Finite Group Databasebeta

← #22601082

Subgroups — #22601082

Order 9088.

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

normal subgroups only

This group has 338 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
1Q8×Dic142C211yesmaximal, characteristic, complemented
2#17986722C211yesmaximal, characteristic
3#17986359C212yesmaximal
4#17986350C211yesmaximal, characteristic, complemented
5#17986290C211yesmaximal, characteristic
6#17986285C212yesmaximal, complemented
7#17986222C212yesmaximal
8#17986210C211yesmaximal, characteristic, complemented
9#17986107C212yesmaximal, complemented
10C4×#11765854C211yesmaximal, characteristic
11#446×C71C211yesmaximal, characteristic, complemented
12C2×Dic284C2212yes—
13C2×#11765854C2211yescharacteristic
14#14556128C2211yescharacteristic
15#14556128C2211yescharacteristic
16#14556128C2212yes—
17#14556127—21no—
18#14556127—22no—
19#14556123—22no—
20#14556116C2212yes—
21#14556104—21no—
22Q8×Dic71—21no—
23C4×Dic142C2211yescharacteristic
24C4×Dic142C2212yes—
25C4×Dic142C2212yes—
26C4×D284C2211yescharacteristic
27#14556086—21no—
28#14556060C2211yescharacteristic
29#14556060C2212yes—
30#14556053C2211yescharacteristic
31#14556053C2212yes—
32#14556053C2212yes—
33#14556053C2212yes—
34#14556050C2211yescharacteristic
35#14556050C2212yes—
36C4×Q8×C71C2211yescharacteristic
37C4⋊C8×C71C2211yescharacteristic
38C4⋊C8×C71C2212yes—
39#97×C71C2212yes—
40C4×C8×C71C2211yescharacteristic
41C2×Dic142—22no—
42C2×Dic142—21no—
43C2×Dic142C2312yes—
44C2×Dic142C2311yescharacteristic
45C2×D284C2311yescharacteristic
46C2×C4×D71—21no—
47Dic284—24no—
48#11765854—22no—
49C4⋊Dic71—21no—
50C4⋊Dic71—22no—
51C4⋊Dic71—21no—
52C4⋊Dic71—21no—
53C4⋊Dic71C2311yescharacteristic
54C4⋊Dic71C2312yes—
55C4⋊Dic71C2311yescharacteristic
56Dic71⋊C4—22no—
57Dic71⋊C4—22no—
58Dic71⋊C4—21no—
59(C2×D71)⋊C4—22no—
60(C2×D71)⋊C4—21no—
61(C2×D71)⋊C4—22no—
62C4×Dic71—22no—
63C4×Dic71—22no—
64C4×Dic71—21no—
65C2×Q8×C71D411yescharacteristic
66C2×C8×C71C2311yescharacteristic
67C2×C8×C71C2311yescharacteristic
68C2×C8×C71C2312yes—
69C4⋊C4×C71D411yescharacteristic
70C4⋊C4×C71D412yes—
71C42×C71C2311yescharacteristic
72C42×C71C2312yes—
73C22×D71—21no—
74Q8×C71—22no—
75C2×C4×C71C2×D412yes—
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D412yes—
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2411yescharacteristic
80C2×Dic71—21no—
81C2×Dic71—21no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—21no—
85D284—21no—
86D284—21no—
87C4×D71—42no—
88Dic142—21no—
89Dic142—22no—
90Dic142—22no—
91Dic142—82no—
92Dic142—81no—
93Dic142#4112yes—
94C8×C71—21no—
95C8×C71—22no—
96C8×C71—21no—
97C22×C71C22×D411yescharacteristic
98C2×D71—41no—
99C2×D71—41no—
100C2×D71—41no—
101C4×C71—22no—
102C4×C71—22no—
103C4×C71—21no—
104C4×C71#13712yes—
105C4×C71C2×#4111yescharacteristic
