Finite Group Databasebeta

← #22601230

Subgroups — #22601230

Order 9088.

324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 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#17986728C211yesmaximal, characteristic
2#17986724C211yesmaximal, characteristic
3#17986402C211yesmaximal, characteristic
4#17986399C212yesmaximal
5#17986309C212yesmaximal
6#17986304C212yesmaximal
7#17986285C211yesmaximal, characteristic
8#17986123C211yesmaximal, characteristic
9C4×#11765855C211yesmaximal, characteristic
10#17986091C212yesmaximal
11#475×C71C211yesmaximal, characteristic
12C2×#11765855C2211yescharacteristic
13#14556128—21no—
14#14556128C2211yescharacteristic
15#14556126—21no—
16#14556119—22no—
17#14556119C2212yes—
18#14556119C2212yes—
19#14556118—22no—
20Q8×Dic71—21no—
21Q8×Dic71C2212yes—
22C4×Dic142—21no—
23C4×Dic142C2211yescharacteristic
24C4×Dic142C2211yescharacteristic
25#14556093C2212yes—
26#14556061C2212yes—
27#14556061C2212yes—
28#14556061C2211yescharacteristic
29#14556060C2212yes—
30Dic71⋊C8C2212yes—
31#14556053C2212yes—
32#14556052C2211yescharacteristic
33#14556051C2211yescharacteristic
34C4×C71⋊C8C2211yescharacteristic
35C8×Dic71C2212yes—
36C4⋊Q8×C71C2211yescharacteristic
37C4×Q8×C71C2211yescharacteristic
38#106×C71C2212yes—
39C4⋊C8×C71C2211yescharacteristic
40#103×C71C2212yes—
41C2×Dic142—21no—
42C2×Dic142D411yescharacteristic
43C2×Dic142C2311yescharacteristic
44#11765855Q814yescomplemented
45C2×C71⋊C8C2311yescharacteristic
46C2×C71⋊C8C2311yescharacteristic
47C4⋊Dic71—21no—
48C4⋊Dic71—22no—
49C4⋊Dic71—22no—
50C4⋊Dic71—22no—
51C4⋊Dic71D411yescharacteristic
52C4⋊Dic71C2311yescharacteristic
53C4⋊Dic71C2312yes—
54Dic71⋊C4—21no—
55Dic71⋊C4—22no—
56Dic71⋊C4—22no—
57Dic71⋊C4—22no—
58Dic71⋊C4D412yes—
59C4×Dic71—21no—
60C4×Dic71—22no—
61C4×Dic71—22no—
62C4×Dic71C2312yes—
63C2×Q8×C71—21no—
64C2×Q8×C71C2311yescharacteristic
65C2×C8×C71C2312yes—
66C4⋊C4×C71—21no—
67C4⋊C4×C71—21no—
68C4⋊C4×C71C2312yes—
69C4⋊C4×C71C2311yescharacteristic
70C42×C71—21no—
71C42×C71C2311yescharacteristic
72Q8×C71—21no—
73Q8×C71—42no—
74Q8×C71C2×Q812yes—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2×D411yescharacteristic
80C2×C4×C71C2411yescharacteristic
81C2×Dic71—21no—
82C2×Dic71—21no—
83C2×Dic71—22no—
84C2×Dic71C2×D412yes—
85C2×Dic71C2×D412yes—
86Dic142—22no—
87Dic142—21no—
88Dic142—42no—
89Dic142C2×Q812yes—
90C8×C71—22no—
91C71⋊C8—21no—
92C71⋊C8C2×Q812yes—
93C22×C71C22×D411yescharacteristic
94C4×C71—22no—
95C4×C71—21no—
96C4×C71—42no—
97C4×C71—41no—
98C4×C71#13512yes—
99C4×C71C22×Q811yescharacteristic
100C4×C712−1+411yescharacteristic
101Dic71—22no—
102Dic71—22no—
103Dic71—22no—
104Dic71—42no—
105Dic71—41no—
106C2×C71D4×Q811yescharacteristic
107C2×C71C2×#13511yescharacteristic
108C2×C71#57811yescharacteristic
109#3383—711nomaximal, Sylow
110C71#338311yescharacteristic, complemented, Sylow
111#557—711no—
112#557—711no—
113#500—711no—
114#499—712no—
115#479—712no—
116#479—712no—
117#475—711no—
118#475D7111yescharacteristic
119C8×Q8—711no—
120C4×Q16—711no—
121C4×Q16—712no—
122C2×Q16—711no—
123C4⋊Q8—711no—
124C4⋊Q8—1421no—
125C4⋊Q8—1421no—
126C4⋊Q8C2×D7111yescharacteristic
127#125—712no—
128#125—712no—
129#125—1422no—
130#125—1422no—
131C4×Q8—711no—
132C4×Q8—712no—
133C4×Q8—712no—
134C4×Q8—711no—
135C4×Q8—1421no—
136C4×Q8—1421no—
137C4×Q8C2×D7111yescharacteristic
138#107—711no—
139#107—712no—
140#107—712no—
141#106—712no—
142#106C2×D7112yes—
143C4⋊C8—712no—
144C4⋊C8C2×D7111yescharacteristic
145#103—711no—
146#103—712no—
147#103—711no—
148#103C2×D7112yes—
149C4×C8—712no—
150C4×C8—711no—
151C2×Q8—21no—
152C2×Q8—711no—
153C2×Q8—711no—
154C2×Q8—1421no—
155C2×Q8C22×D7111yescharacteristic
156Q16—714no—
157C2×C8—711no—
158C2×C8—711no—
159C2×C8C22×D7112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—712no—
163C4⋊C4—711no—
164C4⋊C4—711no—
165C4⋊C4—712no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4—1422no—
170C4⋊C4—1422no—
171C4⋊C4—1422no—
172C4⋊C4—1421no—
173C4⋊C4—1421no—
174C4⋊C4C22×D7111yescharacteristic
175C4⋊C4C22×D7112yes—
176C42—21no—
177C42—712no—
178C42—1422no—
179C42—1422no—
180C42—1421no—
181C42C22×D7111yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—2842no—
185Q8—712no—
186Q8—1421no—
187Q8—1422no—
188Q8Q8×D7112yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—712no—
193C2×C4—712no—
194C2×C4—1421no—
195C2×C4—1422no—
196C2×C4—1421no—
197C2×C4D4×D7111yescharacteristic
198C2×C4D4×D7111yescharacteristic
199C2×C4C23×D7111yescharacteristic
200C8—22no—
201C8—712no—
202C8—1421no—
203C22C2×D4×D7111yescharacteristic
204C4—22no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—2842no—
209C4—2841no—
210C4—1422no—
211C4—1422no—
212C4—1422no—
213C4#1455614912yes—
214C4C2×Q8×D7111yescharacteristic
215C4#1455617511yescharacteristic
216C2#1798666211yescharacteristic
217C2C2×#1455614911yescharacteristic
218C2#1798681511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#475×C71C2
socleC22×C71C22×D4
hypercenter#475D71
hypocenterC71#3383
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
44. #11765855Q8semidirect
110. C71#3383semidirect