Finite Group Databasebeta

← #323×D73 #22608236

Subgroups — #323×D73 #22608236

Order 9344.

456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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×C22⋊C4×D73C211yesmaximal, characteristic
2C22⋊C8×D73C212yesmaximal, complemented
3#17988311C211yesmaximal, characteristic, complemented
4#17988310C212yesmaximal, complemented
5#323×C73C211yesmaximal, characteristic, complemented
6C24×D73C411yescharacteristic
7C22×C4×D73C411yescharacteristic
8C22×C4×D73C2211yescharacteristic
9C2×C8×D73—22no—
10C2×C22⋊Dic73C411yescharacteristic
11C2×#11924005C411yescharacteristic
12C2×#11924005C2211yescharacteristic
13C22⋊C4×D73—22no—
14C22⋊C4×D73—22no—
15C22⋊#10596831C2212yescomplemented
16#14556503—22no—
17C2×C22⋊C4×C73C2211yescharacteristic
18C22⋊C8×C73C2212yescomplemented
19C23×D73—21no—
20C23×D73—21no—
21C23×D73—22no—
22C23×D73—42no—
23C23×D73—42no—
24C23×D73C814yescomplemented
25C23×D73C2×C411yescharacteristic
26C23×D73C2×C411yescharacteristic
27C22×Dic73C2×C411yescharacteristic
28C22×Dic73C2×C411yescharacteristic
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—42no—
32C2×C4×D73—42no—
33C2×C4×D73D412yes—
34C2×C4×D73D412yes—
35C2×#10596831—22no—
36C8×D73—44no—
37C22⋊Dic73—22no—
38#11924005—22no—
39#11924005—22no—
40C24×C73C2×C411yescharacteristic
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C2×C8×C73—22no—
44C22⋊C4×C73—22no—
45C23×C73—21no—
46C23×C73—21no—
47C23×C73—41no—
48C23×C73—41no—
49C23×C73C2×C812yescomplemented
50C23×C73C22×C411yescharacteristic
51C22×D73—22no—
52C22×D73—22no—
53C22×D73—21no—
54C22×D73—21no—
55C22×D73—24no—
56C22×D73—24no—
57C22×D73—42no—
58C22×D73—42no—
59C22×D73—48no—
60C22×D73—48no—
61C22×D73—42no—
62C22×D73—42no—
63C22×D73—41no—
64C22×D73—41no—
65C22×D73C22⋊C411yescharacteristic
66C22×D73C22⋊C411yescharacteristic
67C22×D73C2×C812yes—
68C22×D73C2×C812yescomplemented
69C22×D73M1612yes—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73C2×D412yes—
74C2×Dic73—21no—
75C2×Dic73—41no—
76C2×Dic73—41no—
77C2×Dic73C22⋊C412yes—
78C4×D73—24no—
79C4×D73—42no—
80C4×D73—42no—
81C4×D73—42no—
82C8×C73—42no—
83#10596831—42no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—22no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73C2×C22⋊C411yescharacteristic
92C22×C73C22×C811yescharacteristic
93C22×C73C2×M1611yescharacteristic
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—24no—
97C2×D73—24no—
98C2×D73—22no—
99C2×D73—48no—
100C2×D73—42no—
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—48no—
104C2×D73—42no—
105C2×D73C22⋊C812yes—
106C2×D73C22⋊C812yes—
107C2×D73#9912yes—
108C2×D73#10012yes—
109C4×C73—22no—
110C4×C73—41no—
111Dic73—22no—
112Dic73—41no—
113C2×C73—21no—
114C2×C73—21no—
115C2×C73—42no—
116C2×C73C2×C22⋊C811yescharacteristic
117C2×C73C2×#9911yescharacteristic
118C2×C73C2×#10011yescharacteristic
119D73—22no—
120D73—42no—
121D73#32314yesdirect product factor
122C2×#323—731nomaximal, Sylow
123C73C2×#32311yescharacteristic, complemented, Sylow
124C22×C22⋊C4—731no—
125C2×C22⋊C8—732no—
126#323—731no—
127#323—732no—
128#323D7311yescharacteristic, direct product factor
129C25—731no—
130C23×C4—731no—
131C23×C4—731no—
132C22×C8—1462no—
133C2×C22⋊C4—731no—
134C2×C22⋊C4—731no—
135C2×C22⋊C4—731no—
136C2×C22⋊C4—1462no—
137C2×C22⋊C4—1462no—
138C2×C22⋊C4C2×D7311yescharacteristic
139C22⋊C8—732no—
140C22⋊C8—1462no—
141C22⋊C8C2×D7312yescomplemented
142C24—2922no—
143C24—2922no—
144C24—734no—
145C24—731no—
146C24—731no—
147C24—1461no—
148C24—1461no—
149C24—1462no—
150C24C4×D7311yescharacteristic
151C22×C4—2922no—
152C22×C4—2922no—
153C22×C4—731no—
154C22×C4—732no—
155C22×C4—731no—
156C22×C4—732no—
157C22×C4—1461no—
158C22×C4—1461no—
159C22×C4C4×D7311yescharacteristic
160C22×C4C22×D7311yescharacteristic
161C2×C8—22no—
162C2×C8—2924no—
163C2×C8—1462no—
164C22⋊C4—22no—
165C22⋊C4—1462no—
166C22⋊C4—1462no—
167C22⋊C4—1462no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—2921no—
173C23—2921no—
174C23—2922no—
175C23—2922no—
176C23—2928no—
177C23—2922no—
178C23—2922no—
179C23—2928no—
180C23—732no—
181C23—731no—
182C23—731no—
183C23—732no—
184C23—732no—
185C23—1464no—
186C23—1464no—
187C23—1462no—
188C23—1462no—
189C23—1461no—
190C23—1461no—
191C23C8×D7312yescomplemented
192C23C2×C4×D7311yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—2922no—
199C2×C4—2921no—
200C2×C4—2921no—
201C2×C4—732no—
202C2×C4—1464no—
203C2×C4—1461no—
204C2×C4D4×D7312yes—
205C8—42no—
206C8—2922no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—2922no—
215C22—2922no—
216C22—2928no—
217C22—2928no—
218C22—2921no—
219C22—2921no—
220C22—732no—
221C22—732no—
222C22—732no—
223C22—732no—
224C22—1464no—
225C22—1464no—
226C22—1462no—
227C22—1461no—
228C22—1461no—
229C22C22⋊C4×D7311yescharacteristic
230C22C2×C8×D7311yescharacteristic
231C22M16×D7311yescharacteristic
232C4—22no—
233C4—41no—
234C4—2921no—
235C4—1462no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—2922no—
240C2—734no—
241C2—1462no—
242C2C22⋊C8×D7311yescharacteristic
243C2#99×D7311yescharacteristic
244C2#100×D7311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC22×C73C22×C8
FrattiniC22×C4C22×D73
Fitting#323×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#323D73
hypocenterC73C2×#323
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D73C2semidirect
3. #17988311C2semidirect
4. #17988310C2semidirect
5. #323×C73C2semidirect
15. C22⋊#10596831C22semidirect
18. C22⋊C8×C73C22semidirect
24. C23×D73C8semidirect
49. C23×C73C2×C8semidirect
68. C22×D73C2×C8semidirect
121. D73#323direct (N × H)
123. C73C2×#323semidirect
128. #323D73direct (N × H)
141. C22⋊C8C2×D73semidirect
191. C23C8×D73semidirect