Finite Group Databasebeta

← #22619601

Subgroups — #22619601

Order 9344.

484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14556613C211yesmaximal, characteristic, complemented
2#17989165C212yesmaximal, complemented
3#17988833C214yesmaximal, complemented
4#17988828C212yesmaximal, complemented
5#17988823C212yesmaximal, complemented
6C2×#14556525C211yesmaximal, characteristic, complemented
7#17988589C212yesmaximal, complemented
8C2×#131×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2212yes—
10#14556613—24no—
11C2×Dic292C2211yescharacteristic
12C2×#11924017C2212yes—
13C2×D584C2211yescharacteristic
14#14556570C2214yes—
15#14556567—22no—
16#14556565C2214yes—
17#14556563—24no—
18#14556562—22no—
19C2×C4⋊Dic73C2212yes—
20#14556525C2212yes—
21#14556525C2212yes—
22#14556516C2214yes—
23#14556513C2214yes—
24C2×#41×C73C2211yescharacteristic
25#131×C73—24no—
26C2×M16×C73C2212yes—
27C2×M16×C73C2211yescharacteristic
28C22×C8×C73C2212yes—
29C22×C8×C73C2211yescharacteristic
30#11924028—24no—
31#11924028—24no—
32C2×Dic146C2312yes—
33C2×D292C2312yes—
34C2×C22⋊D73—22no—
35C2×C22⋊D73—24no—
36C22×Dic73—22no—
37C2×C4×D73—22no—
38Dic292—22no—
39#11924017—24no—
40D584—22no—
41C4⋊Dic73—22no—
42C4⋊Dic73C2314yes—
43#11924007—24no—
44C22⋊Dic73—24no—
45#11924005—24no—
46#41×C73—22no—
47#41×C73—22no—
48C2×Q8×C73D411yescharacteristic
49C2×D4×C73D411yescharacteristic
50C2×D4×C73D412yes—
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53M16×C73—22no—
54M16×C73—24no—
55C2×C8×C73—24no—
56C2×C8×C73D414yescomplemented
57C2×C8×C73C2312yes—
58C2×C8×C73C2311yescharacteristic
59C2×C8×C73C2311yescharacteristic
60C23×C73C2×D412yes—
61C23×C73C2×D411yescharacteristic
62C22×D73—22no—
63Q8×C73—22no—
64D4×C73—24no—
65D4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73C2×D412yes—
69C2×C4×C73C2×D412yes—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4112yes—
72C2×C4×C73C2411yescharacteristic
73C22⋊D73—44no—
74C22⋊D73—84no—
75C2×Dic73—24no—
76C2×Dic73—22no—
77C2×Dic73—82no—
78D292—22no—
79D292—22no—
80C4×D73—44no—
81Dic146—22no—
82Dic146—22no—
83C8×C73—22no—
84C8×C73C2×D412yes—
85C8×C73C2×D412yes—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—22no—
89C22×C73—22no—
90C22×C73—22no—
91C22×C73#12112yes—
92C22×C73C22×D411yescharacteristic
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—22no—
97C4×C73#12112yes—
98C4×C73C22×D411yescharacteristic
99C4×C73C2×#4111yescharacteristic
100Dic73—42no—
101Dic73—44no—
102C2×C73—22no—
103C2×C73—42no—
104C2×C73C2×#12111yescharacteristic
105C2×C73#57611yescharacteristic
106C2×C73#57811yescharacteristic
107D73—82no—
108#3061—731nomaximal, Sylow
109C73#306111yescharacteristic, complemented, Sylow
110C2×#135—731no—
111C2×#131D7311yescharacteristic, complemented
112#537—732no—
113#468—734no—
114#467—732no—
115#466—732no—
116C2×#107—731no—
117#417—732no—
118C2×#41—732no—
119C2×#41C2×D7311yescharacteristic
120#135—1464no—
121C2×Q16—731no—
122C2×SD16—732no—
123C2×D8—731no—
124#131—24no—
125C2×M16C2×D7311yescharacteristic
126C2×M16C2×D7312yes—
127C22×C8C2×D7312yes—
128C22×C8C2×D7311yescharacteristic
129C22⋊Q8—734no—
130C22⋊Q8—1462no—
131#121—734no—
132#121—1462no—
133#121—1464no—
134C2×C4⋊C4—732no—
135#107—732no—
136#107—732no—
137#103—734no—
138#102—734no—
139#41—22no—
140#41—22no—
141#41—1464no—
142#41—1464no—
143C2×Q8—732no—
144C2×Q8D29211yescharacteristic
145C2×D4—732no—
146C2×D4—1462no—
147C2×D4—1464no—
148C2×D4D29212yes—
149C2×D4D29211yescharacteristic
150C22×C4—1462no—
151C22×C4—1462no—
152C22×C4C22×D7312yes—
153C22×C4C22×D7311yescharacteristic
154Q16—1462no—
155SD16—1464no—
156D8—1462no—
157M16—22no—
158M16—24no—
159C2×C8—24no—
160C2×C8C22⋊D7314yescomplemented
161C2×C8C22×D7312yes—
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—734no—
165C4⋊C4—1464no—
166C4⋊C4—1462no—
167C22⋊C4—1464no—
168C22⋊C4—1464no—
169C23—1462no—
170C23C2×D29212yes—
171C23C2×D29211yescharacteristic
172Q8—22no—
173Q8—1462no—
174Q8—1462no—
175D4—24no—
176D4—22no—
177D4—2924no—
178D4—5844no—
179D4—1462no—
180D4—1462no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—2924no—
184C2×C4—5842no—
185C2×C4—1464no—
186C2×C4—1462no—
187C2×C4C2×C22⋊D7312yes—
188C2×C4C2×D29212yes—
189C2×C4C2×D29211yescharacteristic
190C2×C4#1192402812yes—
191C2×C4C23×D7311yescharacteristic
192C8—22no—
193C8C2×C22⋊D7312yes—
194C8C2×C22⋊D7312yes—
195C22—21no—
196C22—21no—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—2922no—
201C22—2922no—
202C22—2922no—
203C22#1455656512yes—
204C22C22×D29211yescharacteristic
205C4—22no—
206C4—2924no—
207C4—2922no—
208C4#1455656512yes—
209C4C22×C22⋊D7311yescharacteristic
210C4C2×#1192402811yescharacteristic
211C2—22no—
212C2—42no—
213C2—5842no—
214C2C2×#1455656511yescharacteristic
215C2#1798939211yescharacteristic
216C2#1798940411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#131×C73C2
socleC22×C73C22×D4
hypercenterC2×#131D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#14556613C2semidirect
2. #17989165C2semidirect
3. #17988833C2semidirect
4. #17988828C2semidirect
5. #17988823C2semidirect
6. C2×#14556525C2semidirect
7. #17988589C2semidirect
8. C2×#131×C73C2semidirect
56. C2×C8×C73D4semidirect
109. C73#3061semidirect
111. C2×#131D73semidirect
160. C2×C8C22⋊D73semidirect