Finite Group Databasebeta

← #22619603

Subgroups — #22619603

Order 9344.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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
2C2×#14556597C211yesmaximal, characteristic, complemented
3#17989168C212yesmaximal, complemented
4#17988834C214yesmaximal, complemented
5#17988829C212yesmaximal, complemented
6#17988824C212yesmaximal, complemented
7#17988586C212yesmaximal, complemented
8C2×#107×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2212yes—
10C2×#11924028C2211yescharacteristic
11#14556613—24no—
12C2×Dic292C2211yescharacteristic
13C2×#11924017C2212yes—
14C2×D584C2211yescharacteristic
15#14556597—24no—
16C2×#11924012C2211yescharacteristic
17C2×#11924011C2212yes—
18C2×C8×D73C2212yes—
19#14556571—22no—
20#14556571C2214yes—
21#14556566—22no—
22#14556566C2214yes—
23#14556565—24no—
24#14556514C2214yes—
25#14556511C2214yes—
26C22×C8×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2212yes—
28#107×C73C2212yes—
29#107×C73C2212yes—
30#11924028—22no—
31#11924028—22no—
32#11924028—24no—
33#11924028—24no—
34C2×Dic146D411yescharacteristic
35C2×Dic146C2312yes—
36C2×D292—24no—
37C2×D292D411yescharacteristic
38C2×D292C2312yes—
39C2×C22⋊D73—22no—
40C2×C22⋊D73D412yes—
41C2×C4×D73—22no—
42C2×C4×D73C2312yes—
43Dic292—22no—
44#11924017—24no—
45D584—22no—
46#11924012—22no—
47#11924011—24no—
48C2×#10596831C2312yes—
49C8×D73—24no—
50C4⋊Dic73—24no—
51#11924005—24no—
52#11924005—24no—
53C22×C4×C73—22no—
54C22×C4×C73C2311yescharacteristic
55C2×C8×C73D414yescomplemented
56C2×C8×C73C2311yescharacteristic
57C2×C8×C73C2311yescharacteristic
58C4⋊C4×C73—22no—
59C4⋊C4×C73C2314yes—
60C23×C73C2×D411yescharacteristic
61C22×D73—22no—
62C22×D73C2×D412yes—
63C2×C4×C73—24no—
64C2×C4×C73—82no—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D412yes—
67C2×C4×C73#4112yes—
68C2×C4×C73C2411yescharacteristic
69C22⋊D73—24no—
70C22⋊D73—44no—
71C2×Dic73—22no—
72C2×Dic73C2×D412yes—
73D292—22no—
74D292—22no—
75D292—22no—
76D292—84no—
77C4×D73—22no—
78C4×D73—22no—
79C4×D73—44no—
80Dic146—22no—
81Dic146—22no—
82Dic146—22no—
83C8×C73C2×D412yes—
84C8×C73C2×D412yes—
85#10596831—22no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73#12112yes—
89C22×C73C22×D411yescharacteristic
90C2×D73—22no—
91C2×D73—22no—
92C2×D73—22no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—44no—
97C4×C73#12112yes—
98C4×C73C22×D411yescharacteristic
99C4×C73C2×#4111yescharacteristic
100Dic73—22no—
101Dic73—42no—
102C2×C73—22no—
103C2×C73C2×#12111yescharacteristic
104C2×C73#57611yescharacteristic
105C2×C73#57811yescharacteristic
106D73—42no—
107D73—82no—
108#3061—731nomaximal, Sylow
109C73#306111yescharacteristic, complemented, Sylow
110C2×#135—731no—
111C2×#131—731no—
112#537—732no—
113#468—734no—
114#467—732no—
115#466—732no—
116C2×#107D7311yescharacteristic, complemented
117#417—732no—
118C2×#41—731no—
119C2×#41—732no—
120#135—1464no—
121C2×Q16—731no—
122C2×SD16—732no—
123C2×D8—731no—
124#131—1464no—
125C2×M16—731no—
126C2×M16—732no—
127C22×C8—732no—
128C22×C8C2×D7311yescharacteristic
129C22⋊Q8—734no—
130C22⋊Q8—1462no—
131#121—734no—
132#121—1462no—
133#121—1464no—
134C2×C4⋊C4C2×D7312yes—
135#107C2×D7312yes—
136#107C2×D7312yes—
137#103—734no—
138#102—734no—
139#41—1464no—
140#41—1464no—
141#41—1462no—
142#41—1462no—
143C2×Q8—731no—
144C2×Q8—732no—
145C2×D4—732no—
146C2×D4—731no—
147C2×D4—732no—
148C2×D4—1464no—
149C2×D4—1462no—
150C22×C4—22no—
151C22×C4—732no—
152C22×C4—1462no—
153C22×C4C22×D7311yescharacteristic
154Q16—1462no—
155SD16—1464no—
156D8—1462no—
157M16—1462no—
158M16—1464no—
159C2×C8—732no—
160C2×C8—1464no—
161C2×C8D29214yescomplemented
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—1464no—
166C4⋊C4C22×D7314yes—
167C22⋊C4—1464no—
168C22⋊C4—1464no—
169C23—732no—
170C23—1462no—
171C23D4×D7311yescharacteristic
172Q8—1462no—
173Q8—1462no—
174Q8—1462no—
175D4—2924no—
176D4—5844no—
177D4—1464no—
178D4—1462no—
179D4—1462no—
180D4—1462no—
181C2×C4—24no—
182C2×C4—82no—
183C2×C4—2924no—
184C2×C4—732no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4D4×D7311yescharacteristic
189C2×C4C2×D29212yes—
190C2×C4#1192402912yes—
191C2×C4C23×D7311yescharacteristic
192C8—1462no—
193C8C2×D29212yes—
194C8C2×D29212yes—
195C22—21no—
196C22—21no—
197C22—2922no—
198C22—2922no—
199C22—2922no—
200C22—1462no—
201C22—1462no—
202C22—1462no—
203C22#1455656612yes—
204C22C2×D4×D7311yescharacteristic
205C4—44no—
206C4—2922no—
207C4—1462no—
208C4#1455656612yes—
209C4C22×D29211yescharacteristic
210C4C2×#1192402911yescharacteristic
211C2—22no—
212C2—2922no—
213C2—5842no—
214C2C2×#1455656611yescharacteristic
215C2#1798938811yescharacteristic
216C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#107×C73C2
socleC22×C73C22×D4
hypercenterC2×#107D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14556613C2semidirect
2. C2×#14556597C2semidirect
3. #17989168C2semidirect
4. #17988834C2semidirect
5. #17988829C2semidirect
6. #17988824C2semidirect
7. #17988586C2semidirect
8. C2×#107×C73C2semidirect
55. C2×C8×C73D4semidirect
109. C73#3061semidirect
116. C2×#107D73semidirect
161. C2×C8D292semidirect