Finite Group Databasebeta

← #22621597

Subgroups — #22621597

Order 9344.

482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556621C212yesmaximal, complemented
2D4×Dic146C211yesmaximal, characteristic, complemented
3#17988959C211yesmaximal, characteristic, complemented
4#17988831C212yesmaximal, complemented
5#17988797C211yesmaximal, characteristic, complemented
6#17988784C211yesmaximal, characteristic, complemented
7#17988749C212yesmaximal, complemented
8#17988725C212yesmaximal, complemented
9C4×#11924018C211yesmaximal, characteristic, complemented
10#17988665C211yesmaximal, characteristic, complemented
11#550×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13#14556621—28no—
14C2×#11924018C2212yes—
15C2×#11924018C2211yescharacteristic
16C2×#11924016C2212yes—
17C2×#11924016C2212yes—
18C2×#11924016C2212yes—
19C2×#11924012C2212yes—
20#14556591C2211yescharacteristic
21#14556590—21no—
22#14556570C2212yes—
23#14556568—22no—
24C4×Dic146C2211yescharacteristic
25D4×Dic73—21no—
26#14556524C2211yescharacteristic
27C4⋊#10596831C2211yescharacteristic
28#14556515C2211yescharacteristic
29#14556514C2211yescharacteristic
30#14556514C2212yes—
31#14556512C2212yes—
32C22⋊#10596831C2212yes—
33C4×#10596831C2211yescharacteristic
34C2×#41×C73C2212yes—
35#127×C73—21no—
36#127×C73C2211yescharacteristic
37#121×C73—22no—
38#121×C73C2212yes—
39C4×Q8×C73C2211yescharacteristic
40C4×D4×C73—21no—
41C4×D4×C73C2211yescharacteristic
42C2×Dic146—24no—
43C2×Dic146—22no—
44C2×Dic146—42no—
45C2×Dic146C2312yes—
46C2×Dic146C2311yescharacteristic
47C22×Dic73—22no—
48#11924018—24no—
49#11924018D414yescomplemented
50#11924016—24no—
51#11924016—24no—
52#11924016—42no—
53#11924012—24no—
54C2×#10596831C2311yescharacteristic
55C2×#10596831C2312yes—
56C2×#10596831C2311yescharacteristic
57C4⋊Dic73—21no—
58C4⋊Dic73—21no—
59C4⋊Dic73C2311yescharacteristic
60#11924007—21no—
61#11924007—22no—
62C22⋊Dic73—22no—
63C4×Dic73—21no—
64#41×C73—24no—
65#41×C73—42no—
66C2×Q8×C73C2311yescharacteristic
67C2×D4×C73—22no—
68C2×D4×C73—22no—
69C2×D4×C73—21no—
70C2×D4×C73—21no—
71C2×D4×C73D411yescharacteristic
72C2×D4×C73C2312yes—
73C22×C4×C73—22no—
74C22×C4×C73C2312yes—
75C4⋊C4×C73—21no—
76C4⋊C4×C73D411yescharacteristic
77C4⋊C4×C73C2311yescharacteristic
78C22⋊C4×C73—22no—
79C22⋊C4×C73D412yes—
80C42×C73—21no—
81C42×C73C2311yescharacteristic
82C23×C73—22no—
83C23×C73C2×D412yes—
84Q8×C73—21no—
85Q8×C73C2×D412yes—
86D4×C73—22no—
87D4×C73—22no—
88D4×C73—22no—
89D4×C73—44no—
90D4×C73—42no—
91D4×C73—81no—
92D4×C73—82no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—21no—
97C2×C4×C73—44no—
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D412yes—
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2411yescharacteristic
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—44no—
106Dic146—21no—
107Dic146—22no—
108Dic146—22no—
109Dic146—44no—
110Dic146C2×D412yes—
111#10596831—22no—
112#10596831—21no—
113#10596831C2×D412yes—
114C22×C73—22no—
115C22×C73—22no—
116C22×C73—22no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73C22×D411yescharacteristic
121C4×C73—22no—
122C4×C73—22no—
123C4×C73—21no—
124C4×C73—41no—
125C4×C73#13712yescomplemented
126C4×C73C22×D411yescharacteristic
127C4×C73H(5,𝔽2)11yescharacteristic
