Finite Group Databasebeta

← #22618102

Subgroups — #22618102

Order 9344.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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#17988529C212yesmaximal, complemented
2#17988512C212yesmaximal, complemented
3#17988507C211yesmaximal, characteristic, complemented
4#17988501C212yesmaximal
5#17988499C212yesmaximal, complemented
6#17988499C212yesmaximal, complemented
7#17988492C211yesmaximal, characteristic, complemented
8#17988480C212yesmaximal, complemented
9#394×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C22×Dic146C2211yescharacteristic
12C2×C4⋊Dic73C2212yes—
13C2×#11924007C2212yes—
14C2×C22⋊Dic73C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C4×Dic73C2211yescharacteristic
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2212yes—
30#95×C73C2211yescharacteristic
31C2×Dic146—22no—
32C2×Dic146—41no—
33C2×Dic146—41no—
34C2×Dic146—41no—
35C2×Dic146—42no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—42no—
41#11924007—42no—
42C22⋊Dic73—42no—
43C22⋊Dic73—42no—
44C22⋊Dic73—42no—
45C22⋊Dic73—42no—
46C4×Dic73—41no—
47C24×C73C2312yes—
48C2×D4×C73—41no—
49C2×D4×C73—42no—
50C22×C4×C73C2312yes—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73—41no—
55C22⋊C4×C73—24no—
56C22⋊C4×C73—42no—
57C23×C73—22no—
58C23×C73—22no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73C2411yescharacteristic
65D4×C73—44no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73#4112yes—
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—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88Dic146—44no—
89Dic146—44no—
90C22×C73—42no—
91C22×C73—42no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73—42no—
97C22×C73C2×#4111yescharacteristic
98C22×C73H(5,𝔽2)11yescharacteristic
99C22×C73H(5,𝔽2)12yes—
100C22×C73H(5,𝔽2)11yescharacteristic
101C22×C732−1+412yes—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73—41no—
106Dic73—42no—
107Dic73—42no—
108Dic73—42no—
109Dic73—42no—
110C2×C73—82no—
111C2×C73#53811yescharacteristic
112C2×C73#54212yes—
113C2×C73H(3,𝔽4)11yescharacteristic
114C2×C73#56212yes—
115C2×C73#56311yescharacteristic
116#2832—731nomaximal, Sylow
117C73#283211yescharacteristic, complemented, Sylow
118#400—732no—
119#397—732no—
120#395—731no—
121#394—732no—
122#394D7311yescharacteristic
123#393—732no—
124#393—732no—
125#391—731no—
126#388—732no—
127C22×Q8—731no—
128C22×Q8—731no—
129C22×D4C2×D7311yescharacteristic
130C2×C4⋊C4—732no—
131C2×C4⋊C4—732no—
132C2×C4⋊C4C2×D7311yescharacteristic
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C22⋊C4C2×D7312yes—
138C2×C22⋊C4C2×D7312yes—
139C2×C42—731no—
140#95—732no—
141#95—732no—
142#95—732no—
143#95—732no—
144#95—732no—
145#95—732no—
146#95—731no—
147#95C2×D7311yescharacteristic
148C24C22×D7312yes—
149C2×Q8—2921no—
150C2×Q8—2921no—
151C2×Q8—2922no—
152C2×Q8—2921no—
153C2×Q8—1462no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—732no—
157C22×C4—732no—
158C22×C4—732no—
159C22×C4—732no—
160C22×C4C22×D7312yes—
161C22×C4C22×D7311yescharacteristic
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—2922no—
166C4⋊C4—2922no—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—2922no—
170C22⋊C4—2922no—
171C22⋊C4—2922no—
172C22⋊C4—2922no—
173C42—2921no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C23×D7311yescharacteristic
182Q8—2924no—
183Q8—2924no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
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#1192402712yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#1192402711yescharacteristic
215C22#1455663611yescharacteristic
216C22#1455663612yes—
217C22#1455663711yescharacteristic
218C22#1455663812yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—2922no—
224C4—2922no—
225C4—2922no—
226C4—2922no—
227C2—82no—
228C2#1798917411yescharacteristic
229C2#1798920412yes—
230C2#1798933011yescharacteristic
231C2#1798933412yes—
232C2#1798933711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2832
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #17988529C2semidirect
2. #17988512C2semidirect
3. #17988507C2semidirect
5. #17988499C2semidirect
6. #17988499C2semidirect
7. #17988492C2semidirect
8. #17988480C2semidirect
117. C73#2832semidirect