Finite Group Databasebeta

← #22620560

Subgroups — #22620560

Order 9344.

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

normal subgroups only

This group has 362 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#17989192C211yesmaximal, characteristic
2#17988986C211yesmaximal, characteristic, complemented
3#17988961C211yesmaximal, characteristic, complemented
4#17988955C211yesmaximal, characteristic, complemented
5#17988953C211yesmaximal, characteristic, complemented
6#17988835C212yesmaximal, complemented
7#17988818C212yesmaximal, complemented
8#17988685C212yesmaximal, complemented
9C4×#11924015C212yesmaximal, complemented
10#17988543C211yesmaximal, characteristic, complemented
11#541×C73C211yesmaximal, characteristic, complemented
12C2×#11924015C2212yes—
13C2×#11924015C2212yes—
14C2×#11924012C2211yescharacteristic
15C22×#10596831C2211yescharacteristic
16#14556588C2211yescharacteristic
17#14556583C2211yescharacteristic
18#14556576—22no—
19#14556565C2212yes—
20#14556564—22no—
21C4×D292C2212yes—
22#14556524C2212yes—
23#14556522C2212yes—
24#14556515C2212yes—
25#14556515C2212yes—
26#14556511C2212yes—
27#14556511C2212yes—
28#14556502C2211yescharacteristic
29#14556502C2211yescharacteristic
30C4×#10596831C2211yescharacteristic
31C4×#10596831C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#126×C73—22no—
34#125×C73—22no—
35#125×C73C2211yescharacteristic
36C22⋊Q8×C73C2212yes—
37C4×Q8×C73C2212yes—
38#117×C73C2211yescharacteristic
39C2×D292—22no—
40C2×D292C2312yes—
41C2×C22⋊D73—22no—
42C2×C4×D73—22no—
43#11924015—24no—
44#11924015—24no—
45#11924012—22no—
46C2×#10596831—22no—
47C2×#10596831C2311yescharacteristic
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C2×#10596831C2311yescharacteristic
51C4⋊Dic73C2312yes—
52#11924007—22no—
53#11924005—22no—
54#11924005—22no—
55C2×Q8×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C4⋊C4×C73—22no—
58C4⋊C4×C73—22no—
59C4⋊C4×C73—22no—
60C4⋊C4×C73—22no—
61C4⋊C4×C73D412yes—
62C4⋊C4×C73C2312yes—
63C22⋊C4×C73—22no—
64C22⋊C4×C73D412yes—
65C42×C73—22no—
66C42×C73C2311yescharacteristic
67C42×C73C2311yescharacteristic
68C23×C73C2×D411yescharacteristic
69C22×D73—22no—
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2×D412yes—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C22⋊D73—82no—
81C2×Dic73—22no—
82D292—22no—
83D292—22no—
84D292—82no—
85C4×D73—82no—
86#10596831—21no—
87#10596831—21no—
88#10596831#4112yes—
89#10596831#4112yes—
90C22×C73—21no—
91C22×C73—22no—
92C22×C73C22×D411yescharacteristic
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—21no—
97C4×C73—22no—
98C4×C73—22no—
99C4×C73—42no—
100C4×C73—42no—
101C4×C73C2×#4111yescharacteristic
102C4×C73C2×#4111yescharacteristic
103Dic73—42no—
104C2×C73—41no—
105C2×C73#53211yescharacteristic
106C2×C73#57712yes—
107D73—82no—
108#3174—731nomaximal, Sylow
109C73#317411yescharacteristic, complemented, Sylow
110#541D7311yescharacteristic, complemented
111#540—731no—
112#499—731no—
113#492—731no—
114#491—731no—
115#490—731no—
116#468—732no—
117#465—732no—
118#440—732no—
119C4×SD16—732no—
120#405—731no—
121C2×SD16—732no—
122C2×SD16—732no—
123C2×M16—731no—
124C22×C8—731no—
125C4⋊Q8C2×D7311yescharacteristic
126#127—731no—
127#126—22no—
128#125—22no—
129#125—731no—
130#125C2×D7311yescharacteristic
131#123—1462no—
132C22⋊Q8C2×D7312yes—
133#121—732no—
134#121—1462no—
135C4×Q8C2×D7312yes—
136C4×D4—732no—
137#117C2×D7311yescharacteristic
138#107—732no—
139#106—732no—
140#103—732no—
141#103—732no—
142#102—732no—
143#102—732no—
144#97—731no—
145#97—731no—
146C4×C8—731no—
147C4×C8—731no—
148C2×Q8C22×D7312yes—
149C2×D4—732no—
150C2×D4—1462no—
151C2×D4—1462no—
152C22×C4—1462no—
153C22×C4C22×D7311yescharacteristic
154SD16—1464no—
155SD16—1464no—
156M16—1462no—
157C2×C8—731no—
158C2×C8—731no—
159C2×C8—731no—
160C2×C8—731no—
161C2×C8—1462no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—732no—
167C4⋊C4—1462no—
168C4⋊C4C22⋊D7312yes—
169C4⋊C4C22×D7312yes—
170C22⋊C4—22no—
171C22⋊C4—1462no—
172C22⋊C4—1462no—
173C22⋊C4C22⋊D7312yes—
174C42—22no—
175C42C22×D7311yescharacteristic
176C42C22×D7311yescharacteristic
177C23—1462no—
178C23C2×C22⋊D7311yescharacteristic
179Q8—22no—
180Q8—22no—
181D4—5842no—
182D4—5842no—
183D4—1462no—
184D4—1462no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—5842no—
190C2×C4—1462no—
191C2×C4C2×C22⋊D7312yes—
192C2×C4C2×C22⋊D7312yes—
193C2×C4C2×C22⋊D7311yescharacteristic
194C2×C4C23×D7311yescharacteristic
195C8—732no—
196C8—732no—
197C8—1461no—
198C8—1461no—
199C22—21no—
200C22—22no—
201C22—2922no—
202C22—2922no—
203C22—2922no—
204C22C22×C22⋊D7311yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—42no—
210C4—2922no—
211C4#41×D7311yescharacteristic
212C4#41×D7311yescharacteristic
213C2—41no—
214C2—5842no—
215C2#1798913311yescharacteristic
216C2#1798939512yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#541×C73C2
socleC22×C73C22×D4
hypercenter#541D73
hypocenterC73#3174
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #17988986C2semidirect
3. #17988961C2semidirect
4. #17988955C2semidirect
5. #17988953C2semidirect
6. #17988835C2semidirect
7. #17988818C2semidirect
8. #17988685C2semidirect
9. C4×#11924015C2semidirect
10. #17988543C2semidirect
11. #541×C73C2semidirect
109. C73#3174semidirect
110. #541D73semidirect