Finite Group Databasebeta

← #22618121

Subgroups — #22618121

Order 9344.

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

normal subgroups only

This group has 380 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#17988528C212yesmaximal, complemented
2#17988527C212yesmaximal, complemented
3#17988526C212yesmaximal, complemented
4#17988515C212yesmaximal
5#17988508C212yesmaximal, complemented
6#17988499C211yesmaximal, characteristic
7#17988462C212yesmaximal
8#17988459C211yesmaximal, characteristic
9#397×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C23×Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2212yes—
13C2×C4⋊Dic73C2212yes—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2211yescharacteristic
17C2×C22⋊Dic73C2212yes—
18#14556498C2212yes—
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2212yes—
22#14556498C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C22⋊C4×C73C2212yes—
28C2×C22⋊C4×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2211yescharacteristic
31C2×Dic146—42no—
32C2×Dic146—41no—
33C22×Dic73—42no—
34C22×Dic73—41no—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C4⋊Dic73—42no—
40C4⋊Dic73—42no—
41#11924007—42no—
42#11924007—42no—
43C22⋊Dic73—22no—
44C22⋊Dic73—42no—
45C24×C73C2311yescharacteristic
46C22×C4×C73C2312yes—
47C22×C4×C73C2311yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2312yes—
50C4⋊C4×C73—41no—
51C22⋊C4×C73—24no—
52C22⋊C4×C73—41no—
53C23×C73—21no—
54C23×C73—22no—
55C23×C73—22no—
56C23×C73—21no—
57C23×C73#4112yes—
58C23×C73C2411yescharacteristic
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×Dic73—22no—
70C2×Dic73—22no—
71C2×Dic73—22no—
72C2×Dic73—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—44no—
82Dic146—44no—
83C22×C73—24no—
84C22×C73—22no—
85C22×C73—41no—
86C22×C73—42no—
87C22×C73—41no—
88C22×C73C2×#4111yescharacteristic
89C22×C73H(5,𝔽2)11yescharacteristic
90C22×C73H(5,𝔽2)12yes—
91C22×C732−1+412yes—
92C22×C732−1+411yescharacteristic
93C4×C73—42no—
94C4×C73—42no—
95C4×C73—41no—
96C4×C73—41no—
97Dic73—42no—
98Dic73—42no—
99Dic73—42no—
100Dic73—42no—
101C2×C73—42no—
102C2×C73#53912yes—
103C2×C73#53911yescharacteristic
104C2×C73H(3,𝔽4)11yescharacteristic
105C2×C73#56312yes—
106C2×C73#56311yescharacteristic
107#2835—731nomaximal, Sylow
108C73#283511yescharacteristic, complemented, Sylow
109#400—732no—
110#400—732no—
111#400—732no—
112#397—732no—
113#397D7311yescharacteristic
114#395—732no—
115#393—731no—
116#385—731no—
117#385—732no—
118C22×Q8—731no—
119C23×C4—731no—
120C2×C4⋊C4—732no—
121C2×C4⋊C4—732no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4C2×D7311yescharacteristic
125C2×C22⋊C4—732no—
126C2×C22⋊C4—731no—
127C2×C22⋊C4C2×D7312yes—
128C2×C22⋊C4C2×D7311yescharacteristic
129#95—732no—
130#95—732no—
131#95—732no—
132#95—731no—
133#95—732no—
134#95—732no—
135#95—732no—
136#95—732no—
137#95C2×D7312yes—
138#95C2×D7311yescharacteristic
139C24C22×D7311yescharacteristic
140C2×Q8—2921no—
141C2×Q8—2922no—
142C22×C4—2921no—
143C22×C4—2922no—
144C22×C4—732no—
145C22×C4—732no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4C22×D7311yescharacteristic
149C22×C4C22×D7312yes—
150C22×C4C22×D7312yes—
151C22×C4C22×D7311yescharacteristic
152C4⋊C4—41no—
153C4⋊C4—2922no—
154C4⋊C4—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—2922no—
160C22⋊C4—1462no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23#1192402712yes—
166C23C23×D7311yescharacteristic
167Q8—2924no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2924no—
179C2×C4—1462no—
180C2×C4—1462no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C22—24no—
192C22—22no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22C2×#1192402711yescharacteristic
197C22#1455663611yescharacteristic
198C22#1455663712yes—
199C22#1455663812yes—
200C22#1455663811yescharacteristic
201C4—42no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—2922no—
206C4—2922no—
207C4—2922no—
208C4—2922no—
209C2—42no—
210C2#1798918112yes—
211C2#1798918211yescharacteristic
212C2#1798932911yescharacteristic
213C2#1798933912yes—
214C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2835
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988527C2semidirect
3. #17988526C2semidirect
5. #17988508C2semidirect
108. C73#2835semidirect