Finite Group Databasebeta

← #22620553

Subgroups — #22620553

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#17989199C211yesmaximal, characteristic, complemented
2#17988986C211yesmaximal, characteristic, complemented
3#17988959C211yesmaximal, characteristic, complemented
4#17988957C211yesmaximal, characteristic, complemented
5#17988951C211yesmaximal, characteristic, complemented
6#17988831C212yesmaximal, complemented
7#17988814C212yesmaximal, complemented
8#17988687C212yesmaximal, complemented
9C4×#11924016C212yesmaximal, complemented
10#17988543C211yesmaximal, characteristic, complemented
11#540×C73C211yesmaximal, characteristic
12C2×#11924016C2212yes—
13C2×#11924016C2212yes—
14C2×#11924012C2211yescharacteristic
15C22×#10596831C2211yescharacteristic
16#14556591C2211yescharacteristic
17#14556584—22no—
18#14556583C2211yescharacteristic
19#14556581—22no—
20#14556570C2212yes—
21C4×Dic146C2212yes—
22#14556524C2212yes—
23#14556522C2212yes—
24#14556514C2212yes—
25#14556514C2212yes—
26#14556512C2212yes—
27#14556512C2212yes—
28#14556502C2211yescharacteristic
29#14556502C2211yescharacteristic
30C4×#10596831C2211yescharacteristic
31C4×#10596831C2211yescharacteristic
32#127×C73C2211yescharacteristic
33#125×C73C2211yescharacteristic
34#123×C73—22no—
35#121×C73—22no—
36#121×C73C2212yes—
37C4×D4×C73C2212yes—
38#117×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40#11924016—24no—
41#11924016—24no—
42#11924012—22no—
43C2×#10596831—22no—
44C2×#10596831C2311yescharacteristic
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—22no—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53C22⋊Dic73—22no—
54C4×Dic73—22no—
55C2×D4×C73—22no—
56C2×D4×C73—22no—
57C2×D4×C73C2312yes—
58C22×C4×C73—22no—
59C22×C4×C73C2311yescharacteristic
60C4⋊C4×C73—22no—
61C4⋊C4×C73D412yes—
62C4⋊C4×C73C2312yes—
63C22⋊C4×C73—22no—
64C22⋊C4×C73—22no—
65C22⋊C4×C73D412yes—
66C42×C73C2311yescharacteristic
67C42×C73C2311yescharacteristic
68C23×C73—22no—
69C23×C73C2×D411yescharacteristic
70D4×C73—22no—
71D4×C73—22no—
72D4×C73—82no—
73D4×C73—82no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—82no—
78C2×C4×C73C2×D412yes—
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2411yescharacteristic
82C2×Dic73—22no—
83C2×Dic73—22no—
84Dic146—22no—
85Dic146—22no—
86#10596831—21no—
87#10596831—21no—
88#10596831#4112yes—
89#10596831#4112yes—
90C22×C73—21no—
91C22×C73—22no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73C22×D411yescharacteristic
96C4×C73—21no—
97C4×C73—22no—
98C4×C73—22no—
99C4×C73—42no—
100C4×C73C2×#4111yescharacteristic
101C4×C73C2×#4111yescharacteristic
102Dic73—42no—
103Dic73—42no—
104C2×C73—41no—
105C2×C73—82no—
106C2×C73#53211yescharacteristic
107C2×C73#57712yes—
108#3174—731nomaximal, Sylow
109C73#317411yescharacteristic, complemented, Sylow
110#541—731no—
111#540D7311yescharacteristic
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⋊Q8—731no—
126#127C2×D7311yescharacteristic
127#126—1462no—
128#125—731no—
129#125—1462no—
130#125C2×D7311yescharacteristic
131#123—22no—
132C22⋊Q8—732no—
133#121—22no—
134#121C2×D7312yes—
135C4×Q8—732no—
136C4×D4C2×D7312yes—
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×Q8—732no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4C22×D7312yes—
152C22×C4—22no—
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—732no—
164C4⋊C4—1462no—
165C4⋊C4—1462no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4C22⋊D7312yes—
169C4⋊C4C22×D7312yes—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—1462no—
173C22⋊C4C22⋊D7312yes—
174C42—1462no—
175C42C22×D7311yescharacteristic
176C42C22×D7311yescharacteristic
177C23—22no—
178C23C2×C22⋊D7311yescharacteristic
179Q8—1462no—
180Q8—1462no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—82no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—1462no—
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—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D7311yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—2922no—
210C4—2922no—
211C4#41×D7311yescharacteristic
212C4#41×D7311yescharacteristic
213C2—41no—
214C2—82no—
215C2#1798913311yescharacteristic
216C2#1798939812yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#540×C73C2
socleC22×C73C22×D4
hypercenter#540D73
hypocenterC73#3174
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #17989199C2semidirect
2. #17988986C2semidirect
3. #17988959C2semidirect
4. #17988957C2semidirect
5. #17988951C2semidirect
6. #17988831C2semidirect
7. #17988814C2semidirect
8. #17988687C2semidirect
9. C4×#11924016C2semidirect
10. #17988543C2semidirect
109. C73#3174semidirect