Finite Group Databasebeta

← #22617969

Subgroups — #22617969

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×#14556568C212yesmaximal
2#17988529C212yesmaximal, complemented
3#17988528C212yesmaximal, complemented
4#17988515C212yesmaximal
5#17988512C211yesmaximal, characteristic
6#17988508C212yesmaximal, complemented
7#17988507C212yesmaximal, complemented
8#17988448C211yesmaximal, characteristic
9#397×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C23×Dic73C2211yescharacteristic
12#14556568—28no—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2211yescharacteristic
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31#95×C73C2211yescharacteristic
32C2×Dic146—24no—
33C2×Dic146—42no—
34C2×Dic146—42no—
35C22×Dic73—41no—
36C22×Dic73—41no—
37C22×Dic73D414yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—41no—
44#11924007—24no—
45#11924007—24no—
46#11924007—42no—
47C22⋊Dic73—24no—
48C22⋊Dic73—41no—
49C24×C73C2311yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2312yes—
54C4⋊C4×C73—41no—
55C22⋊C4×C73—24no—
56C22⋊C4×C73—41no—
57C23×C73—21no—
58C23×C73—21no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73C2×D412yes—
62C23×C73C2411yescharacteristic
63C2×C4×C73—22no—
64C2×C4×C73—22no—
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×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—44no—
85C2×Dic73C2×D414yes—
86Dic146—48no—
87C22×C73—22no—
88C22×C73—24no—
89C22×C73—41no—
90C22×C73—42no—
91C22×C73—41no—
92C22×C73C22×D411yescharacteristic
93C22×C73H(5,𝔽2)11yescharacteristic
94C22×C73H(5,𝔽2)11yescharacteristic
95C22×C732−1+412yes—
96C22×C732−1+412yes—
97C4×C73—42no—
98C4×C73—42no—
99C4×C73—41no—
100C4×C73—41no—
101Dic73—24no—
102Dic73—42no—
103Dic73—42no—
104Dic73—42no—
105C2×C73—42no—
106C2×C73#53411yescharacteristic
107C2×C73#53612yes—
108C2×C73#56311yescharacteristic
109C2×C73#56312yes—
110C2×C73#56311yescharacteristic
111#2817—731nomaximal, Sylow
112C73#281711yescharacteristic, complemented, Sylow
113C2×C22⋊Q8—732no—
114#400—732no—
115#400—732no—
116#397—731no—
117#397—732no—
118#397D7311yescharacteristic
119#395—732no—
120#395—732no—
121#381—731no—
122C22×Q8—732no—
123C23×C4—731no—
124C22⋊Q8—1468no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—731no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C22⋊C4—731no—
132C2×C22⋊C4—732no—
133C2×C22⋊C4C2×D7312yes—
134C2×C22⋊C4C2×D7311yescharacteristic
135#95—732no—
136#95—732no—
137#95—732no—
138#95—732no—
139#95—732no—
140#95—732no—
141#95—731no—
142#95C2×D7312yes—
143#95C2×D7311yescharacteristic
144C24C22×D7311yescharacteristic
145C2×Q8—2922no—
146C2×Q8—2922no—
147C2×Q8—1464no—
148C22×C4—2921no—
149C22×C4—2921no—
150C22×C4—734no—
151C22×C4—732no—
152C22×C4—732no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4C22×D7311yescharacteristic
156C22×C4C22×D7311yescharacteristic
157C22×C4C22×D7312yes—
158C22×C4C22×D7312yes—
159C4⋊C4—41no—
160C4⋊C4—2922no—
161C4⋊C4—2921no—
162C4⋊C4—1464no—
163C4⋊C4—1464no—
164C4⋊C4—1464no—
165C22⋊C4—24no—
166C22⋊C4—41no—
167C22⋊C4—2921no—
168C22⋊C4—1464no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23D4×D7312yes—
174C23C23×D7311yescharacteristic
175Q8—2928no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2924no—
187C2×C4—734no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C22—22no—
200C22—24no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22C2×D4×D7311yescharacteristic
205C22#1455663611yescharacteristic
206C22#1455663711yescharacteristic
207C22#1455663812yes—
208C22#1455663812yes—
209C4—42no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—2922no—
214C4—2922no—
215C4—2922no—
216C4—1464no—
217C2—42no—
218C2#1798914511yescharacteristic
219C2#1798915912yes—
220C2#1798933711yescharacteristic
221C2#1798933912yes—
222C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2817
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #17988529C2semidirect
3. #17988528C2semidirect
6. #17988508C2semidirect
7. #17988507C2semidirect
112. C73#2817semidirect