Finite Group Databasebeta

← #22589693

Subgroups — #22589693

Order 9088.

314 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986625C211yesmaximal, characteristic
2#17985872C212yesmaximal
3#17985766C211yesmaximal, characteristic
4#17985765C212yesmaximal
5#385×C71C211yesmaximal, characteristic
6#14556107—21no—
7#14556107—21no—
8#14556105—22no—
9#14556105—22no—
10C2×Dic71⋊C4—22no—
11C2×C22⋊Dic71C2212yes—
12C2×C22⋊Dic71C2212yes—
13C71⋊#95—22no—
14C23×C4×C71C2211yescharacteristic
15C2×C4⋊C4×C71—21no—
16C2×C22⋊C4×C71C2211yescharacteristic
17C2×C22⋊C4×C71C2211yescharacteristic
18#95×C71—21no—
19C2×Dic142—21no—
20C2×Dic142—21no—
21C22×Dic71—22no—
22C22×Dic71D412yes—
23C22×Dic71D412yes—
24C4⋊Dic71—21no—
25C4⋊Dic71—21no—
26Dic71⋊C4—22no—
27Dic71⋊C4—22no—
28Dic71⋊C4—44no—
29C22⋊Dic71—22no—
30C22⋊Dic71—22no—
31C22⋊Dic71—22no—
32C22⋊Dic71Q814yescomplemented
33C24×C71C2311yescharacteristic
34C22×C4×C71—21no—
35C22×C4×C71—21no—
36C22×C4×C71—22no—
37C22×C4×C71—42no—
38C22×C4×C71D411yescharacteristic
39C22×C4×C71D411yescharacteristic
40C4⋊C4×C71—42no—
41C22⋊C4×C71—22no—
42C22⋊C4×C71—21no—
43C22⋊C4×C71Q812yescomplemented
44C23×C71—41no—
45C23×C71—41no—
46C23×C71C2×D412yes—
47C23×C71C2×D411yescharacteristic
48C23×C71C2×Q812yes—
49C23×C71C2×Q811yescharacteristic
50C23×C71#4111yescharacteristic
51C2×C4×C71—22no—
52C2×C4×C71—24no—
53C2×C4×C71—21no—
54C2×C4×C71—21no—
55C2×C4×C71—22no—
56C2×C4×C71—41no—
57C2×C4×C71—41no—
58C2×C4×C71—42no—
59C2×C4×C71—41no—
60C2×C4×C71—41no—
61C2×C4×C71—41no—
62C2×C4×C71—41no—
63C2×Dic71—22no—
64C2×Dic71—22no—
65C2×Dic71—24no—
66C2×Dic71—42no—
67C2×Dic71—42no—
68C2×Dic71—42no—
69C2×Dic71—42no—
70Dic142—81no—
71Dic142—81no—
72C22×C71—22no—
73C22×C71—21no—
74C22×C71—22no—
75C22×C71—21no—
76C22×C71—42no—
77C22×C71—41no—
78C22×C71—41no—
79C22×C71#12011yescharacteristic
80C22×C71C22⋊Q812yes—
81C22×C71C22⋊Q811yescharacteristic
82C22×C71C4⋊Q811yescharacteristic
83C22×C71C4⋊Q812yes—
84C4×C71—42no—
85C4×C71—41no—
86C4×C71—42no—
87C4×C71—41no—
88Dic71—44no—
89Dic71—42no—
90Dic71—42no—
91C2×C71—22no—
92C2×C71—21no—
93C2×C71—21no—
94C2×C71—22no—
95C2×C71#39511yescharacteristic
96C2×C71B(4,𝔽2)11yescharacteristic
97C2×C71#45811yescharacteristic
98#2062—711nomaximal, Sylow
99C71#206211yescharacteristic, complemented, Sylow
100#543—711no—
101#385—712no—
102#385D7111yescharacteristic
103#342—712no—
104#342—711no—
105C23×C4C2×D7111yescharacteristic
106C22⋊Q8—1422no—
107C22⋊Q8—1422no—
108C22⋊Q8—1421no—
109C22⋊Q8—1421no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—1422no—
112C2×C22⋊C4—712no—
113C2×C22⋊C4—712no—
114C2×C22⋊C4C2×D7111yescharacteristic
115C2×C22⋊C4C2×D7111yescharacteristic
116#95—21no—
117#95—1422no—
118C24C22×D7111yescharacteristic
119C2×Q8—1421no—
120C2×Q8—1421no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—42no—
125C22×C4—712no—
126C22×C4—712no—
127C22×C4—1422no—
128C22×C4C22⋊D7111yescharacteristic
129C22×C4C22⋊D7111yescharacteristic
130C4⋊C4—42no—
131C4⋊C4—2844no—
132C4⋊C4—1422no—
133C4⋊C4—1422no—
134C4⋊C4—1421no—
135C4⋊C4—1421no—
136C22⋊C4—22no—
137C22⋊C4—21no—
138C22⋊C4—714no—
139C22⋊C4—1422no—
140C22⋊C4—1422no—
141C22⋊C4—1422no—
142C22⋊C4Dic14212yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D7112yes—
146C23C2×C22⋊D7111yescharacteristic
147C23Q8×D7112yes—
148C23C2×Dic14211yescharacteristic
149C23#1176586511yescharacteristic
150Q8—5681no—
151Q8—5681no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—2842no—
165C2×C4—2842no—
166C2×C4—2842no—
167C2×C4—2842no—
168C2×C4—1422no—
169C2×C4—1422no—
170C2×C4—1424no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22#1455609611yescharacteristic
179C22#1455610612yes—
180C22#1455610711yescharacteristic
181C22#1455612611yescharacteristic
182C22#1455612712yes—
183C4—42no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—2844no—
188C4—2842no—
189C4—2842no—
190C2—21no—
191C2—22no—
192C2—21no—
193C2—22no—
194C2#1798591911yescharacteristic
195C2#1798618511yescharacteristic
196C2#1798618811yescharacteristic
subgroupG/H
centerC22#14556096
commutatorC24×C71C23
FrattiniC24C22×D71
Fitting#385×C71C2
socleC22×C71#120
hypercenter#385D71
hypocenterC71#2062
LCSG ▷ C24×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
32. C22⋊Dic71Q8semidirect
43. C22⋊C4×C71Q8semidirect
99. C71#2062semidirect
142. C22⋊C4Dic142semidirect