Finite Group Databasebeta

← #22620675

Subgroups — #22620675

Order 9344.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#17989142C211yesmaximal, characteristic
2#17989142C211yesmaximal, characteristic
3#17988983C211yesmaximal, characteristic, complemented
4#17988966C211yesmaximal, characteristic, complemented
5#17988938C211yesmaximal, characteristic, complemented
6#17988844C214yesmaximal
7#17988691C214yesmaximal, complemented
8C4×#11924011C211yesmaximal, characteristic
9#487×C73C211yesmaximal, characteristic, complemented
10C2×#11924018C2214yes—
11C2×#11924011C2212yes—
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556582—21no—
15#14556582—21no—
16#14556571—21no—
17#14556571C2212yes—
18#14556567—21no—
19#14556567C2212yes—
20Q8×Dic73—21no—
21Q8×Dic73C2212yes—
22#14556556—21no—
23#14556556C2212yes—
24#14556549—21no—
25#14556549—21no—
26C42×D73C2211yescharacteristic
27#14556522C2214yes—
28#14556516C2214yes—
29#14556501C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#103×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35C2×Dic146—21no—
36C2×Dic146C2312yes—
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73C2311yescharacteristic
40#11924018—28no—
41#11924011—24no—
42C2×#10596831C2312yes—
43C4⋊Dic73—21no—
44C4⋊Dic73—21no—
45C4⋊Dic73—21no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50#11924007—22no—
51#11924005—22no—
52#11924005—22no—
53C4×Dic73—22no—
54C4×Dic73—22no—
55C4×Dic73D411yescharacteristic
56C4×Dic73D411yescharacteristic
57C4×Dic73C2311yescharacteristic
58C2×Q8×C73—21no—
59C2×Q8×C73C2312yes—
60C2×C8×C73C2312yes—
61C4⋊C4×C73—21no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73C2312yes—
65C42×C73C2311yescharacteristic
66C22×D73C2×D411yescharacteristic
67Q8×C73—24no—
68Q8×C73—42no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2411yescharacteristic
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73C2×D411yescharacteristic
77C2×Dic73C2×D411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79C4×D73—22no—
80C4×D73—22no—
81C4×D73—22no—
82Dic146—24no—
83Dic146—42no—
84C8×C73—22no—
85#10596831#4114yes—
86C22×C73C22×D411yescharacteristic
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C4×C73—42no—
91C4×C73—42no—
92C4×C73#13712yes—
93C4×C73#13712yes—
94C4×C73C2×#4112yes—
95Dic73—21no—
96Dic73—21no—
97Dic73—21no—
98Dic73—42no—
99Dic73—42no—
100C2×C73#53211yescharacteristic
101C2×C73C2×#13711yescharacteristic
102C2×C73C2×#13711yescharacteristic
103D73—41no—
104#3185—731nomaximal, Sylow
105C73#318511yescharacteristic, complemented, Sylow
106#533—731no—
107#533—731no—
108#498—731no—
109#494—731no—
110#487—731no—
111#487D7311yescharacteristic, complemented
112#470—734no—
113#441—734no—
114C4×M16—731no—
115C2×Q16—734no—
116C2×M16—732no—
117C4⋊Q8—731no—
118C4⋊Q8—731no—
119C4⋊Q8C2×D7311yescharacteristic
120C4⋊Q8C2×D7311yescharacteristic
121#125—1461no—
122#125—1461no—
123C22⋊Q8—732no—
124C22⋊Q8—732no—
125C22⋊Q8—1461no—
126C22⋊Q8—1461no—
127C4×Q8—732no—
128C4×Q8—732no—
129C4×Q8—1461no—
130C4×Q8—1461no—
131#117—1461no—
132#117—1461no—
133C2×C42—731no—
134#106—734no—
135#103—734no—
136#103C2×D7314yes—
137#97—732no—
138C4×C8—731no—
139C4×C8C2×D7311yescharacteristic
140C2×Q8—21no—
141C2×Q8—732no—
142C2×Q8—1461no—
143C2×Q8C22×D7312yes—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147Q16—1468no—
148M16—1464no—
149C2×C8—732no—
150C2×C8C22×D7312yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—732no—
155C4⋊C4—1462no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1461no—
160C4⋊C4—1461no—
161C4⋊C4—1461no—
162C4⋊C4C22×D7312yes—
163C22⋊C4—1462no—
164C22⋊C4—1462no—
165C42—731no—
166C42—731no—
167C42—731no—
168C42—1462no—
169C42—1462no—
170C42C22×D7311yescharacteristic
171C23—731no—
172Q8—24no—
173Q8—42no—
174Q8—2922no—
175Q8—1464no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—731no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4D4×D7311yescharacteristic
187C2×C4D4×D7311yescharacteristic
188C2×C4C23×D7311yescharacteristic
189C8—22no—
190C8—734no—
191C22—1461no—
192C22—1461no—
193C22—1461no—
194C22C2×D4×D7311yescharacteristic
195C4—42no—
196C4—42no—
197C4—2922no—
198C4—2922no—
199C4—1461no—
200C4—1461no—
201C4—1461no—
202C4#1455662012yes—
203C4#1455662312yes—
204C4#41×D7312yes—
205C2—2921no—
206C2#1798913611yescharacteristic
207C2C2×#1455662011yescharacteristic
208C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#487×C73C2
socleC22×C73C22×D4
hypercenter#487D73
hypocenterC73#3185
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #17988983C2semidirect
4. #17988966C2semidirect
5. #17988938C2semidirect
7. #17988691C2semidirect
9. #487×C73C2semidirect
105. C73#3185semidirect
111. #487D73semidirect