Finite Group Databasebeta

← #22621136

Subgroups — #22621136

Order 9344.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989139C211yesmaximal, characteristic
2C2×#14556582C211yesmaximal, characteristic
3#17988995C212yesmaximal, complemented
4#17988954C212yesmaximal, complemented
5#17988922C211yesmaximal, characteristic
6#17988918C211yesmaximal, characteristic
7#17988915C211yesmaximal, characteristic
8#17988893C212yesmaximal, complemented
9#17988892C212yesmaximal, complemented
10#17988641C211yesmaximal, characteristic
11#484×C73C211yesmaximal, characteristic
12#14556590C2211yescharacteristic
13#14556589C2211yescharacteristic
14#14556582—21no—
15#14556582—21no—
16#14556582C2212yes—
17#14556582C2212yes—
18#14556581—21no—
19#14556570C2211yescharacteristic
20#14556568—21no—
21Q8×Dic73C2211yescharacteristic
22#14556556—21no—
23#14556556C2211yescharacteristic
24#14556547—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73C2211yescharacteristic
29#14556524C2212yes—
30#14556523C2212yes—
31#14556522C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556515C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37#14556501C2212yes—
38C22⋊Q8×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yes—
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146C2311yescharacteristic
45C22×Dic73—21no—
46C22×Dic73D411yescharacteristic
47C22×Dic73D411yescharacteristic
48C2×#10596831C2312yes—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—21no—
53C4⋊Dic73C2312yes—
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—22no—
57#11924007—22no—
58#11924007—21no—
59#11924007—21no—
60#11924007—21no—
61#11924007—21no—
62C22⋊Dic73—21no—
63C4×Dic73—21no—
64C4×Dic73—21no—
65C4×Dic73D411yescharacteristic
66C4×Dic73D411yescharacteristic
67C4×Dic73C2311yescharacteristic
68C4×Dic73C2311yescharacteristic
69C2×Q8×C73C2311yescharacteristic
70C22×C4×C73—21no—
71C22×C4×C73C2311yescharacteristic
72C2×C8×C73C2312yes—
73C4⋊C4×C73—21no—
74C4⋊C4×C73—21no—
75C4⋊C4×C73C2312yes—
76C4⋊C4×C73C2311yescharacteristic
77C22⋊C4×C73—21no—
78C23×C73C2×D411yescharacteristic
79Q8×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—42no—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—22no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—41no—
92C2×Dic73—42no—
93C2×Dic73C2×D411yescharacteristic
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C2×Dic73C2×D411yescharacteristic
97Dic146—22no—
98Dic146—42no—
99C8×C73—22no—
100#10596831—22no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73#13712yes—
104C22×C73C22×D411yescharacteristic
105C4×C73—21no—
106C4×C73—41no—
107C4×C73—41no—
108C4×C73—42no—
109C4×C732−1+412yes—
110Dic73—21no—
111Dic73—21no—
112Dic73—21no—
113Dic73—21no—
114Dic73—41no—
115Dic73—42no—
116Dic73—41no—
117C2×C73—22no—
118C2×C73#53611yescharacteristic
119C2×C73C2×#13711yescharacteristic
120C2×C73#57511yescharacteristic
121#3236—731nomaximal, Sylow
122C73#323611yescharacteristic, complemented, Sylow
123#533—731no—
124C2×#125—731no—
125#501—732no—
126#491—732no—
127#484—731no—
128#484D7311yescharacteristic
129#483—731no—
130#483—731no—
131#479—732no—
132#479—732no—
133#432—731no—
134C4⋊Q8—731no—
135C4⋊Q8—731no—
136#125—732no—
137#125—732no—
138#125—1461no—
139#125—1461no—
140#125—1461no—
141C22⋊Q8—731no—
142C22⋊Q8—1461no—
143C22⋊Q8C2×D7311yescharacteristic
144C4×Q8—731no—
145C4×Q8—731no—
146C4×Q8—1461no—
147#117—1461no—
148C2×C4⋊C4—731no—
149C2×C4⋊C4—1461no—
150C2×C4⋊C4—1461no—
151C2×C4⋊C4C2×D7311yescharacteristic
152C2×C42—731no—
153#107—732no—
154#107C2×D7312yes—
155#106—732no—
156#106—732no—
157C4⋊C8—732no—
158#103—732no—
159#103—732no—
160#103—732no—
161#103C2×D7312yes—
162C22⋊C8—731no—
163C22⋊C8C2×D7311yescharacteristic
164#97—732no—
165C2×Q8—731no—
166C2×Q8—1461no—
167C2×Q8C22×D7311yescharacteristic
168C22×C4—21no—
169C22×C4—731no—
170C22×C4—731no—
171C22×C4—1461no—
172C22×C4C22×D7311yescharacteristic
173C2×C8—732no—
174C2×C8C22×D7312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—732no—
178C4⋊C4—731no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1461no—
182C4⋊C4—1461no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1461no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4C22×D7312yes—
191C4⋊C4C22×D7311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—1461no—
194C42—731no—
195C42—731no—
196C42—731no—
197C42—731no—
198C42—1461no—
199C42—1461no—
200C23D4×D7311yescharacteristic
201Q8—22no—
202Q8—2922no—
203Q8—1462no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2922no—
210C2×C4—2921no—
211C2×C4—731no—
212C2×C4—731no—
213C2×C4—731no—
214C2×C4—731no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4D4×D7311yescharacteristic
220C2×C4C23×D7311yescharacteristic
221C8—22no—
222C8—1462no—
223C22—21no—
224C22—21no—
225C22#1455662312yes—
226C22C2×D4×D7311yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—2922no—
232C4—2921no—
233C4—2921no—
234C4—1461no—
235C4—1461no—
236C4—1461no—
237C4—1461no—
238C4#1455663812yes—
239C2—22no—
240C2#1798915911yescharacteristic
241C2C2×#1455662311yescharacteristic
242C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3236
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #17988995C2semidirect
4. #17988954C2semidirect
8. #17988893C2semidirect
9. #17988892C2semidirect
122. C73#3236semidirect