128Dic73—22no—
129Dic73—42no—
130Dic73—41no—
131C2×C73—42no—
132C2×C73—82no—
133C2×C73D4211yescharacteristic
134C2×C73C2×#13711yescharacteristic
135C2×C73#57711yescharacteristic
136#3278—731nomaximal, Sylow
137C73#327811yescharacteristic, complemented, Sylow
138C2×#137—732no—
139#550D7311yescharacteristic
140D4×Q8—731no—
141#492—731no—
142#468—732no—
143#462—731no—
144#460—731no—
145#452—732no—
146#448—732no—
147C4×Q16—731no—
148#436—731no—
149C2×#41C2×D7312yes—
150C22×Q8—732no—
151#137—1468no—
152C2×Q16—731no—
153C2×Q16—732no—
154C2×SD16—732no—
155C2×SD16—732no—
156C2×SD16—732no—
157C2×M16—732no—
158C4⋊Q8—731no—
159C4⋊Q8—1461no—
160#127—21no—
161#127C2×D7311yescharacteristic
162C22⋊Q8—732no—
163C22⋊Q8—1462no—
164#121—22no—
165#121C2×D7312yes—
166C4×Q8—731no—
167C4×Q8C2×D7311yescharacteristic
168C4×D4—21no—
169C4×D4—1461no—
170C4×D4C2×D7311yescharacteristic
171#107—731no—
172C4⋊C8—731no—
173#103—731no—
174#103—731no—
175#103—732no—
176#102—732no—
177C22⋊C8—732no—
178C4×C8—731no—
179#41—24no—
180#41—42no—
181C2×Q8—2922no—
182C2×Q8—731no—
183C2×Q8—732no—
184C2×Q8—1464no—
185C2×Q8—1462no—
186C2×Q8C22×D7311yescharacteristic
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4C22⋊D7311yescharacteristic
192C2×D4C22×D7312yes—
193C22×C4—22no—
194C22×C4—1462no—
195C22×C4C22×D7312yes—
196Q16—734no—
197Q16—1464no—
198SD16—2922no—
199SD16—1464no—
200SD16—1464no—
201M16—1464no—
202C2×C8—731no—
203C2×C8—731no—
204C2×C8—732no—
205C4⋊C4—21no—
206C4⋊C4—731no—
207C4⋊C4—1461no—
208C4⋊C4—1462no—
209C4⋊C4—1461no—
210C4⋊C4—1461no—
211C4⋊C4C22⋊D7311yescharacteristic
212C4⋊C4C22×D7311yescharacteristic
213C22⋊C4—22no—
214C22⋊C4—1462no—
215C22⋊C4C22⋊D7312yes—
216C42—21no—
217C42—1461no—
218C42C22×D7311yescharacteristic
219C23—22no—
220C23C2×C22⋊D7312yes—
221Q8—21no—
222Q8—2924no—
223Q8—732no—
224Q8—1462no—
225Q8—1462no—
226Q8—1461no—
227Q8D4×D7312yes—
228D4—22no—
229D4—22no—
230D4—22no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—82no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—44no—
240C2×C4—2924no—
241C2×C4—1461no—
242C2×C4—1462no—
243C2×C4—1461no—
244C2×C4C2×C22⋊D7311yescharacteristic
245C2×C4C2×C22⋊D7312yes—
246C2×C4C2×C22⋊D7311yescharacteristic
247C2×C4C23×D7311yescharacteristic
248C8—732no—
249C8—1462no—
250C8—1461no—
251C22—22no—
252C22—22no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—42no—
257C22C22×C22⋊D7311yescharacteristic
258C4—21no—
259C4—22no—
260C4—22no—
261C4—41no—
262C4—2921no—
263C4—2922no—
264C4—1462no—
265C4#1455662112yescomplemented
266C4C2×D4×D7311yescharacteristic
267C4#1455663611yescharacteristic
268C2—42no—
269C2—82no—
270C2D4×C22⋊D7311yescharacteristic
271C2C2×#1455662111yescharacteristic
272C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#550×C73C2
socleC22×C73C22×D4
hypercenter#550D73
hypocenterC73#3278
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14556621C2semidirect
2. D4×Dic146C2semidirect
3. #17988959C2semidirect
4. #17988831C2semidirect
5. #17988797C2semidirect
6. #17988784C2semidirect
7. #17988749C2semidirect
8. #17988725C2semidirect
9. C4×#11924018C2semidirect
10. #17988665C2semidirect
49. #11924018D4semidirect
125. C4×C73#137semidirect
137. C73#3278semidirect
265. C4#14556621semidirect