Finite Group Databasebeta

← #49130927

Subgroups — #49130927

Order 36224.

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×#22583616C211yesmaximal, characteristic, complemented
2#31827043C212yesmaximal, complemented
3#31826708C214yesmaximal, complemented
4#31826703C212yesmaximal, complemented
5#31826698C212yesmaximal, complemented
6C2×#22583544C211yesmaximal, characteristic, complemented
7#31826466C212yesmaximal, complemented
8C2×#135×C283C211yesmaximal, characteristic, complemented
9C2×#17985392C2211yescharacteristic
10#22583616—24no—
11C2×#17985376C2211yescharacteristic
12C2×#17985375C2212yes—
13C2×C8×D283C2212yes—
14#22583589—22no—
15#22583586C2214yes—
16#22583584—22no—
17#22583582—24no—
18#22583581C2214yes—
19C2×C4⋊Dic283C2212yes—
20#22583544C2212yes—
21#22583544C2212yes—
22#22583534C2214yes—
23#22583531C2214yes—
24C2×#41×C283C2212yes—
25#135×C283—24no—
26C2×Q16×C283C2211yescharacteristic
27C2×SD16×C283C2212yes—
28C2×D8×C283C2211yescharacteristic
29C22×C8×C283C2211yescharacteristic
30#17985392—22no—
31#17985392—22no—
32C2×Dic566D411yescharacteristic
33C2×D1132D411yescharacteristic
34C2×C22⋊D283—24no—
35C2×C22⋊D283D412yes—
36C22×Dic283—22no—
37C2×C4×D283C2312yes—
38#17985376—22no—
39#17985375—24no—
40C2×C283⋊C8C2312yes—
41C8×D283—24no—
42C4⋊Dic283—22no—
43C4⋊Dic283C2314yes—
44Dic283⋊C4—24no—
45C22⋊Dic283—24no—
46(C2×D283)⋊C4—24no—
47#41×C283—24no—
48#41×C283—24no—
49C2×Q8×C283C2312yes—
50C2×D4×C283—22no—
51C2×D4×C283C2312yes—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54Q16×C283—22no—
55SD16×C283—24no—
56D8×C283—22no—
57C2×C8×C283D414yescomplemented
58C2×C8×C283C2311yescharacteristic
59C2×C8×C283C2311yescharacteristic
60C22×D283C2×D412yes—
61Dic566—22no—
62D1132—22no—
63C22⋊D283—24no—
64C22⋊D283—84no—
65C2×Dic283—24no—
66C2×Dic283—82no—
67C2×Dic283C2×D412yes—
68C4×D283—22no—
69C4×D283—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283C2×D411yescharacteristic
73Q8×C283—22no—
74Q8×C283—22no—
75D4×C283—22no—
76D4×C283—22no—
77D4×C283—44no—
78C2×C4×C283—22no—
79C2×C4×C283—44no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283C2×D412yes—
85C8×C283C2×D412yes—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283—42no—
89C22×C283—42no—
90C22×C283—42no—
91C22×C283#12112yes—
92C22×C283C22×D411yescharacteristic
93C2×D283—22no—
94C2×D283—22no—
95C2×D283—22no—
96C4×C283—42no—
97C4×C283#12112yes—
98C4×C283C22×D411yescharacteristic
99C4×C283C2×#4111yescharacteristic
100Dic283—22no—
101Dic283—44no—
102C2×C283—22no—
103C2×C283—82no—
104C2×C283C2×#12111yescharacteristic
105C2×C283#57611yescharacteristic
106C2×C283#57811yescharacteristic
107D283—42no—
108C283#306111yescharacteristic, complemented, Sylow
109#3061—2831nomaximal, Sylow
110C2×#135D28311yescharacteristic, complemented
111C2×#131—2831no—
112#537—2832no—
113#468—2834no—
114#467—2832no—
115#466—2832no—
116C2×#107—2831no—
117#417—2832no—
118C2×#41—2831no—
119C2×#41C2×D28312yes—
120#135—24no—
121C2×Q16C2×D28311yescharacteristic
122C2×SD16C2×D28312yes—
123C2×D8C2×D28311yescharacteristic
124#131—5664no—
125C2×M16—2831no—
126C2×M16—2832no—
127C22×C8—2832no—
128C22×C8C2×D28311yescharacteristic
129C22⋊Q8—2834no—
130C22⋊Q8—5662no—
131#121—2834no—
132#121—5662no—
133#121—5664no—
134C2×C4⋊C4—2832no—
135#107—2832no—
136#107—2832no—
137#103—2834no—
138#102—2834no—
139#41—24no—
140#41—24no—
141#41—5662no—
142#41—5662no—
143C2×Q8—2831no—
144C2×Q8C22×D28312yes—
145C2×D4—22no—
146C2×D4—2832no—
147C2×D4—2831no—
148C2×D4—5664no—
149C2×D4C22×D28312yes—
150C22×C4—22no—
151C22×C4—2832no—
152C22×C4—5662no—
153C22×C4C22×D28311yescharacteristic
154Q16—22no—
155SD16—24no—
156D8—22no—
157M16—5662no—
158M16—5664no—
159C2×C8—2832no—
160C2×C8—5664no—
161C2×C8C22⋊D28314yescomplemented
162C2×C8C22×D28311yescharacteristic
163C2×C8C22×D28311yescharacteristic
164C4⋊C4—2834no—
165C4⋊C4—5664no—
166C4⋊C4—5662no—
167C22⋊C4—5664no—
168C22⋊C4—5664no—
169C23—22no—
170C23—2832no—
171C23D4×D28311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—5662no—
175D4—22no—
176D4—22no—
177D4—44no—
178D4—5664no—
179D4—5662no—
180D4—22644no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—2832no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—5664no—
187C2×C4—22642no—
188C2×C4D4×D28311yescharacteristic
189C2×C4C2×C22⋊D28312yes—
190C2×C4#1798539112yes—
191C2×C4C23×D28311yescharacteristic
192C8—5662no—
193C8C2×C22⋊D28312yes—
194C8C2×C22⋊D28312yes—
195C22—21no—
196C22—21no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—5662no—
201C22—5662no—
202C22—5662no—
203C22#2258358112yes—
204C22C2×D4×D28311yescharacteristic
205C4—42no—
206C4—5662no—
207C4—11324no—
208C4#2258358112yes—
209C4C22×C22⋊D28311yescharacteristic
210C4C2×#1798539111yescharacteristic
211C2—22no—
212C2—82no—
213C2—11322no—
214C2C2×#2258358111yescharacteristic
215C2#3182726711yescharacteristic
216C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3061
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22583616C2semidirect
2. #31827043C2semidirect
3. #31826708C2semidirect
4. #31826703C2semidirect
5. #31826698C2semidirect
6. C2×#22583544C2semidirect
7. #31826466C2semidirect
8. C2×#135×C283C2semidirect
57. C2×C8×C283D4semidirect
108. C283#3061semidirect
110. C2×#135D283semidirect
161. C2×C8C22⋊D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#225836162
#318270432
#318267082
#318267032
#318266982
C2×#225835442
#318264662
C2×#135×C2832
#3061283