Finite Group Databasebeta

← #22598012

Subgroups — #22598012

Order 9088.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556150C211yesmaximal, characteristic, complemented
2C2×#14556134C211yesmaximal, characteristic, complemented
3#17986580C212yesmaximal, complemented
4#17986246C214yesmaximal, complemented
5#17986241C212yesmaximal, complemented
6#17986236C212yesmaximal, complemented
7#17985998C212yesmaximal, complemented
8C2×#107×C71C211yesmaximal, characteristic, complemented
9C2×#11765865C2212yes—
10C2×#11765865C2211yescharacteristic
11#14556150—24no—
12C2×Dic284C2211yescharacteristic
13C2×#11765854C2212yes—
14C2×D568C2211yescharacteristic
15#14556134—24no—
16C2×#11765849C2211yescharacteristic
17C2×#11765848C2212yes—
18C2×C8×D71C2212yes—
19#14556108—22no—
20#14556108C2214yes—
21#14556103—22no—
22#14556103C2214yes—
23#14556102—24no—
24#14556051C2214yes—
25#14556048C2214yes—
26C22×C8×C71C2211yescharacteristic
27C2×C4⋊C4×C71C2212yes—
28#107×C71C2212yes—
29#107×C71C2212yes—
30#11765865—22no—
31#11765865—22no—
32#11765865—24no—
33#11765865—24no—
34C2×Dic142D411yescharacteristic
35C2×Dic142C2312yes—
36C2×D284—24no—
37C2×D284D411yescharacteristic
38C2×D284C2312yes—
39C2×C22⋊D71—22no—
40C2×C22⋊D71D412yes—
41C2×C4×D71—22no—
42C2×C4×D71C2312yes—
43Dic284—22no—
44#11765854—24no—
45D568—22no—
46#11765849—22no—
47#11765848—24no—
48C2×C71⋊C8C2312yes—
49C8×D71—24no—
50C4⋊Dic71—24no—
51(C2×D71)⋊C4—24no—
52(C2×D71)⋊C4—24no—
53C22×C4×C71—22no—
54C22×C4×C71C2311yescharacteristic
55C2×C8×C71D414yescomplemented
56C2×C8×C71C2311yescharacteristic
57C2×C8×C71C2311yescharacteristic
58C4⋊C4×C71—22no—
59C4⋊C4×C71C2314yes—
60C23×C71C2×D411yescharacteristic
61C22×D71—22no—
62C22×D71C2×D412yes—
63C2×C4×C71—24no—
64C2×C4×C71—82no—
65C2×C4×C71C2×D411yescharacteristic
66C2×C4×C71C2×D412yes—
67C2×C4×C71#4112yes—
68C2×C4×C71C2411yescharacteristic
69C22⋊D71—24no—
70C22⋊D71—44no—
71C2×Dic71—22no—
72C2×Dic71C2×D412yes—
73D284—22no—
74D284—22no—
75D284—22no—
76D284—84no—
77C4×D71—22no—
78C4×D71—22no—
79C4×D71—44no—
80Dic142—22no—
81Dic142—22no—
82Dic142—22no—
83C8×C71C2×D412yes—
84C8×C71C2×D412yes—
85C71⋊C8—22no—
86C22×C71—21no—
87C22×C71—21no—
88C22×C71#12112yes—
89C22×C71C22×D411yescharacteristic
90C2×D71—22no—
91C2×D71—22no—
92C2×D71—22no—
93C2×D71—42no—
94C2×D71—42no—
95C2×D71—42no—
96C4×C71—44no—
97C4×C71#12112yes—
98C4×C71C22×D411yescharacteristic
99C4×C71C2×#4111yescharacteristic
100Dic71—22no—
101Dic71—42no—
102C2×C71—22no—
103C2×C71C2×#12111yescharacteristic
104C2×C71#57611yescharacteristic
105C2×C71#57811yescharacteristic
106D71—42no—
107D71—82no—
108#3061—711nomaximal, Sylow
109C71#306111yescharacteristic, complemented, Sylow
110C2×#135—711no—
111C2×#131—711no—
112#537—712no—
113#468—714no—
114#467—712no—
115#466—712no—
116C2×#107D7111yescharacteristic, complemented
117#417—712no—
118C2×#41—711no—
119C2×#41—712no—
120#135—1424no—
121C2×Q16—711no—
122C2×SD16—712no—
123C2×D8—711no—
124#131—1424no—
125C2×M16—711no—
126C2×M16—712no—
127C22×C8—712no—
128C22×C8C2×D7111yescharacteristic
129C22⋊Q8—714no—
130C22⋊Q8—1422no—
131#121—714no—
132#121—1422no—
133#121—1424no—
134C2×C4⋊C4C2×D7112yes—
135#107C2×D7112yes—
136#107C2×D7112yes—
137#103—714no—
138#102—714no—
139#41—1424no—
140#41—1424no—
141#41—1422no—
142#41—1422no—
143C2×Q8—711no—
144C2×Q8—712no—
145C2×D4—712no—
146C2×D4—711no—
147C2×D4—712no—
148C2×D4—1424no—
149C2×D4—1422no—
150C22×C4—22no—
151C22×C4—712no—
152C22×C4—1422no—
153C22×C4C22×D7111yescharacteristic
154Q16—1422no—
155SD16—1424no—
156D8—1422no—
157M16—1422no—
158M16—1424no—
159C2×C8—712no—
160C2×C8—1424no—
161C2×C8D28414yescomplemented
162C2×C8C22×D7111yescharacteristic
163C2×C8C22×D7111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—1424no—
166C4⋊C4C22×D7114yes—
167C22⋊C4—1424no—
168C22⋊C4—1424no—
169C23—712no—
170C23—1422no—
171C23D4×D7111yescharacteristic
172Q8—1422no—
173Q8—1422no—
174Q8—1422no—
175D4—2844no—
176D4—5684no—
177D4—1424no—
178D4—1422no—
179D4—1422no—
180D4—1422no—
181C2×C4—24no—
182C2×C4—82no—
183C2×C4—2844no—
184C2×C4—712no—
185C2×C4—1422no—
186C2×C4—1422no—
187C2×C4—1422no—
188C2×C4D4×D7111yescharacteristic
189C2×C4C2×D28412yes—
190C2×C4#1176586612yes—
191C2×C4C23×D7111yescharacteristic
192C8—1422no—
193C8C2×D28412yes—
194C8C2×D28412yes—
195C22—21no—
196C22—21no—
197C22—2842no—
198C22—2842no—
199C22—2842no—
200C22—1422no—
201C22—1422no—
202C22—1422no—
203C22#1455610312yes—
204C22C2×D4×D7111yescharacteristic
205C4—44no—
206C4—2842no—
207C4—1422no—
208C4#1455610312yes—
209C4C22×D28411yescharacteristic
210C4C2×#1176586611yescharacteristic
211C2—22no—
212C2—2842no—
213C2—5682no—
214C2C2×#1455610311yescharacteristic
215C2#1798680011yescharacteristic
216C2#1798681211yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC2×#107×C71C2
socleC22×C71C22×D4
hypercenterC2×#107D71
hypocenterC71#3061
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14556150C2semidirect
2. C2×#14556134C2semidirect
3. #17986580C2semidirect
4. #17986246C2semidirect
5. #17986241C2semidirect
6. #17986236C2semidirect
7. #17985998C2semidirect
8. C2×#107×C71C2semidirect
55. C2×C8×C71D4semidirect
109. C71#3061semidirect
116. C2×#107D71semidirect
161. C2×C8D284semidirect