Finite Group Databasebeta

← #22617765

Subgroups — #22617765

Order 9344.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988509C212yesmaximal, complemented
2#17988505C212yesmaximal
3#17988504C211yesmaximal, characteristic
4#17988479C212yesmaximal, complemented
5#17988479C212yesmaximal, complemented
6#17988476C212yesmaximal, complemented
7#17988470C212yesmaximal, complemented
8#17988456C211yesmaximal, characteristic, complemented
9#400×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C2×C4⋊Dic73C2212yes—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×C4×Dic73C2211yescharacteristic
22C2×C4×Dic73C2212yes—
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×D292—41no—
33C2×D292—42no—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C4⋊Dic73—24no—
38C4⋊Dic73—41no—
39#11924007—42no—
40#11924007—42no—
41#11924005—24no—
42#11924005—24no—
43#11924005—24no—
44#11924005—42no—
45#11924005—42no—
46#11924005—42no—
47C4×Dic73—22no—
48C4×Dic73—42no—
49C22×C4×C73C2312yes—
50C22×C4×C73C2312yes—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73—41no—
55C4⋊C4×C73—41no—
56C23×C73C2411yescharacteristic
57C22×D73—22no—
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73#4112yes—
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#4114yes—
86D292—44no—
87C22×C73C2×#4112yes—
88C22×C73C2×#4111yescharacteristic
89C22×C73H(5,𝔽2)11yescharacteristic
90C22×C73H(5,𝔽2)12yes—
91C22×C732−1+411yescharacteristic
92C2×D73—42no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—42no—
99C4×C73—22no—
100C4×C73—42no—
101C4×C73—42no—
102C4×C73—41no—
103C4×C73—41no—
104Dic73—24no—
105Dic73—42no—
106Dic73—42no—
107C2×C73#53911yescharacteristic
108C2×C73#54212yes—
109C2×C73#55312yes—
110C2×C73#55511yescharacteristic
111C2×C73#56011yescharacteristic
112D73—82no—
113#2795—731nomaximal, Sylow
114C73#279511yescharacteristic, complemented, Sylow
115#400D7311yescharacteristic, complemented
116#396—732no—
117#394—731no—
118#394—732no—
119#388—732no—
120#388—732no—
121#388—732no—
122#387—732no—
123#384—731no—
124C22×D4—731no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—731no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4C2×D7311yescharacteristic
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C22⋊C4—732no—
132C2×C22⋊C4—732no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C42—732no—
138C2×C42—731no—
139#95—731no—
140#95—732no—
141#95—732no—
142#95C2×D7312yes—
143#95C2×D7311yescharacteristic
144#95C2×D7312yes—
145C24—732no—
146C2×D4—2921no—
147C2×D4—2922no—
148C22×C4—732no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4C22×D7312yes—
152C22×C4C22×D7312yes—
153C22×C4C22×D7311yescharacteristic
154C22×C4C22×D7311yescharacteristic
155C22×C4C22×D7311yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—2922no—
159C4⋊C4—2922no—
160C4⋊C4—2921no—
161C4⋊C4—1464no—
162C22⋊C4—2922no—
163C22⋊C4—2922no—
164C22⋊C4—2922no—
165C22⋊C4—1464no—
166C22⋊C4—1464no—
167C22⋊C4—1464no—
168C42—2922no—
169C42—1462no—
170C23—1462no—
171C23—1462no—
172C23—1462no—
173C23—1462no—
174C23—1462no—
175C23—1462no—
176C23—1462no—
177C23C23×D7311yescharacteristic
178D4—2924no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—734no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4#1192402912yes—
201C22—2922no—
202C22—2922no—
203C22—2922no—
204C22—2922no—
205C22—2922no—
206C22—2922no—
207C22—2922no—
208C22#41×D7312yes—
209C22C2×#1192402911yescharacteristic
210C22#1455663611yescharacteristic
211C22#1455663712yes—
212C22#1455663811yescharacteristic
213C4—22no—
214C4—42no—
215C4—42no—
216C4—41no—
217C4—41no—
218C4—2922no—
219C4—2922no—
220C4—1464no—
221C2—5842no—
222C2#1798918611yescharacteristic
223C2#1798920312yes—
224C2#1798929012yes—
225C2#1798929911yescharacteristic
226C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2795
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #17988509C2semidirect
4. #17988479C2semidirect
5. #17988479C2semidirect
6. #17988476C2semidirect
7. #17988470C2semidirect
8. #17988456C2semidirect
9. #400×C73C2semidirect
114. C73#2795semidirect
115. #400D73semidirect