Finite Group Databasebeta

← #22620880

Subgroups — #22620880

Order 9344.

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

normal subgroups only

This group has 384 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#17988967C211yesmaximal, characteristic, complemented
4#17988966C211yesmaximal, characteristic, complemented
5#17988939C211yesmaximal, characteristic, complemented
6#17988796C214yesmaximal, complemented
7#17988744C214yesmaximal
8#17988638C211yesmaximal, characteristic
9#487×C73C211yesmaximal, characteristic, complemented
10C2×Q8×D73C2212yes—
11C2×Dic292C2214yes—
12C2×#11924018C2214yes—
13#14556591C2211yescharacteristic
14#14556591C2211yescharacteristic
15#14556590—21no—
16#14556590—21no—
17#14556589C2212yes—
18#14556582—21no—
19#14556571C2212yes—
20#14556567—21no—
21Q8×Dic73—21no—
22#14556556C2212yes—
23#14556549—21no—
24C4⋊C4×D73—21no—
25C4⋊C4×D73—21no—
26C42×D73C2211yescharacteristic
27#14556520C2212yes—
28#14556514C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#103×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35C2×Dic146—22no—
36C2×Dic146C2312yes—
37C2×Dic146C2312yes—
38Q8×D73—44no—
39C2×C4×D73—22no—
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43Dic292—44no—
44#11924018—44no—
45C2×#10596831C2312yes—
46C4⋊Dic73—21no—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51#11924007—22no—
52#11924007—22no—
53#11924007—22no—
54#11924005—22no—
55C4×Dic73—22no—
56C4×Dic73D411yescharacteristic
57C4×Dic73D411yescharacteristic
58C4×Dic73C2311yescharacteristic
59C2×Q8×C73—21no—
60C2×Q8×C73C2312yes—
61C2×C8×C73C2312yes—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73C2312yes—
66C42×C73C2311yescharacteristic
67C22×D73C2×D411yescharacteristic
68Q8×C73—24no—
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×Dic73—22no—
77C2×Dic73C2×D411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80C4×D73—22no—
81C4×D73—22no—
82C4×D73—44no—
83C4×D73Q1614yescomplemented
84Dic146—24no—
85Dic146—24no—
86Dic146—44no—
87C8×C73—22no—
88#10596831—22no—
89C22×C73C22×D411yescharacteristic
90C2×D73—21no—
91C2×D73—21no—
92C2×D73C2×Q1612yes—
93C4×C73—42no—
94C4×C73—42no—
95C4×C73C2×Q1612yes—
96C4×C73#13712yes—
97C4×C73H(5,𝔽2)12yes—
98Dic73—21no—
99Dic73—21no—
100Dic73—42no—
101Dic73—42no—
102Dic73C2×Q1612yes—
103C2×C73#53511yescharacteristic
104C2×C73C22×Q1611yescharacteristic
105C2×C73C2×#13711yescharacteristic
106D73—22no—
107#3209—731nomaximal, Sylow
108C73#320911yescharacteristic, complemented, Sylow
109#533—731no—
110C2×C4⋊Q8—731no—
111#494—731no—
112#494—731no—
113#487—731no—
114#487D7311yescharacteristic, complemented
115#462—734no—
116#451—734no—
117#431—731no—
118C22×Q8—732no—
119C2×Q16—734no—
120C2×Q16—734no—
121C4⋊Q8—732no—
122C4⋊Q8—731no—
123C4⋊Q8—731no—
124C4⋊Q8—1461no—
125C4⋊Q8—1461no—
126C4⋊Q8C2×D7311yescharacteristic
127C4⋊Q8C2×D7311yescharacteristic
128#125—1461no—
129C22⋊Q8—732no—
130C22⋊Q8—1461no—
131C4×Q8—732no—
132C4×Q8—1461no—
133#117—1461no—
134C2×C4⋊C4—1461no—
135C2×C4⋊C4—1461no—
136C2×C42—731no—
137C4⋊C8—732no—
138#103—734no—
139#103C2×D7314yes—
140C22⋊C8—732no—
141C4×C8—731no—
142C4×C8C2×D7311yescharacteristic
143C2×Q8—21no—
144C2×Q8—2924no—
145C2×Q8—732no—
146C2×Q8—732no—
147C2×Q8—1462no—
148C2×Q8C22×D7312yes—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—1462no—
153Q16—2924no—
154Q16—2924no—
155C2×C8—732no—
156C2×C8C22×D7312yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—1462no—
161C4⋊C4—1462no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C4⋊C4C22×D7312yes—
169C22⋊C4—1462no—
170C42—731no—
171C42—731no—
172C42—731no—
173C42—1462no—
174C42C22×D7311yescharacteristic
175C23—731no—
176Q8—24no—
177Q8—42no—
178Q8—2924no—
179Q8—1464no—
180Q8—1464no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—2924no—
184C2×C4—731no—
185C2×C4—734no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4D4×D7311yescharacteristic
193C2×C4D4×D7311yescharacteristic
194C2×C4C23×D7311yescharacteristic
195C8—22no—
196C8—1462no—
197C22—732no—
198C22—1461no—
199C22—1461no—
200C22C2×D4×D7311yescharacteristic
201C4—42no—
202C4—42no—
203C4—2922no—
204C4—2922no—
205C4—732no—
206C4—1461no—
207C4—1461no—
208C4Q16×D7312yes—
209C4#1455662012yes—
210C4#1455663712yes—
211C2—1462no—
212C2#1798915511yescharacteristic
213C2C2×Q16×D7311yescharacteristic
214C2C2×#1455662011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#487×C73C2
socleC22×C73C22×D4
hypercenter#487D73
hypocenterC73#3209
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. #17988967C2semidirect
4. #17988966C2semidirect
5. #17988939C2semidirect
6. #17988796C2semidirect
9. #487×C73C2semidirect
83. C4×D73Q16semidirect
108. C73#3209semidirect
114. #487D73semidirect