Finite Group Databasebeta

← #22620663

Subgroups — #22620663

Order 9344.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989124C212yesmaximal, complemented
2#17988987C211yesmaximal, characteristic, complemented
3#17988972C211yesmaximal, characteristic, complemented
4#17988943C212yesmaximal, complemented
5#17988842C211yesmaximal, characteristic, complemented
6#17988841C211yesmaximal, characteristic
7#17988836C212yesmaximal, complemented
8#17988700C211yesmaximal, characteristic, complemented
9#17988685C212yesmaximal, complemented
10#17988539C211yesmaximal, characteristic, complemented
11#441×C73C211yesmaximal, characteristic, complemented
12C2×#11924015C2212yes—
13C2×D584C2211yescharacteristic
14C2×#11924011C2211yescharacteristic
15C2×#11924011C2211yescharacteristic
16#14556586—22no—
17#14556582C2212yes—
18#14556580C2212yes—
19#14556576—22no—
20#14556567C2212yes—
21#14556566C2212yes—
22C4×D292—22no—
23C4×D292C2212yes—
24#14556548—22no—
25C42×D73C2211yescharacteristic
26#14556524C2212yes—
27#14556523C2211yescharacteristic
28#14556515C2212yes—
29#14556513C2212yes—
30#14556511C2212yes—
31#14556502C2211yescharacteristic
32C8×Dic73C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2212yes—
36#106×C73C2211yescharacteristic
37#103×C73C2212yes—
38#97×C73C2211yescharacteristic
39C2×D292—22no—
40C2×D292C2312yes—
41C2×C4×D73—22no—
42C2×C4×D73D412yes—
43C2×C4×D73C2311yescharacteristic
44#11924015—24no—
45D584—22no—
46#11924011—22no—
47#11924011—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C4⋊Dic73—22no—
51C4⋊Dic73C2312yes—
52#11924007—22no—
53#11924007—22no—
54#11924005—22no—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005—22no—
59C4×Dic73D412yes—
60C4×Dic73C2311yescharacteristic
61C2×Q8×C73C2312yes—
62Q16×C73—22no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C42×C73—22no—
68C42×C73C2311yescharacteristic
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71Q8×C73—22no—
72Q8×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2411yescharacteristic
77C2×Dic73—22no—
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D412yes—
80D292—22no—
81D292—22no—
82D292—44no—
83C4×D73—21no—
84C4×D73—21no—
85C4×D73—42no—
86C4×D73—44no—
87C8×C73—21no—
88C8×C73#4112yes—
89#10596831—21no—
90#10596831#4112yes—
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#499—731no—
113#495—731no—
114#488—732no—
115#470—731no—
116#469—731no—
117#468—732no—
118#442—731no—
119#441D7311yescharacteristic, complemented
120#440—732no—
121C4×M16—731no—
122C2×Q16C2×D7311yescharacteristic
123C2×SD16—732no—
124C2×D8—731no—
125C2×M16—731no—
126C2×M16—731no—
127#126—1462no—
128#125—732no—
129#124—732no—
130#123—1462no—
131C22⋊Q8—732no—
132#121—732no—
133C4×Q8C2×D7312yes—
134C4×D4—732no—
135C4×D4—1462no—
136#117—1462no—
137C2×C42—731no—
138#107—732no—
139#106—731no—
140#106C2×D7311yescharacteristic
141#103—732no—
142#103C2×D7312yes—
143#102—732no—
144#102—732no—
145#97—731no—
146#97C2×D7311yescharacteristic
147C4×C8—731no—
148C4×C8—731no—
149C2×Q8C22×D7312yes—
150C2×D4—732no—
151C2×D4—1462no—
152C22×C4—732no—
153C22×C4—731no—
154C22×C4—1462no—
155Q16—22no—
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—732no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4C22×D7312yes—
170C22⋊C4—1462no—
171C22⋊C4—1462no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C42—22no—
176C42—732no—
177C42—731no—
178C42C22×D7311yescharacteristic
179C23—731no—
180C23—1462no—
181Q8—22no—
182Q8—22no—
183D4—2924no—
184D4—1462no—
185D4—1462no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—2924no—
189C2×C4—2922no—
190C2×C4—732no—
191C2×C4—731no—
192C2×C4—1462no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4D4×D7312yes—
196C2×C4C23×D7311yescharacteristic
197C8—21no—
198C8—732no—
199C8—1461no—
200C8#1192402812yes—
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—
213C4#41×D7311yescharacteristic
214C4C2×#1192402811yescharacteristic
215C2—2921no—
216C2—5842no—
217C2#1798913411yescharacteristic
218C2#1798938612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#441×C73C2
socleC22×C73C22×D4
hypercenter#441D73
hypocenterC73#3183
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #17989124C2semidirect
2. #17988987C2semidirect
3. #17988972C2semidirect
4. #17988943C2semidirect
5. #17988842C2semidirect
7. #17988836C2semidirect
8. #17988700C2semidirect
9. #17988685C2semidirect
10. #17988539C2semidirect
11. #441×C73C2semidirect
110. C73#3183semidirect
119. #441D73semidirect