Finite Group Databasebeta

← #22621060

Subgroups — #22621060

Order 9344.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989138C211yesmaximal, characteristic
2C4⋊Q8×D73C211yesmaximal, characteristic, complemented
3#17988983C211yesmaximal, characteristic, complemented
4#17988935C211yesmaximal, characteristic, complemented
5#17988934C211yesmaximal, characteristic, complemented
6#17988907C214yesmaximal, complemented
7#17988876C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#498×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×Q8×D73—21no—
12#14556591C2211yescharacteristic
13#14556590—21no—
14#14556590C2212yes—
15#14556589—21no—
16#14556588C2211yescharacteristic
17#14556580—21no—
18#14556566—21no—
19#14556566C2212yes—
20#14556553—21no—
21#14556553C2212yes—
22C4⋊C4×D73—21no—
23C4⋊C4×D73C2212yes—
24C42×D73C2211yescharacteristic
25#14556522C2214yes—
26#14556520C2212yes—
27#14556513C2214yes—
28#14556511C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#106×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36C2×Dic146—21no—
37C2×Dic146—22no—
38Q8×D73—44no—
39C2×D292—22no—
40C2×D292—21no—
41C2×D292—21no—
42C2×D292C2312yes—
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48C2×#10596831C2312yes—
49C4⋊Dic73—21no—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53#11924005—22no—
54#11924005—22no—
55C4×Dic73D411yescharacteristic
56C4×Dic73D411yescharacteristic
57C4×Dic73C2311yescharacteristic
58C2×Q8×C73—21no—
59C2×Q8×C73—21no—
60C2×C8×C73C2312yes—
61C4⋊C4×C73—21no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73C2312yes—
64C4⋊C4×C73C2312yes—
65C42×C73C2311yescharacteristic
66C22×D73—22no—
67C22×D73C2×D411yescharacteristic
68Q8×C73—42no—
69Q8×C73—42no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2411yescharacteristic
75C2×Dic73—22no—
76C2×Dic73C2×D411yescharacteristic
77C2×Dic73C2×D411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79D292—24no—
80D292—44no—
81D292—42no—
82D292—42no—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—44no—
86C4×D73—44no—
87C4×D73SD1614yes—
88Dic146—44no—
89Dic146—42no—
90C8×C73—22no—
91#10596831—22no—
92C22×C73C22×D411yescharacteristic
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73C2×SD1612yes—
99C4×C73—42no—
100C4×C73—42no—
101C4×C73C2×SD1612yes—
102C4×C73AGL(1,ℤ/8)12yes—
103C4×C732−1+412yes—
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107Dic73C2×SD1612yes—
108C2×C73#53611yescharacteristic
109C2×C73C22×SD1611yescharacteristic
110C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
111D73—22no—
112D73—82no—
113#3227—731nomaximal, Sylow
114C73#322711yescharacteristic, complemented, Sylow
115#532—731no—
116C2×C4⋊Q8—731no—
117#498—731no—
118#498D7311yescharacteristic, complemented
119#486—731no—
120#486—731no—
121#481—734no—
122#476—734no—
123#431—731no—
124C2×#41—1461no—
125C22×Q8—1461no—
126C4⋊Q8—732no—
127C4⋊Q8—731no—
128C4⋊Q8—1461no—
129C4⋊Q8—1461no—
130C4⋊Q8C2×D7311yescharacteristic
131C4⋊Q8C2×D7311yescharacteristic
132#127—731no—
133#124—1461no—
134#121—732no—
135#121—1461no—
136C4×D4—732no—
137C4×D4—1461no—
138C2×C4⋊C4—732no—
139C2×C4⋊C4—1461no—
140C2×C42—731no—
141#106—734no—
142#106C2×D7314yes—
143C4⋊C8—732no—
144#102—734no—
145#102—734no—
146C22⋊C8—732no—
147C4×C8—731no—
148C4×C8C2×D7311yescharacteristic
149#41—2924no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—2924no—
153C2×Q8—1462no—
154C2×Q8—1461no—
155C2×D4—732no—
156C2×D4—1462no—
157C2×D4—1461no—
158C2×D4—1461no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—1462no—
163C22×C4—1462no—
164C2×C8—732no—
165C2×C8C22×D7312yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—732no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1461no—
172C4⋊C4C22×D7312yes—
173C4⋊C4C22×D7312yes—
174C22⋊C4—1462no—
175C22⋊C4—1462no—
176C42—731no—
177C42—731no—
178C42—731no—
179C42C22×D7311yescharacteristic
180C23—731no—
181C23—1462no—
182Q8—42no—
183Q8—42no—
184Q8—2924no—
185Q8—2922no—
186D4—2924no—
187D4—2922no—
188D4—2922no—
189D4—1464no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—2924no—
193C2×C4—2924no—
194C2×C4—731no—
195C2×C4—734no—
196C2×C4—731no—
197C2×C4—731no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C2×C4C23×D7311yescharacteristic
204C8—22no—
205C8—1462no—
206C22—2922no—
207C22—2922no—
208C22—2922no—
209C22—732no—
210C22—1461no—
211C22—1461no—
212C22C2×D4×D7311yescharacteristic
213C4—42no—
214C4—42no—
215C4—2922no—
216C4—732no—
217C4—1461no—
218C4—1461no—
219C4SD16×D7312yes—
220C4#1455661812yes—
221C4#1455663912yes—
222C2—5842no—
223C2—1462no—
224C2#1798916211yescharacteristic
225C2C2×SD16×D7311yescharacteristic
226C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#498×C73C2
socleC22×C73C22×D4
hypercenter#498D73
hypocenterC73#3227
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D73C2semidirect
3. #17988983C2semidirect
4. #17988935C2semidirect
5. #17988934C2semidirect
6. #17988907C2semidirect
7. #17988876C2semidirect
8. #17988638C2semidirect
9. #498×C73C2semidirect
114. C73#3227semidirect
118. #498D73semidirect