4—711no—
159C2×C4—711no—
160C2×C4—1422no—
161C2×C4D4×D7111yescharacteristic
162C2×C4D4×D7111yescharacteristic
163C2×C4Q8×D7111yescharacteristic
164C2×C4C2×Dic14211yescharacteristic
165C2×C4#1176586411yescharacteristic
166C2×C4#1176586511yescharacteristic
167C8—22no—
168C8—41no—
169C8—2841no—
170C8—1422no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D7111yescharacteristic
174C22#1455609311yescharacteristic
175C22C4×Dic14211yescharacteristic
176C4—42no—
177C4—2842no—
178C4—1421no—
179C4—1421no—
180C4—1421no—
181C4—1421no—
182C4#1455610511yescharacteristic
183C4#1455610611yescharacteristic
184C4#1455611411yescharacteristic
185C4#1455612711yescharacteristic
186C2—21no—
187C2—21no—
188C2#1798590311yescharacteristic
189C2#1798598011yescharacteristic
190C2#1798598211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#343×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#343D71
hypocenterC71#1998
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
96. C71#1998semidirect