Finite Group Databasebeta

← #22615511

Subgroups — #22615511

Order 9344.

492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14556556C211yesmaximal, characteristic, complemented
2C2×#14556549C211yesmaximal, characteristic
3#17988513C211yesmaximal, characteristic
4#17988507C211yesmaximal, characteristic, complemented
5#17988500C211yesmaximal, characteristic
6#17988476C212yesmaximal
7#17988473C212yesmaximal, complemented
8#17988469C212yesmaximal, complemented
9#17988458C212yesmaximal
10#17988454C211yesmaximal, characteristic, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14#14556556—24no—
15#14556549—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2211yescharacteristic
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2212yes—
25C2×C4×Dic73C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—24no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C2×C4×D73—22no—
46C2×C4×D73—22no—
47C2×C4×D73—22no—
48C4⋊Dic73—22no—
49#11924007—24no—
50#11924007—24no—
51#11924005—24no—
52#11924005—22no—
53#11924005—22no—
54#11924005—24no—
55C4×Dic73—22no—
56C4×Dic73—24no—
57C4×Dic73D414yes—
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—24no—
66C23×C73C2411yescharacteristic
67C22×D73—21no—
68C22×D73—22no—
69C22×D73—21no—
70C22×D73—22no—
71C22×D73#4112yes—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
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×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73#4112yes—
85C2×Dic73—22no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73C2×D412yes—
96C2×Dic73C2×D412yes—
97C2×Dic73#4114yes—
98C4×D73—28no—
99Dic146—28no—
100C22×C73C22×D411yescharacteristic
101C22×C73C2×#4111yescharacteristic
102C22×C73C2×#4112yes—
103C22×C73C2×#4111yescharacteristic
104C22×C732−1+412yes—
105C2×D73—22no—
106C2×D73—24no—
107C2×D73—41no—
108C2×D73—41no—
109C2×D73—42no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—41no—
113C4×C73—42no—
114C4×C73—42no—
115Dic73—24no—
116Dic73—22no—
117Dic73—22no—
118Dic73—41no—
119Dic73—42no—
120C2×C73#52511yescharacteristic
121C2×C73#52511yescharacteristic
122C2×C73#53611yescharacteristic
123C2×C73#55212yes—
124C2×C73#55612yes—
125D73—42no—
126#2599—731nomaximal, Sylow
127C73#259911yescharacteristic, complemented, Sylow
128C2×C4×Q8—731no—
129C2×#117—731no—
130#398D7311yescharacteristic, complemented
131#397—731no—
132#395—731no—
133#393—731no—
134#388—732no—
135#387—732no—
136#387—732no—
137#385—732no—
138#383—731no—
139C22×Q8—731no—
140C23×C4—731no—
141C4×Q8—1464no—
142#117—1464no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C4⋊C4C2×D7312yes—
149C2×C22⋊C4—731no—
150C2×C22⋊C4—731no—
151C2×C22⋊C4—732no—
152C2×C22⋊C4—732no—
153C2×C42—731no—
154C2×C42—731no—
155C2×C42—732no—
156#95—732no—
157#95—732no—
158#95—731no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95C2×D7311yescharacteristic
163#95C2×D7312yes—
164C24—731no—
165C2×Q8—1464no—
166C2×Q8—1462no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4—731no—
172C22×C4—1462no—
173C22×C4—1462no—
174C22×C4—1462no—
175C22×C4C22×D7312yes—
176C22×C4C22×D7312yes—
177C22×C4C22×D7311yescharacteristic
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—1464no—
184C4⋊C4—1464no—
185C4⋊C4—1462no—
186C22⋊C4—1464no—
187C22⋊C4—1462no—
188C22⋊C4—1464no—
189C22⋊C4—1462no—
190C42—734no—
191C42—1462no—
192C42—1464no—
193C23—732no—
194C23—1461no—
195C23—1462no—
196C23—1461no—
197C23—1462no—
198C23C23×D7311yescharacteristic
199Q8—1468no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—732no—
212C2×C4—732no—
213C2×C4—734no—
214C2×C4—1468no—
215C2×C4—1461no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1461no—
222C2×C4—1462no—
223C2×C4—1461no—
224C2×C4—1462no—
225C2×C4D4×D7312yes—
226C2×C4#1192402712yes—
227C22—2921no—
228C22—2922no—
229C22—2921no—
230C22—1464no—
231C22—1462no—
232C22C2×D4×D7311yescharacteristic
233C22#41×D7311yescharacteristic
234C22#41×D7312yes—
235C22C2×#1192402711yescharacteristic
236C22#1455663912yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—41no—
241C4—42no—
242C4—2921no—
243C4—2922no—
244C4—1462no—
245C4—1464no—
246C4—1462no—
247C2—2922no—
248C2#1798909511yescharacteristic
249C2#1798909711yescharacteristic
250C2#1798916211yescharacteristic
251C2#1798926912yes—
252C2#1798930812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2599
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556556C2semidirect
4. #17988507C2semidirect
7. #17988473C2semidirect
8. #17988469C2semidirect
10. #17988454C2semidirect
11. #398×C73C2semidirect
127. C73#2599semidirect
130. #398D73semidirect