Finite Group Databasebeta

← #22589513

Subgroups — #22589513

Order 9088.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#17986556C211yesmaximal, characteristic, complemented
2#17986015C211yesmaximal, characteristic
3C2×#14556056C211yesmaximal, characteristic
4#17985972C211yesmaximal, characteristic
5#17985770C211yesmaximal, characteristic, complemented
6#17985755C211yesmaximal, characteristic, complemented
7#339×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10#14556128—21no—
11#14556120—21no—
12#14556107—22no—
13C4×Dic142—22no—
14#14556087C2211yescharacteristic
15#14556087C2211yescharacteristic
16#14556056—21no—
17#14556056—21no—
18#14556054—22no—
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×Dic142—22no—
28C2×Dic142Q811yescharacteristic, complemented
29C2×D284Q811yescharacteristic, complemented
30C2×C22⋊D71—21no—
31C2×C4×D71—21no—
32#11765849—21no—
33#11765849—21no—
34C2×C71⋊C8—21no—
35C4⋊Dic71—22no—
36C4⋊Dic71—21no—
37C4⋊Dic71—21no—
38Dic71⋊C4—24no—
39C22⋊Dic71—21no—
40C22⋊Dic71D412yes—
41C4×Dic71—21no—
42C4×Dic71D412yes—
43C22×C4×C71—21no—
44C22×C4×C71C2311yescharacteristic
45M16×C71—21no—
46M16×C71—21no—
47C2×C8×C71—21no—
48C4⋊C4×C71—21no—
49C22⋊C4×C71—21no—
50C42×C71—21no—
51C42×C71—21no—
52C42×C71D411yescharacteristic
53C42×C71D411yescharacteristic
54C23×C71C2×D411yescharacteristic
55C22×D71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—21no—
58C2×C4×C71—42no—
59C2×C4×C71—41no—
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C2×C4×C71C2×Q811yescharacteristic
63C2×C4×C71#4111yescharacteristic
64C2×C4×C71#4111yescharacteristic
65C2×C4×C71#4111yescharacteristic
66C22⋊D71—41no—
67C22⋊D71—41no—
68C2×Dic71—22no—
69C2×Dic71—22no—
70C2×Dic71—21no—
71D284—21no—
72D284—21no—
73C4×D71—41no—
74C4×D71—41no—
75Dic142—21no—
76Dic142—21no—
77Dic142—44no—
78C8×C71—41no—
79C71⋊C8—41no—
80C22×C71—41no—
81C22×C71#12011yescharacteristic
82C22×C71C22⋊Q811yescharacteristic
83C22×C71#12411yescharacteristic
84C2×D71—41no—
85C2×D71—81no—
86C4×C71—22no—
87C4×C71—41no—
88C4×C71—81no—
89C4×C71C22⋊Q811yescharacteristic
90C4×C71C22⋊Q811yescharacteristic
91C4×C71#12411yescharacteristic
92C4×C71#12411yescharacteristic
93Dic71—42no—
94Dic71—42no—
95Dic71—41no—
96C2×C71—21no—
97C2×C71—21no—
98C2×C71—21no—
99C2×C71#39311yescharacteristic
100D71—81no—
101#2031—711nomaximal, Sylow
102C71#203111yescharacteristic, complemented, Sylow
103#533—711no—
104#421—711no—
105C2×#104—711no—
106#410—711no—
107#344—711no—
108#339D7111yescharacteristic, complemented
109H(3,ℤ/4)—711no—
110C2×#41—711no—
111C2×M16—711no—
112C2×M16C2×D7111yescharacteristic
113C4⋊Q8—1421no—
114#125—1421no—
115C22⋊Q8—1422no—
116C4×Q8—1422no—
117#117—711no—
118#117—711no—
119#117C2×D7111yescharacteristic
120C2×C42C2×D7111yescharacteristic
121#104—1422no—
122#104—1421no—
123#104—1421no—
124#99—1422no—
125#41—1421no—
126#41—1421no—
127#41—1421no—
128#41—1421no—
129C2×Q8—711no—
130C2×Q8—1422no—
131C2×D4—711no—
132C2×D4—1421no—
133C22×C4—21no—
134C22×C4—1421no—
135C22×C4C22×D7111yescharacteristic
136M16—21no—
137M16—21no—
138M16—1421no—
139M16—1421no—
140C2×C8—21no—
141C2×C8—1421no—
142C4⋊C4—21no—
143C4⋊C4—1424no—
144C4⋊C4—1422no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C22⋊C4—21no—
148C22⋊C4—712no—
149C22⋊C4—1421no—
150C42—21no—
151C42—21no—
152C42—712no—
153C42—1421no—
154C42D28411yescharacteristic
155C42D28411yescharacteristic
156C23—1421no—
157C23D4×D7111yescharacteristic
158Q8—2844no—
159Q8—1421no—
160Q8—1421no—
161D4—2841no—
162D4—2841no—
163D4—1421no—
164D4—1421no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—2841no—
170C2×C4—2841no—
171C2×C4—1422no—
172C2×C4—1422no—
173C2×C4—1421no—
174C2×C4D4×D7111yescharacteristic
175C2×C4C2×D28411yescharacteristic
176C2×C4Q8×D7111yescharacteristic
177C2×C4#1176586411yescharacteristic
178C2×C4#1176586511yescharacteristic
179C2×C4#1176586511yescharacteristic
180C8—41no—
181C8—2841no—
182C22—41no—
183C22—2841no—
184C22—5681no—
185C22#1455609811yescharacteristic
186C22#1455610611yescharacteristic
187C22#1455611411yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—2842no—
192C4—2842no—
193C4—2841no—
194C4#1455610611yescharacteristic
195C4#1455610811yescharacteristic
196C4#1455611411yescharacteristic
197C4#1455611611yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—5681no—
202C2#1798591211yescharacteristic
subgroupG/H
centerC4#14556114
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#339×C71C2
socleC2×C71#393
hypercenter#339D71
hypocenterC71#2031
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #17986556C2semidirect
5. #17985770C2semidirect
6. #17985755C2semidirect
7. #339×C71C2semidirect
28. C2×Dic142Q8semidirect
29. C2×D284Q8semidirect
102. C71#2031semidirect
108. #339D71semidirect