Finite Group Databasebeta

← #22626186

Subgroups — #22626186

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#17989489C212yesmaximal, complemented
4#17989487C212yesmaximal, complemented
5#17989146C211yesmaximal, characteristic
6C2×#11924037—21no—
7C2×C22⋊#64408—21no—
8#14556651—21no—
9#14556651C2212yes—
10#14556649—21no—
11#14556649C2212yes—
12C22×C22⋊D73C2211yescharacteristic
13#14556574C411yescharacteristic, complemented
14#14556574C2211yescharacteristic
15#14556572—21no—
16#14556563—21no—
17#14556563—21no—
18#14556560C411yescharacteristic, complemented
19#14556560C2211yescharacteristic
20#14556559—21no—
21C2×C22⋊Dic73C411yescharacteristic, complemented
22C22×D4×C73C411yescharacteristic, complemented
23C22×#64408—41no—
24#11924037—22no—
25#11924037—41no—
26C2×#10596833—41no—
27C22⋊#64408—22no—
28C22⋊#64408—41no—
29C23×D73D411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C22⋊D73—41no—
33C2×C22⋊D73—41no—
34C2×C22⋊D73C2×C411yescharacteristic
35C2×C22⋊D73D411yescharacteristic
36C2×C22⋊D73D411yescharacteristic
37C2×C22⋊D73C2311yescharacteristic
38C22×Dic73—21no—
39C22×Dic73D411yescharacteristic
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44C22⋊Dic73—21no—
45C22⋊Dic73C2×C411yescharacteristic, complemented
46C22⋊Dic73C2×C411yescharacteristic, complemented
47#11924005—21no—
48#11924005—21no—
49C24×C73C2×C411yescharacteristic
50C24×C73C2×C411yescharacteristic, complemented
51C2×D4×C73—21no—
52C2×D4×C73—21no—
53C2×D4×C73—41no—
54C2×D4×C73—41no—
55C22×C4×C73C2×C411yescharacteristic, complemented
56C23×C73—21no—
57C23×C73—21no—
58C23×C73—21no—
59C23×C73—41no—
60C23×C73—81no—
61C23×C73—81no—
62C23×C73C22⋊C411yescharacteristic
63C23×C73C22⋊C411yescharacteristic
64C23×C73C22×C411yescharacteristic
65C22×D73—21no—
66C22×D73—21no—
67C22×D73—81no—
68C22×D73C22⋊C411yescharacteristic
69C22×D73C2×D411yescharacteristic
70C2×#64408—42no—
71C2×#64408—82no—
72D4×C73—42no—
73D4×C73—41no—
74D4×C73—41no—
75C2×C4×C73—21no—
76C2×C4×C73—41no—
77C22⋊D73—41no—
78C22⋊D73—41no—
79C22⋊D73—41no—
80C22⋊D73—41no—
81C22⋊D73—81no—
82C22⋊D73—81no—
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—81no—
88C2×Dic73C22⋊C411yescharacteristic
89C2×Dic73C2×D411yescharacteristic
90#10596833—42no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—81no—
100C22×C73—81no—
101C22×C73—82no—
102C22×C73#9911yescharacteristic
103C22×C73#9911yescharacteristic
104C22×C73C2×C22⋊C411yescharacteristic
105C2×D73—21no—
106C2×D73—21no—
107C2×D73—42no—
108C2×D73—41no—
109C2×D73—41no—
110C2×D73—81no—
111#64408—82no—
112C4×C73—41no—
113Dic73—21no—
114Dic73—21no—
115Dic73—41no—
116Dic73—41no—
117C2×C73—21no—
118C2×C73—21no—
119C2×C73—21no—
120C2×C73—41no—
121C2×C73—41no—
122C2×C73—81no—
123C2×C73C2×#9911yescharacteristic
124D73—41no—
125D73—41no—
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#6440811yescharacteristic, complemented
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—731no—
145C2×C22⋊C4—1461no—
146#100—732no—
147#100—1461no—
148#99—732no—
149#99—1461no—
150C24—731no—
151C24C2×#6440811yescharacteristic
152C24C2×#6440811yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—2921no—
158C2×D4—2921no—
159C2×D4—731no—
160C2×D4—731no—
161C2×D4—731no—
162C2×D4—731no—
163C2×D4—1461no—
164C2×D4—1461no—
165C22×C4—2921no—
166C22×C4—731no—
167C22×C4—1461no—
168C22×C4C2×#6440811yescharacteristic, complemented
169M16—2921no—
170M16—1462no—
171C2×C8—2921no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C22⋊C4—2921no—
175C22⋊C4—731no—
176C22⋊C4—731no—
177C22⋊C4—1461no—
178C22⋊C4—1461no—
179C22⋊C4—1462no—
180C22⋊C4—1461no—
181C22⋊C4—1461no—
182C22⋊C4—1461no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—81no—
188C23—81no—
189C23—5841no—
190C23—731no—
191C23—731no—
192C23—1461no—
193C23—1461no—
194C23C22⋊#6440811yescharacteristic
195C23C22⋊#6440811yescharacteristic
196C23C22×#6440811yescharacteristic
197D4—42no—
198D4—41no—
199D4—41no—
200D4—2921no—
201D4—2921no—
202D4—2921no—
203D4—2921no—
204D4—5841no—
205D4—5841no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—2922no—
209C2×C4—5841no—
210C2×C4—5842no—
211C2×C4—731no—
212C2×C4—731no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4—1461no—
217C8—2922no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—81no—
227C22—81no—
228C22—82no—
229C22—2921no—
230C22—2921no—
231C22—2922no—
232C22—5841no—
233C22—1461no—
234C22—1461no—
235C22#1455664911yescharacteristic
236C22#1455664911yescharacteristic
237C22C2×C22⋊#6440811yescharacteristic
238C4—41no—
239C4—2921no—
240C4—2921no—
241C4—5842no—
242C4—1461no—
243C4—1461no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2—2921no—
251C2—2921no—
252C2C2×#1455664911yescharacteristic
subgroupG/H
centerC2C2×#14556649
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC2×C73C2×#99
hypercenterC22×D4#64408
hypocenterC73#2121
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14556651C2semidirect
2. C2×#14556649C2semidirect
3. #17989489C2semidirect
4. #17989487C2semidirect
13. #14556574C4semidirect
18. #14556560C4semidirect
21. C2×C22⋊Dic73C4semidirect
22. C22×D4×C73C4semidirect
45. C22⋊Dic73C2×C4semidirect
46. C22⋊Dic73C2×C4semidirect
50. C24×C73C2×C4semidirect
55. C22×C4×C73C2×C4semidirect
127. C73#2121semidirect
134. C22×D4#64408semidirect
152. C24C2×#64408semidirect
168. C22×C4C2×#64408semidirect