Finite Group Databasebeta

← #22609962

Subgroups — #22609962

Order 9344.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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
2C2×#14556524C211yesmaximal, characteristic, complemented
3C2×#14556522C211yesmaximal, characteristic, complemented
4#17988447C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7#380×C73C211yesmaximal, characteristic
8C2×#11924012—22no—
9C2×#11924012—22no—
10C2×#11924012C414yescomplemented
11C22×#10596831C2211yescharacteristic
12C22×#10596831C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C22⋊Dic73—21no—
16#14556524—22no—
17#14556522—22no—
18#14556498—21no—
19C23×C4×C73C2211yescharacteristic
20C2×C4⋊C4×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C22⋊C4×C73—21no—
23#95×C73—21no—
24C22×Dic73—21no—
25C22×Dic73—21no—
26#11924012—28no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831C2×C412yes—
30C2×#10596831C2×C412yes—
31C2×#10596831D412yes—
32C2×#10596831D412yes—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C22⋊Dic73—42no—
38C24×C73D411yescharacteristic
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73—21no—
42C22×C4×C73—21no—
43C22×C4×C73—21no—
44C22×C4×C73—21no—
45C22×C4×C73C2×C412yes—
46C22×C4×C73D411yescharacteristic
47C22×C4×C73Q812yes—
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C22⋊C4×C73—42no—
54C23×C73—21no—
55C23×C73—21no—
56C23×C73—21no—
57C23×C73—21no—
58C23×C73—21no—
59C23×C73—21no—
60C23×C73C4⋊C412yes—
61C23×C73C2×D411yescharacteristic
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73C4⋊C412yes—
75C2×C4×C73C22×C411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×Q811yescharacteristic
79C2×C4×C73#4111yescharacteristic
80C2×C4×C73#4111yescharacteristic
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86C2×Dic73—41no—
87#10596831—22no—
88#10596831C22⋊C414yescomplemented
89C22×C73—22no—
90C22×C73—22no—
91C22×C73—22no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73—41no—
96C22×C73C2×C4⋊C411yescharacteristic
97C22×C73#12111yescharacteristic
98C22×C73#12111yescharacteristic
99C22×C73AGL(1,ℤ/8)11yescharacteristic
100C22×C73AGL(1,ℤ/8)11yescharacteristic
101C22×C73#13711yescharacteristic
102C22×C73#13711yescharacteristic
103C4×C73—22no—
104C4×C73—81no—
105C4×C73—81no—
106C4×C73C2×C22⋊C411yescharacteristic
107C4×C73#11711yescharacteristic
108C4×C73C22⋊Q811yescharacteristic
109C4×C73C22⋊Q811yescharacteristic
110Dic73—81no—
111Dic73—81no—
112C2×C73—42no—
113C2×C73#38011yescharacteristic
114C2×C73#42811yescharacteristic
115C2×C73#42811yescharacteristic
116C2×C73#46811yescharacteristic
117C2×C73#46811yescharacteristic
118C2×C73#46911yescharacteristic
119C2×C73#47011yescharacteristic
120#1809—731nomaximal, Sylow
121C73#180911yescharacteristic, complemented, Sylow
122C22×M16—731no—
123C2×#107—731no—
124C2×#106—731no—
125#380—731no—
126#380D7311yescharacteristic
127#340—731no—
128#340—731no—
129C23×C4C2×D7311yescharacteristic
130C2×M16—734no—
131C2×M16—1462no—
132C2×M16—1462no—
133C22×C8—731no—
134C22×C8—731no—
135C2×C4⋊C4—731no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C22⋊C4—21no—
140C2×C22⋊C4—1461no—
141#107—1462no—
142#106—1462no—
143#95—21no—
144#95—1461no—
145C24C22⋊D7311yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—1461no—
153C22×C4—1461no—
154C22×C4Dic14612yes—
155C22×C4C4×D7312yes—
156C22×C4C22⋊D7311yescharacteristic
157C22×C4C22×D7311yescharacteristic
158M16—1468no—
159C2×C8—732no—
160C2×C8—732no—
161C2×C8—732no—
162C2×C8—732no—
163C2×C8—1461no—
164C2×C8—1461no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C4⋊C4—1461no—
172C4⋊C4—1461no—
173C22⋊C4—42no—
174C22⋊C4—2922no—
175C23—21no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23#1192400712yes—
182C23C2×C22⋊D7311yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—2921no—
200C2×C4—2921no—
201C2×C4#1192400712yes—
202C2×C4C2×C4×D7311yescharacteristic
203C2×C4D4×D7311yescharacteristic
204C2×C4D4×D7311yescharacteristic
205C2×C4C2×Dic14611yescharacteristic
206C2×C4#1192402711yescharacteristic
207C2×C4#1192402711yescharacteristic
208C8—734no—
209C8—1462no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×#1192400711yescharacteristic
218C22#1455656311yescharacteristic
219C22#1455656311yescharacteristic
220C22#1455661611yescharacteristic
221C22#1455661711yescharacteristic
222C22#1455662111yescharacteristic
223C22#1455662211yescharacteristic
224C4—22no—
225C4—81no—
226C4—81no—
227C4—5841no—
228C4—5841no—
229C4C22⋊C4×D7311yescharacteristic
230C4#1455654711yescharacteristic
231C4#1455656811yescharacteristic
232C4#1455656811yescharacteristic
233C2—42no—
234C2#1798844511yescharacteristic
235C2#1798862711yescharacteristic
236C2#1798863011yescharacteristic
237C2#1798883111yescharacteristic
238C2#1798883511yescharacteristic
239C2#1798883811yescharacteristic
240C2#1798884311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#380×C73C2
socleC23×C73C2×D4
hypercenter#380D73
hypocenterC73#1809
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#14556524C2semidirect
3. C2×#14556522C2semidirect
5. #17988349C2semidirect
6. #17988349C2semidirect
10. C2×#11924012C4semidirect
88. #10596831C22⋊C4semidirect
121. C73#1809semidirect