Finite Group Databasebeta

← #22589515

Subgroups — #22589515

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#17986552C211yesmaximal, characteristic, complemented
2#17986015C211yesmaximal, characteristic
3C2×#14556054C211yesmaximal, characteristic
4#17985972C211yesmaximal, characteristic
5#17985760C211yesmaximal, characteristic, complemented
6#17985756C211yesmaximal, characteristic, complemented
7#344×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9#14556127—21no—
10#14556119—21no—
11#14556105—22no—
12C4×Dic142—22no—
13#14556087C2211yescharacteristic
14#14556087C2211yescharacteristic
15C2×C4×Dic71C2211yescharacteristic
16#14556054—21no—
17#14556054—21no—
18#14556054—22no—
19#14556042—22no—
20C2×M16×C71C2211yescharacteristic
21C2×M16×C71C2211yescharacteristic
22#117×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—
31C22×Dic71—21no—
32C2×C4×D71—21no—
33C4⋊Dic71—22no—
34C4⋊Dic71—21no—
35C4⋊Dic71—21no—
36Dic71⋊C4—22no—
37Dic71⋊C4—22no—
38C22⋊Dic71—21no—
39C22⋊Dic71—21no—
40C4×Dic71—21no—
41C4×Dic71—21no—
42C4×Dic71D411yescharacteristic
43C4×Dic71D411yescharacteristic
44C4×Dic71D412yes—
45C22×C4×C71C2311yescharacteristic
46M16×C71—21no—
47M16×C71—21no—
48M16×C71—21no—
49M16×C71—21no—
50C2×C8×C71—21no—
51C2×C8×C71—21no—
52C4⋊C4×C71—21no—
53C22⋊C4×C71D412yes—
54C42×C71—21no—
55C23×C71C2×D411yescharacteristic
56C22×D71—21no—
57C2×C4×C71—22no—
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×Q811yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×C4×C71#4111yescharacteristic
63C2×C4×C71#4111yescharacteristic
64C22⋊D71—41no—
65C22⋊D71—41no—
66C2×Dic71—21no—
67C2×Dic71—21no—
68C2×Dic71—22no—
69C2×Dic71—21no—
70C2×Dic71—42no—
71C2×Dic71—41no—
72D284—21no—
73D284—21no—
74C4×D71—41no—
75C4×D71—41no—
76Dic142—21no—
77Dic142—21no—
78Dic142—44no—
79C8×C71—41no—
80C8×C71—41no—
81C22×C71—41no—
82C22×C71#12011yescharacteristic
83C22×C71C22⋊Q811yescharacteristic
84C22×C71#12411yescharacteristic
85C2×D71—41no—
86C2×D71—81no—
87C4×C71—42no—
88C4×C71C22⋊Q811yescharacteristic
89C4×C71C22⋊Q811yescharacteristic
90C4×C71#12411yescharacteristic
91C4×C71#12411yescharacteristic
92Dic71—22no—
93Dic71—42no—
94Dic71—41no—
95Dic71—41no—
96Dic71—81no—
97C2×C71—21no—
98C2×C71—21no—
99C2×C71—21no—
100C2×C71#39311yescharacteristic
101D71—81no—
102#2031—711nomaximal, Sylow
103C71#203111yescharacteristic, complemented, Sylow
104#533—711no—
105#421—711no—
106C2×#104—711no—
107#410—711no—
108#344D7111yescharacteristic, complemented
109#339—711no—
110H(3,ℤ/4)—711no—
111C2×#41—711no—
112C2×M16C2×D7111yescharacteristic
113C2×M16C2×D7111yescharacteristic
114C4⋊Q8—1421no—
115#125—1421no—
116C22⋊Q8—1422no—
117C4×Q8—1422no—
118#117—711no—
119#117—711no—
120#117C2×D7111yescharacteristic
121C2×C42—711no—
122#104—1421no—
123#104—1421no—
124#104—1422no—
125#99—1422no—
126#41—1421no—
127#41—1421no—
128#41—1421no—
129#41—1421no—
130C2×Q8—711no—
131C2×Q8—1422no—
132C2×D4—711no—
133C2×D4—1421no—
134C22×C4—1421no—
135C22×C4—1421no—
136C22×C4C22×D7111yescharacteristic
137M16—21no—
138M16—21no—
139M16—21no—
140M16—21no—
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—1422no—
145C4⋊C4—1422no—
146C4⋊C4—1422no—
147C4⋊C4—1421no—
148C4⋊C4—1421no—
149C22⋊C4—1421no—
150C22⋊C4—1421no—
151C22⋊C4D28412yes—
152C42—21no—
153C42—711no—
154C42—711no—
155C42—712no—
156C42—1421no—
157C42—1421no—
158C23—1421no—
159C23C2×D28411yescharacteristic
160Q8—2844no—
161Q8—1421no—
162Q8—1421no—
163D4—2841no—
164D4—2841no—
165D4—1421no—
166D4—1421no—
167C2×C4—22no—
168C2×C4—2842no—
169C2×C4—2841no—
170C2×C4—2841no—
171C2×C4—2841no—
172C2×C4—1421no—
173C2×C4—1422no—
174C2×C4—1421no—
175C2×C4—1421no—
176C2×C4D4×D7111yescharacteristic
177C2×C4D4×D7111yescharacteristic
178C2×C4Q8×D7111yescharacteristic
179C2×C4#1176586411yescharacteristic
180C2×C4#1176586511yescharacteristic
181C2×C4#1176586511yescharacteristic
182C8—41no—
183C8—41no—
184C22—41no—
185C22—2841no—
186C22—5681no—
187C22#1455609811yescharacteristic
188C22#1455610811yescharacteristic
189C22#1455611611yescharacteristic
190C4—42no—
191C4—2841no—
192C4—2842no—
193C4—2841no—
194C4—5681no—
195C4—1422no—
196C4#1455610611yescharacteristic
197C4#1455610611yescharacteristic
198C4#1455611411yescharacteristic
199C4#1455611411yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—5681no—
204C2#1798591211yescharacteristic
subgroupG/H
centerC4#14556114
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#344×C71C2
socleC2×C71#393
hypercenter#344D71
hypocenterC71#2031
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #17986552C2semidirect
5. #17985760C2semidirect
6. #17985756C2semidirect
7. #344×C71C2semidirect
28. C2×Dic142Q8semidirect
29. C2×D284Q8semidirect
103. C71#2031semidirect
108. #344D71semidirect