Finite Group Databasebeta

← #22621151

Subgroups — #22621151

Order 9344.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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⋊Q8×D73C211yesmaximal, characteristic, complemented
2#17989119C211yesmaximal, characteristic
3#17988994C212yesmaximal, complemented
4#17988945C212yesmaximal, complemented
5#17988919C212yesmaximal, complemented
6#17988899C212yesmaximal
7#17988883C211yesmaximal, characteristic, complemented
8#17988879C211yesmaximal, characteristic, complemented
9#17988877C211yesmaximal, characteristic, complemented
10#17988643C211yesmaximal, characteristic, complemented
11#476×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73—21no—
13#14556591C2211yescharacteristic
14#14556590—21no—
15#14556590C2212yes—
16#14556589—21no—
17#14556584—21no—
18#14556582C2211yescharacteristic
19#14556578C2211yescharacteristic
20#14556573—21no—
21#14556571C2211yescharacteristic
22#14556562C2211yescharacteristic
23C4×Dic146C2211yescharacteristic
24C4×C22⋊D73—21no—
25#14556550—21no—
26C4⋊C4×D73—21no—
27C4⋊C4×D73C2212yes—
28C42×D73C2211yescharacteristic
29#14556525C2212yes—
30#14556524C2212yes—
31#14556522C2212yes—
32C4⋊#10596831C2211yescharacteristic
33#14556516C2212yes—
34#14556514C2212yes—
35#14556512C2212yes—
36#14556503C2212yes—
37#14556501C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40#106×C73C2212yes—
41C4⋊C8×C73C2211yescharacteristic
42#102×C73C2212yes—
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146C2311yescharacteristic
46Q8×D73—44no—
47C2×C22⋊D73—21no—
48C2×C4×D73—22no—
49C2×C4×D73D411yescharacteristic
50C2×C4×D73D411yescharacteristic
51C2×C4×D73C2311yescharacteristic
52C2×#10596831C2312yes—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73C2312yes—
57C4⋊Dic73C2311yescharacteristic
58#11924007—21no—
59#11924007—22no—
60#11924007—22no—
61#11924007—21no—
62C22⋊Dic73—21no—
63C22⋊Dic73—21no—
64C22⋊Dic73—21no—
65#11924005—21no—
66C4×Dic73—21no—
67C4×Dic73D411yescharacteristic
68C4×Dic73D411yescharacteristic
69C4×Dic73C2311yescharacteristic
70C2×Q8×C73—21no—
71C2×D4×C73C2311yescharacteristic
72C22×C4×C73—21no—
73C2×C8×C73C2312yes—
74C4⋊C4×C73—21no—
75C4⋊C4×C73C2312yes—
76C4⋊C4×C73C2311yescharacteristic
77C22⋊C4×C73—21no—
78C42×C73C2311yescharacteristic
79C23×C73—21no—
80C22×D73C2×D411yescharacteristic
81Q8×C73—42no—
82D4×C73—21no—
83D4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—42no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C22⋊D73—42no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C2×Dic73C2×D411yescharacteristic
97C4×D73—22no—
98C4×D73—22no—
99C4×D73—21no—
100C4×D73—21no—
101C4×D73—44no—
102Dic146—21no—
103Dic146—21no—
104Dic146—44no—
105Dic146—42no—
106C8×C73—22no—
107#10596831—22no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73C22×D411yescharacteristic
112C2×D73—21no—
113C2×D73—21no—
114C2×D73AGL(1,ℤ/8)12yes—
115C4×C73—21no—
116C4×C73—42no—
117C4×C73—41no—
118C4×C73#13712yes—
119C4×C732−1+411yescharacteristic
120C4×C732−1+411yescharacteristic
121Dic73—21no—
122Dic73—21no—
123Dic73—21no—
124Dic73—41no—
125Dic73—42no—
126Dic73—41no—
127C2×C73—81no—
128C2×C73#53611yescharacteristic
129C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C73C2×#13711yescharacteristic
131D73—22no—
132#3238—731nomaximal, Sylow
133C73#323811yescharacteristic, complemented, Sylow
134C2×C4⋊Q8—731no—
135#529—731no—
136#501—732no—
137#489—732no—
138#483—732no—
139#480—732no—
140#477—731no—
141#477—731no—
142#476—731no—
143#476D7311yescharacteristic, complemented
144#432—731no—
145C22×Q8—1461no—
146C4⋊Q8—732no—
147C4⋊Q8—731no—
148C4⋊Q8—1461no—
149C4⋊Q8—1461no—
150C4⋊Q8C2×D7311yescharacteristic
151#126—1461no—
152#125—731no—
153#124—731no—
154#123—1461no—
155C22⋊Q8—731no—
156#121—731no—
157C4×Q8—731no—
158C4×D4—1461no—
159C4×D4C2×D7311yescharacteristic
160#117—1461no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—1461no—
163C2×C42—731no—
164#107—732no—
165#107—732no—
166#106—732no—
167#106C2×D7312yes—
168C4⋊C8—731no—
169C4⋊C8C2×D7311yescharacteristic
170#103—732no—
171#103—732no—
172#102—732no—
173#102C2×D7312yes—
174C22⋊C8—732no—
175#97—732no—
176C2×Q8—21no—
177C2×Q8—2924no—
178C2×Q8—731no—
179C2×Q8—1462no—
180C2×Q8—1461no—
181C2×D4—1461no—
182C2×D4C22×D7311yescharacteristic
183C22×C4—21no—
184C22×C4—731no—
185C22×C4—731no—
186C22×C4—731no—
187C22×C4—1462no—
188C2×C8—732no—
189C2×C8C22×D7312yes—
190C4⋊C4—21no—
191C4⋊C4—732no—
192C4⋊C4—731no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4—1461no—
199C4⋊C4—1461no—
200C4⋊C4C22×D7312yes—
201C4⋊C4C22×D7311yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C22⋊C4—1461no—
206C22⋊C4—1461no—
207C42—731no—
208C42—731no—
209C42—731no—
210C42—1461no—
211C42C22×D7311yescharacteristic
212C23—21no—
213C23—731no—
214Q8—42no—
215Q8—2922no—
216Q8—2924no—
217Q8—1461no—
218Q8—1461no—
219D4—21no—
220D4—21no—
221D4—2922no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—2924no—
226C2×C4—731no—
227C2×C4—731no—
228C2×C4—731no—
229C2×C4—1462no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4D4×D7311yescharacteristic
237C2×C4D4×D7311yescharacteristic
238C2×C4C23×D7311yescharacteristic
239C8—22no—
240C8—1462no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—732no—
245C22—1461no—
246C22—1461no—
247C22C2×D4×D7311yescharacteristic
248C4—21no—
249C4—41no—
250C4—42no—
251C4—2921no—
252C4—2922no—
253C4—2921no—
254C4—1461no—
255C4—1461no—
256C4—1461no—
257C4#1455662012yes—
258C4#1455663811yescharacteristic
259C4#1455663911yescharacteristic
260C2—81no—
261C2—1462no—
262C2#1798916011yescharacteristic
263C2AGL(1,ℤ/8)×D7311yescharacteristic
264C2C2×#1455662011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#476×C73C2
socleC22×C73C22×D4
hypercenter#476D73
hypocenterC73#3238
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D73C2semidirect
3. #17988994C2semidirect
4. #17988945C2semidirect
5. #17988919C2semidirect
7. #17988883C2semidirect
8. #17988879C2semidirect
9. #17988877C2semidirect
10. #17988643C2semidirect
11. #476×C73C2semidirect
133. C73#3238semidirect
143. #476D73semidirect