Finite Group Databasebeta

← #22589598

Subgroups — #22589598

Order 9088.

276 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 71 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#17986025C211yesmaximal, characteristic, complemented
2#17986008C211yesmaximal, characteristic, complemented
3#17986004C211yesmaximal, characteristic
4C2×#14556047C211yesmaximal, characteristic, complemented
5C2×#14556045C211yesmaximal, characteristic
6#17985764C211yesmaximal, characteristic, complemented
7C22×SD16×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C2×#11765849C2211yescharacteristic
11#14556087C2211yescharacteristic
12Dic71⋊C8—22no—
13#14556052—22no—
14#14556049—22no—
15#14556047—22no—
16#14556045—22no—
17C22×Q8×C71C2211yescharacteristic
18C22×D4×C71C2211yescharacteristic
19C2×SD16×C71—22no—
20C2×SD16×C71—22no—
21C2×SD16×C71—22no—
22C22×C8×C71C2211yescharacteristic
23#11765849—21no—
24#11765849—21no—
25#11765849—21no—
26#11765849—21no—
27#11765849—21no—
28#11765849—21no—
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C4⋊Dic71D412yes—
33C22⋊Dic71—21no—
34C4×Dic71—21no—
35C24×C71—21no—
36C2×Q8×C71—21no—
37C2×Q8×C71—21no—
38C2×Q8×C71—21no—
39C2×Q8×C71—21no—
40C2×Q8×C71—21no—
41C2×Q8×C71D412yes—
42C2×D4×C71—21no—
43C2×D4×C71—21no—
44C2×D4×C71—21no—
45C2×D4×C71—21no—
46C2×D4×C71—21no—
47C2×D4×C71D412yes—
48C22×C4×C71—21no—
49C22×C4×C71C2311yescharacteristic
50SD16×C71—28no—
51C2×C8×C71—21no—
52C2×C8×C71—21no—
53C2×C8×C71D412yes—
54C23×C71—22no—
55C23×C71—41no—
56C23×C71—41no—
57C23×C71—82no—
58C23×C71#4111yescharacteristic
59Q8×C71—22no—
60Q8×C71—22no—
61Q8×C71—41no—
62Q8×C71—41no—
63D4×C71—22no—
64D4×C71—22no—
65D4×C71—41no—
66D4×C71—41no—
67C2×C4×C71—22no—
68C2×C4×C71—41no—
69C2×C4×C71—41no—
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C2×C4×C71#4111yescharacteristic
75C2×C4×C71#4111yescharacteristic
76C2×Dic71—22no—
77C8×C71—22no—
78C71⋊C8—41no—
79C71⋊C8—41no—
80C71⋊C8—41no—
81C22×C71—22no—
82C22×C71—42no—
83C22×C71—82no—
84C22×C71—82no—
85C22×C71—82no—
86C22×C71#12111yescharacteristic
87C22×C71#12311yescharacteristic
88C22×C71#12311yescharacteristic
89C4×C71—42no—
90C4×C71#12011yescharacteristic
91C4×C71#12111yescharacteristic
92C4×C71#12111yescharacteristic
93C4×C71#12411yescharacteristic
94Dic71—42no—
95C2×C71—21no—
96C2×C71—21no—
97C2×C71—82no—
98C2×C71#39411yescharacteristic
99C2×C71#47112yes—
100#2046—711nomaximal, Sylow
101C71#204611yescharacteristic, complemented, Sylow
102C22×SD16D7111yescharacteristic
103#424—711no—
104#419—711no—
105#418—711no—
106C2×#101—711no—
107C2×#100—711no—
108#341—711no—
109C22×Q8C2×D7111yescharacteristic
110C22×D4C2×D7111yescharacteristic
111C2×SD16—22no—
112C2×SD16—22no—
113C2×SD16—22no—
114C2×M16—711no—
115C2×M16—711no—
116C2×M16—711no—
117C22×C8C2×D7111yescharacteristic
118#117—711no—
119C4⋊C8—1422no—
120#103—1422no—
121#102—1422no—
122#101—1422no—
123#100—1422no—
124C24—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8C22⋊D7112yes—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4C22⋊D7112yes—
137C22×C4—21no—
138C22×C4C22×D7111yescharacteristic
139SD16—28no—
140M16—1421no—
141M16—1421no—
142M16—1421no—
143M16—1421no—
144M16—1421no—
145M16—1421no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—1421no—
149C2×C8—1421no—
150C2×C8—1421no—
151C2×C8C22⋊D7112yes—
152C4⋊C4—712no—
153C22⋊C4—1421no—
154C42—1421no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#1176586411yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1422no—
172C2×C4D4×D7111yescharacteristic
173C2×C4C2×C22⋊D7111yescharacteristic
174C2×C4C2×C22⋊D7111yescharacteristic
175C2×C4C2×C22⋊D7111yescharacteristic
176C2×C4#1176586411yescharacteristic
177C2×C4#1176586411yescharacteristic
178C8—22no—
179C8—2841no—
180C8—2841no—
181C8—2841no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#1455609911yescharacteristic
188C22#1455610911yescharacteristic
189C22#1455610911yescharacteristic
190C4—42no—
191C4—2842no—
192C4#1455609711yescharacteristic
193C4#1455610011yescharacteristic
194C4#1455610011yescharacteristic
195C4#1455611511yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1798591311yescharacteristic
200C2#1798625912yes—
subgroupG/H
centerC22#14556099
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC22×SD16×C71C2
socleC22×C71#121
hypercenterC22×SD16D71
hypocenterC71#2046
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. #17986025C2semidirect
2. #17986008C2semidirect
4. C2×#14556047C2semidirect
6. #17985764C2semidirect
101. C71#2046semidirect