Finite Group Databasebeta

← #22626188

Subgroups — #22626188

Order 9344.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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×#14556651C211yesmaximal, characteristic, complemented
2C2×#14556649C211yesmaximal, characteristic, complemented
3#17989490C212yesmaximal, complemented
4#17989488C212yesmaximal, complemented
5#17989149C211yesmaximal, characteristic
6C2×#11924037—21no—
7C2×C22⋊#64408—21no—
8#14556651—21no—
9#14556651C2212yes—
10#14556649—21no—
11#14556649C2212yes—
12C22×C22⋊D73C411yescharacteristic, complemented
13C22×C22⋊D73C2211yescharacteristic
14#14556575—21no—
15#14556575C411yescharacteristic, complemented
16#14556575C2211yescharacteristic
17#14556565—21no—
18#14556565—21no—
19#14556561—21no—
20#14556561C411yescharacteristic, complemented
21#14556561C2211yescharacteristic
22C2×C22⋊C4×C73C411yescharacteristic, complemented
23C22×#64408—41no—
24#11924037—22no—
25#11924037—41no—
26C2×#10596833—41no—
27C22⋊#64408—22no—
28C22⋊#64408—41no—
29C23×D73C2×C411yescharacteristic, complemented
30C23×D73D411yescharacteristic
31C2×D292—21no—
32C2×D292—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35C2×C22⋊D73—41no—
36C2×C22⋊D73—41no—
37C2×C22⋊D73—41no—
38C2×C22⋊D73—41no—
39C2×C22⋊D73C2×C411yescharacteristic
40C2×C22⋊D73D411yescharacteristic
41C2×C22⋊D73D411yescharacteristic
42C2×C22⋊D73C2311yescharacteristic
43C22×Dic73C2×C411yescharacteristic, complemented
44C22×Dic73D411yescharacteristic
45C4⋊Dic73—21no—
46C4⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49#11924005—21no—
50#11924005—21no—
51C24×C73C2×C411yescharacteristic
52C22×C4×C73—21no—
53C22⋊C4×C73—21no—
54C22⋊C4×C73C2×C411yescharacteristic, complemented
55C22⋊C4×C73C2×C411yescharacteristic, complemented
56C23×C73—21no—
57C23×C73—21no—
58C23×C73—81no—
59C23×C73C22⋊C411yescharacteristic
60C23×C73C22⋊C411yescharacteristic
61C23×C73C22×C411yescharacteristic
62C22×D73—21no—
63C22×D73—21no—
64C22×D73—21no—
65C22×D73—41no—
66C22×D73—81no—
67C22×D73—81no—
68C22×D73C22⋊C411yescharacteristic
69C22×D73C2×D411yescharacteristic
70C2×#64408—42no—
71C2×#64408—82no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—81no—
75C22⋊D73—41no—
76C22⋊D73—41no—
77C22⋊D73—41no—
78C22⋊D73—41no—
79C22⋊D73—42no—
80C22⋊D73—41no—
81C22⋊D73—41no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—41no—
86C2×Dic73C22⋊C411yescharacteristic
87C2×Dic73C2×D411yescharacteristic
88D292—81no—
89D292—81no—
90#10596833—42no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73—41no—
96C22×C73—81no—
97C22×C73—81no—
98C22×C73#9911yescharacteristic
99C22×C73#9911yescharacteristic
100C22×C73C2×C22⋊C411yescharacteristic
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—42no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—41no—
109C2×D73—81no—
110C2×D73—82no—
111#64408—82no—
112C4×C73—41no—
113C4×C73—41no—
114Dic73—21no—
115Dic73—21no—
116Dic73—41no—
117C2×C73—21no—
118C2×C73—21no—
119C2×C73—21no—
120C2×C73—41no—
121C2×C73—41no—
122C2×C73C2×#9911yescharacteristic
123D73—41no—
124D73—41no—
125D73—81no—
126#2121—731nomaximal, Sylow
127C73#212111yescharacteristic, complemented, Sylow
128#534—731no—
129C2×#100—731no—
130C2×#99—731no—
131#352—732no—
132AΣL(1,𝔽16)—732no—
133C22×D4—731no—
134C22×D4—731no—
135C2×M16—1461no—
136#123—731no—
137#123—731no—
138#123—1461no—
139#121—1461no—
140#121—1461no—
141#120—731no—
142#120—731no—
143#120—1461no—
144C2×C22⋊C4—1461no—
145C2×C22⋊C4#6440811yescharacteristic, complemented
146#100—732no—
147#100—1461no—
148#99—732no—
149#99—1461no—
150C24—731no—
151C24—731no—
152C24C2×#6440811yescharacteristic
153C2×D4—2921no—
154C2×D4—2921no—
155C2×D4—2921no—
156C2×D4—2921no—
157C2×D4—731no—
158C2×D4—731no—
159C2×D4—731no—
160C2×D4—731no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1461no—
164C2×D4—1461no—
165C22×C4—21no—
166C22×C4—2921no—
167C22×C4—731no—
168C22×C4—731no—
169M16—2921no—
170M16—1462no—
171C2×C8—2921no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C22⋊C4—21no—
175C22⋊C4—2921no—
176C22⋊C4—1461no—
177C22⋊C4—1461no—
178C22⋊C4—1461no—
179C22⋊C4—1461no—
180C22⋊C4—1462no—
181C22⋊C4C2×#6440811yescharacteristic, complemented
182C22⋊C4C2×#6440811yescharacteristic, complemented
183C23—21no—
184C23—21no—
185C23—81no—
186C23—2921no—
187C23—5841no—
188C23—5841no—
189C23—731no—
190C23—731no—
191C23—1461no—
192C23—1461no—
193C23—1461no—
194C23C22⋊#6440811yescharacteristic
195C23C22⋊#6440811yescharacteristic
196C23C22×#6440811yescharacteristic
197D4—2922no—
198D4—2921no—
199D4—2921no—
200D4—2921no—
201D4—2921no—
202D4—2921no—
203D4—2921no—
204D4—5841no—
205D4—5841no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—81no—
209C2×C4—2921no—
210C2×C4—2922no—
211C2×C4—5842no—
212C2×C4—731no—
213C2×C4—731no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4—1461no—
217C8—2922no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—2921no—
226C22—2921no—
227C22—2922no—
228C22—2921no—
229C22—2921no—
230C22—2921no—
231C22—5841no—
232C22—5842no—
233C22—1461no—
234C22—1461no—
235C22#1455665011yescharacteristic
236C22#1455665011yescharacteristic
237C22C2×C22⋊#6440811yescharacteristic
238C4—41no—
239C4—41no—
240C4—2921no—
241C4—5842no—
242C4—1461no—
243C4—1461no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—2921no—
250C2—2921no—
251C2—5841no—
252C2C2×#1455665011yescharacteristic
subgroupG/H
centerC2C2×#14556650
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC2×C73C2×#99
hypercenterC2×C22⋊C4#64408
hypocenterC73#2121
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556651C2semidirect
2. C2×#14556649C2semidirect
3. #17989490C2semidirect
4. #17989488C2semidirect
12. C22×C22⋊D73C4semidirect
15. #14556575C4semidirect
20. #14556561C4semidirect
22. C2×C22⋊C4×C73C4semidirect
29. C23×D73C2×C4semidirect
43. C22×Dic73C2×C4semidirect
54. C22⋊C4×C73C2×C4semidirect
55. C22⋊C4×C73C2×C4semidirect
127. C73#2121semidirect
145. C2×C22⋊C4#64408semidirect
181. C22⋊C4C2×#64408semidirect
182. C22⋊C4C2×#64408semidirect