Finite Group Databasebeta

← #22599482

Subgroups — #22599482

Order 9088.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#17986551C211yesmaximal, characteristic
2C2×#14556127C211yesmaximal, characteristic
3#17986396C212yesmaximal, complemented
4#17986348C212yesmaximal, complemented
5#17986330C211yesmaximal, characteristic
6#17986329C211yesmaximal, characteristic
7#17986327C211yesmaximal, characteristic
8#17986283C212yesmaximal, complemented
9#17986282C212yesmaximal, complemented
10#17986049C211yesmaximal, characteristic
11#483×C71C211yesmaximal, characteristic
12C22×Dic142—21no—
13#14556127—21no—
14#14556127—21no—
15#14556127C2212yes—
16#14556127C2211yescharacteristic
17#14556127C2212yes—
18#14556126C2211yescharacteristic
19#14556118—21no—
20#14556107C2211yescharacteristic
21#14556105—21no—
22Q8×Dic71C2211yescharacteristic
23#14556093—21no—
24#14556093C2211yescharacteristic
25#14556084—21no—
26C2×C4⋊Dic71C2211yescharacteristic
27C2×Dic71⋊C4—21no—
28C2×C4×Dic71C2211yescharacteristic
29#14556060C2212yes—
30#14556059C2212yes—
31#14556059C2212yes—
32Dic71⋊C8C2212yes—
33#14556053C2212yes—
34#14556052C2212yes—
35#14556051C2212yes—
36C22⋊(C71⋊C8)C2211yescharacteristic
37C8×Dic71C2212yes—
38C22⋊Q8×C71C2211yescharacteristic
39C2×C4⋊C4×C71C2211yescharacteristic
40#106×C71C2212yes—
41#103×C71C2212yes—
42C22⋊C8×C71C2211yescharacteristic
43C2×Dic142—22no—
44C2×Dic142—22no—
45C2×Dic142—21no—
46C2×Dic142—44no—
47C2×Dic142C2311yescharacteristic
48C22×Dic71—21no—
49C22×Dic71D411yescharacteristic
50C22×Dic71D411yescharacteristic
51C2×C71⋊C8C2312yes—
52C4⋊Dic71—21no—
53C4⋊Dic71—21no—
54C4⋊Dic71C2312yes—
55C4⋊Dic71C2311yescharacteristic
56Dic71⋊C4—21no—
57Dic71⋊C4—22no—
58Dic71⋊C4—22no—
59Dic71⋊C4—21no—
60Dic71⋊C4—21no—
61Dic71⋊C4—21no—
62Dic71⋊C4—21no—
63C22⋊Dic71—21no—
64C4×Dic71—21no—
65C4×Dic71—21no—
66C4×Dic71D411yescharacteristic
67C4×Dic71D411yescharacteristic
68C4×Dic71C2311yescharacteristic
69C4×Dic71C2311yescharacteristic
70C2×Q8×C71C2311yescharacteristic
71C22×C4×C71—21no—
72C22×C4×C71C2311yescharacteristic
73C2×C8×C71C2312yes—
74C4⋊C4×C71—21no—
75C4⋊C4×C71—21no—
76C4⋊C4×C71C2312yes—
77C4⋊C4×C71C2311yescharacteristic
78C22⋊C4×C71—21no—
79C23×C71C2×D411yescharacteristic
80Q8×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—21no—
83C2×C4×C71—21no—
84C2×C4×C71—22no—
85C2×C4×C71—42no—
86C2×C4×C71C2×D411yescharacteristic
87C2×C4×C71C2411yescharacteristic
88C2×Dic71—22no—
89C2×Dic71—21no—
90C2×Dic71—21no—
91C2×Dic71—22no—
92C2×Dic71—42no—
93C2×Dic71SD1614yes—
94C2×Dic71C2×D411yescharacteristic
95C2×Dic71C2×D411yescharacteristic
96C2×Dic71C2×D411yescharacteristic
97C2×Dic71C2×D411yescharacteristic
98Dic142—22no—
99Dic142—44no—
100Dic142—44no—
101Dic142—42no—
102C8×C71—22no—
103C71⋊C8—22no—
104C22×C71—21no—
105C22×C71—21no—
106C22×C71C2×SD1612yes—
107C22×C71C22×D411yescharacteristic
108C4×C71—21no—
109C4×C71—41no—
