Finite Group Databasebeta

← #22617967

Subgroups — #22617967

Order 9344.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556571C211yesmaximal, characteristic
2C2×#14556569C211yesmaximal, characteristic
3#17988529C212yesmaximal, complemented
4#17988525C211yesmaximal, characteristic, complemented
5#17988516C212yesmaximal
6#17988514C212yesmaximal
7#17988508C211yesmaximal, characteristic, complemented
8#17988508C212yesmaximal, complemented
9#17988507C211yesmaximal, characteristic, complemented
10#17988449C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556571—24no—
16#14556569—24no—
17C2×C4⋊Dic73C2212yes—
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26#14556498C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×Dic146—42no—
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C2×C4×D73—42no—
48C2×C4×D73D414yes—
49C4⋊Dic73—24no—
50C4⋊Dic73—42no—
51#11924007—22no—
52#11924007—22no—
53#11924007—42no—
54#11924005—22no—
55#11924005—22no—
56#11924005—24no—
57#11924005—42no—
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C23×C73C2411yescharacteristic
66C22×D73—22no—
67C22×D73—21no—
68C22×D73—22no—
69C22×D73—21no—
70C22×D73C2×D412yes—
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—24no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73C2×D412yes—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73C2×D412yes—
96C4×D73—44no—
97Dic146—44no—
98Dic146—44no—
99C22×C73C22×D411yescharacteristic
100C22×C73H(5,𝔽2)12yes—
101C22×C732−1+412yes—
102C22×C732−1+411yescharacteristic
103C22×C732−1+411yescharacteristic
104C2×D73—22no—
105C2×D73—22no—
106C2×D73—22no—
107C2×D73—42no—
108C2×D73—42no—
109C4×C73—22no—
110C4×C73—41no—
111C4×C73—42no—
112C4×C73—41no—
113C4×C73—42no—
114Dic73—22no—
115Dic73—41no—
116Dic73—42no—
117Dic73—41no—
118Dic73—42no—
119C2×C73#53411yescharacteristic
120C2×C73#53611yescharacteristic
121C2×C73#53611yescharacteristic
122C2×C73#56312yes—
123C2×C73#56312yes—
124D73—42no—
125#2817—731nomaximal, Sylow
126C73#281711yescharacteristic, complemented, Sylow
127C2×C22⋊Q8—731no—
128C2×C22⋊Q8—731no—
129#400—731no—
130#400—732no—
131#400D7311yescharacteristic, complemented
132#397—732no—
133#397—732no—
134#395—731no—
135#395—732no—
136#395—731no—
137#381—731no—
138C22×Q8—731no—
139C22×Q8—731no—
140C23×C4—731no—
141C22⋊Q8—1464no—
142C22⋊Q8—1464no—
143C2×C4⋊C4—732no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4—731no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4C2×D7311yescharacteristic
149C2×C4⋊C4C2×D7311yescharacteristic
150C2×C22⋊C4—732no—
151C2×C22⋊C4—731no—
152C2×C22⋊C4—731no—
153C2×C22⋊C4—732no—
154#95—732no—
155#95—731no—
156#95—732no—
157#95—732no—
158#95—732no—
159#95—732no—
160#95C2×D7311yescharacteristic
161#95C2×D7312yes—
162#95C2×D7312yes—
163C24—731no—
164C2×Q8—2922no—
165C2×Q8—2922no—
166C2×Q8—1462no—
167C2×Q8—1462no—
168C22×C4—2922no—
169C22×C4—734no—
170C22×C4—731no—
171C22×C4—732no—
172C22×C4—731no—
173C22×C4—732no—
174C22×C4—731no—
175C22×C4C22×D7312yes—
176C22×C4C22×D7312yes—
177C22×C4C22×D7311yescharacteristic
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—2922no—
183C4⋊C4—2922no—
184C4⋊C4—1462no—
185C4⋊C4—1464no—
186C4⋊C4—1462no—
187C22⋊C4—2922no—
188C22⋊C4—1462no—
189C22⋊C4—1464no—
190C22⋊C4—1462no—
191C23—732no—
192C23—1462no—
193C23—1461no—
194C23—1462no—
195C23—1461no—
196C23C23×D7311yescharacteristic
197Q8—2924no—
198Q8—2924no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—24no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—2924no—
211C2×C4—732no—
212C2×C4—1461no—
213C2×C4—1462no—
214C2×C4—1461no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1461no—
220C2×C4—1462no—
221C2×C4—1461no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4D4×D7312yes—
225C22—2922no—
226C22—2922no—
227C22—1462no—
228C22—1462no—
229C22—1462no—
230C22C2×D4×D7311yescharacteristic
231C22#1455663712yes—
232C22#1455663812yes—
233C22#1455663811yescharacteristic
234C22#1455663911yescharacteristic
235C4—22no—
236C4—41no—
237C4—42no—
238C4—41no—
239C4—42no—
240C4—2922no—
241C4—2921no—
242C4—2921no—
243C4—2922no—
244C4—1462no—
245C2—2922no—
246C2#1798914811yescharacteristic
247C2#1798915711yescharacteristic
248C2#1798916011yescharacteristic
249C2#1798933912yes—
250C2#1798934112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2817
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #17988529C2semidirect
4. #17988525C2semidirect
7. #17988508C2semidirect
8. #17988508C2semidirect
9. #17988507C2semidirect
11. #400×C73C2semidirect
126. C73#2817semidirect
131. #400D73semidirect