Finite Group Databasebeta

← #22619597

Subgroups — #22619597

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×#14556597C211yesmaximal, characteristic, complemented
2#17989165C212yesmaximal, complemented
3#17988830C214yesmaximal, complemented
4#17988825C212yesmaximal, complemented
5#17988820C212yesmaximal, complemented
6C2×#14556525C211yesmaximal, characteristic, complemented
7#17988588C212yesmaximal, complemented
8C2×#135×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2211yescharacteristic
10#14556597—24no—
11C2×#11924012C2211yescharacteristic
12C2×#11924011C2212yes—
13C2×C8×D73C2212yes—
14#14556570—22no—
15#14556567C2214yes—
16#14556565—22no—
17#14556563—24no—
18#14556562C2214yes—
19C2×C4⋊Dic73C2212yes—
20#14556525C2212yes—
21#14556525C2212yes—
22#14556515C2214yes—
23#14556512C2214yes—
24C2×#41×C73C2212yes—
25#135×C73—24no—
26C2×Q16×C73C2211yescharacteristic
27C2×SD16×C73C2212yes—
28C2×D8×C73C2211yescharacteristic
29C22×C8×C73C2211yescharacteristic
30#11924028—22no—
31#11924028—22no—
32C2×Dic146D411yescharacteristic
33C2×D292D411yescharacteristic
34C2×C22⋊D73—24no—
35C2×C22⋊D73D412yes—
36C22×Dic73—22no—
37C2×C4×D73C2312yes—
38#11924012—22no—
39#11924011—24no—
40C2×#10596831C2312yes—
41C8×D73—24no—
42C4⋊Dic73—22no—
43C4⋊Dic73C2314yes—
44#11924007—24no—
45C22⋊Dic73—24no—
46#11924005—24no—
47#41×C73—24no—
48#41×C73—24no—
49C2×Q8×C73C2312yes—
50C2×D4×C73—22no—
51C2×D4×C73C2312yes—
52C22×C4×C73—22no—
53C22×C4×C73C2311yescharacteristic
54Q16×C73—22no—
55SD16×C73—24no—
56D8×C73—22no—
57C2×C8×C73D414yescomplemented
58C2×C8×C73C2311yescharacteristic
59C2×C8×C73C2311yescharacteristic
60C23×C73—22no—
61C23×C73C2×D411yescharacteristic
62C22×D73C2×D412yes—
63Q8×C73—22no—
64Q8×C73—22no—
65D4×C73—22no—
66D4×C73—22no—
67D4×C73—44no—
68C2×C4×C73—22no—
69C2×C4×C73—44no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D412yes—
72C2×C4×C73#4112yes—
73C2×C4×C73C2411yescharacteristic
74C22⋊D73—24no—
75C22⋊D73—84no—
76C2×Dic73—24no—
77C2×Dic73—82no—
78C2×Dic73C2×D412yes—
79D292—22no—
80C4×D73—22no—
81C4×D73—22no—
82Dic146—22no—
83C8×C73C2×D412yes—
84C8×C73C2×D412yes—
85#10596831—22no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73—42no—
91C22×C73#12112yes—
92C22×C73C22×D411yescharacteristic
93C2×D73—22no—
94C2×D73—22no—
95C2×D73—22no—
96C4×C73—42no—
97C4×C73#12112yes—
98C4×C73C22×D411yescharacteristic
99C4×C73C2×#4111yescharacteristic
100Dic73—22no—
101Dic73—44no—
102C2×C73—22no—
103C2×C73—82no—
104C2×C73C2×#12111yescharacteristic
105C2×C73#57611yescharacteristic
106C2×C73#57811yescharacteristic
107D73—42no—
108#3061—731nomaximal, Sylow
109C73#306111yescharacteristic, complemented, Sylow
110C2×#135D7311yescharacteristic, complemented
111C2×#131—731no—
112#537—732no—
113#468—734no—
114#467—732no—
115#466—732no—
116C2×#107—731no—
117#417—732no—
118C2×#41—731no—
119C2×#41C2×D7312yes—
120#135—24no—
121C2×Q16C2×D7311yescharacteristic
122C2×SD16C2×D7312yes—
123C2×D8C2×D7311yescharacteristic
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⋊C4—732no—
135#107—732no—
136#107—732no—
137#103—734no—
138#102—734no—
139#41—24no—
140#41—24no—
141#41—1462no—
142#41—1462no—
143C2×Q8—731no—
144C2×Q8C22×D7312yes—
145C2×D4—22no—
146C2×D4—732no—
147C2×D4—731no—
148C2×D4—1464no—
149C2×D4C22×D7312yes—
150C22×C4—22no—
151C22×C4—732no—
152C22×C4—1462no—
153C22×C4C22×D7311yescharacteristic
154Q16—22no—
155SD16—24no—
156D8—22no—
157M16—1462no—
158M16—1464no—
159C2×C8—732no—
160C2×C8—1464no—
161C2×C8C22⋊D7314yescomplemented
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—734no—
165C4⋊C4—1464no—
166C4⋊C4—1462no—
167C22⋊C4—1464no—
168C22⋊C4—1464no—
169C23—22no—
170C23—732no—
171C23D4×D7311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—1462no—
175D4—22no—
176D4—22no—
177D4—44no—
178D4—5844no—
179D4—1464no—
180D4—1462no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—5842no—
184C2×C4—732no—
185C2×C4—1464no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4D4×D7311yescharacteristic
189C2×C4C2×C22⋊D7312yes—
190C2×C4#1192402712yes—
191C2×C4C23×D7311yescharacteristic
192C8—1462no—
193C8C2×C22⋊D7312yes—
194C8C2×C22⋊D7312yes—
195C22—21no—
196C22—21no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—1462no—
201C22—1462no—
202C22—1462no—
203C22#1455656212yes—
204C22C2×D4×D7311yescharacteristic
205C4—42no—
206C4—2924no—
207C4—1462no—
208C4#1455656212yes—
209C4C22×C22⋊D7311yescharacteristic
210C4C2×#1192402711yescharacteristic
211C2—22no—
212C2—82no—
213C2—2922no—
214C2C2×#1455656211yescharacteristic
215C2#1798938911yescharacteristic
216C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#135×C73C2
socleC22×C73C22×D4
hypercenterC2×#135D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14556597C2semidirect
2. #17989165C2semidirect
3. #17988830C2semidirect
4. #17988825C2semidirect
5. #17988820C2semidirect
6. C2×#14556525C2semidirect
7. #17988588C2semidirect
8. C2×#135×C73C2semidirect
57. C2×C8×C73D4semidirect
109. C73#3061semidirect
110. C2×#135D73semidirect
161. C2×C8C22⋊D73semidirect