Finite Group Databasebeta

← #22601270

Subgroups — #22601270

Order 9088.

326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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
1Q8×Dic142C211yesmaximal, characteristic
2#17986728C211yesmaximal, characteristic
3#17986407C212yesmaximal
4#17986397C211yesmaximal, characteristic
5#17986304C212yesmaximal
6#17986294C211yesmaximal, characteristic
7#17986284C211yesmaximal, characteristic
8#17986282C212yesmaximal
9#17986129C211yesmaximal, characteristic
10#17986106C212yesmaximal
11C4×Q16×C71C211yesmaximal, characteristic
12#14556128—21no—
13#14556128—21no—
14#14556128C2211yescharacteristic
15#14556128C2211yescharacteristic
16#14556127—22no—
17#14556127C2212yes—
18#14556119—22no—
19#14556119C2212yes—
20Q8×Dic71C2212yes—
21Q8×Dic71C2212yes—
22C4×Dic142—21no—
23C4×Dic142—21no—
24C4×Dic142C2211yescharacteristic
25#14556061C2212yes—
26#14556060C2212yes—
27#14556060C2212yes—
28#14556059C2212yes—
29C4⋊(C71⋊C8)C2211yescharacteristic
30Dic71⋊C8C2212yes—
31#14556052C2212yes—
32#14556052C2212yes—
33#14556038C2212yes—
34C2×Q16×C71C2211yescharacteristic
35C4×Q8×C71C2211yescharacteristic
36C4×Q8×C71C2211yescharacteristic
37#107×C71C2211yescharacteristic
38#103×C71C2211yescharacteristic
39#103×C71C2211yescharacteristic
40C4×C8×C71C2211yescharacteristic
41C2×Dic142—21no—
42C2×Dic142—21no—
43C2×Dic142—22no—
44C2×Dic142D411yescharacteristic
45C2×C71⋊C8C2312yes—
46C4⋊Dic71—21no—
47C4⋊Dic71—21no—
48C4⋊Dic71—22no—
49C4⋊Dic71—22no—
50C4⋊Dic71—22no—
51C4⋊Dic71D411yescharacteristic
52C4⋊Dic71C2312yes—
53C4⋊Dic71C2312yes—
54Dic71⋊C4—22no—
55Dic71⋊C4—22no—
56Dic71⋊C4D412yes—
57C4×Dic71—22no—
58C4×Dic71—22no—
59C4×Dic71C2312yes—
60C2×Q8×C71C2311yescharacteristic
61C2×Q8×C71C2311yescharacteristic
62Q16×C71Q814yescomplemented
63C2×C8×C71C2311yescharacteristic
64C2×C8×C71C2311yescharacteristic
65C4⋊C4×C71—21no—
66C4⋊C4×C71—21no—
67C4⋊C4×C71C2311yescharacteristic
68C4⋊C4×C71C2311yescharacteristic
69C42×C71—21no—
70C42×C71—21no—
71C42×C71C2311yescharacteristic
72Q8×C71—21no—
73Q8×C71—21no—
74Q8×C71C2×Q812yes—
75Q8×C71C2×Q812yes—
76C2×C4×C71—21no—
77C2×C4×C71—21no—
78C2×C4×C71—21no—
79C2×C4×C71—21no—
80C2×C4×C71C2×D411yescharacteristic
81C2×C4×C71C2×D411yescharacteristic
82C2×C4×C71C2411yescharacteristic
83C2×Dic71—22no—
84C2×Dic71—22no—
85C2×Dic71C2×D412yes—
86C2×Dic71C2×D412yes—
87Dic142—22no—
88Dic142—42no—
89Dic142—82no—
90Dic142—81no—
91C8×C71—21no—
92C8×C71C2×Q812yes—
93C71⋊C8—22no—
94C22×C71C22×D411yescharacteristic
95C4×C71—22no—
96C4×C71—22no—
97C4×C71—21no—
98C4×C71—41no—
99C4×C71—41no—
100C4×C71#13712yes—
101C4×C71C22×Q811yescharacteristic
