Finite Group Databasebeta

← #22588443

Subgroups — #22588443

Order 9088.

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

normal subgroups only

This group has 262 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
1C4×#11765865C211yesmaximal, characteristic
2#17985981C211yesmaximal, characteristic
3#17985972C211yesmaximal, characteristic
4#17985759C211yesmaximal, characteristic, complemented
5#17985756C211yesmaximal, characteristic, complemented
6#17985755C211yesmaximal, characteristic, complemented
7#339×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C4×Dic142—21no—
11C4×D284—21no—
12C4×C22⋊D71—22no—
13#14556087C2211yescharacteristic
14#14556087C2211yescharacteristic
15#14556085C412yescomplemented
16C42×D71C412yescomplemented
17#14556046—21no—
18#14556044—21no—
19#14556042—22no—
20C2×M16×C71C2211yescharacteristic
21#117×C71C2211yescharacteristic
22C2×C42×C71C2211yescharacteristic
23#11765865—21no—
24#11765865—21no—
25#11765865—21no—
26#11765865—21no—
27C2×Dic142D411yescharacteristic
28C2×D284D411yescharacteristic
29C2×C22⋊D71D412yes—
30C2×C4×D71—22no—
31C2×C4×D71C2×C412yes—
32#11765849—21no—
33#11765849—21no—
34C2×C71⋊C8—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37Dic71⋊C4—22no—
38C22⋊Dic71—21no—
39C22⋊Dic71—21no—
40(C2×D71)⋊C4—22no—
41C4×Dic71—22no—
42C4×Dic71—21no—
43C4×Dic71C2×C412yes—
44C22×C4×C71—21no—
45C22×C4×C71C2311yescharacteristic
46M16×C71—21no—
47M16×C71—21no—
48C2×C8×C71—21no—
49C4⋊C4×C71—21no—
50C22⋊C4×C71—21no—
51C42×C71—21no—
52C42×C71—21no—
53C42×C71C2×C411yescharacteristic
54C42×C71C2×C411yescharacteristic
55C23×C71C2×D411yescharacteristic
56C22×D71C22⋊C412yes—
57C2×C4×C71—21no—
58C2×C4×C71—21no—
59C2×C4×C71—42no—
60C2×C4×C71—41no—
61C2×C4×C71C22×C411yescharacteristic
62C2×C4×C71C2×D411yescharacteristic
63C2×C4×C71#4111yescharacteristic
64C2×C4×C71#4111yescharacteristic
65C2×C4×C71#4111yescharacteristic
66C2×C4×C71#4111yescharacteristic
67C22⋊D71—22no—
68C22⋊D71—22no—
69C2×Dic71—22no—
70C2×Dic71—41no—
71C2×Dic71C22⋊C412yes—
72D284—21no—
73D284—21no—
74C4×D71—22no—
75C4×D71—22no—
76C4×D71—44no—
77Dic142—21no—
78Dic142—21no—
79C8×C71—41no—
80C71⋊C8—41no—
81C22×C71—41no—
82C22×C71C2×C22⋊C411yescharacteristic
83C22×C71#12311yescharacteristic
84C22×C71#12311yescharacteristic
85C2×D71—22no—
86C2×D71—42no—
87C4×C71—22no—
88C4×C71—41no—
89C4×C71—81no—
90C4×C71#11711yescharacteristic
91C4×C71#11711yescharacteristic
92C4×C71#12311yescharacteristic
93C4×C71#12311yescharacteristic
94Dic71—22no—
95Dic71—42no—
96Dic71—81no—
97C2×C71—21no—
98C2×C71—21no—
99C2×C71—21no—
100C2×C71#38111yescharacteristic
101D71—42no—
102#1827—711nomaximal, Sylow
103C71#182711yescharacteristic, complemented, Sylow
104C4×#41—711no—
105#413—711no—
106#410—711no—
107#339—711no—
108#339D7111yescharacteristic, complemented
109H(3,ℤ/4)—711no—
110H(3,ℤ/4)—711no—
111C2×#41—711no—
112C2×M16—711no—
113C2×M16C2×D7111yescharacteristic
114C4×Q8—1421no—
115C4×D4—1421no—
116C4×D4—1422no—
117#117—711no—
118#117—712no—
119#117—711no—
120#117C2×D7111yescharacteristic
121C2×C42—712no—
122C2×C42C2×D7111yescharacteristic
123#101—1421no—
124#100—1421no—
125#99—1422no—
126#41—1421no—
127#41—1421no—
128#41—1421no—
129#41—1421no—
130C2×Q8—711no—
131C2×D4—712no—
132C2×D4—711no—
133C22×C4—21no—
134C22×C4—712no—
135C22×C4—1422no—
136C22×C4C22×D7111yescharacteristic
137M16—21no—
138M16—21no—
139M16—1421no—
140M16—1421no—
141C2×C8—21no—
142C2×C8—1421no—
143C4⋊C4—21no—
144C4⋊C4—1422no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C22⋊C4—21no—
148C22⋊C4—1422no—
149C22⋊C4—1421no—
150C22⋊C4—1421no—
151C42—21no—
152C42—21no—
153C42—712no—
154C42—1422no—
155C42—1421no—
156C42C4×D7111yescharacteristic
157C42C4×D7111yescharacteristic
158C23—712no—
159C23D4×D7111yescharacteristic
160Q8—1421no—
161Q8—1421no—
162D4—1422no—
163D4—1422no—
164D4—1421no—
165D4—1421no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—2844no—
171C2×C4—2841no—
172C2×C4—712no—
173C2×C4—1422no—
174C2×C4—1422no—
175C2×C4—1422no—
176C2×C4C2×C4×D7111yescharacteristic
177C2×C4D4×D7111yescharacteristic
178C2×C4#1176586411yescharacteristic
179C2×C4#1176586511yescharacteristic
180C2×C4#1176586511yescharacteristic
181C2×C4#1176586611yescharacteristic
182C8—41no—
183C8—2841no—
184C22—41no—
185C22—2842no—
186C22—1422no—
187C22C22⋊C4×D7111yescharacteristic
188C22#1455611011yescharacteristic
189C22#1455611311yescharacteristic
190C4—22no—
191C4—41no—
192C4—81no—
193C4—2842no—
194C4—5681no—
195C4—1422no—
196C4#1455608511yescharacteristic
197C4#1455608611yescharacteristic
198C4#1455611011yescharacteristic
199C4#1455611311yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—2842no—
204C2#1798586111yescharacteristic
subgroupG/H
centerC4#14556086
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#339×C71C2
socleC2×C71#381
hypercenter#339D71
hypocenterC71#1827
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #17985759C2semidirect
5. #17985756C2semidirect
6. #17985755C2semidirect
7. #339×C71C2semidirect
15. #14556085C4semidirect
16. C42×D71C4semidirect
103. C71#1827semidirect
108. #339D71semidirect