Finite Group Databasebeta

← #22621306

Subgroups — #22621306

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#17989119C211yesmaximal, characteristic
3#17988897C212yesmaximal, complemented
4#17988879C211yesmaximal, characteristic, complemented
5#17988846C212yesmaximal, complemented
6#17988832C212yesmaximal
7#17988808C212yesmaximal, complemented
8#17988798C211yesmaximal, characteristic, complemented
9#17988792C211yesmaximal, characteristic, complemented
10#17988609C211yesmaximal, characteristic, complemented
11#476×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2212yes—
13C2×#11924016C2212yes—
14C2×#11924011C2212yes—
15#14556591C2211yescharacteristic
16#14556584—21no—
17#14556582—21no—
18#14556582C2211yescharacteristic
19#14556578C2211yescharacteristic
20#14556573—21no—
21#14556571C2212yes—
22#14556571C2211yescharacteristic
23#14556567—21no—
24#14556562C2211yescharacteristic
25Q8×Dic73—21no—
26C4×Dic146C2211yescharacteristic
27#14556556C2212yes—
28C4×C22⋊D73—21no—
29#14556550—21no—
30#14556549—21no—
31C42×D73C2211yescharacteristic
32#14556524C2212yes—
33C4⋊#10596831C2211yescharacteristic
34#14556520C2212yes—
35#14556516C2212yes—
36#14556514C2212yes—
37#14556514C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40#106×C73C2212yes—
41C4⋊C8×C73C2211yescharacteristic
42#102×C73C2212yes—
43C2×Dic146C2311yescharacteristic
44C2×Dic146C2312yes—
45C2×C22⋊D73—21no—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49Dic292—42no—
50#11924016—42no—
51#11924011—42no—
52C2×#10596831C2312yes—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73—21no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2311yescharacteristic
59#11924007—21no—
60#11924007—21no—
61#11924007—22no—
62C22⋊Dic73—21no—
63C22⋊Dic73—21no—
64C22⋊Dic73—21no—
65#11924005—22no—
66#11924005—21no—
67C4×Dic73—21no—
68C4×Dic73—22no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73—21no—
73C2×D4×C73C2311yescharacteristic
74C22×C4×C73—21no—
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2312yes—
78C4⋊C4×C73C2311yescharacteristic
79C22⋊C4×C73—21no—
80C42×C73C2311yescharacteristic
81C23×C73—21no—
82C22×D73C2×D411yescharacteristic
83Q8×C73—42no—
84D4×C73—21no—
85D4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—42no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2411yescharacteristic
92C22⋊D73—42no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96C2×Dic73C2×D411yescharacteristic
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C4×D73—22no—
100C4×D73—21no—
101C4×D73—21no—
102C4×D73—41no—
103Dic146—22no—
104Dic146—21no—
105Dic146—21no—
106Dic146—22no—
107C8×C73—22no—
108#10596831—22no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73C22×D411yescharacteristic
113C2×D73—21no—
114C2×D73—21no—
115C2×D73—21no—
116C4×C73—21no—
117C4×C73—41no—
118C4×C73—42no—
119C4×C73#13712yes—
120C4×C73H(5,𝔽2)11yescharacteristic
121C4×C732−1+411yescharacteristic
122Dic73—21no—
123Dic73—21no—
124Dic73—21no—
125Dic73—42no—
126Dic73—41no—
127Dic73—41no—
128C2×C73—81no—
129C2×C73#53711yescharacteristic
130C2×C73C2×#13711yescharacteristic
131C2×C73#57511yescharacteristic
132D73—41no—
133#3252—731nomaximal, Sylow
134C73#325211yescharacteristic, complemented, Sylow
135#533—731no—
136#529—731no—
137#479—732no—
138#477—731no—
139#476D7311yescharacteristic, complemented
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—731no—
162C4×Q8—1461no—
163C4×D4—1461no—
164C4×D4C2×D7311yescharacteristic
165#117—1461no—
166#117—1461no—
167C2×C42—731no—
168#107—732no—
169#106C2×D7312yes—
170C4⋊C8—732no—
171C4⋊C8—731no—
172C4⋊C8C2×D7311yescharacteristic
173#103—732no—
174#103—732no—
175#103—732no—
176#102C2×D7312yes—
177C2×Q8—21no—
178C2×Q8—731no—
179C2×Q8—732no—
180C2×D4—1461no—
181C2×D4C22×D7311yescharacteristic
182C22×C4—21no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—731no—
186Q16—2922no—
187SD16—2922no—
188M16—2922no—
189C2×C8—732no—
190C2×C8C22×D7312yes—
191C4⋊C4—21no—
192C4⋊C4—731no—
193C4⋊C4—1461no—
194C4⋊C4—1462no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1462no—
198C4⋊C4—1461no—
199C4⋊C4—1461no—
200C4⋊C4—1461no—
201C4⋊C4C22×D7312yes—
202C4⋊C4C22×D7311yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—1462no—
205C22⋊C4—1461no—
206C22⋊C4—1461no—
207C22⋊C4—1461no—
208C22⋊C4—1461no—
209C42—731no—
210C42—731no—
211C42—731no—
212C42—1462no—
213C42—1461no—
214C42C22×D7311yescharacteristic
215C23—21no—
216C23—731no—
217Q8—42no—
218Q8—1462no—
219Q8—1461no—
220Q8—1461no—
221Q8—1462no—
222D4—21no—
223D4—21no—
224D4—2922no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—2921no—
229C2×C4—731no—
230C2×C4—731no—
231C2×C4—731no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4D4×D7311yescharacteristic
239C2×C4D4×D7311yescharacteristic
240C2×C4C23×D7311yescharacteristic
241C8—22no—
242C8—1462no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—1461no—
247C22—1461no—
248C22—1461no—
249C22C2×D4×D7311yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—2921no—
254C4—2921no—
255C4—2922no—
256C4—1461no—
257C4—1461no—
258C4—1461no—
259C4#1455662012yes—
260C4#1455663711yescharacteristic
261C4#1455663911yescharacteristic
262C2—81no—
263C2—2921no—
264C2#1798916711yescharacteristic
265C2C2×#1455662011yescharacteristic
266C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#476×C73C2
socleC22×C73C22×D4
hypercenter#476D73
hypocenterC73#3252
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. #17989142C2semidirect
3. #17988897C2semidirect
4. #17988879C2semidirect
5. #17988846C2semidirect
7. #17988808C2semidirect
8. #17988798C2semidirect
9. #17988792C2semidirect
10. #17988609C2semidirect
11. #476×C73C2semidirect
134. C73#3252semidirect
139. #476D73semidirect