Finite Group Databasebeta

← #22615842

Subgroups — #22615842

Order 9344.

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

normal subgroups only

This group has 450 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
1C2×#14556586C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic, complemented
3#17988518C212yesmaximal, complemented
4#17988513C211yesmaximal, characteristic
5#17988511C212yesmaximal
6#17988507C211yesmaximal, characteristic, complemented
7#17988500C211yesmaximal, characteristic
8#17988477C212yesmaximal
9#17988474C212yesmaximal, complemented
10#17988451C211yesmaximal, characteristic, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13#14556586—24no—
14#14556556—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924005C2211yescharacteristic
21C2×#11924005C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×C4×Dic73C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—24no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C4⋊Dic73—22no—
46#11924007—24no—
47#11924007—22no—
48#11924007—24no—
49#11924007—42no—
50#11924005—22no—
51#11924005—22no—
52#11924005—22no—
53#11924005—24no—
54#11924005—42no—
55C4×Dic73—24no—
56C4×Dic73D414yes—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2312yes—
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—22no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—42no—
65C23×C73C2411yescharacteristic
66C22×D73—21no—
67C22×D73—22no—
68C22×D73—21no—
69C22×D73—21no—
70C22×D73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73C2×D412yes—
95C2×Dic73C2×D412yes—
96C2×Dic73#4114yes—
97Dic146—28no—
98C22×C73C22×D411yescharacteristic
99C22×C73C2×#4112yes—
100C22×C73H(5,𝔽2)11yescharacteristic
101C22×C732−1+411yescharacteristic
102C22×C732−1+412yes—
103C2×D73—41no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—42no—
107C2×D73—42no—
108C4×C73—22no—
109C4×C73—41no—
110C4×C73—42no—
111C4×C73—41no—
112C4×C73—42no—
113Dic73—24no—
114Dic73—22no—
115Dic73—22no—
116Dic73—41no—
117Dic73—42no—
118C2×C73#52511yescharacteristic
119C2×C73#53611yescharacteristic
120C2×C73#53711yescharacteristic
121C2×C73#54112yes—
122C2×C73#54212yes—
123D73—81no—
124#2637—731nomaximal, Sylow
125C73#263711yescharacteristic, complemented, Sylow
126C2×#126—731no—
127C2×C4×Q8—731no—
128#398—732no—
129#398D7311yescharacteristic, complemented
130#397—731no—
131#396—732no—
132#395—731no—
133#393—731no—
134#388—732no—
135#387—732no—
136#382—731no—
137C22×Q8—731no—
138#126—1464no—
139C4×Q8—1464no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C4⋊C4C2×D7312yes—
148C2×C22⋊C4—732no—
149C2×C22⋊C4—731no—
150C2×C22⋊C4—731no—
151C2×C22⋊C4—731no—
152C2×C22⋊C4—732no—
153C2×C42—731no—
154C2×C42—732no—
155#95—732no—
156#95—731no—
157#95—732no—
158#95—732no—
159#95—732no—
160#95C2×D7311yescharacteristic
161#95C2×D7312yes—
162C24—731no—
163C2×Q8—1464no—
164C2×Q8—1462no—
165C22×C4—731no—
166C22×C4—732no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—732no—
170C22×C4C22×D7312yes—
171C22×C4C22×D7311yescharacteristic
172C22×C4C22×D7312yes—
173C22×C4C22×D7311yescharacteristic
174C22×C4C22×D7311yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—2922no—
179C4⋊C4—1464no—
180C4⋊C4—1464no—
181C4⋊C4—1462no—
182C4⋊C4—1462no—
183C22⋊C4—2922no—
184C22⋊C4—1464no—
185C22⋊C4—1462no—
186C22⋊C4—1462no—
187C22⋊C4—1462no—
188C42—734no—
189C42—1464no—
190C23—1461no—
191C23—1462no—
192C23—1461no—
193C23—1461no—
194C23—1462no—
195C23C23×D7311yescharacteristic
196Q8—1468no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—732no—
210C2×C4—732no—
211C2×C4—734no—
212C2×C4—1461no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1461no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4D4×D7312yes—
223C22—2921no—
224C22—2921no—
225C22—2922no—
226C22—2922no—
227C22—2921no—
228C22C2×D4×D7311yescharacteristic
229C22#41×D7312yes—
230C22#1455663611yescharacteristic
231C22#1455663811yescharacteristic
232C22#1455663912yes—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—42no—
237C4—41no—
238C4—2921no—
239C4—2922no—
240C4—1462no—
241C4—1462no—
242C4—1464no—
243C2—5841no—
244C2#1798909511yescharacteristic
245C2#1798916211yescharacteristic
246C2#1798916611yescharacteristic
247C2#1798919612yes—
248C2#1798920712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2637
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#14556556C2semidirect
3. #17988518C2semidirect
6. #17988507C2semidirect
9. #17988474C2semidirect
10. #17988451C2semidirect
11. #398×C73C2semidirect
125. C73#2637semidirect
129. #398D73semidirect