Finite Group Databasebeta

← #22620561

Subgroups — #22620561

Order 9344.

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

normal subgroups only

This group has 362 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#17989200C211yesmaximal, characteristic, complemented
2#17989193C211yesmaximal, characteristic
3#17988960C211yesmaximal, characteristic, complemented
4#17988957C211yesmaximal, characteristic, complemented
5#17988953C211yesmaximal, characteristic, complemented
6#17988834C212yesmaximal, complemented
7#17988817C212yesmaximal, complemented
8#17988686C212yesmaximal, complemented
9#17988674C212yesmaximal, complemented
10#17988541C211yesmaximal, characteristic, complemented
11#499×C73C211yesmaximal, characteristic, complemented
12C2×#11924017C2212yes—
13C2×#11924017C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×C8×D73C2211yescharacteristic
16#14556591C2211yescharacteristic
17#14556588C2211yescharacteristic
18#14556586—22no—
19#14556582—22no—
20#14556576—22no—
21#14556571C2212yes—
22#14556566—22no—
23#14556566C2212yes—
24#14556556C2212yes—
25#14556553C2212yes—
26#14556548C2211yescharacteristic
27#14556514C2212yes—
28#14556514C2212yes—
29#14556511C2212yes—
30#14556511C2212yes—
31#14556502C2211yescharacteristic
32#14556501C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34#125×C73C2211yescharacteristic
35#125×C73C2211yescharacteristic
36#107×C73C2212yes—
37#106×C73C2212yes—
38C4×C8×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40C2×D292—22no—
41C2×D292—22no—
42C2×D292C2312yes—
43C2×C4×D73—22no—
44C2×C4×D73C2311yescharacteristic
45#11924017—24no—
46#11924017—24no—
47#11924011—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C8×D73—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—22no—
53#11924007—22no—
54#11924007D412yes—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005D412yes—
59C4×Dic73—22no—
60C4×Dic73C2311yescharacteristic
61C2×C8×C73C2311yescharacteristic
62C2×C8×C73C2311yescharacteristic
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73C2312yes—
66C4⋊C4×C73C2312yes—
67C42×C73C2311yescharacteristic
68C22×D73—22no—
69C22×D73C2×D411yescharacteristic
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73C2×D412yes—
73C2×C4×C73C2411yescharacteristic
74C2×Dic73—22no—
75C2×Dic73C2×D412yes—
76C2×Dic73C2×D411yescharacteristic
77D292—22no—
78D292—22no—
79D292—82no—
80D292—82no—
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—82no—
84Dic146—22no—
85Dic146—22no—
86C8×C73#4112yes—
87C8×C73#4112yes—
88#10596831—21no—
89#10596831—21no—
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#499D7311yescharacteristic, complemented
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#127—731no—
127#126—1462no—
128#125—1462no—
129#125C2×D7311yescharacteristic
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#107C2×D7312yes—
139#106C2×D7312yes—
140#103—732no—
141#103—732no—
142#102—732no—
143#102—732no—
144#97—731no—
145#97—731no—
146C4×C8—731no—
147C4×C8C2×D7311yescharacteristic
148C2×Q8—732no—
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—1462no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4C22×D7312yes—
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—1462no—
180Q8—1462no—
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—1461no—
196C8—1461no—
197C8#1192402912yes—
198C8#1192402912yes—
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—
211C4C2×#1192402911yescharacteristic
212C4C2×#1192402911yescharacteristic
213C2—2921no—
214C2—5842no—
215C2#1798913811yescharacteristic
216C2#1798939412yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#499×C73C2
socleC22×C73C22×D4
hypercenter#499D73
hypocenterC73#3174
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #17989200C2semidirect
3. #17988960C2semidirect
4. #17988957C2semidirect
5. #17988953C2semidirect
6. #17988834C2semidirect
7. #17988817C2semidirect
8. #17988686C2semidirect
9. #17988674C2semidirect
10. #17988541C2semidirect
11. #499×C73C2semidirect
109. C73#3174semidirect
112. #499D73semidirect