Finite Group Databasebeta

← #22587414

Subgroups — #22587414

Order 9088.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#17986706C211yesmaximal, characteristic, complemented
2#17986372C211yesmaximal, characteristic, complemented
3#17986200C211yesmaximal, characteristic, complemented
4#17986194C211yesmaximal, characteristic
5#17985747C211yesmaximal, characteristic, complemented
6#17985731C211yesmaximal, characteristic, complemented
7D4⋊C8×C71C211yesmaximal, characteristic, complemented
8C2×#11765854—22no—
9C2×#11765854—21no—
10C2×#11765850—21no—
11#14556128C2211yescharacteristic
12#14556125C2211yescharacteristic
13#14556119—21no—
14#14556107—21no—
15#14556105—22no—
16C4×Dic142C2211yescharacteristic
17D4×Dic71—21no—
18C2×C4⋊Dic71—21no—
19C4⋊(C71⋊C8)C2211yescharacteristic
20#14556050—21no—
21#14556048—21no—
22C4×D4×C71C2211yescharacteristic
23C4⋊C8×C71C2211yescharacteristic
24C4×C8×C71C2211yescharacteristic
25C2×Dic142D411yescharacteristic
26C2×Dic142D412yes—
27C2×D284—21no—
28C2×D284—21no—
29C2×D284—21no—
30C22×Dic71—22no—
31#11765854—44no—
32#11765854—42no—
33#11765850—42no—
34C2×C71⋊C8—21no—
35C4⋊Dic71—22no—
36C4⋊Dic71—21no—
37C4⋊Dic71—21no—
38C4⋊Dic71D411yescharacteristic
39Dic71⋊C4—22no—
40Dic71⋊C4—21no—
41C22⋊Dic71—22no—
42C4×Dic71—21no—
43C2×D4×C71D411yescharacteristic
44C22×C4×C71—21no—
45C2×C8×C71—21no—
46C2×C8×C71—21no—
47C4⋊C4×C71D411yescharacteristic
48C22⋊C4×C71—21no—
49C42×C71C2311yescharacteristic
50C23×C71—21no—
51C22×D71—41no—
52D4×C71—21no—
53D4×C71SD1612yescomplemented
54C2×C4×C71—21no—
55C2×C4×C71—41no—
56C2×C4×C71—41no—
57C2×C4×C71C2×D411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×Dic71—21no—
61C2×Dic71—21no—
62C2×Dic71—22no—
63C2×Dic71—82no—
64D284—42no—
65D284—41no—
66D284—41no—
67D284—41no—
68D284—41no—
69Dic142—21no—
70Dic142—21no—
71Dic142—42no—
72C8×C71—22no—
73C8×C71—41no—
74C71⋊C8—41no—
75C22×C71—22no—
76C22×C71—41no—
77C22×C71—41no—
78C22×C71#12011yescharacteristic
79C2×D71—81no—
80C2×D71—81no—
81C2×D71—81no—
82C4×C71—21no—
83C4×C71—41no—
84C4×C71C2×SD1611yescharacteristic
85C4×C71#13511yescharacteristic
86C4×C71AGL(1,ℤ/8)11yescharacteristic
87C4×C71#13711yescharacteristic
88Dic71—41no—
89Dic71—42no—
90Dic71—41no—
91C2×C71—42no—
92C2×C71#44811yescharacteristic
93C2×C71#44911yescharacteristic
94C2×C71#45311yescharacteristic
95D71—161no—
96#1622—711nomaximal, Sylow
97C71#162211yescharacteristic, complemented, Sylow
98#554—711no—
99#492—711no—
100#460—711no—
101#459—711no—
102#333—711no—
103Q8⋊C8—711no—
104D4⋊C8D7111yescharacteristic, complemented
105C2×SD16—1421no—
106C2×SD16—1422no—
107C2×D8—1421no—
108C4⋊Q8—711no—
109#127—711no—
110#125—1421no—
111C22⋊Q8—1422no—
112C22⋊Q8—1421no—
113C4×Q8—711no—
114C4×D4—1421no—
115C4×D4C2×D7111yescharacteristic
116C2×C4⋊C4—1421no—
117C4⋊C8—711no—
118C4⋊C8C2×D7111yescharacteristic
119#102—1421no—
120#102—1421no—
121C4×C8C2×D7111yescharacteristic
122C2×Q8—712no—
123C2×Q8—711no—
124C2×D4—1421no—
125C2×D4—1421no—
126C2×D4—1421no—
127C2×D4D28411yescharacteristic
128C22×C4—21no—
129C22×C4—1422no—
130SD16—2844no—
131SD16—2842no—
132D8—2842no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1421no—
136C4⋊C4—711no—
137C4⋊C4—1422no—
138C4⋊C4—1422no—
139C4⋊C4—1421no—
140C4⋊C4—1421no—
141C4⋊C4—1421no—
142C4⋊C4D28411yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1422no—
145C42—1421no—
146C42C22×D7111yescharacteristic
147C23—21no—
148C23—2841no—
149Q8—2842no—
150Q8—1421no—
151Q8—1421no—
152D4—21no—
153D4—2842no—
154D4—2841no—
155D4—2841no—
156D4—2841no—
157D4—2841no—
158D4#1176585412yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—5682no—
163C2×C4—1421no—
164C2×C4—1421no—
165C2×C4—1422no—
166C2×C4D4×D7111yescharacteristic
167C2×C4D4×D7111yescharacteristic
168C2×C4C2×D28411yescharacteristic
169C8—22no—
170C8—41no—
171C8—2841no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—5681no—
176C22—5681no—
177C22—5681no—
178C22#1455609811yescharacteristic
179C4—21no—
180C4—41no—
181C4—2841no—
182C4—2841no—
183C4—2842no—
184C4C2×#1176585411yescharacteristic
185C4#1455614911yescharacteristic
186C4#1455615211yescharacteristic
187C4#1455616111yescharacteristic
188C2—42no—
189C2—11361no—
190C2#1798614011yescharacteristic
191C2#1798614511yescharacteristic
192C2#1798616811yescharacteristic
subgroupG/H
centerC22#14556098
commutatorC42×C71C23
FrattiniC42C22×D71
FittingD4⋊C8×C71C2
socleC22×C71#120
hypercenterD4⋊C8D71
hypocenterC71#1622
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #17986706C2semidirect
2. #17986372C2semidirect
3. #17986200C2semidirect
5. #17985747C2semidirect
6. #17985731C2semidirect
7. D4⋊C8×C71C2semidirect
53. D4×C71SD16semidirect
97. C71#1622semidirect
104. D4⋊C8D71semidirect
158. D4#11765854semidirect