Finite Group Databasebeta

← #22593551

Subgroups — #22593551

Order 9088.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14556127C211yesmaximal, characteristic
2C2×#14556093C211yesmaximal, characteristic
3#17985939C211yesmaximal, characteristic
4#17985938C211yesmaximal, characteristic
5#17985937C211yesmaximal, characteristic
6#17985903C212yesmaximal
7#17985903C212yesmaximal
8#17985903C212yesmaximal
9#17985863C212yesmaximal
10#17985850C211yesmaximal, characteristic
11#400×C71C211yesmaximal, characteristic
12C22×Dic142C2212yes—
13C22×Dic142C2211yescharacteristic
14#14556127—24no—
15#14556093—24no—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2211yescharacteristic
19C2×Dic71⋊C4C2212yes—
20C2×Dic71⋊C4C2211yescharacteristic
21C2×C4×Dic71C2212yes—
22C2×C4×Dic71C2211yescharacteristic
23C2×C4×Dic71C2211yescharacteristic
24C2×C4×Dic71C2211yescharacteristic
25C71⋊#95C2211yescharacteristic
26C71⋊#95C2212yes—
27C71⋊#95C2212yes—
28C71⋊#95C2212yes—
29C71⋊#95C2212yes—
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C2×C4⋊C4×C71C2211yescharacteristic
33C2×C4⋊C4×C71C2211yescharacteristic
34#95×C71C2211yescharacteristic
35#95×C71C2212yes—
36#95×C71C2212yes—
37C2×Dic142—22no—
38C2×Dic142—22no—
39C2×Dic142—24no—
40C2×Dic142—28no—
41C2×Dic142Q814yescomplemented
42C22×Dic71C2312yes—
43C22×Dic71C2312yes—
44C22×Dic71C2311yescharacteristic
45C22×Dic71C2311yescharacteristic
46C22×Dic71C2311yescharacteristic
47C22×Dic71C2311yescharacteristic
48C4⋊Dic71—22no—
49Dic71⋊C4—22no—
50Dic71⋊C4—22no—
51Dic71⋊C4—24no—
52Dic71⋊C4—24no—
53C4×Dic71—22no—
54C4×Dic71—22no—
55C4×Dic71—24no—
56C4×Dic71D414yes—
57C22×C4×C71C2312yes—
58C22×C4×C71C2312yes—
59C22×C4×C71C2311yescharacteristic
60C22×C4×C71C2311yescharacteristic
61C22×C4×C71C2311yescharacteristic
62C4⋊C4×C71—22no—
63C4⋊C4×C71—22no—
64C23×C71C2411yescharacteristic
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—22no—
68C2×C4×C71—21no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—24no—
73C2×C4×C71—22no—
74C2×C4×C71—22no—
75C2×C4×C71C2×D412yes—
76C2×C4×C71C2×Q812yes—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—24no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71C2×D412yes—
87C2×Dic71C2×D412yes—
88C2×Dic71C2×Q812yes—
89C2×Dic71C2×Q812yes—
90C2×Dic71#4112yes—
91C2×Dic71#4114yes—
92Dic142—28no—
93Dic142—48no—
94C22×C71C22×D411yescharacteristic
95C22×C71C22×Q811yescharacteristic
96C22×C71C2×#4111yescharacteristic
97C22×C71C2×#4112yes—
98C22×C712−1+412yes—
99C4×C71—22no—
100C4×C71—22no—
101C4×C71—42no—
102C4×C71—41no—
103C4×C71—42no—
104Dic71—22no—
105Dic71—42no—
106Dic71—41no—
107Dic71—42no—
108Dic71C22⋊Q814yes—
109Dic71#12414yes—
110C2×C71C2×C22⋊Q811yescharacteristic
111C2×C71C2×#12411yescharacteristic
112C2×C71#53611yescharacteristic
113C2×C71#55612yes—
114C2×C71#55712yes—
115#2568—711nomaximal, Sylow
116C71#256811yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—711no—
118C2×C4×Q8—711no—
119#400—711no—
120#400—711no—
121#400—711no—
122#400D7111yescharacteristic
123#391—712no—
124#391—712no—
125#391—712no—
126#382—712no—
127C4×C4⋊C4—711no—
128C22×Q8—711no—
129C22×Q8—712no—
130C4⋊Q8—1424no—
131C4×Q8—1424no—
132C2×C4⋊C4—711no—
133C2×C4⋊C4—711no—
134C2×C4⋊C4—712no—
135C2×C4⋊C4—711no—
136C2×C4⋊C4—712no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C4⋊C4C2×D7111yescharacteristic
139C2×C42—711no—
140C2×C42—711no—
141C2×C42—711no—
142C2×C42—712no—
143#95—711no—
144#95—712no—
145#95—712no—
146#95—712no—
147#95—712no—
148#95—712no—
149#95—712no—
150#95C2×D7111yescharacteristic
151#95C2×D7112yes—
152#95C2×D7112yes—
153C2×Q8—714no—
154C2×Q8—1424no—
155C2×Q8—1428no—
156C2×Q8—1422no—
157C2×Q8—1422no—
158C22×C4—711no—
159C22×C4—711no—
160C22×C4—711no—
161C22×C4—712no—
162C22×C4—711no—
163C22×C4—712no—
164C22×C4C22×D7112yes—
165C22×C4C22×D7111yescharacteristic
166C22×C4C22×D7112yes—
167C22×C4C22×D7111yescharacteristic
168C22×C4C22×D7111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1424no—
172C4⋊C4—1422no—
173C4⋊C4—1424no—
174C4⋊C4—1422no—
175C4⋊C4—1422no—
176C42—714no—
177C42—1424no—
178C42—1422no—
179C42—1422no—
180C23C23×D7111yescharacteristic
181Q8—2848no—
182Q8—1428no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—712no—
194C2×C4—712no—
195C2×C4—712no—
196C2×C4—712no—
197C2×C4—714no—
198C2×C4—712no—
199C2×C4—1421no—
200C2×C4—1422no—
201C2×C4—1422no—
202C2×C4—1422no—
203C2×C4—1424no—
204C2×C4—1422no—
205C2×C4—1422no—
206C2×C4—1421no—
207C2×C4—1421no—
208C2×C4D4×D7112yes—
209C2×C4Q8×D7112yes—
210C22C2×D4×D7111yescharacteristic
211C22C2×Q8×D7111yescharacteristic
212C22#41×D7111yescharacteristic
213C22#41×D7112yes—
214C22#1455617512yes—
215C4—22no—
216C4—22no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—2841no—
221C4—2842no—
222C4—2842no—
223C4—714no—
224C4—714no—
225C4—1422no—
226C2C22⋊Q8×D7111yescharacteristic
227C2#124×D7111yescharacteristic
228C2#1798657111yescharacteristic
229C2#1798671612yes—
230C2#1798672612yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#400×C71C2
hypercenter#400D71
hypocenterC71#2568
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
41. C2×Dic142Q8semidirect
116. C71#2568semidirect