Finite Group Databasebeta

← #22616097

Subgroups — #22616097

Order 9344.

434 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556582C211yesmaximal, characteristic, complemented
3#17988526C211yesmaximal, characteristic, complemented
4#17988524C211yesmaximal, characteristic
5#17988519C212yesmaximal, complemented
6#17988513C211yesmaximal, characteristic
7#17988509C212yesmaximal
8#17988483C212yesmaximal, complemented
9#17988476C212yesmaximal
10#17988438C211yesmaximal, characteristic, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12#14556586—24no—
13#14556582—24no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×C4×Dic73C2212yes—
27C2×C4×Dic73C2211yescharacteristic
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
38C22×Dic73C2312yes—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C4⋊Dic73—22no—
44C4⋊Dic73—24no—
45C4⋊Dic73—24no—
46C4⋊Dic73—22no—
47#11924007—24no—
48#11924007—24no—
49#11924007—22no—
50#11924005—22no—
51#11924005—24no—
52#11924005—22no—
53#11924005—22no—
54#11924005—42no—
55C4×Dic73—42no—
56C4×Dic73D414yes—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2312yes—
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—22no—
70C22×D73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
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×C73C2×D412yes—
83C2×C4×C73#4114yes—
84C2×Dic73—22no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73C2×D412yes—
96C2×Dic73C2×D412yes—
97C22×C73C22×D411yescharacteristic
98C22×C73C2×#4112yes—
99C22×C73H(5,𝔽2)11yescharacteristic
100C22×C732−1+412yes—
101C22×C732−1+411yescharacteristic
102C2×D73—41no—
103C2×D73—41no—
104C2×D73—41no—
105C2×D73—42no—
106C2×D73—42no—
107C4×C73—22no—
108C4×C73—24no—
109C4×C73—41no—
110C4×C73—41no—
111C4×C73—42no—
112Dic73—22no—
113Dic73—22no—
114Dic73—41no—
115Dic73—42no—
116Dic73—42no—
117C2×C73#53211yescharacteristic
118C2×C73#53611yescharacteristic
119C2×C73#53711yescharacteristic
120C2×C73#53912yes—
121C2×C73#54112yes—
122D73—81no—
123#2664—731nomaximal, Sylow
124C73#266411yescharacteristic, complemented, Sylow
125C2×#126—731no—
126C2×#125—731no—
127#400—731no—
128#399—731no—
129#398—732no—
130#398D7311yescharacteristic, complemented
131#397—731no—
132#396—732no—
133#389—732no—
134#388—732no—
135C4×C4⋊C4—731no—
136#126—1464no—
137#125—1464no—
138C2×C4⋊C4—732no—
139C2×C4⋊C4—732no—
140C2×C4⋊C4—731no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—732no—
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—732no—
154C2×C42—731no—
155#95—731no—
156#95—732no—
157#95—732no—
158#95—732no—
159#95C2×D7311yescharacteristic
160#95C2×D7312yes—
161C24—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—732no—
165C22×C4—731no—
166C22×C4—732no—
167C22×C4C22×D7311yescharacteristic
168C22×C4C22×D7311yescharacteristic
169C22×C4C22×D7312yes—
170C22×C4C22×D7311yescharacteristic
171C22×C4C22×D7312yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—1464no—
176C4⋊C4—1462no—
177C4⋊C4—1464no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1464no—
181C4⋊C4—1464no—
182C22⋊C4—2922no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C22⋊C4—1462no—
186C22⋊C4—1464no—
187C42—2922no—
188C42—734no—
189C23—1461no—
190C23—1462no—
191C23—1461no—
192C23—1462no—
193C23—1461no—
194C23C23×D7311yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—732no—
207C2×C4—732no—
208C2×C4—1461no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1461no—
218C2×C4—1461no—
219C2×C4D4×D7312yes—
220C2×C4#1192402914yes—
221C22—2921no—
222C22—2921no—
223C22—2921no—
224C22—2922no—
225C22—2922no—
226C22C2×D4×D7311yescharacteristic
227C22C2×#1192402912yes—
228C22#1455663611yescharacteristic
229C22#1455663812yes—
230C22#1455663811yescharacteristic
231C4—22no—
232C4—24no—
233C4—41no—
234C4—41no—
235C4—42no—
236C4—2921no—
237C4—2922no—
238C4—2922no—
239C4—1462no—
240C4—1462no—
241C2—5841no—
242C2#1798913811yescharacteristic
243C2#1798915911yescharacteristic
244C2#1798916611yescharacteristic
245C2#1798918612yes—
246C2#1798920012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2664
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#14556582C2semidirect
3. #17988526C2semidirect
5. #17988519C2semidirect
8. #17988483C2semidirect
10. #17988438C2semidirect
11. #398×C73C2semidirect
124. C73#2664semidirect
130. #398D73semidirect