Finite Group Databasebeta

← #22621048

Subgroups — #22621048

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#17989135C211yesmaximal, characteristic
2C4⋊Q8×D73C211yesmaximal, characteristic, complemented
3#17988992C211yesmaximal, characteristic, complemented
4#17988990C211yesmaximal, characteristic, complemented
5#17988933C211yesmaximal, characteristic, complemented
6#17988899C214yesmaximal, complemented
7#17988865C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#486×C73C211yesmaximal, characteristic, complemented
10C2×#11924027—21no—
11C2×Q8×D73—21no—
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556590—21no—
15#14556590C2212yes—
16#14556589—21no—
17#14556578—21no—
18#14556562—21no—
19#14556562C2212yes—
20D4×Dic73—21no—
21D4×Dic73C2212yes—
22C4⋊C4×D73—21no—
23C4⋊C4×D73C2212yes—
24C42×D73C2211yescharacteristic
25#14556525C2214yes—
26#14556524C2214yes—
27#14556520C2212yes—
28#14556512C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32#127×C73C2211yescharacteristic
33#102×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924027—44no—
36C2×Dic146—21no—
37C2×Dic146—21no—
38C2×Dic146—22no—
39Q8×D73—44no—
40C2×C22⋊D73—22no—
41C22×Dic73—22no—
42C2×C4×D73—22no—
43C2×C4×D73D411yescharacteristic
44C2×C4×D73D411yescharacteristic
45C2×C4×D73C2311yescharacteristic
46C2×#10596831C2312yes—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49C4⋊Dic73C2312yes—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55C4×Dic73D411yescharacteristic
56C4×Dic73D411yescharacteristic
57C4×Dic73C2311yescharacteristic
58C2×Q8×C73—21no—
59C2×D4×C73—21no—
60C2×D4×C73—21no—
61C2×D4×C73C2312yes—
62C2×C8×C73C2312yes—
63C4⋊C4×C73—21no—
64C4⋊C4×C73C2312yes—
65C42×C73C2311yescharacteristic
66C23×C73—22no—
67C22×D73C2×D411yescharacteristic
68Q8×C73—42no—
69D4×C73—24no—
70D4×C73—42no—
71D4×C73—42no—
72C2×C4×C73—22no—
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2411yescharacteristic
76C22⋊D73—44no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—44no—
80C2×Dic73C2×D411yescharacteristic
81C2×Dic73C2×D411yescharacteristic
82C2×Dic73C2×D411yescharacteristic
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—44no—
86C4×D73D814yes—
87Dic146—42no—
88Dic146—42no—
89Dic146—44no—
90C8×C73—22no—
91#10596831—22no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73C22×D411yescharacteristic
96C2×D73—21no—
97C2×D73—21no—
98C2×D73C2×D812yes—
99C4×C73—42no—
100C4×C73C2×D812yes—
101C4×C73#13712yes—
102C4×C732−1+412yes—
103Dic73—21no—
104Dic73—21no—
105Dic73—42no—
106Dic73—42no—
107Dic73C2×D812yes—
108C2×C73—82no—
109C2×C73#53611yescharacteristic
110C2×C73C22×D811yescharacteristic
111C2×C73C2×#13711yescharacteristic
112D73—22no—
113#3226—731nomaximal, Sylow
114C73#322611yescharacteristic, complemented, Sylow
115#532—731no—
116C2×C4⋊Q8—731no—
117#500—731no—
118#500—731no—
119#486—731no—
120#486D7311yescharacteristic, complemented
121#480—734no—
122#474—734no—
123#431—731no—
124C2×#41—1461no—
125C22×Q8—1461no—
126C4⋊Q8—732no—
127C4⋊Q8—731no—
128C4⋊Q8—731no—
129C4⋊Q8—1461no—
130C4⋊Q8—1461no—
131C4⋊Q8C2×D7311yescharacteristic
132#127C2×D7311yescharacteristic
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#107—734no—
142#107—734no—
143C4⋊C8—732no—
144#102—734no—
145#102C2×D7314yes—
146C22⋊C8—732no—
147C4×C8—731no—
148C4×C8C2×D7311yescharacteristic
149#41—2924no—
150C2×Q8—21no—
151C2×Q8—2924no—
152C2×Q8—1462no—
153C2×Q8—1461no—
154C2×Q8—1461no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—1462no—
158C2×D4C22×D7312yes—
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—732no—
168C4⋊C4—732no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1461no—
172C4⋊C4—1461no—
173C4⋊C4C22×D7312yes—
174C22⋊C4—1462no—
175C22⋊C4—1462no—
176C42—731no—
177C42—731no—
178C42—731no—
179C42C22×D7311yescharacteristic
180C23—22no—
181C23—731no—
182Q8—42no—
183Q8—2924no—
184Q8—2922no—
185Q8—2922no—
186D4—24no—
187D4—42no—
188D4—42no—
189D4—2924no—
190C2×C4—22no—
191C2×C4—2924no—
192C2×C4—2924no—
193C2×C4—731no—
194C2×C4—734no—
195C2×C4—731no—
196C2×C4—731no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C2×C4C23×D7311yescharacteristic
204C8—22no—
205C8—1462no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—732no—
210C22—1461no—
211C22—1461no—
212C22C2×D4×D7311yescharacteristic
213C4—42no—
214C4—2922no—
215C4—2922no—
216C4—732no—
217C4—1461no—
218C4—1461no—
219C4D8×D7312yes—
220C4#1455662012yes—
221C4#1455663812yes—
222C2—82no—
223C2—1462no—
224C2#1798915711yescharacteristic
225C2C2×D8×D7311yescharacteristic
226C2C2×#1455662011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#486×C73C2
socleC22×C73C22×D4
hypercenter#486D73
hypocenterC73#3226
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D73C2semidirect
3. #17988992C2semidirect
4. #17988990C2semidirect
5. #17988933C2semidirect
6. #17988899C2semidirect
7. #17988865C2semidirect
8. #17988638C2semidirect
9. #486×C73C2semidirect
114. C73#3226semidirect
120. #486D73semidirect