Finite Group Databasebeta

← #22620657

Subgroups — #22620657

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#17989116C212yesmaximal, complemented
2#17988989C211yesmaximal, characteristic, complemented
3#17988941C212yesmaximal, complemented
4#17988842C211yesmaximal, characteristic, complemented
5#17988837C211yesmaximal, characteristic
6#17988830C212yesmaximal, complemented
7#17988699C211yesmaximal, characteristic, complemented
8#17988694C211yesmaximal, characteristic, complemented
9#17988688C212yesmaximal, complemented
10C4×#11924011C211yesmaximal, characteristic, complemented
11#495×C73C211yesmaximal, characteristic, complemented
12C2×#11924011C2211yescharacteristic
13C2×#11924011C2211yescharacteristic
14#14556584—22no—
15#14556583C2212yes—
16#14556573—22no—
17#14556567C2212yes—
18#14556562C2212yes—
19Q8×Dic73C2212yes—
20D4×Dic73C2212yes—
21#14556551—22no—
22#14556547—22no—
23C42×D73C2211yescharacteristic
24#14556525C2212yes—
25#14556523C2211yescharacteristic
26#14556523C2211yescharacteristic
27#14556515C2212yes—
28#14556515C2212yes—
29#14556512C2212yes—
30#14556512C2212yes—
31#14556501C2211yescharacteristic
32#14556501C2211yescharacteristic
33C4×#10596831C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C2×SD16×C73C2212yes—
36C2×D8×C73C2211yescharacteristic
37#124×C73C2212yes—
38C4×C8×C73C2211yescharacteristic
39C2×C22⋊D73—22no—
40C22×Dic73—22no—
41C2×C4×D73D412yes—
42C2×C4×D73C2311yescharacteristic
43#11924011—22no—
44#11924011—22no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55#11924005—22no—
56C4×Dic73—22no—
57C4×Dic73D412yes—
58C4×Dic73C2311yescharacteristic
59C2×Q8×C73C2312yes—
60C2×D4×C73C2312yes—
61Q16×C73—22no—
62SD16×C73—24no—
63D8×C73—22no—
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C22⋊C4×C73—22no—
67C22⋊C4×C73—22no—
68C42×C73C2311yescharacteristic
69C23×C73—22no—
70C22×D73C2×D411yescharacteristic
71Q8×C73—22no—
72Q8×C73—22no—
73D4×C73—22no—
74D4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2411yescharacteristic
78C22⋊D73—44no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—44no—
82C2×Dic73C2×D412yes—
83C2×Dic73C2×D411yescharacteristic
84C4×D73—21no—
85C4×D73—21no—
86C4×D73—42no—
87C8×C73#4112yes—
88C8×C73#4112yes—
89#10596831—21no—
90#10596831—21no—
91C22×C73—42no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73C22×D411yescharacteristic
95C2×D73—21no—
96C2×D73—22no—
97C4×C73—22no—
98C4×C73—42no—
99C4×C73C2×#4111yescharacteristic
100C4×C73C2×#4111yescharacteristic
101Dic73—21no—
102Dic73—22no—
103Dic73—42no—
104Dic73—42no—
105C2×C73—82no—
106C2×C73#53211yescharacteristic
107C2×C73#57512yes—
108D73—41no—
109#3183—731nomaximal, Sylow
110C73#318311yescharacteristic, complemented, Sylow
111#529—732no—
112#499—731no—
113#495D7311yescharacteristic, complemented
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×Q16C2×D7311yescharacteristic
123C2×SD16C2×D7312yes—
124C2×D8C2×D7311yescharacteristic
125C2×M16—731no—
126C2×M16—731no—
127#126—1462no—
128#125—732no—
129#124C2×D7312yes—
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#107—732no—
139#106—731no—
140#106—731no—
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×Q8C22×D7312yes—
150C2×D4—1462no—
151C2×D4C22×D7312yes—
152C22×C4—732no—
153C22×C4—731no—
154C22×C4—1462no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—1462no—
159M16—1462no—
160C2×C8—731no—
161C2×C8—731no—
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—732no—
165C4⋊C4—732no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—732no—
176C42—731no—
177C42—1462no—
178C42C22×D7311yescharacteristic
179C23—22no—
180C23—731no—
181Q8—22no—
182Q8—22no—
183D4—22no—
184D4—22no—
185D4—2924no—
186C2×C4—22no—
187C2×C4—2922no—
188C2×C4—2924no—
189C2×C4—732no—
190C2×C4—731no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4D4×D7312yes—
196C2×C4C23×D7311yescharacteristic
197C8—1461no—
198C8—1461no—
199C8#1192402712yes—
200C8#1192402712yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1462no—
205C22—1461no—
206C22C2×D4×D7311yescharacteristic
207C4—22no—
208C4—42no—
209C4—2922no—
210C4—2922no—
211C4—1462no—
212C4—1461no—
213C4C2×#1192402711yescharacteristic
214C4C2×#1192402711yescharacteristic
215C2—82no—
216C2—2921no—
217C2#1798913511yescharacteristic
218C2#1798938412yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#495×C73C2
socleC22×C73C22×D4
hypercenter#495D73
hypocenterC73#3183
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17989116C2semidirect
2. #17988989C2semidirect
3. #17988941C2semidirect
4. #17988842C2semidirect
6. #17988830C2semidirect
7. #17988699C2semidirect
8. #17988694C2semidirect
9. #17988688C2semidirect
10. C4×#11924011C2semidirect
11. #495×C73C2semidirect
110. C73#3183semidirect
113. #495D73semidirect