Finite Group Databasebeta

← #22621307

Subgroups — #22621307

Order 9344.

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

normal subgroups only

This group has 348 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#17989142C211yesmaximal, characteristic, complemented
2#17989124C211yesmaximal, characteristic
3#17988893C212yesmaximal, complemented
4#17988874C211yesmaximal, characteristic, complemented
5#17988844C212yesmaximal, complemented
6#17988834C212yesmaximal
7#17988812C212yesmaximal, complemented
8#17988797C211yesmaximal, characteristic, complemented
9#17988793C211yesmaximal, characteristic, complemented
10#17988609C211yesmaximal, characteristic, complemented
11#477×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924017C2212yes—
14C2×#11924011C2212yes—
15#14556591C2211yescharacteristic
16#14556586—21no—
17#14556582—21no—
18#14556582C2211yescharacteristic
19#14556580C2211yescharacteristic
20#14556576—21no—
21#14556571C2212yes—
22#14556567—21no—
23#14556567C2211yescharacteristic
24#14556566C2211yescharacteristic
25Q8×Dic73—21no—
26#14556556C2212yes—
27C4×D292—21no—
28C4×D292C2211yescharacteristic
29#14556549—21no—
30#14556548—21no—
31C42×D73C2211yescharacteristic
32#14556522C2212yes—
33C4⋊#10596831C2211yescharacteristic
34#14556520C2212yes—
35#14556516C2212yes—
36#14556514C2212yes—
37#14556511C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39C4×Q8×C73C2211yescharacteristic
40#107×C73C2212yes—
41C4⋊C8×C73C2211yescharacteristic
42#103×C73C2212yes—
43C2×Dic146C2312yes—
44C2×D292—21no—
45C2×D292C2311yescharacteristic
46C2×C4×D73—21no—
47C2×C4×D73D411yescharacteristic
48C2×C4×D73D411yescharacteristic
49C2×C4×D73C2311yescharacteristic
50#11924018—42no—
51#11924017—42no—
52#11924011—42no—
53C2×#10596831C2312yes—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73—21no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2311yescharacteristic
59#11924007—21no—
60#11924007—21no—
61#11924007—22no—
62#11924005—22no—
63#11924005—21no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67#11924005—21no—
68C4×Dic73—22no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73—21no—
73C2×Q8×C73C2311yescharacteristic
74C2×C8×C73C2312yes—
75C4⋊C4×C73—21no—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2312yes—
78C4⋊C4×C73C2311yescharacteristic
79C42×C73—21no—
80C42×C73C2311yescharacteristic
81C22×D73—21no—
82C22×D73C2×D411yescharacteristic
83Q8×C73—21no—
84Q8×C73—21no—
85Q8×C73—42no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2411yescharacteristic
92C2×Dic73—22no—
93C2×Dic73—21no—
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C2×Dic73C2×D411yescharacteristic
97D292—21no—
98D292—21no—
99D292—42no—
100C4×D73—22no—
101C4×D73—21no—
102C4×D73—21no—
103C4×D73—41no—
104C4×D73—42no—
105Dic146—22no—
106Dic146—22no—
107C8×C73—22no—
108#10596831—22no—
109C22×C73C22×D411yescharacteristic
110C2×D73—21no—
111C2×D73—21no—
112C2×D73—21no—
113C2×D73—41no—
114C2×D73—41no—
115C2×D73—41no—
116C4×C73—21no—
117C4×C73—41no—
118C4×C73—41no—
119C4×C73—42no—
120C4×C73#13712yes—
121C4×C73H(5,𝔽2)11yescharacteristic
122C4×C732−1+411yescharacteristic
123Dic73—21no—
124Dic73—21no—
125Dic73—21no—
126Dic73—42no—
127Dic73—41no—
128C2×C73#53711yescharacteristic
129C2×C73C2×#13711yescharacteristic
130C2×C73#57511yescharacteristic
131D73—41no—
132D73—81no—
133#3252—731nomaximal, Sylow
134C73#325211yescharacteristic, complemented, Sylow
135#533—731no—
136#529—731no—
137#479—732no—
138#477D7311yescharacteristic, complemented
139#476—731no—
140#470—732no—
141#468—732no—
142#464—732no—
143#462—731no—
144#461—731no—
145#423—731no—
146C2×Q16—732no—
147C2×SD16—732no—
148C2×M16—732no—
149C4⋊Q8—731no—
150C4⋊Q8C2×D7311yescharacteristic
151#126—1461no—
152#125—731no—
153#125—1461no—
154#124—731no—
155#123—1461no—
156C22⋊Q8—731no—
157C22⋊Q8—732no—
158C22⋊Q8—1461no—
159#121—731no—
160C4×Q8—732no—
161C4×Q8—1461no—
162C4×Q8C2×D7311yescharacteristic
163C4×D4—731no—
164C4×D4—1461no—
165#117—1461no—
166#117—1461no—
167C2×C42—731no—
168#107C2×D7312yes—
169#106—732no—
170C4⋊C8—732no—
171C4⋊C8—731no—
172C4⋊C8C2×D7311yescharacteristic
173#103—732no—
174#103—732no—
175#103C2×D7312yes—
176#102—732no—
177C2×Q8—21no—
178C2×Q8—732no—
179C2×Q8C22×D7311yescharacteristic
180C2×D4—731no—
181C2×D4—1461no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—1461no—
186Q16—2922no—
187SD16—2922no—
188M16—2922no—
189C2×C8—732no—
190C2×C8C22×D7312yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—731no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1462no—
197C4⋊C4—1461no—
198C4⋊C4—1462no—
199C4⋊C4—1461no—
200C4⋊C4—1461no—
201C4⋊C4C22×D7312yes—
202C4⋊C4C22×D7311yescharacteristic
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C22⋊C4—1461no—
206C22⋊C4—1462no—
207C22⋊C4—1461no—
208C22⋊C4—1461no—
209C42—21no—
210C42—731no—
211C42—731no—
212C42—731no—
213C42—1462no—
214C42C22×D7311yescharacteristic
215C23—731no—
216C23—1461no—
217Q8—21no—
218Q8—21no—
219Q8—42no—
220Q8—1462no—
221Q8—1462no—
222D4—2922no—
223D4—1461no—
224D4—1461no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—2921no—
229C2×C4—2922no—
230C2×C4—731no—
231C2×C4—731no—
232C2×C4—731no—
233C2×C4—1462no—
234C2×C4—1461no—
235C2×C4—1462no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4D4×D7311yescharacteristic
239C2×C4D4×D7311yescharacteristic
240C2×C4C23×D7311yescharacteristic
241C8—22no—
242C8—1462no—
243C22—2921no—
244C22—2921no—
245C22—2921no—
246C22—1461no—
247C22—1461no—
248C22—1461no—
249C22C2×D4×D7311yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—41no—
254C4—2921no—
255C4—2922no—
256C4—1461no—
257C4—1461no—
258C4—1461no—
259C4#1455662312yes—
260C4#1455663711yescharacteristic
261C4#1455663911yescharacteristic
262C2—2921no—
263C2—5841no—
264C2#1798916711yescharacteristic
265C2C2×#1455662311yescharacteristic
266C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#477×C73C2
socleC22×C73C22×D4
hypercenter#477D73
hypocenterC73#3252
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988893C2semidirect
4. #17988874C2semidirect
5. #17988844C2semidirect
7. #17988812C2semidirect
8. #17988797C2semidirect
9. #17988793C2semidirect
10. #17988609C2semidirect
11. #477×C73C2semidirect
134. C73#3252semidirect
138. #477D73semidirect