Finite Group Databasebeta

← #22608354

Subgroups — #22608354

Order 9344.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×D4×D73C211yesmaximal, characteristic
2#17988638C211yesmaximal, characteristic, complemented
3#17988609C211yesmaximal, characteristic, complemented
4#17988316C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic, complemented
8C2×D4×D73C411yescharacteristic
9C22×C4×D73—21no—
10C2×#11924011—21no—
11C4×D292C2211yescharacteristic
12D4×Dic73C411yescharacteristic
13#14556553C411yescharacteristic
14C4×C22⋊D73—21no—
15#14556551—21no—
16C4⋊C4×D73C411yescharacteristic
17C22⋊C4×D73—21no—
18C42×D73C2211yescharacteristic
19C4⋊#10596831C2211yescharacteristic, complemented
20#14556520—21no—
21#14556520—21no—
22#14556503—21no—
23C4×#10596831C2211yescharacteristic, complemented
24C4×D4×C73C2211yescharacteristic
25C4⋊C8×C73C2211yescharacteristic, complemented
26C4×C8×C73C2211yescharacteristic, complemented
27C23×D73—21no—
28C2×D292C2×C411yescharacteristic
29C2×C22⋊D73—21no—
30D4×D73—22no—
31D4×D73—22no—
32C22×Dic73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73—42no—
37C2×C4×D73—42no—
38C2×C4×D73C2×C411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73D411yescharacteristic
41#11924011—42no—
42C2×#10596831—21no—
43C2×#10596831—21no—
44C4⋊Dic73C2×C411yescharacteristic
45#11924007—21no—
46C22⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49C4×Dic73C2×C411yescharacteristic
50C4×Dic73D411yescharacteristic
51C4×Dic73D411yescharacteristic
52C2×D4×C73C2×C411yescharacteristic
53C22×C4×C73—21no—
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C4⋊C4×C73C2×C411yescharacteristic
57C22⋊C4×C73—21no—
58C42×C73C2311yescharacteristic
59C23×C73—21no—
60C22×D73—24no—
61C22×D73—21no—
62C22×D73—42no—
63C22×D73—42no—
64C22×D73C22⋊C411yescharacteristic
65D4×C73—21no—
66D4×C73M1612yescomplemented
67C2×C4×C73—21no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73C22×C411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C22⋊D73—24no—
74C2×Dic73—21no—
75C2×Dic73—42no—
76C2×Dic73C22⋊C411yescharacteristic
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C22⋊C411yescharacteristic
79D292—21no—
80D292M1612yescomplemented
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—41no—
84C4×D73—42no—
85C4×D73—41no—
86C4×D73—41no—
87C4×D73—42no—
88C4×D73D812yes—
89C4×D73SD1612yes—
90C8×C73—41no—
91C8×C73—41no—
92#10596831—41no—
93#10596831—41no—
94C22×C73—22no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73C2×C22⋊C411yescharacteristic
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—22no—
101C2×D73—48no—
102C2×D73—41no—
103C2×D73—41no—
104C2×D73#10212yes—
105C4×C73—21no—
106C4×C73—41no—
107C4×C73C2×M1611yescharacteristic
108C4×C73C2×M1611yescharacteristic
109C4×C73C2×D811yescharacteristic
110C4×C73C2×SD1611yescharacteristic
111Dic73—21no—
112Dic73—21no—
113Dic73—41no—
114Dic73#10212yes—
115C2×C73—42no—
116C2×C73#40711yescharacteristic
117C2×C73C2×#10211yescharacteristic
118C2×C73#42111yescharacteristic
119D73—22no—
120D73—42no—
121#1486—731nomaximal, Sylow
122C73#148611yescharacteristic, complemented, Sylow
123C2×C4×D4—731no—
124#431—731no—
125#423—731no—
126D4⋊C8—731no—
127D4⋊C8—731no—
128D4⋊C8—731no—
129D4⋊C8D7311yescharacteristic, complemented
130C22×D4—731no—
131C23×C4—1461no—
132C2×M16—1461no—
133C4×D4—731no—
134C4×D4—731no—
135C4×D4—731no—
136C4×D4—1461no—
137C4×D4—1461no—
138C4×D4C2×D7311yescharacteristic
139C2×C4⋊C4—731no—
140C2×C22⋊C4—1461no—
141C2×C42—731no—
142C4⋊C8—731no—
143C4⋊C8—1461no—
144C4⋊C8—1461no—
145C4⋊C8C2×D7311yescharacteristic, complemented
146C22⋊C8—1461no—
147C4×C8—731no—
148C4×C8C2×D7311yescharacteristic, complemented
149C24—1461no—
150C2×D4—731no—
151C2×D4—1461no—
152C2×D4—1462no—
153C2×D4—1462no—
154C2×D4C4×D7311yescharacteristic
155C22×C4—21no—
156C22×C4—2922no—
157C22×C4—2922no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—1461no—
162C22×C4—1461no—
163C22×C4—1461no—
164C22×C4—1461no—
165M16—2922no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1461no—
169C2×C8—1461no—
170C4⋊C4—731no—
171C4⋊C4—1461no—
172C4⋊C4C4×D7311yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—1461no—
175C22⋊C4—1461no—
176C22⋊C4—1461no—
177C42—731no—
178C42—731no—
179C42—731no—
180C42C22×D7311yescharacteristic
181C23—21no—
182C23—2922no—
183C23—2922no—
184C23—731no—
185C23—1464no—
186C23—1461no—
187D4—21no—
188D4—732no—
189D4—1464no—
190D4—1461no—
191D4#1192401112yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—2921no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—2922no—
199C2×C4—2921no—
200C2×C4—2921no—
201C2×C4—731no—
202C2×C4—732no—
203C2×C4—732no—
204C2×C4—731no—
205C2×C4—731no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4—1461no—
209C2×C4C2×C4×D7311yescharacteristic
210C2×C4D4×D7311yescharacteristic
211C2×C4D4×D7311yescharacteristic
212C8—41no—
213C8—41no—
214C8—2921no—
215C8—2921no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—2928no—
220C22—2921no—
221C22—2921no—
222C22—732no—
223C22—1462no—
224C22—1461no—
225C22—1461no—
226C22C22⋊C4×D7311yescharacteristic
227C4—21no—
228C4—41no—
229C4—2921no—
230C4—732no—
231C4—1461no—
232C4—1461no—
233C4M16×D7311yescharacteristic
234C4C2×#1192401111yescharacteristic
235C4D8×D7311yescharacteristic
236C4SD16×D7311yescharacteristic
237C2—42no—
238C2—2922no—
239C2—1462no—
240C2#1798854911yescharacteristic
241C2#102×D7311yescharacteristic
242C2#1798860211yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73C2×C22⋊C4
hypercenterD4⋊C8D73
hypocenterC73#1486
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988638C2semidirect
3. #17988609C2semidirect
4. #17988316C2semidirect
5. D4⋊#10596831C2semidirect
6. #17988314C2semidirect
7. D4⋊C8×C73C2semidirect
19. C4⋊#10596831C22semidirect
23. C4×#10596831C22semidirect
25. C4⋊C8×C73C22semidirect
26. C4×C8×C73C22semidirect
66. D4×C73M16semidirect
80. D292M16semidirect
122. C73#1486semidirect
129. D4⋊C8D73semidirect
145. C4⋊C8C2×D73semidirect
148. C4×C8C2×D73semidirect
191. D4#11924011semidirect