Finite Group Databasebeta

← #22620651

Subgroups — #22620651

Order 9344.

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

normal subgroups only

This group has 402 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, complemented
2#17989138C211yesmaximal, characteristic
3#17988960C211yesmaximal, characteristic, complemented
4#17988939C211yesmaximal, characteristic, complemented
5#17988935C211yesmaximal, characteristic, complemented
6#17988834C214yesmaximal, complemented
7#17988686C214yesmaximal, complemented
8C4×#11924011C211yesmaximal, characteristic, complemented
9#500×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×#11924017C2214yes—
12C2×#11924011C2212yes—
13#14556591C2211yescharacteristic
14#14556588C2211yescharacteristic
15#14556582—21no—
16#14556580—21no—
17#14556571C2212yes—
18#14556567—21no—
19#14556566—21no—
20#14556566C2212yes—
21Q8×Dic73—21no—
22#14556556C2212yes—
23#14556553—21no—
24#14556553C2212yes—
25#14556549—21no—
26C42×D73C2211yescharacteristic
27#14556514C2214yes—
28#14556511C2214yes—
29#14556501C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#107×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36C2×Dic146C2312yes—
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#11924017—28no—
46#11924011—24no—
47C2×#10596831C2312yes—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51#11924007—22no—
52#11924005—22no—
53#11924005—22no—
54#11924005—22no—
55C4×Dic73—22no—
56C4×Dic73D411yescharacteristic
57C4×Dic73D411yescharacteristic
58C4×Dic73C2311yescharacteristic
59C2×Q8×C73—21no—
60C2×Q8×C73—21no—
61C2×C8×C73C2312yes—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73C2312yes—
65C4⋊C4×C73C2312yes—
66C42×C73C2311yescharacteristic
67C22×D73—22no—
68C22×D73C2×D411yescharacteristic
69Q8×C73—42no—
70Q8×C73—42no—
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—24no—
89C8×C73#4114yescomplemented
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×C73AGL(1,ℤ/8)12yes—
101C4×C73#13712yes—
102C4×C73C2×#4112yes—
103Dic73—21no—
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107C2×C73#53211yescharacteristic
108C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C73C2×#13711yescharacteristic
110D73—41no—
111D73—82no—
112#3182—731nomaximal, Sylow
113C73#318211yescharacteristic, complemented, Sylow
114#533—731no—
115#532—731no—
116#500D7311yescharacteristic, complemented
117#492—731no—
118#487—731no—
119#486—731no—
120#468—734no—
121#440—734no—
122C4×M16—731no—
123C2×#41—1461no—
124C2×SD16—734no—
125C2×M16—732no—
126C4⋊Q8—731no—
127C4⋊Q8C2×D7311yescharacteristic
128C4⋊Q8C2×D7311yescharacteristic
129#127—731no—
130#125—1461no—
131#124—1461no—
132C22⋊Q8—732no—
133C22⋊Q8—1461no—
134#121—732no—
135#121—1461no—
136C4×Q8—732no—
137C4×Q8—1461no—
138C4×D4—732no—
139C4×D4—1461no—
140#117—1461no—
141C2×C42—731no—
142#107C2×D7314yes—
143#103—734no—
144#102—734no—
145#97—732no—
146C4×C8—731no—
147C4×C8C2×D7311yescharacteristic
148#41—2924no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—732no—
152C2×D4—732no—
153C2×D4—1462no—
154C2×D4—1461no—
155C2×D4—1461no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—1462no—
160SD16—1468no—
161M16—1464no—
162C2×C8—732no—
163C2×C8C22×D7312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1461no—
169C4⋊C4—1461no—
170C4⋊C4C22×D7312yes—
171C4⋊C4C22×D7312yes—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—731no—
176C42—731no—
177C42—731no—
178C42—1462no—
179C42C22×D7311yescharacteristic
180C23—731no—
181C23—1462no—
182Q8—42no—
183Q8—42no—
184Q8—1464no—
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—1462no—
203C8#1192402914yescomplemented
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#1455661512yes—
218C4#1455662312yes—
219C4C2×#1192402912yes—
220C2—2921no—
221C2—5842no—
222C2#1798913811yescharacteristic
223C2C2×#1455661511yescharacteristic
224C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#500×C73C2
socleC22×C73C22×D4
hypercenter#500D73
hypocenterC73#3182
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988960C2semidirect
4. #17988939C2semidirect
5. #17988935C2semidirect
6. #17988834C2semidirect
7. #17988686C2semidirect
8. C4×#11924011C2semidirect
9. #500×C73C2semidirect
89. C8×C73#41semidirect
113. C73#3182semidirect
116. #500D73semidirect
203. C8#11924029semidirect