Finite Group Databasebeta

← #22616858

Subgroups — #22616858

Order 9344.

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

normal subgroups only

This group has 504 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×#14556576C212yesmaximal
2#17988517C211yesmaximal, characteristic, complemented
3#17988516C212yesmaximal, complemented
4#17988516C212yesmaximal, complemented
5#17988488C211yesmaximal, characteristic
6#17988482C212yesmaximal, complemented
7#17988461C212yesmaximal, complemented
8#17988458C212yesmaximal, complemented
9#398×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C4×D73C2212yes—
12#14556576—28no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×C4×Dic73C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27C2×C4⋊C4×C73C2212yes—
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C4⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31#95×C73C2211yescharacteristic
32C23×D73C2312yes—
33C2×D292—41no—
34C2×D292—41no—
35C2×D292D414yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C2×C4×D73—24no—
40C2×C4×D73—42no—
41C2×C4×D73—42no—
42C4⋊Dic73—41no—
43#11924007—24no—
44#11924007—24no—
45#11924007—42no—
46#11924005—24no—
47#11924005—24no—
48#11924005—24no—
49#11924005—24no—
50#11924005—24no—
51C4×Dic73—41no—
52C22×C4×C73C2312yes—
53C22×C4×C73C2311yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C4⋊C4×C73—24no—
58C4⋊C4×C73—41no—
59C4⋊C4×C73—41no—
60C23×C73C2411yescharacteristic
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73—22no—
65C22×D73—22no—
66C22×D73—22no—
67C22×D73C2×D414yes—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73C2×D412yes—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73#4114yes—
90D292—44no—
91C4×D73—48no—
92C22×C73C22×D411yescharacteristic
93C22×C73C2×#4112yes—
94C22×C73H(5,𝔽2)11yescharacteristic
95C22×C73H(5,𝔽2)11yescharacteristic
96C22×C732−1+412yes—
97C2×D73—24no—
98C2×D73—24no—
99C2×D73—24no—
100C2×D73—42no—
101C2×D73—42no—
102C2×D73—42no—
103C2×D73—42no—
104C4×C73—22no—
105C4×C73—42no—
106C4×C73—42no—
107C4×C73—41no—
108C4×C73—41no—
109Dic73—24no—
110Dic73—42no—
111Dic73—42no—
112C2×C73#53411yescharacteristic
113C2×C73#53912yes—
114C2×C73#54712yes—
115C2×C73#55911yescharacteristic
116C2×C73#56311yescharacteristic
117D73—44no—
118#2724—731nomaximal, Sylow
119C73#272411yescharacteristic, complemented, Sylow
120C2×#123—732no—
121#398—731no—
122#398D7311yescharacteristic, complemented
123#397—732no—
124#397—732no—
125#390—731no—
126#389—732no—
127#385—732no—
128#385—732no—
129C22×D4—731no—
130C23×C4—732no—
131#123—1468no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—731no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4C2×D7312yes—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C22⋊C4—732no—
140C2×C22⋊C4—732no—
141C2×C22⋊C4—732no—
142C2×C22⋊C4—732no—
143C2×C22⋊C4—732no—
144C2×C42—731no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—731no—
149#95C2×D7312yes—
150#95C2×D7311yescharacteristic
151C24—732no—
152C2×D4—2921no—
153C2×D4—2921no—
154C2×D4—734no—
155C22×C4—2922no—
156C22×C4—2922no—
157C22×C4—732no—
158C22×C4—732no—
159C22×C4—732no—
160C22×C4—1464no—
161C22×C4C22×D7311yescharacteristic
162C22×C4C22×D7312yes—
163C22×C4C22×D7311yescharacteristic
164C22×C4C22×D7312yes—
165C22×C4C22×D7311yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—2922no—
170C4⋊C4—2921no—
171C4⋊C4—1464no—
172C4⋊C4—1464no—
173C22⋊C4—1464no—
174C22⋊C4—1464no—
175C22⋊C4—1464no—
176C22⋊C4—1464no—
177C22⋊C4—1464no—
178C42—2921no—
179C23—734no—
180C23—1462no—
181C23—1462no—
182C23—1462no—
183C23—1462no—
184C23—1462no—
185C23—1462no—
186C23C23×D7311yescharacteristic
187D4—2924no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—2928no—
201C2×C4—734no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4D4×D7312yes—
211C22—2922no—
212C22—2922no—
213C22—2922no—
214C22—2922no—
215C22—1464no—
216C22—1464no—
217C22—1464no—
218C22C2×D4×D7311yescharacteristic
219C22#41×D7312yes—
220C22#1455663611yescharacteristic
221C22#1455663711yescharacteristic
222C22#1455663912yes—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—2922no—
229C4—2922no—
230C4—1464no—
231C2—2924no—
232C2#1798914511yescharacteristic
233C2#1798918512yes—
234C2#1798923912yes—
235C2#1798932111yescharacteristic
236C2#1798933611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2724
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #17988517C2semidirect
3. #17988516C2semidirect
4. #17988516C2semidirect
6. #17988482C2semidirect
7. #17988461C2semidirect
8. #17988458C2semidirect
9. #398×C73C2semidirect
119. C73#2724semidirect
122. #398D73semidirect