Finite Group Databasebeta

← #22620580

Subgroups — #22620580

Order 9344.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#17989193C211yesmaximal, characteristic, complemented
2#17989191C211yesmaximal, characteristic, complemented
3#17988986C211yesmaximal, characteristic, complemented
4#17988963C211yesmaximal, characteristic, complemented
5#17988952C211yesmaximal, characteristic, complemented
6#17988839C212yesmaximal, complemented
7#17988822C212yesmaximal, complemented
8#17988696C212yesmaximal, complemented
9#17988667C212yesmaximal, complemented
10#17988544C211yesmaximal, characteristic, complemented
11#490×C73C211yesmaximal, characteristic, complemented
12C2×#11924013C2212yes—
13C2×#11924013C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×C8×D73C2211yescharacteristic
16#14556588C2211yescharacteristic
17#14556583C2211yescharacteristic
18#14556576—22no—
19#14556572—22no—
20#14556566—22no—
21#14556566C2212yes—
22#14556563—22no—
23#14556562C2212yes—
24D4×Dic73C2212yes—
25#14556553C2212yes—
26#14556548C2211yescharacteristic
27#14556524C2212yes—
28#14556522C2212yes—
29#14556513C2212yes—
30#14556513C2212yes—
31#14556501C2211yescharacteristic
32C4×#10596831C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34#127×C73C2211yescharacteristic
35#125×C73C2211yescharacteristic
36#102×C73C2212yes—
37#102×C73C2212yes—
38#97×C73C2211yescharacteristic
39C2×D292—22no—
40C2×D292—22no—
41C2×D292C2312yes—
42C2×C22⋊D73—22no—
43C22×Dic73—22no—
44C2×C4×D73—22no—
45C2×C4×D73C2311yescharacteristic
46#11924013—24no—
47#11924013—24no—
48#11924011—22no—
49C2×#10596831C2311yescharacteristic
50C2×#10596831C2311yescharacteristic
51C8×D73—22no—
52C4⋊Dic73C2312yes—
53#11924007—22no—
54#11924007D412yes—
55C22⋊Dic73—22no—
56C22⋊Dic73—22no—
57#11924005—22no—
58#11924005—22no—
59#11924005D412yes—
60C4×Dic73C2311yescharacteristic
61C2×D4×C73—22no—
62C2×D4×C73C2312yes—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C42×C73C2311yescharacteristic
68C23×C73—22no—
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71D4×C73—22no—
72D4×C73—22no—
73D4×C73—82no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2411yescharacteristic
77C22⋊D73—82no—
78C2×Dic73—22no—
79C2×Dic73—82no—
80C2×Dic73C2×D412yes—
81C2×Dic73C2×D411yescharacteristic
82D292—22no—
83D292—22no—
84D292—82no—
85D292—82no—
86C4×D73—21no—
87C4×D73—21no—
88C4×D73—82no—
89C8×C73—21no—
90C8×C73—21no—
91#10596831#4112yes—
92#10596831#4112yes—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73C22×D411yescharacteristic
97C2×D73—21no—
98C2×D73—22no—
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—42no—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73C2×#4111yescharacteristic
105C4×C73C2×#4111yescharacteristic
106Dic73—21no—
107Dic73—22no—
108Dic73—42no—
109C2×C73—82no—
110C2×C73#53211yescharacteristic
111C2×C73#57612yes—
112D73—41no—
113D73—82no—
114#3176—731nomaximal, Sylow
115C73#317611yescharacteristic, complemented, Sylow
116#540—731no—
117#540—731no—
118#499—731no—
119#493—731no—
120#490—731no—
121#490D7311yescharacteristic, complemented
122#469—732no—
123#466—732no—
124#442—732no—
125C4×D8—732no—
126#405—731no—
127C2×D8—732no—
128C2×D8—732no—
129C2×M16—731no—
130C22×C8—731no—
131#127—731no—
132#127C2×D7311yescharacteristic
133#125—731no—
134#125C2×D7311yescharacteristic
135#123—1462no—
136#123—1462no—
137#121—732no—
138#121—732no—
139#121—1462no—
140#121—1462no—
141C4×D4—732no—
142C4×D4—732no—
143#117—731no—
144#107—732no—
145#106—732no—
146#102—732no—
147#102—732no—
148#102C2×D7312yes—
149#102C2×D7312yes—
150#97—731no—
151#97C2×D7311yescharacteristic
152C4×C8—731no—
153C4×C8—731no—
154C2×D4—22no—
155C2×D4—732no—
156C2×D4—1462no—
157C2×D4—1462no—
158C2×D4—1462no—
159C2×D4C22×D7312yes—
160C22×C4—731no—
161C22×C4—1462no—
162C22×C4—1462no—
163D8—1464no—
164D8—1464no—
165M16—1462no—
166C2×C8—731no—
167C2×C8—731no—
168C2×C8—1462no—
169C2×C8C22×D7311yescharacteristic
170C2×C8C22×D7311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—732no—
173C4⋊C4—732no—
174C4⋊C4—1462no—
175C4⋊C4C22×D7312yes—
176C22⋊C4—732no—
177C22⋊C4—1462no—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C22⋊C4—1462no—
181C42—731no—
182C42C22×D7311yescharacteristic
183C23—22no—
184C23—731no—
185C23—1462no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—5842no—
190D4—5842no—
191D4—5842no—
192D4—1462no—
193D4—1462no—
194C2×C4—22no—
195C2×C4—5842no—
196C2×C4—5842no—
197C2×C4—732no—
198C2×C4—731no—
199C2×C4—1462no—
200C2×C4—1461no—
201C2×C4—1461no—
202C2×C4D4×D7312yes—
203C2×C4C23×D7311yescharacteristic
204C8—21no—
205C8—21no—
206C8—732no—
207C8—732no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—2922no—
212C22—2922no—
213C22—2922no—
214C22—1462no—
215C22—1461no—
216C22C2×D4×D7311yescharacteristic
217C4—22no—
218C4—42no—
219C4—2922no—
220C4—1462no—
221C4—1461no—
222C4#41×D7311yescharacteristic
223C4#41×D7311yescharacteristic
224C2—82no—
225C2—2921no—
226C2—5842no—
227C2#1798913611yescharacteristic
228C2#1798939112yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3176
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17989193C2semidirect
2. #17989191C2semidirect
3. #17988986C2semidirect
4. #17988963C2semidirect
5. #17988952C2semidirect
6. #17988839C2semidirect
7. #17988822C2semidirect
8. #17988696C2semidirect
9. #17988667C2semidirect
10. #17988544C2semidirect
11. #490×C73C2semidirect
115. C73#3176semidirect
121. #490D73semidirect