Finite Group Databasebeta

← #22588985

Subgroups — #22588985

Order 9088.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#14556063C211yesmaximal, characteristic, complemented
2C2×#14556055C211yesmaximal, characteristic
3#17985995C211yesmaximal, characteristic
4#17985954C211yesmaximal, characteristic, complemented
5#17985760C211yesmaximal, characteristic, complemented
6#17985753C211yesmaximal, characteristic, complemented
7#408×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10#14556087C2211yescharacteristic
11C2×C4×Dic71C2211yescharacteristic
12#14556063—22no—
13#14556055—22no—
14#14556052C411yescharacteristic, complemented
15#14556052C411yescharacteristic, complemented
16#14556049C411yescharacteristic, complemented
17#14556049C411yescharacteristic, complemented
18#14556038—21no—
19C8×Dic71—21no—
20C2×#41×C71C2211yescharacteristic
21C2×M16×C71C2211yescharacteristic
22C22×C8×C71C2211yescharacteristic
23C22⋊C8×C71—21no—
24C22⋊C8×C71—21no—
25C22×Dic71—21no—
26#11765849—21no—
27#11765849D412yes—
28C2×C71⋊C8—21no—
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8C2×C411yescharacteristic
32C2×C71⋊C8C2×C411yescharacteristic
33C4⋊Dic71C2×C411yescharacteristic
34C4⋊Dic71C2×C411yescharacteristic
35C22⋊Dic71—21no—
36C4×Dic71—21no—
37C4×Dic71—21no—
38C4×Dic71—21no—
39#41×C71—21no—
40#41×C71—21no—
41#41×C71—21no—
42#41×C71—21no—
43C2×Q8×C71C2×C411yescharacteristic
44C2×D4×C71—21no—
45C2×D4×C71C2×C411yescharacteristic
46C22×C4×C71—21no—
47C22×C4×C71C2311yescharacteristic
48M16×C71—21no—
49M16×C71—21no—
50C2×C8×C71—21no—
51C2×C8×C71—21no—
52C2×C8×C71—21no—
53C2×C8×C71D411yescharacteristic
54C2×C8×C71D411yescharacteristic
55C23×C71—21no—
56C23×C71#4111yescharacteristic
57Q8×C71—21no—
58Q8×C71—21no—
59D4×C71—21no—
60D4×C71—21no—
61D4×C71—41no—
62D4×C71—41no—
63C2×C4×C71—21no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71C22×C411yescharacteristic
67C2×C4×C71C2×D411yescharacteristic
68C2×C4×C71C2×D411yescharacteristic
69C2×C4×C71#4111yescharacteristic
70C2×C4×C71#4111yescharacteristic
71C2×C4×C71#4111yescharacteristic
72C2×Dic71—22no—
73C2×Dic71—21no—
74C2×Dic71—21no—
75C2×Dic71—41no—
76C2×Dic71—41no—
77C8×C71—21no—
78C8×C71—21no—
79C8×C71—41no—
80C71⋊C8—21no—
81C71⋊C8—21no—
82C71⋊C8—22no—
83C22×C71—21no—
84C22×C71—21no—
85C22×C71—41no—
86C22×C71—41no—
87C22×C71—41no—
88C22×C71C4×D411yescharacteristic
89C22×C71#12411yescharacteristic
90C22×C71#12611yescharacteristic
91C4×C71—41no—
92C4×C71#11711yescharacteristic
93C4×C71C4×D411yescharacteristic
94C4×C71#12111yescharacteristic
95C4×C71#12311yescharacteristic
96Dic71—42no—
97Dic71—41no—
98Dic71—41no—
99C2×C71—21no—
100C2×C71—21no—
101C2×C71—81no—
102C2×C71#38811yescharacteristic
103C2×C71#44311yescharacteristic
104C2×C71#44411yescharacteristic
105#1929—711nomaximal, Sylow
106C71#192911yescharacteristic, complemented, Sylow
107C2×#108—711no—
108C2×#104—711no—
109#416—711no—
110#408D7111yescharacteristic
111#405—711no—
112#339—711no—
113#336—711no—
114C2×#41C2×D7111yescharacteristic
115C2×M16—711no—
116C2×M16C2×D7111yescharacteristic
117C22×C8—711no—
118C22×C8C2×D7111yescharacteristic
119#117—711no—
120C2×C42—711no—
121#108—1422no—
122#104—1422no—
123#103—711no—
124#103—711no—
125#102—711no—
126#102—711no—
127C22⋊C8—21no—
128C22⋊C8—21no—
129#97—1421no—
130C4×C8—1421no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8C4×D7111yescharacteristic
136C2×D4—21no—
137C2×D4C4×D7111yescharacteristic
138C22×C4—21no—
139C22×C4—1421no—
140C22×C4C22×D7111yescharacteristic
141M16—21no—
142M16—21no—
143M16—712no—
144M16—1421no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—711no—
149C2×C8—711no—
150C2×C8—1421no—
151C2×C8—1421no—
152C2×C8—1421no—
153C2×C8C22⋊D7111yescharacteristic
154C2×C8C22⋊D7111yescharacteristic
155C4⋊C4—711no—
156C4⋊C4—711no—
157C22⋊C4—1421no—
158C42—1421no—
159C42—1421no—
160C42—1421no—
161C23—21no—
162C23#1176586511yescharacteristic
163Q8—21no—
164Q8—21no—
165D4—21no—
166D4—21no—
167D4—41no—
168D4—41no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—2841no—
173C2×C4—2841no—
174C2×C4—1422no—
175C2×C4—1421no—
176C2×C4—1421no—
177C2×C4C2×C4×D7111yescharacteristic
178C2×C4D4×D7111yescharacteristic
179C2×C4C2×C22⋊D7111yescharacteristic
180C2×C4#1176586411yescharacteristic
181C2×C4#1176586411yescharacteristic
182C2×C4#1176586411yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—1421no—
187C8—1421no—
188C8—1422no—
189C22—21no—
190C22—21no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22C4×C22⋊D7111yescharacteristic
195C22#1455611411yescharacteristic
196C22#1455612111yescharacteristic
197C4—41no—
198C4—2842no—
199C4—2841no—
200C4—2841no—
201C4#1455608411yescharacteristic
202C4(C22⋊D71)⋊C411yescharacteristic
203C4#1455609911yescharacteristic
204C4#1455610911yescharacteristic
205C2—21no—
206C2—21no—
207C2—81no—
208C2#1798588711yescharacteristic
209C2#1798611411yescharacteristic
210C2#1798611911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#408×C71C2
socleC22×C71C4×D4
hypercenter#408D71
hypocenterC71#1929
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14556063C2semidirect
4. #17985954C2semidirect
5. #17985760C2semidirect
6. #17985753C2semidirect
14. #14556052C4semidirect
15. #14556052C4semidirect
16. #14556049C4semidirect
17. #14556049C4semidirect
106. C71#1929semidirect