Finite Group Databasebeta

← #22610873

Subgroups — #22610873

Order 9344.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#17989140C211yesmaximal, characteristic
2M16×Dic73C211yesmaximal, characteristic
3C4×#11924007C211yesmaximal, characteristic
4#17988348C211yesmaximal, characteristic
5#17988347C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic
7#339×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556590C411yescharacteristic, complemented
10#14556590C411yescharacteristic, complemented
11#14556582C411yescharacteristic, complemented
12#14556582C411yescharacteristic, complemented
13#14556568—21no—
14#14556568—21no—
15C4×Dic146—21no—
16C4×Dic146—21no—
17#14556550C2211yescharacteristic
18C2×#11924007—21no—
19C2×C4×Dic73C2211yescharacteristic
20C2×C4×Dic73C2211yescharacteristic
21#14556501—21no—
22C8×Dic73—21no—
23#14556498—21no—
24C2×M16×C73C2211yescharacteristic
25#117×C73C2211yescharacteristic
26C2×C42×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×Dic146—21no—
29C22×Dic73—21no—
30C22×Dic73D411yescharacteristic
31C22×Dic73D411yescharacteristic
32#11924012—21no—
33#11924012Q812yescomplemented
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73C2×C411yescharacteristic
38C4⋊Dic73C2×C411yescharacteristic
39#11924007—24no—
40#11924007—21no—
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44C22⋊Dic73—21no—
45C4×Dic73—21no—
46C4×Dic73—21no—
47C4×Dic73—21no—
48C4×Dic73C2×C411yescharacteristic
49C4×Dic73C2×C411yescharacteristic
50C4×Dic73D411yescharacteristic
51C4×Dic73D411yescharacteristic
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54M16×C73—21no—
55M16×C73Q812yescomplemented
56C2×C8×C73—21no—
57C4⋊C4×C73C2×C411yescharacteristic
58C4⋊C4×C73C2×C411yescharacteristic
59C22⋊C4×C73—21no—
60C42×C73—21no—
61C42×C73—21no—
62C42×C73—21no—
63C23×C73C2×D411yescharacteristic
64C2×C4×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73C22×C411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×Q811yescharacteristic
72C2×C4×C73C2×Q811yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73C22⋊C411yescharacteristic
83C2×Dic73C22⋊C411yescharacteristic
84C2×Dic73C22⋊C411yescharacteristic
85C2×Dic73C22⋊C411yescharacteristic
86Dic146—42no—
87Dic146—42no—
88C8×C73—22no—
89#10596831—22no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73C2×C22⋊C411yescharacteristic
93C22×C73#12411yescharacteristic
94C22×C73C4⋊Q811yescharacteristic
95C4×C73—42no—
96C4×C73—41no—
97C4×C73—41no—
98C4×C73C4×Q811yescharacteristic
99C4×C73C4×Q811yescharacteristic
100C4×C73C22⋊Q811yescharacteristic
101C4×C73C22⋊Q811yescharacteristic
102Dic73—21no—
103Dic73—21no—
104Dic73—21no—
105Dic73—42no—
106Dic73—41no—
107Dic73—41no—
108Dic73#10412yes—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73#39111yescharacteristic
112C2×C73C2×#10411yescharacteristic
113C2×C73#42111yescharacteristic
114#1986—731nomaximal, Sylow
115C73#198611yescharacteristic, complemented, Sylow
116#533—731no—
117C4×M16—731no—
118C4×C4⋊C4—731no—
119#339—731no—
120#339—731no—
121#339—731no—
122#339D7311yescharacteristic
123C2×M16—731no—
124C2×M16C2×D7311yescharacteristic
125C4⋊Q8—731no—
126C4⋊Q8—731no—
127#125—731no—
128#125—731no—
129C22⋊Q8—1461no—
130C22⋊Q8—1461no—
131C4×Q8—1461no—
132C4×Q8—1461no—
133#117—731no—
134#117C2×D7311yescharacteristic
135C2×C4⋊C4—1461no—
136C2×C42—731no—
137C2×C42—731no—
138C2×C42C2×D7311yescharacteristic
139#97—1461no—
140C4×C8—1461no—
141#95—1461no—
142C2×Q8—1461no—
143C2×Q8—1461no—
144C22×C4—21no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—1461no—
148C22×C4C22×D7311yescharacteristic
149M16—21no—
150M16—732no—
151M16—1461no—
152M16Dic14612yescomplemented
153C2×C8—21no—
154C2×C8—1461no—
155C4⋊C4—731no—
156C4⋊C4—731no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C4⋊C4—1461no—
160C4⋊C4—1461no—
161C4⋊C4—1461no—
162C4⋊C4—1461no—
163C4⋊C4—1464no—
164C4⋊C4C4×D7311yescharacteristic
165C4⋊C4C4×D7311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1461no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—731no—
172C42—731no—
173C42—731no—
174C42—731no—
175C42—1461no—
176C42—1461no—
177C42—1461no—
178C23D4×D7311yescharacteristic
179Q8—2922no—
180Q8—2922no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2921no—
187C2×C4—2921no—
188C2×C4—2921no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—1462no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4—1462no—
197C2×C4C2×C4×D7311yescharacteristic
198C2×C4D4×D7311yescharacteristic
199C2×C4Q8×D7311yescharacteristic
200C2×C4C2×Dic14611yescharacteristic
201C2×C4#1192402711yescharacteristic
202C2×C4#1192402811yescharacteristic
203C8—22no—
204C8—1462no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D7311yescharacteristic
208C22#1455657711yescharacteristic
209C22#1455659011yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—2922no—
214C4—2921no—
215C4—2921no—
216C4—732no—
217C4—1461no—
218C4—1461no—
219C4—1461no—
220C4#1455655611yescharacteristic
221C4C4×Dic14611yescharacteristic
222C4#1455656811yescharacteristic
223C4#1455656911yescharacteristic
224C2—21no—
225C2—21no—
226C2#1798849111yescharacteristic
227C2#104×D7311yescharacteristic
228C2#1798860211yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#339D73
hypocenterC73#1986
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14556590C4semidirect
10. #14556590C4semidirect
11. #14556582C4semidirect
12. #14556582C4semidirect
33. #11924012Q8semidirect
55. M16×C73Q8semidirect
115. C73#1986semidirect
152. M16Dic146semidirect