Finite Group Databasebeta

← #22587364

Subgroups — #22587364

Order 9088.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#17986334C212yesmaximal, complemented
3#17985735C212yesmaximal, complemented
4#17985723C211yesmaximal, characteristic
5#399×C71C211yesmaximal, characteristic
6#14556107—21no—
7#14556107C2212yes—
8#14556105—22no—
9#14556105—22no—
10C2×C22⋊Dic71—21no—
11#14556061—22no—
12#14556051—22no—
13C22⋊(C71⋊C8)C2212yes—
14C2×C4⋊C4×C71—21no—
15C2×C4⋊C4×C71C2211yescharacteristic
16C2×C22⋊C4×C71—21no—
17C2×C22⋊C4×C71C2211yescharacteristic
18#95×C71C2211yescharacteristic
19C2×Dic142—21no—
20C2×Dic142D412yes—
21C22×Dic71—21no—
22C22×Dic71—21no—
23C2×C71⋊C8—22no—
24C4⋊Dic71—21no—
25C4⋊Dic71D412yes—
26Dic71⋊C4—22no—
27Dic71⋊C4—22no—
28C22⋊Dic71—22no—
29C22⋊Dic71—22no—
30C24×C71D411yescharacteristic
31C22×C4×C71—21no—
32C22×C4×C71—21no—
33C22×C4×C71D411yescharacteristic
34C22×C4×C71C2311yescharacteristic
35C4⋊C4×C71—22no—
36C4⋊C4×C71—42no—
37C22⋊C4×C71—22no—
38C22⋊C4×C71—42no—
39C23×C71—21no—
40C23×C71—21no—
41C23×C71—41no—
42C23×C71—41no—
43C23×C71Q1612yes—
44C23×C71C2×D411yescharacteristic
45C2×C4×C71—22no—
46C2×C4×C71—21no—
47C2×C4×C71—41no—
48C2×C4×C71—41no—
49C2×C4×C71—41no—
50C2×C4×C71—41no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71—41no—
54C2×C4×C71C2×D412yes—
55C2×Dic71—22no—
56C2×Dic71—22no—
57C2×Dic71—81no—
58C2×Dic71—81no—
59Dic142—42no—
60Dic142—81no—
61C71⋊C8—42no—
62C22×C71—21no—
63C22×C71—21no—
64C22×C71—22no—
65C22×C71—42no—
66C22×C71—41no—
67C22×C71—41no—
68C22×C71—81no—
69C22×C71#12011yescharacteristic
70C22×C71C2×Q1611yescharacteristic
71C22×C71#13711yescharacteristic
72C4×C71—22no—
73C4×C71—42no—
74C4×C71—41no—
75C4×C71—81no—
76Dic71—42no—
77Dic71—42no—
78C2×C71—21no—
79C2×C71—21no—
80C2×C71—42no—
81C2×C71#45111yescharacteristic
82C2×C71#45311yescharacteristic
83C2×C71#45811yescharacteristic
84#1614—711nomaximal, Sylow
85C71#161411yescharacteristic, complemented, Sylow
86#543—711no—
87#484—712no—
88#399D7111yescharacteristic
89#328—712no—
90#323—711no—
91C22⋊Q8—712no—
92C22⋊Q8—1422no—
93C22⋊Q8—1422no—
94C22⋊Q8—1421no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D7111yescharacteristic
97C2×C22⋊C4—21no—
98C2×C22⋊C4—1421no—
99C2×C22⋊C4C2×D7111yescharacteristic
100#107—1422no—
101#103—1422no—
102C22⋊C8—712no—
103#95C2×D7111yescharacteristic
104C24C22⋊D7111yescharacteristic
105C2×Q8—712no—
106C2×Q8—1421no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—1421no—
110C22×C4—1421no—
111C22×C4C22⋊D7111yescharacteristic
112C22×C4C22×D7111yescharacteristic
113C2×C8—1422no—
114C4⋊C4—22no—
115C4⋊C4—42no—
116C4⋊C4—712no—
117C4⋊C4—1422no—
118C4⋊C4—1421no—
119C4⋊C4—1422no—
120C22⋊C4—22no—
121C22⋊C4—42no—
122C22⋊C4—1422no—
123C22⋊C4—1422no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1176585512yes—
129C23C2×C22⋊D7111yescharacteristic
130Q8—2842no—
131Q8—5681no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—5681no—
142C2×C4—5681no—
143C2×C4—1422no—
144C2×C4—1422no—
145C2×C4D4×D7112yes—
146C8—2842no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1455609611yescharacteristic
155C22C2×#1176585511yescharacteristic
156C22#1455615811yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—81no—
161C4—2842no—
162C4—2842no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1798615411yescharacteristic
167C2#1798616611yescharacteristic
168C2#1798618811yescharacteristic
subgroupG/H
centerC22#14556096
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#399×C71C2
socleC22×C71#120
hypercenter#399D71
hypocenterC71#1614
LCSG ▷ C22×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #17986334C2semidirect
3. #17985735C2semidirect
85. C71#1614semidirect