102C4×C712−1+411yescharacteristic
103Dic71—22no—
104Dic71—22no—
105Dic71—42no—
106Dic71—42no—
107C2×C71D4×Q811yescharacteristic
108C2×C71C2×#13711yescharacteristic
109C2×C71#57711yescharacteristic
110#3387—711nomaximal, Sylow
111C71#338711yescharacteristic, complemented, Sylow
112Q82—711no—
113#557—711no—
114#501—712no—
115#498—711no—
116#479—712no—
117#477—711no—
118#475—711no—
119#475—712no—
120#446—711no—
121#441—712no—
122C4×Q16D7111yescharacteristic
123C2×Q16C2×D7111yescharacteristic
124C4⋊Q8—712no—
125C4⋊Q8—711no—
126C4⋊Q8—711no—
127C4⋊Q8—1421no—
128C4⋊Q8—1421no—
129C4⋊Q8—1422no—
130#125—712no—
131#125—1422no—
132C4×Q8—711no—
133C4×Q8—712no—
134C4×Q8—712no—
135C4×Q8—1421no—
136C4×Q8—1421no—
137C4×Q8C2×D7111yescharacteristic
138C4×Q8C2×D7111yescharacteristic
139#107—712no—
140#107C2×D7111yescharacteristic
141#106—712no—
142#106—712no—
143#106—712no—
144C4⋊C8—712no—
145C4⋊C8—711no—
146#103—712no—
147#103—712no—
148#103C2×D7111yescharacteristic
149#103C2×D7111yescharacteristic
150#97—712no—
151C4×C8C2×D7111yescharacteristic
152C2×Q8—711no—
153C2×Q8—1422no—
154C2×Q8—1421no—
155C2×Q8—1421no—
156C2×Q8C22×D7111yescharacteristic
157C2×Q8C22×D7111yescharacteristic
158Q16Dic14214yescomplemented
159C2×C8—712no—
160C2×C8C22×D7111yescharacteristic
161C2×C8C22×D7111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—712no—
165C4⋊C4—711no—
166C4⋊C4—712no—
167C4⋊C4—712no—
168C4⋊C4—1422no—
169C4⋊C4—1422no—
170C4⋊C4—1422no—
171C4⋊C4—1422no—
172C4⋊C4—1422no—
173C4⋊C4—1421no—
174C4⋊C4—1421no—
175C4⋊C4C22×D7111yescharacteristic
176C4⋊C4C22×D7111yescharacteristic
177C42—21no—
178C42—21no—
179C42—712no—
180C42—1422no—
181C42—1422no—
182C42C22×D7111yescharacteristic
183Q8—21no—
184Q8—21no—
185Q8—2842no—
186Q8—5681no—
187Q8—5682no—
188Q8—1422no—
189Q8C2×Dic14212yes—
190Q8C2×Dic14212yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—712no—
196C2×C4—712no—
197C2×C4—1422no—
198C2×C4—1422no—
199C2×C4D4×D7111yescharacteristic
200C2×C4D4×D7111yescharacteristic
201C2×C4C23×D7111yescharacteristic
202C8—21no—
203C8—1422no—
204C8C2×Dic14212yes—
205C22C2×D4×D7111yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—41no—
210C4—41no—
211C4—2842no—
212C4—2842no—
213C4—1422no—
214C4—1422no—
215C4#1455616012yes—
216C4C22×Dic14211yescharacteristic
217C4#1455617511yescharacteristic
218C2D4×Dic14211yescharacteristic
219C2C2×#1455616011yescharacteristic
220C2#1798680611yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC4×Q16×C71C2
socleC22×C71C22×D4
hypercenterC4×Q16D71
hypocenterC71#3387
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
62. Q16×C71Q8semidirect
111. C71#3387semidirect
158. Q16Dic142semidirect