Finite Group Databasebeta

← #22621071

Subgroups — #22621071

Order 9344.

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

normal subgroups only

This group has 360 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#17989142C211yesmaximal, characteristic
2C4⋊Q8×D73C211yesmaximal, characteristic
3#17988985C211yesmaximal, characteristic, complemented
4#17988983C211yesmaximal, characteristic, complemented
5#17988937C211yesmaximal, characteristic, complemented
6#17988916C214yesmaximal
7#17988870C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic
9#487×C73C211yesmaximal, characteristic, complemented
10C2×Q8×D73—21no—
11#14556591C2211yescharacteristic
12#14556591C2211yescharacteristic
13#14556590—21no—
14#14556590C2212yes—
15#14556589—21no—
16#14556582—21no—
17#14556571—21no—
18#14556567C2212yes—
19Q8×Dic73C2212yes—
20#14556556—21no—
21#14556549—21no—
22C4⋊C4×D73—21no—
23C4⋊C4×D73C2212yes—
24C42×D73C2211yescharacteristic
25#14556523C2214yes—
26#14556522C2214yes—
27#14556520C2212yes—
28#14556515C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#103×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×Dic146—22no—
38Q8×D73—44no—
39C2×C4×D73—22no—
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43C2×#10596831C2312yes—
44C4⋊Dic73—21no—
45C4⋊Dic73—21no—
46C4⋊Dic73—22no—
47C4⋊Dic73C2312yes—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50#11924007—22no—
51#11924007—22no—
52#11924005—22no—
53C4×Dic73—22no—
54C4×Dic73D411yescharacteristic
55C4×Dic73D411yescharacteristic
56C4×Dic73C2311yescharacteristic
57C2×Q8×C73—21no—
58C2×Q8×C73C2312yes—
59C2×C8×C73C2312yes—
60C4⋊C4×C73—21no—
61C4⋊C4×C73—21no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73C2312yes—
64C42×C73C2311yescharacteristic
65C22×D73C2×D411yescharacteristic
66Q8×C73—24no—
67Q8×C73—42no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2411yescharacteristic
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73C2×D411yescharacteristic
76C2×Dic73C2×D411yescharacteristic
77C2×Dic73C2×D411yescharacteristic
78C4×D73—22no—
79C4×D73—22no—
80C4×D73—44no—
81C4×D73SD1614yes—
82Dic146—42no—
83Dic146—42no—
84Dic146—44no—
85C8×C73—22no—
86#10596831—22no—
87C22×C73C22×D411yescharacteristic
88C2×D73—21no—
89C2×D73—21no—
90C2×D73C2×SD1612yes—
91C4×C73—42no—
92C4×C73—42no—
93C4×C73C2×SD1612yes—
94C4×C73#13712yes—
95C4×C732−1+412yes—
96Dic73—21no—
97Dic73—21no—
98Dic73—42no—
99Dic73—42no—
100Dic73C2×SD1612yes—
101C2×C73#53611yescharacteristic
102C2×C73C22×SD1611yescharacteristic
103C2×C73C2×#13711yescharacteristic
104D73—22no—
105#3229—731nomaximal, Sylow
106C73#322911yescharacteristic, complemented, Sylow
107#533—731no—
108C2×C4⋊Q8—731no—
109#498—731no—
110#498—731no—
111#487—731no—
112#487D7311yescharacteristic, complemented
113#483—734no—
114#475—734no—
115#431—731no—
116C22×Q8—1461no—
117C4⋊Q8—732no—
118C4⋊Q8—731no—
119C4⋊Q8—731no—
120C4⋊Q8—1461no—
121C4⋊Q8—1461no—
122C4⋊Q8C2×D7311yescharacteristic
123C4⋊Q8C2×D7311yescharacteristic
124#125—1461no—
125C22⋊Q8—732no—
126C22⋊Q8—1461no—
127C4×Q8—732no—
128C4×Q8—1461no—
129#117—1461no—
130C2×C4⋊C4—732no—
131C2×C4⋊C4—1461no—
132C2×C42—731no—
133#106—734no—
134#106—734no—
135C4⋊C8—732no—
136#103—734no—
137#103C2×D7314yes—
138C22⋊C8—732no—
139C4×C8—731no—
140C4×C8C2×D7311yescharacteristic
141C2×Q8—21no—
142C2×Q8—2924no—
143C2×Q8—1462no—
144C2×Q8—1461no—
145C2×Q8—1461no—
146C2×Q8C22×D7312yes—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—1462no—
151C2×C8—732no—
152C2×C8C22×D7312yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—732no—
157C4⋊C4—732no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1462no—
161C4⋊C4—1462no—
162C4⋊C4—1461no—
163C4⋊C4—1461no—
164C4⋊C4C22×D7312yes—
165C22⋊C4—1462no—
166C42—731no—
167C42—731no—
168C42—731no—
169C42—1462no—
170C42C22×D7311yescharacteristic
171C23—731no—
172Q8—24no—
173Q8—42no—
174Q8—2924no—
175Q8—2922no—
176Q8—2922no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2924no—
180C2×C4—731no—
181C2×C4—734no—
182C2×C4—731no—
183C2×C4—731no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4D4×D7311yescharacteristic
189C2×C4D4×D7311yescharacteristic
190C2×C4C23×D7311yescharacteristic
191C8—22no—
192C8—1462no—
193C22—732no—
194C22—1461no—
195C22—1461no—
196C22C2×D4×D7311yescharacteristic
197C4—42no—
198C4—42no—
199C4—2922no—
200C4—2922no—
201C4—732no—
202C4—1461no—
203C4—1461no—
204C4SD16×D7312yes—
205C4#1455662312yes—
206C4#1455663812yes—
207C2—1462no—
208C2#1798915711yescharacteristic
209C2C2×SD16×D7311yescharacteristic
210C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#487×C73C2
socleC22×C73C22×D4
hypercenter#487D73
hypocenterC73#3229
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. #17988985C2semidirect
4. #17988983C2semidirect
5. #17988937C2semidirect
7. #17988870C2semidirect
9. #487×C73C2semidirect
106. C73#3229semidirect
112. #487D73semidirect