Finite Group Databasebeta

← #22620662

Subgroups — #22620662

Order 9344.

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

normal subgroups only

This group has 370 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#17989122C212yesmaximal, complemented
2#17988971C211yesmaximal, characteristic, complemented
3#17988944C212yesmaximal, complemented
4#17988846C211yesmaximal, characteristic, complemented
5#17988841C211yesmaximal, characteristic
6#17988834C212yesmaximal, complemented
7#17988698C211yesmaximal, characteristic, complemented
8#17988693C211yesmaximal, characteristic, complemented
9#17988686C212yesmaximal, complemented
10C4×#11924011C211yesmaximal, characteristic, complemented
11#499×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×#11924017C2212yes—
14C2×D584C2211yescharacteristic
15C2×#11924011C2211yescharacteristic
16C2×#11924011C2211yescharacteristic
17#14556586—22no—
18#14556579C2212yes—
19#14556576—22no—
20#14556571C2212yes—
21#14556566C2212yes—
22#14556556C2212yes—
23#14556553—22no—
24#14556553C2212yes—
25#14556549—22no—
26C42×D73C2211yescharacteristic
27#14556514C2212yes—
28#14556514C2212yes—
29#14556511C2212yes—
30#14556511C2212yes—
31#14556501C2211yescharacteristic
32#14556501C2211yescharacteristic
33C4×#10596831C2211yescharacteristic
34#125×C73C2212yes—
35#107×C73C2212yes—
36#106×C73C2211yescharacteristic
37#106×C73C2211yescharacteristic
38C4×C8×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40C2×D292—22no—
41C2×D292C2312yes—
42C2×C4×D73—22no—
43C2×C4×D73D412yes—
44C2×C4×D73C2311yescharacteristic
45Dic292—22no—
46#11924017—24no—
47D584—22no—
48#11924011—22no—
49#11924011—22no—
50C2×#10596831C2311yescharacteristic
51C2×#10596831C2311yescharacteristic
52C4⋊Dic73—22no—
53#11924007—22no—
54#11924005—22no—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005—22no—
59C4×Dic73—22no—
60C4×Dic73D412yes—
61C4×Dic73C2311yescharacteristic
62C2×C8×C73C2311yescharacteristic
63C2×C8×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C4⋊C4×C73C2312yes—
68C42×C73C2311yescharacteristic
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73C2×D412yes—
74C2×C4×C73C2411yescharacteristic
75C2×Dic73—22no—
76C2×Dic73C2×D412yes—
77C2×Dic73C2×D411yescharacteristic
78D292—22no—
79D292—22no—
80D292—44no—
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—42no—
84C4×D73—44no—
85Dic146—22no—
86Dic146—22no—
87C8×C73#4112yes—
88C8×C73#4112yes—
89#10596831—21no—
90#10596831—21no—
91C22×C73C22×D411yescharacteristic
92C2×D73—21no—
93C2×D73—22no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C4×C73—22no—
98C4×C73—42no—
99C4×C73—42no—
100C4×C73C2×#4111yescharacteristic
101C4×C73C2×#4111yescharacteristic
102Dic73—21no—
103Dic73—22no—
104Dic73—42no—
105C2×C73#53211yescharacteristic
106C2×C73#57512yes—
107D73—41no—
108D73—82no—
109#3183—731nomaximal, Sylow
110C73#318311yescharacteristic, complemented, Sylow
111#529—732no—
112#499D7311yescharacteristic, complemented
113#495—731no—
114#488—732no—
115#470—731no—
116#469—731no—
117#468—732no—
118#442—731no—
119#441—731no—
120#440—732no—
121C4×M16—731no—
122C2×Q16—731no—
123C2×SD16—732no—
124C2×D8—731no—
125C2×M16—731no—
126C2×M16—731no—
127#126—1462no—
128#125C2×D7312yes—
129#124—732no—
130#123—1462no—
131C22⋊Q8—732no—
132#121—732no—
133C4×Q8—732no—
134C4×D4—732no—
135C4×D4—1462no—
136#117—1462no—
137C2×C42—731no—
138#107C2×D7312yes—
139#106C2×D7311yescharacteristic
140#106C2×D7311yescharacteristic
141#103—732no—
142#103—732no—
143#102—732no—
144#102—732no—
145#97—731no—
146#97—731no—
147C4×C8—731no—
148C4×C8C2×D7311yescharacteristic
149C2×Q8—732no—
150C2×D4—732no—
151C2×D4—1462no—
152C22×C4—732no—
153C22×C4—731no—
154C22×C4—1462no—
155Q16—1462no—
156SD16—1464no—
157D8—1462no—
158M16—1462no—
159M16—1462no—
160C2×C8—731no—
161C2×C8—731no—
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4C22×D7312yes—
169C4⋊C4C22×D7312yes—
170C22⋊C4—1462no—
171C22⋊C4—1462no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—732no—
176C42—731no—
177C42—1462no—
178C42C22×D7311yescharacteristic
179C23—731no—
180C23—1462no—
181Q8—1462no—
182Q8—1462no—
183D4—2924no—
184D4—1462no—
185D4—1462no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—2922no—
189C2×C4—2924no—
190C2×C4—732no—
191C2×C4—731no—
192C2×C4—1462no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4D4×D7312yes—
196C2×C4C23×D7311yescharacteristic
197C8—1461no—
198C8—1461no—
199C8#1192402912yes—
200C8#1192402912yes—
201C22—2922no—
202C22—2922no—
203C22—2922no—
204C22—1462no—
205C22—1461no—
206C22C2×D4×D7311yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—2922no—
211C4—1462no—
212C4—1461no—
213C4C2×#1192402911yescharacteristic
214C4C2×#1192402911yescharacteristic
215C2—2921no—
216C2—5842no—
217C2#1798913811yescharacteristic
218C2#1798938412yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#499×C73C2
socleC22×C73C22×D4
hypercenter#499D73
hypocenterC73#3183
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. #17989122C2semidirect
2. #17988971C2semidirect
3. #17988944C2semidirect
4. #17988846C2semidirect
6. #17988834C2semidirect
7. #17988698C2semidirect
8. #17988693C2semidirect
9. #17988686C2semidirect
10. C4×#11924011C2semidirect
11. #499×C73C2semidirect
110. C73#3183semidirect
112. #499D73semidirect