Finite Group Databasebeta

← #22626070

Subgroups — #22626070

Order 9344.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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×#14556649C214yesmaximal, complemented
2#17989529C211yesmaximal, characteristic, complemented
3C4×C22⋊#64408C211yesmaximal, characteristic, complemented
4C2×#14556562C211yesmaximal, characteristic
5C2×C4⋊#64408—21no—
6C2×C22⋊#64408C2212yes—
7C2×C22⋊#64408C2212yes—
8C2×C4×#64408—21no—
9#14556649—28no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4—21no—
12C22×C22⋊D73C2212yes—
13C22×C4×D73C2211yescharacteristic
14#14556562—21no—
15#14556562—21no—
16#14556562—21no—
17#14556562—21no—
18C2×C4⋊Dic73C411yescharacteristic, complemented
19C2×C22⋊Dic73C412yescomplemented
20C22×D4×C73C411yescharacteristic, complemented
21C22×#64408—22no—
22C22×#64408—22no—
23C4⋊#64408—42no—
24C22⋊#64408—22no—
25C22⋊#64408—24no—
26C22⋊#64408D414yescomplemented
27C4×#64408—42no—
28C23×D73C2311yescharacteristic
29C2×C22⋊D73—22no—
30C2×C22⋊D73—22no—
31C2×C22⋊D73—24no—
32C2×C22⋊D73—24no—
33C22×Dic73C2×C412yes—
34C22×Dic73C2×C411yescharacteristic
35C2×C4×D73—42no—
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42C22⋊Dic73—22no—
43C22⋊Dic73—22no—
44C24×C73C2×C412yes—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—42no—
48C22×C4×C73C2×C411yescharacteristic
49C23×C73—22no—
50C23×C73—24no—
51C23×C73—42no—
52C23×C73—42no—
53C23×C73C22×C411yescharacteristic
54C22×D73—41no—
55C22×D73—41no—
56C22×D73C2×D411yescharacteristic
57C22×D73C2×D411yescharacteristic
58C22×D73C2×D412yes—
59C22×D73#4112yes—
60C2×#64408—24no—
61C2×#64408—42no—
62C2×#64408—42no—
63C2×#64408—42no—
64C2×#64408—42no—
65C2×#64408—42no—
66D4×C73—42no—
67D4×C73—42no—
68C2×C4×C73—22no—
69C2×C4×C73C22⋊C411yescharacteristic
70C2×C4×C73C22⋊C411yescharacteristic
71C22⋊D73—44no—
72C22⋊D73—42no—
73C22⋊D73—42no—
74C2×Dic73—22no—
75C2×Dic73—24no—
76C2×Dic73—41no—
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C22⋊C411yescharacteristic
79C4×D73—22no—
80C4×D73—22no—
81C4×D73—41no—
82C4×D73—41no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73—42no—
86C22×C73—42no—
87C22×C73—42no—
88C22×C73—84no—
89C22×C73C2×C22⋊C411yescharacteristic
90C22×C73C4×D412yes—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73#12112yes—
98C2×D73#12411yescharacteristic
99C2×D73#12711yescharacteristic
100#64408—44no—
101#64408—82no—
102C4×C73—21no—
103C4×C73#9912yescomplemented
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107C2×C73—22no—
108C2×C73—82no—
109C2×C73#39011yescharacteristic
110C2×C73C2×#9911yescharacteristic
111C2×C73#41011yescharacteristic
112D73—22no—
113D73—21no—
114D73—21no—
115#1964—731nomaximal, Sylow
116C73#196411yescharacteristic, complemented, Sylow
117C2×#121—731no—
118C2×#99—734no—
119#380—731no—
120C4×C22⋊C4—731no—
121C22×D4—732no—
122C22×D4#6440811yescharacteristic, complemented
123C23×C4—731no—
124#121—1461no—
125#121—1461no—
126#121—1461no—
127#121—1461no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—1461no—
130C2×C22⋊C4—732no—
131C2×C22⋊C4—732no—
132C2×C22⋊C4—732no—
133C2×C42—1461no—
134#99—1468no—
135#95—1461no—
136#95—1461no—
137C24—731no—
138C24C2×#6440812yes—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—42no—
142C2×D4—1464no—
143C2×D4—1462no—
144C2×D4—1462no—
145C2×D4—1464no—
146C22×C4—2922no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—732no—
153C22×C4—1462no—
154C22×C4—1462no—
155C22×C4C2×#6440811yescharacteristic
156C4⋊C4—2922no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C22⋊C4—734no—
160C22⋊C4—1464no—
161C22⋊C4—1462no—
162C22⋊C4—1462no—
163C22⋊C4—1462no—
164C42—2922no—
165C23—22no—
166C23—24no—
167C23—42no—
168C23—42no—
169C23—2921no—
170C23—2921no—
171C23—732no—
172C23—732no—
173C23—731no—
174C23—731no—
175C23C22×#6440811yescharacteristic
176D4—42no—
177D4—42no—
178D4—2922no—
179D4—2924no—
180D4—2922no—
181C2×C4—22no—
182C2×C4—2921no—
183C2×C4—2921no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—2921no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—1464no—
193C2×C4—1462no—
194C2×C4—1464no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4C22⋊#6440811yescharacteristic
198C2×C4C22⋊#6440811yescharacteristic
199C22—21no—
200C22—21no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—84no—
205C22—2922no—
206C22—2922no—
207C22—731no—
208C22—732no—
209C22—731no—
210C22—1461no—
211C22—1461no—
212C22—1461no—
213C22—1461no—
214C22C2×C22⋊#6440811yescharacteristic
215C22D4×#6440812yes—
216C4—21no—
217C4—2924no—
218C4—2922no—
219C4—5842no—
220C4—1461no—
221C4—1461no—
222C4#1455664912yescomplemented
223C2—22no—
224C2—82no—
225C2—1462no—
226C2—1461no—
227C2—1461no—
228C2#1798953911yescharacteristic
229C2C2×#1455664911yescharacteristic
230C2#1798956711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1964
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14556649C2semidirect
2. #17989529C2semidirect
3. C4×C22⋊#64408C2semidirect
18. C2×C4⋊Dic73C4semidirect
19. C2×C22⋊Dic73C4semidirect
20. C22×D4×C73C4semidirect
26. C22⋊#64408D4semidirect
103. C4×C73#99semidirect
116. C73#1964semidirect
122. C22×D4#64408semidirect
222. C4#14556649semidirect