Finite Group Databasebeta

← #22593324

Subgroups — #22593324

Order 9088.

540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14556127C212yesmaximal
3C2×#14556093C211yesmaximal, characteristic
4#17985931C211yesmaximal, characteristic
5#17985930C211yesmaximal, characteristic
6#17985929C211yesmaximal, characteristic
7#17985903C212yesmaximal
8#17985896C212yesmaximal
9#17985894C212yesmaximal
10#17985850C211yesmaximal, characteristic
11#398×C71C211yesmaximal, characteristic
12C22×Dic142C2212yes—
13C22×Dic142C2211yescharacteristic
14#14556127—28no—
15#14556127—24no—
16#14556093—24no—
17C2×C4⋊Dic71C2212yes—
18C2×C4⋊Dic71C2211yescharacteristic
19C2×Dic71⋊C4C2212yes—
20C2×Dic71⋊C4C2212yes—
21C2×Dic71⋊C4C2212yes—
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2212yes—
25C2×C4×Dic71C2212yes—
26C2×C4×Dic71C2211yescharacteristic
27C2×C4×Dic71C2211yescharacteristic
28C2×C4×Dic71C2211yescharacteristic
29C71⋊#95C2211yescharacteristic
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C71⋊#95C2212yes—
33C2×C4⋊C4×C71C2212yes—
34C2×C4⋊C4×C71C2211yescharacteristic
35C2×C4⋊C4×C71C2211yescharacteristic
36#95×C71C2211yescharacteristic
37#95×C71C2212yes—
38C2×Dic142—22no—
39C2×Dic142—22no—
40C2×Dic142—24no—
41C2×Dic142—24no—
42C2×Dic142—24no—
43C2×Dic142D414yes—
44C22×Dic71C2312yes—
45C22×Dic71C2311yescharacteristic
46C22×Dic71C2311yescharacteristic
47C22×Dic71C2312yes—
48C22×Dic71C2311yescharacteristic
49C22×Dic71C2311yescharacteristic
50C4⋊Dic71—22no—
51C4⋊Dic71—24no—
52Dic71⋊C4—22no—
53Dic71⋊C4—24no—
54Dic71⋊C4—22no—
55Dic71⋊C4—24no—
56Dic71⋊C4—24no—
57Dic71⋊C4Q818yescomplemented
58C4×Dic71—22no—
59C4×Dic71—22no—
60C4×Dic71—24no—
61C4×Dic71D414yes—
62C22×C4×C71C2312yes—
63C22×C4×C71C2311yescharacteristic
64C22×C4×C71C2311yescharacteristic
65C22×C4×C71C2311yescharacteristic
66C22×C4×C71C2312yes—
67C4⋊C4×C71—22no—
68C4⋊C4×C71—24no—
69C4⋊C4×C71—22no—
70C23×C71C2411yescharacteristic
71C2×C4×C71—22no—
72C2×C4×C71—21no—
73C2×C4×C71—21no—
74C2×C4×C71—22no—
75C2×C4×C71—22no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71C2×D412yes—
82C2×C4×C71C2×D412yes—
83C2×C4×C71C2×Q814yes—
84C2×Dic71—22no—
85C2×Dic71—21no—
86C2×Dic71—21no—
87C2×Dic71—22no—
88C2×Dic71—21no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71C2×D412yes—
94C2×Dic71C2×D412yes—
95C2×Dic71C2×D412yes—
96C2×Dic71C2×D412yes—
97C2×Dic71C2×Q814yes—
98C2×Dic71C2×Q814yes—
99C2×Dic71#4112yes—
100Dic142—28no—
101Dic142—48no—
102C22×C71C22×D411yescharacteristic
103C22×C71C22×D411yescharacteristic
104C22×C71C22×Q812yes—
105C22×C71C2×#4111yescharacteristic
106C22×C712−1+412yes—
107C4×C71—22no—
108C4×C71—22no—
109C4×C71—24no—
110C4×C71—42no—
111C4×C71—41no—
112Dic71—22no—
113Dic71—24no—
114Dic71—42no—
