Finite Group Databasebeta

← #22615631

Subgroups — #22615631

Order 9344.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#14556548C211yesmaximal, characteristic
2#17988525C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic
4#17988518C211yesmaximal, characteristic, complemented
5#17988513C211yesmaximal, characteristic
6#17988482C212yesmaximal, complemented
7#17988477C212yesmaximal
8#17988468C212yesmaximal, complemented
9#17988458C212yesmaximal
10#17988433C211yesmaximal, characteristic, complemented
11C2×#125×C73C211yesmaximal, characteristic, complemented
12C22×C4×D73C2211yescharacteristic
13#14556548—24no—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×#11924007C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×C4×Dic73C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#125×C73—24no—
32C2×C4⋊C4×C73C2212yes—
33C2×C4⋊C4×C73C2212yes—
34C2×C4⋊C4×C73C2211yescharacteristic
35C2×C4⋊C4×C73C2211yescharacteristic
36C2×C42×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C22×Dic73C2312yes—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73—22no—
46#11924007—22no—
47#11924007—22no—
48#11924007—24no—
49#11924007—24no—
50#11924005—24no—
51#11924005—22no—
52#11924005—22no—
53#11924005—24no—
54C4×Dic73—22no—
55C4×Dic73—24no—
56C22×C4×C73C2312yes—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C4⋊C4×C73—24no—
62C4⋊C4×C73—24no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C42×C73D414yes—
66C23×C73C2411yescharacteristic
67C22×D73—21no—
68C22×D73—22no—
69C22×D73—21no—
70C22×D73—22no—
71C22×D73#4112yes—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D412yes—
85C2×Dic73—21no—
86C2×Dic73—22no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73#4114yes—
97C2×Dic73#4112yes—
98C4×D73—28no—
99C22×C73C22×D411yescharacteristic
100C22×C73C2×#4111yescharacteristic
101C22×C73C2×#4111yescharacteristic
102C22×C73C2×#4112yes—
103C22×C732−1+412yes—
104C2×D73—22no—
105C2×D73—24no—
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—42no—
109C4×C73—22no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—42no—
113C4×C73—42no—
114Dic73—22no—
115Dic73—24no—
116Dic73—41no—
117Dic73—41no—
118Dic73—42no—
119C2×C73#52511yescharacteristic
120C2×C73#53211yescharacteristic
121C2×C73#53611yescharacteristic
122C2×C73#55212yes—
123C2×C73#55212yes—
124D73—42no—
125#2611—731nomaximal, Sylow
126C73#261111yescharacteristic, complemented, Sylow
127C2×#125D7311yescharacteristic, complemented
128C2×#117—731no—
129#400—731no—
130#399—731no—
131#398—731no—
132#397—731no—
133#389—732no—
134#388—732no—
135#387—732no—
136#385—732no—
137#376—731no—
138C23×C4—731no—
139#125—24no—
140#117—1464no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—732no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4C2×D7312yes—
146C2×C4⋊C4C2×D7312yes—
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C4⋊C4C2×D7311yescharacteristic
149C2×C22⋊C4—731no—
150C2×C22⋊C4—731no—
151C2×C22⋊C4—732no—
152C2×C22⋊C4—732no—
153C2×C42—731no—
154C2×C42—732no—
155C2×C42C2×D7311yescharacteristic
156#95—732no—
157#95—731no—
158#95—731no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95—732no—
163C24—731no—
164C22×C4—732no—
165C22×C4—731no—
166C22×C4—732no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—1462no—
170C22×C4—1462no—
171C22×C4—1462no—
172C22×C4C22×D7312yes—
173C22×C4C22×D7312yes—
174C22×C4C22×D7311yescharacteristic
175C22×C4C22×D7311yescharacteristic
176C22×C4C22×D7311yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—1464no—
182C4⋊C4—1464no—
183C4⋊C4—1462no—
184C4⋊C4—1462no—
185C22⋊C4—1464no—
186C22⋊C4—1464no—
187C22⋊C4—1462no—
188C22⋊C4—1462no—
189C42—1464no—
190C42—1462no—
191C42C22⋊D7314yes—
192C23—732no—
193C23—1461no—
194C23—1462no—
195C23—1461no—
196C23—1462no—
197C23C23×D7311yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—734no—
209C2×C4—732no—
210C2×C4—1468no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4C2×C22⋊D7312yes—
223C2×C4C2×C22⋊D7312yes—
224C2×C4C2×C22⋊D7312yes—
225C22—2921no—
226C22—2921no—
227C22—2922no—
228C22—1464no—
229C22—1462no—
230C22C22×C22⋊D7311yescharacteristic
231C22#41×D7312yes—
232C22#41×D7311yescharacteristic
233C22#41×D7311yescharacteristic
234C22#1455663912yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—2921no—
241C4—2921no—
242C4—2922no—
243C4—1464no—
244C4—1462no—
245C2—2922no—
246C2#1798909411yescharacteristic
247C2#1798913311yescharacteristic
248C2#1798916111yescharacteristic
249C2#1798926912yes—
250C2#1798926912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#125×C73C2
hypercenterC2×#125D73
hypocenterC73#2611
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #17988525C2semidirect
4. #17988518C2semidirect
6. #17988482C2semidirect
8. #17988468C2semidirect
10. #17988433C2semidirect
11. C2×#125×C73C2semidirect
126. C73#2611semidirect
127. C2×#125D73semidirect