Finite Group Databasebeta

← #22589261

Subgroups — #22589261

Order 9088.

324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14556126C211yesmaximal, characteristic
2C2×Dic71⋊C8C211yesmaximal, characteristic
3C2×#14556053C211yesmaximal, characteristic
4C2×#14556052C211yesmaximal, characteristic
5C2×#14556051C211yesmaximal, characteristic
6C4⋊C4×Dic71C211yesmaximal, characteristic
7C2×#103×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10#14556126—22no—
11#14556126C414yescomplemented
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4—21no—
14C2×Dic71⋊C4—21no—
15C2×C4×Dic71—21no—
16C2×C4×Dic71C2211yescharacteristic
17Dic71⋊C8—22no—
18#14556053—22no—
19#14556052—22no—
20#14556051—22no—
21C71⋊#95—21no—
22C22×Q8×C71C2211yescharacteristic
23C22×C8×C71C2211yescharacteristic
24C2×C4⋊C4×C71C2211yescharacteristic
25#103×C71—22no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142—21no—
29C2×Dic142—21no—
30C2×Dic142—21no—
31C2×Dic142C2×C412yes—
32C22×Dic71—21no—
33C22×Dic71—21no—
34C22×Dic71D411yescharacteristic
35C22×Dic71D411yescharacteristic
36C2×C71⋊C8—21no—
37C2×C71⋊C8—21no—
38C2×C71⋊C8—21no—
39C4⋊Dic71—21no—
40C4⋊Dic71D412yes—
41Dic71⋊C4—24no—
42Dic71⋊C4—24no—
43C4×Dic71—42no—
44C4×Dic71C2×C412yes—
45C4×Dic71D412yes—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71—21no—
50C2×Q8×C71—21no—
51C2×Q8×C71C2×C412yes—
52C22×C4×C71—21no—
53C22×C4×C71—21no—
54C22×C4×C71C2311yescharacteristic
55C2×C8×C71—21no—
56C2×C8×C71—21no—
57C2×C8×C71—21no—
58C4⋊C4×C71—21no—
59C4⋊C4×C71D412yes—
60C23×C71C2×D411yescharacteristic
61Q8×C71—22no—
62Q8×C71—22no—
63Q8×C71—41no—
64Q8×C71—41no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—41no—
68C2×C4×C71—41no—
69C2×C4×C71—41no—
70C2×C4×C71—41no—
71C2×C4×C71C22×C411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71#4111yescharacteristic
76C2×C4×C71#4111yescharacteristic
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—41no—
82C2×Dic71—41no—
83C2×Dic71—41no—
84C2×Dic71—41no—
85C2×Dic71C22⋊C412yes—
86C2×Dic71C22⋊C412yes—
87C2×Dic71SD1612yes—
88C2×Dic71Q1612yes—
89Dic142—22no—
90Dic142—22no—
91Dic142—41no—
92Dic142—41no—
93C8×C71—41no—
94C71⋊C8—41no—
95C22×C71C2×C22⋊C411yescharacteristic
96C22×C71#12111yescharacteristic
97C22×C71#12111yescharacteristic
98C22×C71C2×SD1611yescharacteristic
99C22×C71C2×Q1611yescharacteristic
100C22×C71#13711yescharacteristic
101C22×C71#13711yescharacteristic
102C4×C71—42no—
103C4×C71—42no—
104C4×C71C4×D411yescharacteristic
105C4×C71C4×D411yescharacteristic
106C4×C71#12411yescharacteristic
107C4×C71#12711yescharacteristic
108Dic71—22no—
109Dic71—42no—
110Dic71—42no—
111Dic71#10314yescomplemented
112C2×C71#39011yescharacteristic
113C2×C71C2×#10311yescharacteristic
114C2×C71#41911yescharacteristic
115C2×C71#46111yescharacteristic
116C2×C71#46111yescharacteristic
117C2×C71#46211yescharacteristic
118C2×C71#46211yescharacteristic
119#1981—711nomaximal, Sylow
120C71#198111yescharacteristic, complemented, Sylow
121C2×C4⋊Q8—711no—
122C2×C4⋊C8—711no—
123C2×#103—711no—
124C2×#103—711no—
125C2×#103—711no—
126C2×#103D7111yescharacteristic
127C4×C4⋊C4—711no—
128C22×Q8—711no—
129C22×Q8C2×D7111yescharacteristic
130C22×C8—711no—
131C22×C8C2×D7111yescharacteristic
132C4⋊Q8—714no—
133C4⋊Q8—1422no—
134C2×C4⋊C4—711no—
135C2×C4⋊C4—1421no—
136C2×C4⋊C4—1421no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C42—711no—
139C2×C42—1421no—
140C4⋊C8—1422no—
141#103—22no—
142#103—1422no—
143#103—1422no—
144#103—1422no—
145#95—1421no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—712no—
152C2×Q8—1421no—
153C2×Q8—1421no—
154C2×Q8—1421no—
155C2×Q8—1421no—
156C2×Q8—1421no—
157C2×Q8C4×D7112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—711no—
161C22×C4—711no—
162C22×C4—1421no—
163C22×C4—1421no—
164C22×C4C22×D7111yescharacteristic
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1421no—
169C2×C8—1421no—
170C2×C8—1421no—
171C4⋊C4—21no—
172C4⋊C4—712no—
173C4⋊C4—1424no—
174C4⋊C4—1424no—
175C4⋊C4—1421no—
176C4⋊C4C22⋊D7112yes—
177C42—2842no—
178C42—712no—
179C42—712no—
180C23D4×D7111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—2841no—
186Q8—2841no—
187Q8—1422no—
188Q8—1422no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—2841no—
196C2×C4—2841no—
197C2×C4—2841no—
198C2×C4—2841no—
199C2×C4—712no—
200C2×C4—712no—
201C2×C4—712no—
202C2×C4—712no—
203C2×C4—1422no—
204C2×C4—1422no—
205C2×C4—1421no—
206C2×C4—1421no—
207C2×C4C2×C4×D7111yescharacteristic
208C2×C4D4×D7111yescharacteristic
209C2×C4D4×D7111yescharacteristic
210C2×C4C2×C22⋊D7111yescharacteristic
211C2×C4#1176586411yescharacteristic
212C2×C4#1176586511yescharacteristic
213C8—41no—
214C8—2841no—
215C22C22⋊C4×D7111yescharacteristic
216C22#1455610011yescharacteristic
217C22#1455610111yescharacteristic
218C22SD16×D7111yescharacteristic
219C22Q16×D7111yescharacteristic
220C22#1455615711yescharacteristic
221C22#1455616011yescharacteristic
222C4—42no—
223C4—42no—
224C4—2842no—
225C4—2842no—
226C4—714no—
227C4—1422no—
228C4(C22⋊D71)⋊C411yescharacteristic
229C4C4×C22⋊D7111yescharacteristic
230C4#1455611411yescharacteristic
231C4#1455612411yescharacteristic
232C2#1798589911yescharacteristic
233C2#103×D7111yescharacteristic
234C2#1798600611yescharacteristic
235C2#1798620211yescharacteristic
236C2#1798620311yescharacteristic
237C2#1798620711yescharacteristic
238C2#1798620811yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
FittingC2×#103×C71C2
socleC23×C71C2×D4
hypercenterC2×#103D71
hypocenterC71#1981
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. #14556126C4semidirect
111. Dic71#103semidirect
120. C71#1981semidirect