115Dic71—41no—
116Dic71#12114yes—
117Dic71C4⋊Q814yescomplemented
118C2×C71C2×#12111yescharacteristic
119C2×C71C2×C4⋊Q811yescharacteristic
120C2×C71#53611yescharacteristic
121C2×C71D4×Q812yes—
122C2×C71#55712yes—
123#2546—711nomaximal, Sylow
124C71#254611yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—711no—
126C2×C4⋊Q8—712no—
127C2×C4×Q8—711no—
128#398—711no—
129#398—711no—
130#398—711no—
131#398D7111yescharacteristic
132#391—712no—
133#389—712no—
134#389—712no—
135C4×C4⋊C4—711no—
136C22×Q8—711no—
137C22×Q8—712no—
138C4⋊Q8—1424no—
139C4⋊Q8—1428no—
140C4×Q8—1424no—
141C2×C4⋊C4—712no—
142C2×C4⋊C4—711no—
143C2×C4⋊C4—711no—
144C2×C4⋊C4—712no—
145C2×C4⋊C4—712no—
146C2×C4⋊C4—712no—
147C2×C4⋊C4—712no—
148C2×C4⋊C4—711no—
149C2×C4⋊C4C2×D7111yescharacteristic
150C2×C4⋊C4C2×D7112yes—
151C2×C4⋊C4C2×D7111yescharacteristic
152C2×C42—711no—
153C2×C42—711no—
154C2×C42—711no—
155C2×C42—712no—
156#95—711no—
157#95—712no—
158#95—712no—
159#95—712no—
160#95C2×D7111yescharacteristic
161#95C2×D7112yes—
162C2×Q8—714no—
163C2×Q8—1424no—
164C2×Q8—1424no—
165C2×Q8—1424no—
166C2×Q8—1422no—
167C2×Q8—1422no—
168C22×C4—711no—
169C22×C4—711no—
170C22×C4—712no—
171C22×C4—711no—
172C22×C4—711no—
173C22×C4—712no—
174C22×C4C22×D7111yescharacteristic
175C22×C4C22×D7112yes—
176C22×C4C22×D7111yescharacteristic
177C22×C4C22×D7111yescharacteristic
178C22×C4C22×D7112yes—
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—718no—
183C4⋊C4—1422no—
184C4⋊C4—1424no—
185C4⋊C4—1424no—
186C4⋊C4—1424no—
187C4⋊C4—1422no—
188C4⋊C4—1424no—
189C4⋊C4—1422no—
190C42—714no—
191C42—1422no—
192C42—1422no—
193C42—1424no—
194C23C23×D7111yescharacteristic
195Q8—2848no—
196Q8—1428no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—712no—
208C2×C4—712no—
209C2×C4—712no—
210C2×C4—714no—
211C2×C4—712no—
212C2×C4—712no—
213C2×C4—714no—
214C2×C4—1421no—
215C2×C4—1422no—
216C2×C4—1422no—
217C2×C4—1422no—
218C2×C4—1422no—
219C2×C4—1422no—
220C2×C4—1421no—
221C2×C4—1421no—
222C2×C4—1422no—
223C2×C4D4×D7112yes—
224C2×C4D4×D7112yes—
225C2×C4Q8×D7114yes—
226C22C2×D4×D7111yescharacteristic
227C22C2×D4×D7111yescharacteristic
228C22C2×Q8×D7112yes—
229C22#41×D7111yescharacteristic
230C22#1455617512yes—
231C4—22no—
232C4—24no—
233C4—22no—
234C4—41no—
235C4—42no—
236C4—2841no—
237C4—2842no—
238C4—714no—
239C4—714no—
240C4—1424no—
241C4—1422no—
242C2#121×D7111yescharacteristic
243C2C4⋊Q8×D7111yescharacteristic
244C2#1798657111yescharacteristic
245C2#1798666212yes—
246C2#1798672612yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#398×C71C2
hypercenter#398D71
hypocenterC71#2546
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
57. Dic71⋊C4Q8semidirect
117. Dic71C4⋊Q8semidirect
124. C71#2546semidirect