Finite Group Databasebeta

← #22615629

Subgroups — #22615629

Order 9344.

476 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556583C211yesmaximal, characteristic, complemented
2#17988526C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic
4#17988517C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic
6#17988482C212yesmaximal, complemented
7#17988481C212yesmaximal
8#17988471C212yesmaximal, complemented
9#17988460C212yesmaximal
10#17988433C211yesmaximal, characteristic, complemented
11C2×#117×C73C211yesmaximal, characteristic
12#14556583—24no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C4×Dic73C2212yes—
22#14556498C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29C23×C4×C73C2211yescharacteristic
30#117×C73—24no—
31C2×C4⋊C4×C73C2211yescharacteristic
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C42×C73C2211yescharacteristic
36C2×C42×C73C2211yescharacteristic
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C4⋊Dic73—22no—
42C4⋊Dic73—22no—
43#11924007—24no—
44#11924007—24no—
45#11924007—24no—
46#11924007—24no—
47C22⋊Dic73—24no—
48C22⋊Dic73—24no—
49C4×Dic73—24no—
50C24×C73C2311yescharacteristic
51C22×C4×C73—22no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C4⋊C4×C73—22no—
61C4⋊C4×C73—22no—
62C22⋊C4×C73—22no—
63C22⋊C4×C73—22no—
64C42×C73—22no—
65C42×C73D414yes—
66C23×C73—21no—
67C23×C73—21no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73#4112yes—
71C23×C73C2411yescharacteristic
72C2×C4×C73—28no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2×D412yes—
86C2×C4×C73#4112yes—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73#4114yes—
99C22×C73—22no—
100C22×C73—24no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—42no—
104C22×C73C22×D411yescharacteristic
105C22×C73C2×#4112yes—
106C22×C73C2×#4111yescharacteristic
107C22×C73C2×#4111yescharacteristic
108C22×C732−1+412yes—
109C4×C73—22no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—22no—
113C4×C73—41no—
114C4×C73—41no—
115Dic73—24no—
116Dic73—42no—
117Dic73—42no—
118Dic73—42no—
119C2×C73—42no—
120C2×C73#52511yescharacteristic
121C2×C73#53211yescharacteristic
122C2×C73#53611yescharacteristic
123C2×C73#55212yes—
124C2×C73#55212yes—
125#2611—731nomaximal, Sylow
126C73#261111yescharacteristic, complemented, Sylow
127C2×#125—731no—
128C2×#117D7311yescharacteristic
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×C4C2×D7311yescharacteristic
139#125—1464no—
140#117—24no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—732no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—731no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—732no—
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C4⋊C4C2×D7311yescharacteristic
149C2×C22⋊C4—732no—
150C2×C22⋊C4—732no—
151C2×C22⋊C4C2×D7311yescharacteristic
152C2×C22⋊C4C2×D7311yescharacteristic
153C2×C42—732no—
154C2×C42C2×D7311yescharacteristic
155C2×C42C2×D7311yescharacteristic
156#95—732no—
157#95—731no—
158#95—731no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95—732no—
163C24C22×D7311yescharacteristic
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—732no—
168C22×C4—732no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4C22×D7311yescharacteristic
172C22×C4C22×D7311yescharacteristic
173C22×C4C22×D7311yescharacteristic
174C22×C4C22×D7311yescharacteristic
175C22×C4C22×D7311yescharacteristic
176C22×C4C22×D7311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—1464no—
180C4⋊C4—1464no—
181C4⋊C4—1464no—
182C4⋊C4—1462no—
183C4⋊C4—1462no—
184C4⋊C4—1464no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—1464no—
188C22⋊C4—1464no—
189C42—22no—
190C42—1464no—
191C42C22⋊D7314yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#1192402812yes—
197C23C23×D7311yescharacteristic
198C2×C4—28no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—734no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4C2×C22⋊D7312yes—
222C2×C4C2×C22⋊D7312yes—
223C2×C4C2×C22⋊D7312yes—
224C2×C4#1192402812yes—
225C22—24no—
226C22—22no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C22×C22⋊D7311yescharacteristic
231C22#41×D7312yes—
232C22C2×#1192402811yescharacteristic
233C22C2×#1192402811yescharacteristic
234C22#1455663812yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—41no—
241C4—2922no—
242C4—2922no—
243C4—2922no—
244C4—1464no—
245C2—42no—
246C2#1798909811yescharacteristic
247C2#1798913311yescharacteristic
248C2#1798915811yescharacteristic
249C2#1798927012yes—
250C2#1798927612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#117×C73C2
hypercenterC2×#117D73
hypocenterC73#2611
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14556583C2semidirect
2. #17988526C2semidirect
4. #17988517C2semidirect
6. #17988482C2semidirect
8. #17988471C2semidirect
10. #17988433C2semidirect
126. C73#2611semidirect