Finite Group Databasebeta

← #22620884

Subgroups — #22620884

Order 9344.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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, complemented
2#17989138C211yesmaximal, characteristic
3#17988961C211yesmaximal, characteristic, complemented
4#17988937C211yesmaximal, characteristic, complemented
5#17988934C211yesmaximal, characteristic, complemented
6#17988811C214yesmaximal, complemented
7#17988748C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#494×C73C211yesmaximal, characteristic, complemented
10C2×#11924029C2212yes—
11C2×#11924015C2214yes—
12#14556591C2211yescharacteristic
13#14556588C2211yescharacteristic
14#14556582—21no—
15#14556580C2212yes—
16#14556571—21no—
17#14556567C2212yes—
18#14556566—21no—
19#14556566—21no—
20Q8×Dic73C2212yes—
21#14556556—21no—
22#14556553—21no—
23#14556553—21no—
24#14556549—21no—
25C42×D73C2211yescharacteristic
26#14556520C2212yes—
27#14556515C2214yes—
28#14556513C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C2×Q16×C73C2214yes—
32C4⋊Q8×C73C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36C2×Dic146—21no—
37C2×D292—22no—
38C2×D292—21no—
39C2×D292—21no—
40C2×D292C2312yes—
41C2×C4×D73—22no—
42C2×C4×D73D411yescharacteristic
43C2×C4×D73D411yescharacteristic
44C2×C4×D73C2311yescharacteristic
45#11924015—44no—
46C2×#10596831C2312yes—
47C4⋊Dic73—21no—
48C4⋊Dic73—22no—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924005—22no—
52#11924005—22no—
53#11924005—22no—
54C4×Dic73—22no—
55C4×Dic73D411yescharacteristic
56C4×Dic73D411yescharacteristic
57C4×Dic73C2311yescharacteristic
58C2×Q8×C73C2312yes—
59C2×Q8×C73C2312yes—
60Q16×C73—44no—
61C2×C8×C73C2312yes—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—21no—
66C42×C73C2311yescharacteristic
67C22×D73—22no—
68C22×D73C2×D411yescharacteristic
69Q8×C73—24no—
70Q8×C73—24no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73C2×D411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80D292—24no—
81D292—44no—
82D292—42no—
83D292—42no—
84C4×D73—22no—
85C4×D73—22no—
86C4×D73—22no—
87C4×D73—44no—
88Dic146—42no—
89C8×C73—22no—
90#10596831—22no—
91C22×C73C22×D411yescharacteristic
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C4×C73—42no—
99C4×C73—42no—
100C4×C73#13512yes—
101C4×C73#13712yes—
102C4×C73H(5,𝔽2)12yes—
103Dic73—21no—
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107C2×C73#53511yescharacteristic
108C2×C73C2×#13511yescharacteristic
109C2×C73C2×#13711yescharacteristic
110D73—41no—
111D73—82no—
112#3210—731nomaximal, Sylow
113C73#321011yescharacteristic, complemented, Sylow
114#533—731no—
115#532—731no—
116#494D7311yescharacteristic, complemented
117#492—731no—
118#487—731no—
119#486—731no—
120#464—734no—
121#452—734no—
122#431—731no—
123C2×#41—732no—
124C2×Q16C2×D7314yes—
125C2×SD16—734no—
126C4⋊Q8—731no—
127C4⋊Q8C2×D7311yescharacteristic
128C4⋊Q8C2×D7311yescharacteristic
129#127—731no—
130#125—1461no—
131#124—732no—
132C22⋊Q8—732no—
133C22⋊Q8—1461no—
134#121—1461no—
135#121—1461no—
136C4×Q8—732no—
137C4×Q8—1461no—
138C4×D4—1461no—
139C4×D4—1461no—
140#117—1461no—
141C2×C42—731no—
142C4⋊C8—732no—
143#103—734no—
144#102—734no—
145C22⋊C8—732no—
146C4×C8—731no—
147C4×C8C2×D7311yescharacteristic
148#41—2924no—
149C2×Q8—1461no—
150C2×Q8C22×D7312yes—
151C2×Q8C22×D7312yes—
152C2×D4—732no—
153C2×D4—1462no—
154C2×D4—1461no—
155C2×D4—1461no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—1462no—
160Q16—44no—
161SD16—2924no—
162C2×C8—732no—
163C2×C8C22×D7312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—732no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1461no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—731no—
176C42—731no—
177C42—731no—
178C42—1462no—
179C42C22×D7311yescharacteristic
180C23—731no—
181C23—1462no—
182Q8—24no—
183Q8—24no—
184Q8—2922no—
185D4—2924no—
186D4—2922no—
187D4—2922no—
188D4—1464no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—2924no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4D4×D7311yescharacteristic
200C2×C4D4×D7311yescharacteristic
201C2×C4C23×D7311yescharacteristic
202C8—22no—
203C8—1462no—
204C22—2922no—
205C22—2922no—
206C22—2922no—
207C22—1461no—
208C22—1461no—
209C22—1461no—
210C22C2×D4×D7311yescharacteristic
211C4—42no—
212C4—42no—
213C4—2922no—
214C4—1461no—
215C4—1461no—
216C4—1461no—
217C4#1455661412yes—
218C4#1455662312yes—
219C4#1455663612yes—
220C2—2921no—
221C2—5842no—
222C2#1798915011yescharacteristic
223C2C2×#1455661411yescharacteristic
224C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#494×C73C2
socleC22×C73C22×D4
hypercenter#494D73
hypocenterC73#3210
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988961C2semidirect
4. #17988937C2semidirect
5. #17988934C2semidirect
6. #17988811C2semidirect
7. #17988748C2semidirect
8. #17988638C2semidirect
9. #494×C73C2semidirect
113. C73#3210semidirect
116. #494D73semidirect