Finite Group Databasebeta

← #22620955

Subgroups — #22620955

Order 9344.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556591C211yesmaximal, characteristic, complemented
2#17988982C212yesmaximal, complemented
3#17988957C212yesmaximal, complemented
4#17988797C212yesmaximal, complemented
5#17988792C212yesmaximal, complemented
6#17988742C212yesmaximal, complemented
7#17988725C212yesmaximal
8#17988644C211yesmaximal, characteristic, complemented
9#529×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C2×#11924018C2214yes—
12C2×#11924016C2214yes—
13#14556591—21no—
14#14556591—21no—
15#14556591C2212yes—
16#14556591C2212yes—
17C2×C4⋊Dic73—21no—
18C2×C4⋊Dic73—21no—
19C4⋊#10596831C2212yes—
20#14556514C2214yes—
21#14556514C2214yes—
22C22⋊#10596831C2212yes—
23#14556502C2212yes—
24#126×C73—21no—
25#125×C73C2211yescharacteristic
26#124×C73C2211yescharacteristic
27#123×C73—21no—
28C22⋊Q8×C73C2211yescharacteristic
29#121×C73C2211yescharacteristic
30C4×Q8×C73C2211yescharacteristic
31C4×D4×C73—21no—
32C4×D4×C73C2211yescharacteristic
33#117×C73—21no—
34C2×C42×C73C2211yescharacteristic
35C2×Dic146—22no—
36C2×Dic146—44no—
37C2×Dic146C2314yes—
38C22×Dic73—22no—
39#11924018—44no—
40#11924016—44no—
41C2×#10596831C2314yes—
42C4⋊Dic73—22no—
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45C4⋊Dic73—22no—
46C2×Q8×C73C2311yescharacteristic
47C2×D4×C73—21no—
48C2×D4×C73C2311yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73D411yescharacteristic
51C22×C4×C73D411yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C4⋊C4×C73C2311yescharacteristic
58C4⋊C4×C73C2311yescharacteristic
59C22⋊C4×C73—21no—
60C22⋊C4×C73—21no—
61C22⋊C4×C73—21no—
62C22⋊C4×C73—21no—
63C22⋊C4×C73—21no—
64C42×C73—21no—
65C42×C73D411yescharacteristic
66C42×C73D411yescharacteristic
67C42×C73C2311yescharacteristic
68C42×C73C2311yescharacteristic
69C23×C73—21no—
70C23×C73C2×D411yescharacteristic
71Q8×C73—22no—
72D4×C73—22no—
73D4×C73—42no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—42no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—24no—
88C2×Dic73—44no—
89Dic146—24no—
90Dic146—24no—
91Dic146—44no—
92#10596831—24no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73#13712yes—
99C22×C73C22×D411yescharacteristic
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73#13712yes—
108C4×C73H(5,𝔽2)12yes—
109Dic73—44no—
110C2×C73—22no—
111C2×C73—81no—
112C2×C73#53511yescharacteristic
113C2×C73C2×#13711yescharacteristic
114C2×C73C2×#13711yescharacteristic
115#3218—731nomaximal, Sylow
116C73#321811yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—731no—
118#529D7311yescharacteristic
119#497—732no—
120#491—732no—
121#462—732no—
122#461—732no—
123#451—732no—
124#448—732no—
125#432—731no—
126C22×Q8—732no—
127C2×Q16—734no—
128C2×SD16—734no—
129C4⋊Q8—732no—
130C4⋊Q8—732no—
131C4⋊Q8—1461no—
132C4⋊Q8—1461no—
133#126—21no—
134#125C2×D7311yescharacteristic
135#124C2×D7311yescharacteristic
136#123—21no—
137C22⋊Q8C2×D7311yescharacteristic
138#121C2×D7311yescharacteristic
139C4×Q8C2×D7311yescharacteristic
140C4×D4—21no—
141C4×D4C2×D7311yescharacteristic
142#117—21no—
143C2×C4⋊C4—1461no—
144C2×C4⋊C4—1461no—
145C2×C42C2×D7311yescharacteristic
146C4⋊C8—732no—
147#103—734no—
148#103—734no—
149C22⋊C8—732no—
150#97—732no—
151C2×Q8—2924no—
152C2×Q8—734no—
153C2×Q8—1462no—
154C2×Q8C22×D7311yescharacteristic
155C2×D4—21no—
156C2×D4C22×D7311yescharacteristic
157C22×C4—21no—
158C22×C4—1462no—
159C22×C4C22⋊D7311yescharacteristic
160C22×C4C22⋊D7311yescharacteristic
161C22×C4C22×D7311yescharacteristic
162Q16—2924no—
163SD16—2924no—
164C2×C8—734no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4C22×D7311yescharacteristic
174C4⋊C4C22×D7311yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C42—21no—
181C42C22⋊D7311yescharacteristic
182C42C22⋊D7311yescharacteristic
183C42C22×D7311yescharacteristic
184C42C22×D7311yescharacteristic
185C23—21no—
186C23C2×C22⋊D7311yescharacteristic
187Q8—22no—
188Q8—2924no—
189Q8—1464no—
190Q8—1464no—
191D4—22no—
192D4—42no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—2924no—
201C2×C4—1464no—
202C2×C4C2×C22⋊D7311yescharacteristic
203C2×C4C2×C22⋊D7311yescharacteristic
204C2×C4C2×C22⋊D7311yescharacteristic
205C2×C4C2×C22⋊D7311yescharacteristic
206C2×C4C2×C22⋊D7311yescharacteristic
207C2×C4C23×D7311yescharacteristic
208C8—1464no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22#1455662112yes—
215C22C22×C22⋊D7311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—41no—
222C4—41no—
223C4—2924no—
224C4#1455662112yes—
225C4#1455663712yes—
226C2—22no—
227C2—81no—
228C2#1798915111yescharacteristic
229C2C2×#1455662111yescharacteristic
230C2C2×#1455662111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#529×C73C2
socleC22×C73C22×D4
hypercenter#529D73
hypocenterC73#3218
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×#14556591C2semidirect
2. #17988982C2semidirect
3. #17988957C2semidirect
4. #17988797C2semidirect
5. #17988792C2semidirect
6. #17988742C2semidirect
8. #17988644C2semidirect
116. C73#3218semidirect