Finite Group Databasebeta

← #22615181

Subgroups — #22615181

Order 9344.

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

normal subgroups only

This group has 476 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
1#17988504C211yesmaximal, characteristic
2#17988500C212yesmaximal, complemented
3#17988492C211yesmaximal, characteristic, complemented
4#17988477C212yesmaximal, complemented
5#17988465C212yesmaximal
6#17988454C212yesmaximal, complemented
7#17988449C212yesmaximal, complemented
8#17988434C212yesmaximal, complemented
9#400×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C22×C4×D73C2212yes—
13C2×#11924005C2212yes—
14C2×#11924005C2212yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×C4×Dic73C2212yes—
19C2×C4×Dic73C2211yescharacteristic
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2212yes—
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28#95×C73C2212yes—
29#95×C73C2211yescharacteristic
30#95×C73C2212yes—
31C23×D73C2312yes—
32C2×Dic146—22no—
33C2×Dic146—41no—
34C2×Dic146—41no—
35C2×D292—24no—
36C2×D292—41no—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C2×C4×D73—24no—
41C2×C4×D73—24no—
42C2×C4×D73—42no—
43#11924005—24no—
44#11924005—24no—
45#11924005—24no—
46#11924005—42no—
47#11924005—42no—
48C4×Dic73—24no—
49C4×Dic73—41no—
50C22×C4×C73C2312yes—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2312yes—
53C22×C4×C73C2311yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—41no—
56C4⋊C4×C73—41no—
57C23×C73C2411yescharacteristic
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73#4114yes—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73#4112yes—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73#4114yes—
87D292—44no—
88C4×D73—48no—
89Dic146—44no—
90C22×C73C2×#4112yes—
91C22×C73C2×#4112yes—
92C22×C73C2×#4111yescharacteristic
93C22×C73H(5,𝔽2)11yescharacteristic
94C22×C73H(5,𝔽2)11yescharacteristic
95C2×D73—24no—
96C2×D73—24no—
97C2×D73—24no—
98C2×D73—42no—
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—42no—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73—42no—
107Dic73—24no—
108Dic73—42no—
109Dic73—42no—
110C2×C73#52912yes—
111C2×C73#53811yescharacteristic
112C2×C73#55112yes—
113C2×C73#55111yescharacteristic
114C2×C73#55511yescharacteristic
115D73—44no—
116#2572—731nomaximal, Sylow
117C73#257211yescharacteristic, complemented, Sylow
118#400D7311yescharacteristic, complemented
119#394—731no—
120#393—732no—
121#391—731no—
122#388—732no—
123#386—732no—
124#383—732no—
125#381—732no—
126C4×C22⋊C4—732no—
127C22×Q8—731no—
128C22×D4—731no—
129C23×C4—732no—
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C4⋊C4C2×D7311yescharacteristic
132C2×C22⋊C4—732no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C42—731no—
138C2×C42—732no—
139#95—732no—
140#95—732no—
141#95—732no—
142#95—731no—
143#95—732no—
144#95—732no—
145#95C2×D7312yes—
146#95C2×D7311yescharacteristic
147#95C2×D7312yes—
148C24—732no—
149C2×Q8—2921no—
150C2×Q8—2921no—
151C2×Q8—1462no—
152C2×D4—2921no—
153C2×D4—1464no—
154C22×C4—2922no—
155C22×C4—732no—
156C22×C4—732no—
157C22×C4—732no—
158C22×C4—1464no—
159C22×C4—1464no—
160C22×C4C22×D7311yescharacteristic
161C22×C4C22×D7312yes—
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7312yes—
164C22×C4C22×D7311yescharacteristic
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—2922no—
168C22⋊C4—2922no—
169C22⋊C4—1464no—
170C22⋊C4—1464no—
171C22⋊C4—1464no—
172C42—2921no—
173C42—1464no—
174C23—734no—
175C23—1462no—
176C23—1462no—
177C23—1462no—
178C23—1462no—
179C23—1462no—
180C23—1462no—
181C23C23×D7311yescharacteristic
182Q8—2924no—
183D4—2924no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—2928no—
197C2×C4—734no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4#1192402912yes—
207C22—2922no—
208C22—2922no—
209C22—2922no—
210C22—2922no—
211C22—1464no—
212C22—1464no—
213C22—1464no—
214C22#41×D7312yes—
215C22#41×D7312yes—
216C22C2×#1192402911yescharacteristic
217C22#1455663611yescharacteristic
218C22#1455663711yescharacteristic
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—2922no—
225C4—2922no—
226C4—1464no—
227C2—2924no—
228C2#1798912212yes—
229C2#1798917711yescharacteristic
230C2#1798926212yes—
231C2#1798926511yescharacteristic
232C2#1798929911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2572
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #17988500C2semidirect
3. #17988492C2semidirect
4. #17988477C2semidirect
6. #17988454C2semidirect
7. #17988449C2semidirect
8. #17988434C2semidirect
9. #400×C73C2semidirect
117. C73#2572semidirect
118. #400D73semidirect