Finite Group Databasebeta

← #22620562

Subgroups — #22620562

Order 9344.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989198C211yesmaximal, characteristic, complemented
2#17989193C211yesmaximal, characteristic
3#17988986C211yesmaximal, characteristic, complemented
4#17988961C211yesmaximal, characteristic, complemented
5#17988952C211yesmaximal, characteristic, complemented
6#17988836C212yesmaximal, complemented
7#17988819C212yesmaximal, complemented
8#17988690C212yesmaximal, complemented
9#17988672C212yesmaximal, complemented
10#17988544C211yesmaximal, characteristic, complemented
11#491×C73C211yesmaximal, characteristic, complemented
12C2×#11924015C2212yes—
13C2×#11924015C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×C8×D73C2211yescharacteristic
16#14556588C2211yescharacteristic
17#14556586—22no—
18#14556583C2211yescharacteristic
19#14556581—22no—
20#14556576—22no—
21#14556567C2212yes—
22#14556566—22no—
23#14556566C2212yes—
24Q8×Dic73C2212yes—
25#14556553C2212yes—
26#14556548C2211yescharacteristic
27#14556524C2212yes—
28#14556522C2212yes—
29#14556513C2212yes—
30#14556513C2212yes—
31#14556501C2211yescharacteristic
32C4×#10596831C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C4⋊Q8×C73C2211yescharacteristic
35#125×C73C2211yescharacteristic
36#103×C73C2212yes—
37#103×C73C2212yes—
38#97×C73C2211yescharacteristic
39C2×D292—22no—
40C2×D292—22no—
41C2×D292C2312yes—
42C2×C4×D73—22no—
43C2×C4×D73C2311yescharacteristic
44#11924015—24no—
45#11924015—24no—
46#11924011—22no—
47C2×#10596831C2311yescharacteristic
48C2×#10596831C2311yescharacteristic
49C8×D73—22no—
50C4⋊Dic73—22no—
51C4⋊Dic73C2312yes—
52#11924007—22no—
53#11924007—22no—
54#11924007D412yes—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005D412yes—
59C4×Dic73—22no—
60C4×Dic73C2311yescharacteristic
61C2×Q8×C73C2312yes—
62C2×C8×C73C2311yescharacteristic
63C2×C8×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C42×C73C2311yescharacteristic
68C22×D73—22no—
69C22×D73C2×D411yescharacteristic
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73C2411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73C2×D412yes—
78C2×Dic73C2×D411yescharacteristic
79D292—22no—
80D292—22no—
81D292—82no—
82D292—82no—
83C4×D73—21no—
84C4×D73—21no—
85C4×D73—82no—
86C8×C73—21no—
87C8×C73—21no—
88#10596831#4112yes—
89#10596831#4112yes—
90C22×C73C22×D411yescharacteristic
91C2×D73—21no—
92C2×D73—22no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—22no—
97C4×C73—42no—
98C4×C73—42no—
99C4×C73C2×#4111yescharacteristic
100C4×C73C2×#4111yescharacteristic
101Dic73—21no—
102Dic73—22no—
103Dic73—42no—
104C2×C73#53211yescharacteristic
105C2×C73#57712yes—
106D73—41no—
107D73—82no—
108#3174—731nomaximal, Sylow
109C73#317411yescharacteristic, complemented, Sylow
110#541—731no—
111#540—731no—
112#499—731no—
113#492—731no—
114#491D7311yescharacteristic, complemented
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—1462no—
128#125—731no—
129#125—1462no—
130#125C2×D7311yescharacteristic
131#123—1462no—
132C22⋊Q8—732no—
133#121—732no—
134#121—1462no—
135C4×Q8—732no—
136C4×D4—732no—
137#117—731no—
138#107—732no—
139#106—732no—
140#103C2×D7312yes—
141#103C2×D7312yes—
142#102—732no—
143#102—732no—
144#97—731no—
145#97C2×D7311yescharacteristic
146C4×C8—731no—
147C4×C8—731no—
148C2×Q8C22×D7312yes—
149C2×D4—732no—
150C2×D4—1462no—
151C2×D4—1462no—
152C22×C4—731no—
153C22×C4—1462no—
154SD16—1464no—
155SD16—1464no—
156M16—1462no—
157C2×C8—731no—
158C2×C8—731no—
159C2×C8—1462no—
160C2×C8C22×D7311yescharacteristic
161C2×C8C22×D7311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—732no—
165C4⋊C4—732no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4C22×D7312yes—
170C22⋊C4—732no—
171C22⋊C4—1462no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C42—731no—
175C42—1462no—
176C42C22×D7311yescharacteristic
177C23—731no—
178C23—1462no—
179Q8—22no—
180Q8—22no—
181D4—5842no—
182D4—5842no—
183D4—1462no—
184D4—1462no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—5842no—
188C2×C4—732no—
189C2×C4—731no—
190C2×C4—1462no—
191C2×C4—1461no—
192C2×C4—1461no—
193C2×C4D4×D7312yes—
194C2×C4C23×D7311yescharacteristic
195C8—21no—
196C8—21no—
197C8—732no—
198C8—732no—
199C22—2922no—
200C22—2922no—
201C22—2922no—
202C22—1461no—
203C22—1462no—
204C22C2×D4×D7311yescharacteristic
205C4—22no—
206C4—42no—
207C4—42no—
208C4—2922no—
209C4—1461no—
210C4—1462no—
211C4#41×D7311yescharacteristic
212C4#41×D7311yescharacteristic
213C2—2921no—
214C2—5842no—
215C2#1798913611yescharacteristic
216C2#1798939612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#491×C73C2
socleC22×C73C22×D4
hypercenter#491D73
hypocenterC73#3174
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #17989198C2semidirect
3. #17988986C2semidirect
4. #17988961C2semidirect
5. #17988952C2semidirect
6. #17988836C2semidirect
7. #17988819C2semidirect
8. #17988690C2semidirect
9. #17988672C2semidirect
10. #17988544C2semidirect
11. #491×C73C2semidirect
109. C73#3174semidirect
114. #491D73semidirect