Finite Group Databasebeta

← #22620640

Subgroups — #22620640

Order 9344.

366 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989144C211yesmaximal, characteristic, complemented
2#17989121C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic, complemented
4#17988981C211yesmaximal, characteristic, complemented
5#17988956C211yesmaximal, characteristic, complemented
6#17988947C211yesmaximal, characteristic, complemented
7#17988828C212yesmaximal, complemented
8#17988816C212yesmaximal
9#17988695C212yesmaximal, complemented
10#17988689C212yesmaximal, complemented
11C2×#97×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2212yes—
13C2×#11924017C2212yes—
14#14556591C2211yescharacteristic
15#14556591C2211yescharacteristic
16#14556585—21no—
17#14556583—21no—
18#14556583C2211yescharacteristic
19#14556579C2211yescharacteristic
20#14556574—21no—
21#14556570—21no—
22#14556570C2211yescharacteristic
23#14556570C2212yes—
24#14556565C2211yescharacteristic
25C4×Dic146—21no—
26C4×Dic146C2211yescharacteristic
27C4×Dic146C2212yes—
28C4×D292C2211yescharacteristic
29C4×C22⋊D73—21no—
30#14556550—21no—
31#14556548—21no—
32#14556525C2212yes—
33#14556523C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556516C2212yes—
37#14556513C2212yes—
38C22×C8×C73C2212yes—
39C2×C42×C73C2211yescharacteristic
40#97×C73C2212yes—
41#97×C73C2211yescharacteristic
42#97×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146C2311yescharacteristic
45C2×Dic146C2312yes—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49Dic292—24no—
50#11924017—24no—
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53C4⋊Dic73—21no—
54C4⋊Dic73C2312yes—
55C4⋊Dic73C2311yescharacteristic
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—21no—
59#11924007—21no—
60#11924007—22no—
61#11924007—22no—
62#11924007—21no—
63C22⋊Dic73—22no—
64C22⋊Dic73—21no—
65#11924005—21no—
66#11924005—21no—
67#11924005—21no—
68#11924005—21no—
69C4×Dic73—21no—
70C4×Dic73—22no—
71C22×C4×C73D411yescharacteristic
72C22×C4×C73D411yescharacteristic
73C22×C4×C73C2311yescharacteristic
74C2×C8×C73—24no—
75C2×C8×C73C2312yes—
76C2×C8×C73C2312yes—
77C42×C73D411yescharacteristic
78C42×C73D411yescharacteristic
79C42×C73C2311yescharacteristic
80C42×C73C2311yescharacteristic
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—41no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2411yescharacteristic
92C22⋊D73—42no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98D292—22no—
99C4×D73—42no—
100Dic146—22no—
101Dic146—22no—
102Dic146—22no—
103Dic146—42no—
104C8×C73—22no—
105C8×C73#4114yes—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73#13712yes—
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—21no—
118C4×C73C2×#4112yes—
119Dic73—42no—
120Dic73—41no—
121Dic73—41no—
122Dic73—42no—
123Dic73—41no—
124C2×C73—22no—
125C2×C73#53211yescharacteristic
126C2×C73C2×#13711yescharacteristic
127C2×C73#57511yescharacteristic
128D73—81no—
129#3181—731nomaximal, Sylow
130C73#318111yescharacteristic, complemented, Sylow
131#533—731no—
132#529—731no—
133#501—731no—
134#497—731no—
135#491—731no—
136#489—731no—
137#467—732no—
138#465—732no—
139#441—732no—
140#440—732no—
141C2×#97D7311yescharacteristic, complemented
142C2×Q16—732no—
143C2×SD16—732no—
144C22×C8C2×D7312yes—
145C4⋊Q8—731no—
146C4⋊Q8—731no—
147#126—1461no—
148#125—731no—
149#125—1461no—
150#124—731no—
151#123—1461no—
152C22⋊Q8—731no—
153C22⋊Q8—732no—
154C22⋊Q8—1461no—
155#121—731no—
156C4×Q8—731no—
157C4×Q8—732no—
158C4×Q8—1461no—
159C4×D4—731no—
160C4×D4—1461no—
161#117—1461no—
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#97C2×D7312yes—
171#97C2×D7311yescharacteristic
172#97C2×D7311yescharacteristic
173C2×Q8—731no—
174C2×Q8—732no—
175C2×Q8—1461no—
176C2×D4—731no—
177C2×D4—1461no—
178C22×C4—1461no—
179C22×C4D29211yescharacteristic
180C22×C4D29211yescharacteristic
181C22×C4C22×D7311yescharacteristic
182Q16—1464no—
183SD16—1464no—
184C2×C8—24no—
185C2×C8C22×D7312yes—
186C2×C8C22×D7312yes—
187C4⋊C4—732no—
188C4⋊C4—731no—
189C4⋊C4—731no—
190C4⋊C4—1461no—
191C4⋊C4—1461no—
192C4⋊C4—1461no—
193C4⋊C4—1462no—
194C4⋊C4—1461no—
195C4⋊C4—1462no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4—1461no—
199C22⋊C4—1462no—
200C22⋊C4—1461no—
201C22⋊C4—1461no—
202C22⋊C4—1461no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C42—1461no—
206C42—1462no—
207C42D29211yescharacteristic
208C42D29211yescharacteristic
209C42C22×D7311yescharacteristic
210C42C22×D7311yescharacteristic
211C23—1461no—
212C23C2×D29211yescharacteristic
213Q8—2922no—
214Q8—1462no—
215Q8—1462no—
216Q8—1462no—
217D4—2922no—
218D4—1462no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—2922no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1461no—
228C2×C4C2×D29211yescharacteristic
229C2×C4C2×D29211yescharacteristic
230C2×C4C2×D29211yescharacteristic
231C2×C4C2×D29211yescharacteristic
232C2×C4C2×D29211yescharacteristic
233C2×C4C23×D7311yescharacteristic
234C8—22no—
235C8#1192402814yes—
236C22—21no—
237C22—21no—
238C22—2921no—
239C22—2921no—
240C22—2921no—
241C22#1455662412yes—
242C22C22×D29211yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—2921no—
249C4—2921no—
250C4—2922no—
251C4—2921no—
252C4—2922no—
253C4C2×#1192402812yes—
254C2—22no—
255C2—5841no—
256C2#1798913711yescharacteristic
257C2C2×#1455662411yescharacteristic
258C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#97×C73C2
socleC22×C73C22×D4
hypercenterC2×#97D73
hypocenterC73#3181
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
3. #17988996C2semidirect
4. #17988981C2semidirect
5. #17988956C2semidirect
6. #17988947C2semidirect
7. #17988828C2semidirect
9. #17988695C2semidirect
10. #17988689C2semidirect
11. C2×#97×C73C2semidirect
130. C73#3181semidirect
141. C2×#97D73semidirect