Finite Group Databasebeta

← #22620531

Subgroups — #22620531

Order 9344.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989121C211yesmaximal, characteristic
2#17988993C211yesmaximal, characteristic, complemented
3#17988979C211yesmaximal, characteristic, complemented
4#17988955C211yesmaximal, characteristic, complemented
5#17988949C211yesmaximal, characteristic, complemented
6#17988843C212yesmaximal, complemented
7#17988835C212yesmaximal
8C4×#11924018C212yesmaximal, complemented
9C4×#11924015C212yesmaximal, complemented
10C4×#11924012C211yesmaximal, characteristic, complemented
11#533×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924015C2212yes—
14C2×#11924012C2212yes—
15#14556585—21no—
16#14556583C2211yescharacteristic
17#14556579C2211yescharacteristic
18#14556574—21no—
19#14556570C2211yescharacteristic
20#14556565C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22C4×D292C2211yescharacteristic
23C4×C22⋊D73—21no—
24#14556548—21no—
25#14556524C2212yes—
26#14556522C2212yes—
27#14556515C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30#14556511C2212yes—
31#14556502C2211yescharacteristic
32#14556502C2211yescharacteristic
33C4×#10596831C2212yes—
34C4⋊Q8×C73C2211yescharacteristic
35C4⋊Q8×C73C2211yescharacteristic
36#125×C73—21no—
37C22⋊Q8×C73—21no—
38C22⋊Q8×C73C2212yes—
39C4×Q8×C73—21no—
40C4×Q8×C73C2212yes—
41#117×C73—21no—
42C2×C42×C73C2211yescharacteristic
43C2×Dic146C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C4×D73—21no—
47#11924018—24no—
48#11924015—24no—
49#11924012—24no—
50C2×#10596831C2312yes—
51C2×#10596831C2312yes—
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54#11924007—21no—
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58C22⋊Dic73—21no—
59#11924005—21no—
60#11924005—21no—
61#11924005—21no—
62#11924005—21no—
63C4×Dic73—21no—
64C2×Q8×C73—21no—
65C2×Q8×C73C2312yes—
66C22×C4×C73D411yescharacteristic
67C22×C4×C73D411yescharacteristic
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—21no—
70C4⋊C4×C73—21no—
71C4⋊C4×C73—21no—
72C4⋊C4×C73—22no—
73C4⋊C4×C73—22no—
74C4⋊C4×C73C2312yes—
75C22⋊C4×C73—22no—
76C42×C73—22no—
77C42×C73D411yescharacteristic
78C42×C73D411yescharacteristic
79C42×C73C2311yescharacteristic
80C42×C73C2311yescharacteristic
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83Q8×C73—22no—
84Q8×C73—22no—
85Q8×C73—42no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2411yescharacteristic
97C22⋊D73—42no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101D292—22no—
102C4×D73—42no—
103Dic146—22no—
104#10596831—22no—
105#10596831#4114yes—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—21no—
109C22×C73C22×D411yescharacteristic
110C2×D73—41no—
111C2×D73—41no—
112C2×D73—41no—
113C4×C73—21no—
114C4×C73—21no—
115C4×C73—21no—
116C4×C73—21no—
117C4×C73—42no—
118C4×C73—42no—
119C4×C73#13712yes—
120C4×C73C2×#4112yes—
121Dic73—41no—
122Dic73—41no—
123Dic73—41no—
124C2×C73—41no—
125C2×C73#53211yescharacteristic
126C2×C73C2×#13711yescharacteristic
127C2×C73#57511yescharacteristic
128D73—81no—
129#3172—731nomaximal, Sylow
130C73#317211yescharacteristic, complemented, Sylow
131#533D7311yescharacteristic, complemented
132#529—731no—
133#501—731no—
134#497—731no—
135#491—731no—
136#489—731no—
137#470—732no—
138#468—732no—
139C4×Q16—732no—
140C4×SD16—732no—
141C4×M16—731no—
142C2×Q16—732no—
143C2×SD16—732no—
144C2×M16—732no—
145C4⋊Q8C2×D7311yescharacteristic
146C4⋊Q8C2×D7311yescharacteristic
147#126—1461no—
148#125—21no—
149#125—731no—
150#124—731no—
151#123—1461no—
152C22⋊Q8—21no—
153C22⋊Q8—731no—
154C22⋊Q8C2×D7312yes—
155#121—731no—
156C4×Q8—21no—
157C4×Q8—731no—
158C4×Q8C2×D7312yes—
159C4×D4—731no—
160C4×D4—1461no—
161#117—21no—
162#117—1461no—
163C2×C42C2×D7311yescharacteristic
164#107—732no—
165#106—732no—
166#103—732no—
167#103—732no—
168#103—732no—
169#102—732no—
170#97—731no—
171#97—731no—
172C4×C8—732no—
173C2×Q8—21no—
174C2×Q8—731no—
175C2×Q8C22×D7312yes—
176C2×D4—731no—
177C2×D4—1461no—
178C22×C4—1461no—
179C22×C4C22⋊D7311yescharacteristic
180C22×C4C22⋊D7311yescharacteristic
181C22×C4C22×D7311yescharacteristic
182Q16—1464no—
183SD16—1464no—
184M16—1464no—
185C2×C8—732no—
186C2×C8—732no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—731no—
193C4⋊C4—731no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4C22×D7312yes—
199C22⋊C4—22no—
200C22⋊C4—1461no—
201C22⋊C4—1461no—
202C22⋊C4—1461no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C42—22no—
206C42—1461no—
207C42C22⋊D7311yescharacteristic
208C42C22⋊D7311yescharacteristic
209C42C22×D7311yescharacteristic
210C42C22×D7311yescharacteristic
211C23—1461no—
212C23C2×C22⋊D7311yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—1462no—
217D4—2922no—
218D4—1462no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—2922no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4C2×C22⋊D7311yescharacteristic
229C2×C4C2×C22⋊D7311yescharacteristic
230C2×C4C2×C22⋊D7311yescharacteristic
231C2×C4C2×C22⋊D7311yescharacteristic
232C2×C4C2×C22⋊D7311yescharacteristic
233C2×C4C23×D7311yescharacteristic
234C8—734no—
235C8—1462no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—2921no—
240C22—2921no—
241C22—2921no—
242C22C22×C22⋊D7311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—2921no—
250C4—2921no—
251C4—2921no—
252C4#1455662212yes—
253C4#41×D7312yes—
254C2—41no—
255C2—5841no—
256C2#1798913311yescharacteristic
257C2C2×#1455662211yescharacteristic
258C2#1798938511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3172
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988993C2semidirect
3. #17988979C2semidirect
4. #17988955C2semidirect
5. #17988949C2semidirect
6. #17988843C2semidirect
8. C4×#11924018C2semidirect
9. C4×#11924015C2semidirect
10. C4×#11924012C2semidirect
11. #533×C73C2semidirect
130. C73#3172semidirect
131. #533D73semidirect