Finite Group Databasebeta

← #22588577

Subgroups — #22588577

Order 9088.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#17986765C211yesmaximal, characteristic
2#17986022C211yesmaximal, characteristic, complemented
3#17986015C211yesmaximal, characteristic
4C2×#14556054C211yesmaximal, characteristic
5#17985771C211yesmaximal, characteristic, complemented
6#17985760C211yesmaximal, characteristic, complemented
7#430×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9#14556136—22no—
10#14556134—22no—
11C2×#11765849C2211yescharacteristic
12M16×D71—22no—
13#14556087C2211yescharacteristic
14C2×C4×Dic71C2211yescharacteristic
15Dic71⋊C8—22no—
16#14556054—22no—
17#14556054C412yescomplemented
18#14556054C412yescomplemented
19C2×M16×C71C2211yescharacteristic
20C2×M16×C71C2211yescharacteristic
21C2×M16×C71C2211yescharacteristic
22#108×C71—22no—
23#11765865—21no—
24#11765865—21no—
25#11765865C2×C412yes—
26#11765865D412yes—
27C2×Dic142Q811yescharacteristic
28C2×D284Q811yescharacteristic
29C2×C22⋊D71—21no—
30C22×Dic71—21no—
31C2×C4×D71—21no—
32#11765849—21no—
33#11765849—21no—
34#11765848—24no—
35C2×C71⋊C8D412yes—
36C8×D71—24no—
37C4⋊Dic71—21no—
38C22⋊Dic71—21no—
39C4×Dic71—21no—
40C4×Dic71—21no—
41C4×Dic71C2×C411yescharacteristic
42C4×Dic71C2×C411yescharacteristic
43C22×C4×C71C2311yescharacteristic
44M16×C71—21no—
45M16×C71—21no—
46M16×C71—21no—
47M16×C71—21no—
48M16×C71C2×C412yes—
49M16×C71D412yes—
50C2×C8×C71—21no—
51C2×C8×C71—21no—
52C2×C8×C71—21no—
53C23×C71#4111yescharacteristic
54C22×D71—21no—
55C2×C4×C71C22×C411yescharacteristic
56C2×C4×C71C2×D411yescharacteristic
57C2×C4×C71C2×D411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×Q811yescharacteristic
60C2×C4×C71#4111yescharacteristic
61C22⋊D71—22no—
62C22⋊D71—22no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—21no—
66C2×Dic71—42no—
67C2×Dic71—41no—
68D284—21no—
69D284C4⋊C412yes—
70C4×D71—22no—
71C4×D71—22no—
72Dic142—21no—
73Dic142C4⋊C412yes—
74C8×C71—22no—
75C8×C71—22no—
76C8×C71—41no—
77C71⋊C8—22no—
78C22×C71—41no—
79C22×C71C4×D411yescharacteristic
80C22×C71C22⋊Q811yescharacteristic
81C22×C71#12311yescharacteristic
82C2×D71—22no—
83C2×D71—81no—
84C4×C71C2×C4⋊C411yescharacteristic
85C4×C71C4×D411yescharacteristic
86C4×C71#12011yescharacteristic
87C4×C71C22⋊Q811yescharacteristic
88Dic71—22no—
89Dic71—22no—
90Dic71—41no—
91Dic71—81no—
92C2×C71—21no—
93C2×C71—21no—
94C2×C71—21no—
95C2×C71#38511yescharacteristic
96D71—42no—
97#1861—711nomaximal, Sylow
98C71#186111yescharacteristic, complemented, Sylow
99#568—711no—
100#430D7111yescharacteristic, complemented
101#423—711no—
102#421—711no—
103C2×#104—711no—
104#344—711no—
105#339—711no—
106C2×#41—711no—
107#131—1422no—
108#131—1422no—
109C2×M16—711no—
110C2×M16—1422no—
111C2×M16C2×D7111yescharacteristic
112C2×M16C2×D7111yescharacteristic
113C2×M16C2×D7111yescharacteristic
114#117—711no—
115C2×C42—711no—
116#108—22no—
117C4⋊C8—1422no—
118#104—712no—
119#104—712no—
120#104—1422no—
121#41—712no—
122#41—712no—
123#41—1421no—
124#41—1421no—
125C2×Q8—711no—
126C2×D4—711no—
127C2×D4—1421no—
128C22×C4—1421no—
129C22×C4—1421no—
130C22×C4C22×D7111yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—1424no—
136M16—1421no—
137M16—1421no—
138M16C4×D7112yes—
139M16C22⋊D7112yes—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—712no—
144C2×C8—1424no—
145C4⋊C4—1421no—
146C22⋊C4—1421no—
147C42—711no—
148C42—711no—
149C42—1421no—
150C42—1421no—
151C23—1421no—
152C23#1176586611yescharacteristic
153Q8—712no—
154Q8—1421no—
155D4—712no—
156D4—1422no—
157D4—1422no—
158D4—1421no—
159C2×C4—2842no—
160C2×C4—2841no—
161C2×C4—1421no—
162C2×C4—1421no—
163C2×C4—1421no—
164C2×C4—1422no—
165C2×C4—1422no—
166C2×C4C2×C4×D7111yescharacteristic
167C2×C4D4×D7111yescharacteristic
168C2×C4D4×D7111yescharacteristic
169C2×C4C2×C22⋊D7111yescharacteristic
170C2×C4Q8×D7111yescharacteristic
171C2×C4#1176586511yescharacteristic
172C8—22no—
173C8—22no—
174C8—41no—
175C8—1422no—
176C22—41no—
177C22—5681no—
178C22—1422no—
179C22#1455609011yescharacteristic
180C22#1455610411yescharacteristic
181C22#1455611311yescharacteristic
182C4—2841no—
183C4—5681no—
184C4—1422no—
185C4—1422no—
186C4C4⋊C4×D7111yescharacteristic
187C4C4×C22⋊D7111yescharacteristic
188C4#1455609611yescharacteristic
189C4#1455610611yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—2842no—
194C2#1798587011yescharacteristic
subgroupG/H
centerC4#14556096
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#430×C71C2
socleC2×C71#385
hypercenter#430D71
hypocenterC71#1861
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #17986022C2semidirect
5. #17985771C2semidirect
6. #17985760C2semidirect
7. #430×C71C2semidirect
17. #14556054C4semidirect
18. #14556054C4semidirect
98. C71#1861semidirect
100. #430D71semidirect