Finite Group Databasebeta

← #22625793

Subgroups — #22625793

Order 9344.

380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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×#14556649C212yesmaximal
2#17989529C212yesmaximal, complemented
3#17989465C212yesmaximal, complemented
4C2×#14556551C211yesmaximal, characteristic
5C2×C4⋊#64408—22no—
6C2×C22⋊#64408C2214yes—
7#14556649—24no—
8(C2×#64408)⋊C4—22no—
9C22×C22⋊D73C2211yescharacteristic
10C23×Dic73C411yescharacteristic, complemented
11C22×C4×D73C2211yescharacteristic
12#14556551—22no—
13#14556551—22no—
14C2×#11924007C411yescharacteristic, complemented
15C2×#11924005C2211yescharacteristic
16C2×C4×Dic73C411yescharacteristic, complemented
17C2×C22⋊C4×C73C411yescharacteristic, complemented
18C22×#64408—24no—
19C4⋊#64408—44no—
20C22⋊#64408—24no—
21C22⋊#64408—24no—
22C23×D73C2311yescharacteristic
23C2×C22⋊D73—22no—
24C2×C22⋊D73—22no—
25C2×C22⋊D73D412yes—
26C2×C22⋊D73Q812yes—
27C22×Dic73—21no—
28C22×Dic73—21no—
29C22×Dic73—42no—
30C22×Dic73C2×C411yescharacteristic
31C22×Dic73C2×C411yescharacteristic
32C22×Dic73C2×C411yescharacteristic
33C2×C4×D73—42no—
34C2×C4×D73D412yes—
35C2×C4×D73D412yes—
36#11924007—22no—
37#11924005—22no—
38C4×Dic73—21no—
39C4×Dic73—21no—
40C24×C73C2×C411yescharacteristic
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73C2×C411yescharacteristic
43C22⋊C4×C73—22no—
44C23×C73—21no—
45C23×C73—21no—
46C23×C73—41no—
47C23×C73—41no—
48C23×C73C4⋊C412yescomplemented
49C23×C73C22×C411yescharacteristic
50C22×D73—41no—
51C22×D73—41no—
52C22×D73C2×D412yes—
53C22×D73C2×D411yescharacteristic
54C22×D73C2×Q811yescharacteristic
55C22×D73#4112yes—
56C2×#64408—44no—
57C2×#64408—44no—
58C2×#64408—44no—
59C2×C4×C73—21no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73C22⋊C412yes—
63C22⋊D73—24no—
64C22⋊D73—24no—
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—22no—
68C2×Dic73—21no—
69C2×Dic73—42no—
70C2×Dic73—42no—
71C2×Dic73—41no—
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C22⋊C411yescharacteristic
74C2×Dic73C4⋊C412yescomplemented
75C4×D73—24no—
76C4×D73—42no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73—22no—
80C22×C73—42no—
81C22×C73—42no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73C2×C22⋊C411yescharacteristic
85C22×C73C2×C4⋊C411yescharacteristic
86C22×C73#11711yescharacteristic
87C2×D73—22no—
88C2×D73—22no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73—42no—
92C2×D73#12112yes—
93C2×D73C22⋊Q812yes—
94#64408—84no—
95C4×C73—22no—
96C4×C73—41no—
97Dic73—22no—
98Dic73—21no—
99Dic73—41no—
100Dic73#9912yescomplemented
101C2×C73—21no—
102C2×C73—21no—
103C2×C73—42no—
104C2×C73#38011yescharacteristic
105C2×C73C2×#9911yescharacteristic
106C2×C73#41011yescharacteristic
107D73—22no—
108D73—22no—
109#1799—731nomaximal, Sylow
110C73#179911yescharacteristic, complemented, Sylow
111C2×C4×D4—731no—
112C2×#99—732no—
113#380—732no—
114#342—732no—
115C22×D4—731no—
116C23×C4—731no—
117C23×C4—731no—
118C4×D4—1462no—
119C4×D4—1462no—
120C2×C4⋊C4—731no—
121C2×C4⋊C4—1462no—
122C2×C22⋊C4—731no—
123C2×C22⋊C4—734no—
124C2×C22⋊C4#6440811yescharacteristic, complemented
125C2×C42—731no—
126#99—1464no—
127#95—1462no—
128C24—731no—
129C24C2×#6440811yescharacteristic
130C2×D4—732no—
131C2×D4—732no—
132C2×D4—1462no—
133C2×D4—1462no—
134C22×C4—2922no—
135C22×C4—2922no—
136C22×C4—732no—
137C22×C4—731no—
138C22×C4—731no—
139C22×C4—731no—
140C22×C4—732no—
141C22×C4—1464no—
142C22×C4—1461no—
143C22×C4—1461no—
144C22×C4C2×#6440811yescharacteristic
145C22×C4C2×#6440811yescharacteristic
146C4⋊C4—2924no—
147C4⋊C4—1462no—
148C22⋊C4—22no—
149C22⋊C4—1462no—
150C22⋊C4—1464no—
151C22⋊C4—1464no—
152C42—1461no—
153C42—1461no—
154C23—21no—
155C23—21no—
156C23—41no—
157C23—41no—
158C23—2921no—
159C23—2921no—
160C23—731no—
161C23—731no—
162C23—732no—
163C23—732no—
164C23C4⋊#6440812yescomplemented
165C23C22×#6440811yescharacteristic
166D4—1464no—
167D4—1464no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2922no—
172C2×C4—2922no—
173C2×C4—2922no—
174C2×C4—2921no—
175C2×C4—2924no—
176C2×C4—2924no—
177C2×C4—2924no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—732no—
181C2×C4—1464no—
182C2×C4—1461no—
183C2×C4—1462no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4C22⋊#6440812yes—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—2921no—
195C22—2921no—
196C22—2922no—
197C22—732no—
198C22—732no—
199C22—1462no—
200C22—1462no—
201C22C2×C22⋊#6440811yescharacteristic
202C22C2×C4⋊#6440811yescharacteristic
203C22#1455667011yescharacteristic
204C4—22no—
205C4—41no—
206C4—2921no—
207C4—5844no—
208C4—732no—
209C4—1462no—
210C4—1461no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2—1462no—
215C2—1462no—
216C2#1798952911yescharacteristic
217C2D73⋊#9911yescharacteristic
218C2#1798956711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1799
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #17989529C2semidirect
3. #17989465C2semidirect
10. C23×Dic73C4semidirect
14. C2×#11924007C4semidirect
16. C2×C4×Dic73C4semidirect
17. C2×C22⋊C4×C73C4semidirect
48. C23×C73C4⋊C4semidirect
74. C2×Dic73C4⋊C4semidirect
100. Dic73#99semidirect
110. C73#1799semidirect
124. C2×C22⋊C4#64408semidirect
164. C23C4⋊#64408semidirect