106C4×C712−1+411yescharacteristic
107Dic71—22no—
108Dic71—42no—
109Dic71—41no—
110Dic71—41no—
111Dic71—42no—
112C2×C71#54811yescharacteristic
113C2×C71C2×#13711yescharacteristic
114C2×C71#57711yescharacteristic
115D71—81no—
116#3369—711nomaximal, Sylow
117C71#336911yescharacteristic, complemented, Sylow
118Q82—711no—
119#556—711no—
120#489—712no—
121#487—711no—
122#476—711no—
123#475—712no—
124#464—712no—
125#462—711no—
126#446D7111yescharacteristic, complemented
127#441—712no—
128C4×SD16—711no—
129C2×Q16—712no—
130C2×SD16—711no—
131C4⋊Q8—712no—
132C4⋊Q8—711no—
133C4⋊Q8—711no—
134C4⋊Q8—1421no—
135C4⋊Q8—1422no—
136#126—1422no—
137#124—712no—
138C22⋊Q8—1421no—
139C4×Q8—712no—
140C4×Q8—711no—
141C4×Q8—712no—
142C4×Q8—1421no—
143C4×Q8C2×D7111yescharacteristic
144C4×D4—711no—
145#117—1421no—
146#106—711no—
147#106—712no—
148C4⋊C8C2×D7111yescharacteristic
149C4⋊C8C2×D7112yes—
150#103—711no—
151#103—712no—
152#103—712no—
153#103—712no—
154#102—711no—
155#102—712no—
156#97C2×D7112yes—
157C4×C8C2×D7111yescharacteristic
158C2×Q8—711no—
159C2×Q8—712no—
160C2×Q8—1422no—
161C2×Q8—1421no—
162C2×Q8D28411yescharacteristic
163C2×D4—711no—
164C22×C4—1421no—
165Q16—1424no—
166SD16—1422no—
167C2×C8C22×D7111yescharacteristic
168C2×C8C22×D7111yescharacteristic
169C2×C8C22×D7112yes—
170C4⋊C4—711no—
171C4⋊C4—712no—
172C4⋊C4—711no—
173C4⋊C4—1422no—
174C4⋊C4—1422no—
175C4⋊C4—1421no—
176C4⋊C4—1421no—
177C4⋊C4—1422no—
178C4⋊C4—1421no—
179C4⋊C4—1421no—
180C4⋊C4D28411yescharacteristic
181C4⋊C4D28412yes—
182C22⋊C4—1422no—
183C22⋊C4—1421no—
184C22⋊C4—1422no—
185C42—1422no—
186C42—1422no—
187C42—1421no—
188C42C22×D7111yescharacteristic
189C42C22×D7112yes—
190C23—1421no—
191Q8—22no—
192Q8—5682no—
193Q8—5681no—
194Q8—712no—
195Q8—1422no—
196Q8—1422no—
197Q8—1421no—
198D4—1421no—
199D4—1421no—
200C2×C4—2842no—
201C2×C4—1421no—
202C2×C4—1422no—
203C2×C4—1422no—
204C2×C4—1421no—
205C2×C4—1421no—
206C2×C4C2×D28412yes—
207C2×C4C2×D28412yes—
208C2×C4C2×D28411yescharacteristic
209C2×C4C2×D28411yescharacteristic
210C2×C4C23×D7111yescharacteristic
211C8—21no—
212C8—22no—
213C8—21no—
214C22—2841no—
215C22—2841no—
216C22—2841no—
217C22C22×D28411yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—2842no—
222C4—2841no—
223C4—2842no—
224C4—2841no—
225C4—1422no—
226C4#1455616112yes—
227C4#41×D7111yescharacteristic
228C4#1455617611yescharacteristic
229C2—5681no—
230C2#1798666111yescharacteristic
231C2C2×#1455616111yescharacteristic
232C2#1798681111yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#446×C71C2
socleC22×C71C22×D4
hypercenter#446D71
hypocenterC71#3369
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. Q8×Dic142C2semidirect
4. #17986350C2semidirect
6. #17986285C2semidirect
8. #17986210C2semidirect
9. #17986107C2semidirect
11. #446×C71C2semidirect
117. C71#3369semidirect
126. #446D71semidirect