110C4×C71—42no—
111C4×C71—41no—
112C4×C712−1+412yes—
113Dic71—21no—
114Dic71—41no—
115Dic71—42no—
116Dic71—41no—
117Dic71C2×SD1612yes—
118Dic71C2×SD1612yes—
119Dic71#13712yes—
120C2×C71—22no—
121C2×C71#53611yescharacteristic
122C2×C71C22×SD1611yescharacteristic
123C2×C71C2×#13711yescharacteristic
124#3229—711nomaximal, Sylow
125C71#322911yescharacteristic, complemented, Sylow
126#533—711no—
127C2×C4⋊Q8—711no—
128#498—712no—
129#487—712no—
130#483—711no—
131#483—711no—
132#483—711no—
133#483D7111yescharacteristic
134#475—712no—
135#475—712no—
136#431—711no—
137C22×Q8—1421no—
138C4⋊Q8—712no—
139C4⋊Q8—712no—
140C4⋊Q8—711no—
141C4⋊Q8—711no—
142C4⋊Q8—1421no—
143C4⋊Q8—1421no—
144#125—1421no—
145C22⋊Q8—711no—
146C22⋊Q8—1421no—
147C22⋊Q8C2×D7111yescharacteristic
148C4×Q8—711no—
149C4×Q8—711no—
150C4×Q8—1421no—
151#117—1421no—
152C2×C4⋊C4—711no—
153C2×C4⋊C4—1421no—
154C2×C4⋊C4C2×D7111yescharacteristic
155C2×C42—711no—
156#106—712no—
157#106—712no—
158#106—712no—
159#106C2×D7112yes—
160C4⋊C8—712no—
161#103—712no—
162#103—712no—
163#103—712no—
164#103C2×D7112yes—
165C22⋊C8—711no—
166C22⋊C8C2×D7111yescharacteristic
167C4×C8—712no—
168C2×Q8—2844no—
169C2×Q8—711no—
170C2×Q8—1421no—
171C2×Q8—1422no—
172C2×Q8—1422no—
173C2×Q8C22×D7111yescharacteristic
174C22×C4—21no—
175C22×C4—711no—
176C22×C4—711no—
177C22×C4—1421no—
178C22×C4C22×D7111yescharacteristic
179C2×C8—712no—
180C2×C8C22×D7112yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—712no—
184C4⋊C4—711no—
185C4⋊C4—1422no—
186C4⋊C4—1422no—
187C4⋊C4—1421no—
188C4⋊C4—1421no—
189C4⋊C4—1421no—
190C4⋊C4—1421no—
191C4⋊C4—1421no—
192C4⋊C4—1421no—
193C4⋊C4—1421no—
194C4⋊C4C22×D7112yes—
195C4⋊C4C22×D7111yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1421no—
198C42—711no—
199C42—711no—
200C42—711no—
201C42—711no—
202C42—1421no—
203C42—1421no—
204C23D4×D7111yescharacteristic
205Q8—22no—
206Q8—2844no—
207Q8—2844no—
208Q8—2842no—
209Q8—1422no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—2842no—
216C2×C4—711no—
217C2×C4—711no—
218C2×C4—711no—
219C2×C4—714no—
220C2×C4—711no—
221C2×C4—1421no—
222C2×C4—1421no—
223C2×C4—1422no—
224C2×C4—1422no—
225C2×C4D4×D7111yescharacteristic
226C2×C4C23×D7111yescharacteristic
227C8—22no—
228C8—1422no—
229C22—21no—
230C22—21no—
231C22SD16×D7112yes—
232C22C2×D4×D7111yescharacteristic
233C4—21no—
234C4—41no—
235C4—42no—
236C4—41no—
237C4—2841no—
238C4—2842no—
239C4—2841no—
240C4—712no—
241C4—712no—
242C4—712no—
243C4—1421no—
244C4#1455617512yes—
245C2—22no—
246C2#1798657111yescharacteristic
247C2C2×SD16×D7111yescharacteristic
248C2#137×D7111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#483×C71C2
socleC22×C71C22×D4
hypercenter#483D71
hypocenterC71#3229
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #17986396C2semidirect
4. #17986348C2semidirect
8. #17986283C2semidirect
9. #17986282C2semidirect
125. C71#3229semidirect