Finite Group Databasebeta

← #22610395

Subgroups — #22610395

Order 9344.

390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#11924012C211yesmaximal, characteristic, complemented
2C2×#14556508C212yesmaximal, complemented
3#17988551C211yesmaximal, characteristic, complemented
4#17988356C212yesmaximal, complemented
5C2×#121×C73C211yesmaximal, characteristic
6C2×#11924012—24no—
7C2×#11924012—21no—
8C2×#11924012C2212yes—
9C2×#11924012C2212yes—
10C22×#10596831—21no—
11#14556508—24no—
12C22⋊#10596831—21no—
13C22⋊#10596831—21no—
14C22×D4×C73C412yes—
15C22×D4×C73C2211yescharacteristic
16C23×C4×C73C2211yescharacteristic
17#121×C73—21no—
18#121×C73—21no—
19#121×C73—21no—
20#121×C73—21no—
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C22⋊C4×C73C412yes—
23#11924012—24no—
24#11924012—22no—
25#11924012—22no—
26#11924012—22no—
27#11924012D414yescomplemented
28C2×#10596831—24no—
29C2×#10596831—22no—
30C2×#10596831—22no—
31C24×C73C2×C411yescharacteristic
32C24×C73C2×C412yes—
33C2×D4×C73—22no—
34C2×D4×C73—22no—
35C2×D4×C73—21no—
36C2×D4×C73—21no—
37C2×D4×C73—22no—
38C2×D4×C73—22no—
39C2×D4×C73—44no—
40C22×C4×C73—22no—
41C22×C4×C73—22no—
42C22×C4×C73C2×C411yescharacteristic
43C22×C4×C73C2×C412yes—
44C22×C4×C73D411yescharacteristic
45C22×C4×C73D411yescharacteristic
46C22×C4×C73D411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C22⋊C4×C73—22no—
52C22⋊C4×C73—22no—
53C23×C73—22no—
54C23×C73—22no—
55C23×C73—22no—
56C23×C73—24no—
57C23×C73—41no—
58C23×C73—42no—
59C23×C73—42no—
60C23×C73C22⋊C411yescharacteristic
61C23×C73C22⋊C411yescharacteristic
62C23×C73C22×C411yescharacteristic
63D4×C73—44no—
64D4×C73—44no—
65D4×C73—41no—
66D4×C73—42no—
67D4×C73—41no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—42no—
77C2×C4×C73C22⋊C411yescharacteristic
78C2×C4×C73C22⋊C411yescharacteristic
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73#4112yes—
83#10596831—24no—
84#10596831—42no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—44no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73—84no—
97C22×C73#10012yescomplemented
98C22×C73C2×C22⋊C411yescharacteristic
99C22×C73C4×D412yes—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—42no—
103C4×C73#12011yescharacteristic
104C4×C73#12112yes—
105C4×C73#12311yescharacteristic
106C2×C73—22no—
107C2×C73—22no—
108C2×C73—41no—
109C2×C73—82no—
110C2×C73#38611yescharacteristic
111C2×C73C2×#10011yescharacteristic
112C2×C73#41311yescharacteristic
113#1900—731nomaximal, Sylow
114C73#190011yescharacteristic, complemented, Sylow
115C22×M16—731no—
116C2×#121D7311yescharacteristic
117C2×#100—732no—
118#407—731no—
119#343—732no—
120C22×D4Dic7312yes—
121C22×D4C2×D7311yescharacteristic
122C23×C4C2×D7311yescharacteristic
123C2×M16—732no—
124C2×M16—732no—
125C2×M16—1464no—
126C2×M16—1461no—
127C22×C8—1461no—
128#121—21no—
129#121—21no—
130#121—21no—
131#121—21no—
132C2×C4⋊C4C2×D7311yescharacteristic
133C2×C22⋊C4Dic7312yes—
134#100—1464no—
135C22⋊C8—1461no—
136C22⋊C8—1461no—
137C24C2×Dic7311yescharacteristic
138C24C2×Dic7312yes—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4—44no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4C2×Dic7311yescharacteristic
149C22×C4C2×Dic7312yes—
150C22×C4C22⋊D7311yescharacteristic
151C22×C4C22⋊D7311yescharacteristic
152C22×C4C22⋊D7311yescharacteristic
153C22×C4C22⋊D7311yescharacteristic
154C22×C4C22×D7311yescharacteristic
155M16—734no—
156M16—1462no—
157M16—1462no—
158M16—1464no—
159M16—1462no—
160C2×C8—1462no—
161C2×C8—1464no—
162C2×C8—1462no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C23—22no—
168C23—22no—
169C23—22no—
170C23—24no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23C22⋊Dic7311yescharacteristic
175C23C22⋊Dic7311yescharacteristic
176C23C22×Dic7311yescharacteristic
177D4—44no—
178D4—44no—
179D4—41no—
180D4—42no—
181D4—41no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C22⋊Dic7311yescharacteristic
192C2×C4C22⋊Dic7311yescharacteristic
193C2×C4D4×D7312yes—
194C2×C4C2×C22⋊D7311yescharacteristic
195C2×C4C2×C22⋊D7311yescharacteristic
196C2×C4#1192402712yes—
197C8—2922no—
198C8—1464no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22#1455650812yescomplemented
212C22C2×C22⋊Dic7311yescharacteristic
213C22D4×Dic7312yes—
214C4—21no—
215C4—21no—
216C4—42no—
217C4#1455655911yescharacteristic
218C4#1455656312yes—
219C4#1455657211yescharacteristic
220C2—22no—
221C2—22no—
222C2—41no—
223C2—82no—
224C2#1798846711yescharacteristic
225C2C2×#1455650811yescharacteristic
226C2#1798857111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic73
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#121×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC2×#121D73
hypocenterC73#1900
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#11924012C2semidirect
2. C2×#14556508C2semidirect
3. #17988551C2semidirect
4. #17988356C2semidirect
27. #11924012D4semidirect
97. C22×C73#100semidirect
114. C73#1900semidirect
211. C22#14556508semidirect