Finite Group Databasebeta

← #22626187

Subgroups — #22626187

Order 9344.

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D73⋊#100C211yesmaximal, characteristic, complemented
2D73⋊#99C211yesmaximal, characteristic, complemented
3#17989490C212yesmaximal, complemented
4#17989487C212yesmaximal, complemented
5#17989147C211yesmaximal, characteristic
6D73⋊M16—21no—
7C2×C22⋊#64408—21no—
8#14556651—21no—
9#14556651C2212yes—
10#14556650—21no—
11#14556649C2212yes—
12C22×C22⋊D73C411yescharacteristic, complemented
13C2×D4×D73C2211yescharacteristic
14#14556575C2211yescharacteristic
15#14556573—21no—
16#14556572C411yescharacteristic, complemented
17#14556564—21no—
18#14556562—21no—
19#14556560C2211yescharacteristic
20#14556559—21no—
21C22⋊C4×D73C411yescharacteristic, complemented
22#120×C73C411yescharacteristic, complemented
23C22×#64408—41no—
24#11924038—41no—
25#11924037—22no—
26#11924036—41no—
27C22⋊#64408—22no—
28C22⋊#64408—41no—
29C23×D73C2×C411yescharacteristic
30C23×D73D411yescharacteristic
31C2×D292D411yescharacteristic
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35C2×C22⋊D73—41no—
36C2×C22⋊D73—41no—
37C2×C22⋊D73D411yescharacteristic
38C2×C22⋊D73C2311yescharacteristic
39D4×D73—41no—
40D4×D73—41no—
41C22×Dic73C2×C411yescharacteristic, complemented
42C2×C4×D73—21no—
43C2×C4×D73D411yescharacteristic
44C4⋊Dic73—21no—
45#11924007—21no—
46C22⋊Dic73—21no—
47C22⋊Dic73—21no—
48C22⋊Dic73C2×C411yescharacteristic, complemented
49#11924005—21no—
50#11924005—21no—
51C24×C73C2×C411yescharacteristic, complemented
52C2×D4×C73—21no—
53C2×D4×C73C2×C411yescharacteristic
54C22⋊C4×C73—21no—
55C22⋊C4×C73C2×C411yescharacteristic, complemented
56C23×C73—21no—
57C23×C73—41no—
58C23×C73—81no—
59C23×C73C22⋊C411yescharacteristic
60C23×C73C22×C411yescharacteristic
61C22×D73—21no—
62C22×D73—21no—
63C22×D73—21no—
64C22×D73—21no—
65C22×D73—81no—
66C22×D73—81no—
67C22×D73C22⋊C411yescharacteristic
68C22×D73C22⋊C411yescharacteristic
69C22×D73C2×D411yescharacteristic
70C2×#64408—42no—
71C2×#64408—82no—
72D4×C73—41no—
73D4×C73—81no—
74C2×C4×C73—21no—
75C2×C4×C73C22⋊C411yescharacteristic
76C22⋊D73—41no—
77C22⋊D73—41no—
78C22⋊D73—42no—
79C22⋊D73—41no—
80C22⋊D73—41no—
81C22⋊D73—81no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—41no—
85C2×Dic73C2×D411yescharacteristic
86D292—41no—
87C4×D73—21no—
88C4×D73—21no—
89C4×D73—81no—
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—82no—
99C22×C73C2×C22⋊C411yescharacteristic
100C2×D73—21no—
101C2×D73—21no—
102C2×D73—41no—
103C2×D73—42no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—81no—
107C2×D73—81no—
108C2×D73—81no—
109C2×D73#9911yescharacteristic
110C2×D73#9911yescharacteristic
111#64408—82no—
112C4×C73—21no—
113C4×C73—41no—
114Dic73—21no—
115Dic73—41no—
116Dic73—41no—
117C2×C73—21no—
118C2×C73—41no—
119C2×C73—41no—
120C2×C73—81no—
121C2×C73C2×#9911yescharacteristic
122D73—21no—
123D73—21no—
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—731no—
135C2×M16—1461no—
136#123—731no—
137#123—731no—
138#123—1461no—
139#121—1461no—
140#121—1461no—
141#120—731no—
142#120—1461no—
143#120#6440811yescharacteristic, complemented
144C2×C22⋊C4—731no—
145C2×C22⋊C4—1461no—
146#100—732no—
147#100—1461no—
148#99—732no—
149#99—1461no—
150C24—731no—
151C24—731no—
152C24C2×#6440811yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—2921no—
155C2×D4—2921no—
156C2×D4—2921no—
157C2×D4—2921no—
158C2×D4—731no—
159C2×D4—731no—
160C2×D4—731no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1461no—
164C2×D4C2×#6440811yescharacteristic
165C22×C4—2921no—
166C22×C4—731no—
167C22×C4—731no—
168C22×C4—1461no—
169M16—2921no—
170M16—1462no—
171C2×C8—2921no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C22⋊C4—21no—
175C22⋊C4—2921no—
176C22⋊C4—731no—
177C22⋊C4—1461no—
178C22⋊C4—1461no—
179C22⋊C4—1462no—
180C22⋊C4—1461no—
181C22⋊C4—1461no—
182C22⋊C4C2×#6440811yescharacteristic, complemented
183C23—21no—
184C23—41no—
185C23—81no—
186C23—5841no—
187C23—5841no—
188C23—731no—
189C23—731no—
190C23—731no—
191C23—1461no—
192C23—1461no—
193C23—1461no—
194C23—1461no—
195C23C22⋊#6440811yescharacteristic
196C23C22×#6440811yescharacteristic
197D4—41no—
198D4—81no—
199D4—2921no—
200D4—2921no—
201D4—2921no—
202D4—2922no—
203D4—2921no—
204D4—2921no—
205D4—5841no—
206C2×C4—21no—
207C2×C4—2921no—
208C2×C4—2922no—
209C2×C4—5841no—
210C2×C4—5842no—
211C2×C4—731no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4C22⋊#6440811yescharacteristic
217C8—2922no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—82no—
226C22—2921no—
227C22—2921no—
228C22—2921no—
229C22—2922no—
230C22—5841no—
231C22—5841no—
232C22—5841no—
233C22—731no—
234C22—731no—
235C22—1461no—
236C22—1461no—
237C22C2×C22⋊#6440811yescharacteristic
238C4—21no—
239C4—41no—
240C4—2921no—
241C4—2921no—
242C4—5842no—
243C4—1461no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—81no—
248C2—2921no—
249C2—2921no—
250C2—1461no—
251C2—1461no—
252C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
Fitting#120×C73C4
socleC2×C73C2×#99
hypercenter#120#64408
hypocenterC73#2121
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
1. D73⋊#100C2semidirect
2. D73⋊#99C2semidirect
3. #17989490C2semidirect
4. #17989487C2semidirect
12. C22×C22⋊D73C4semidirect
16. #14556572C4semidirect
21. C22⋊C4×D73C4semidirect
22. #120×C73C4semidirect
41. C22×Dic73C2×C4semidirect
48. C22⋊Dic73C2×C4semidirect
51. C24×C73C2×C4semidirect
55. C22⋊C4×C73C2×C4semidirect
127. C73#2121semidirect
143. #120#64408semidirect
152. C24C2×#64408semidirect
182. C22⋊C4C2×#64408semidirect