Finite Group Databasebeta

← #49130843

Subgroups — #49130843

Order 36224.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22583632C211yesmaximal, characteristic, complemented
2C22×C8×D283C211yesmaximal, characteristic, complemented
3#31826977C212yesmaximal, complemented
4#31826707C212yesmaximal, complemented
5#31826702C212yesmaximal, complemented
6#31826695C214yesmaximal, complemented
7#31826459C212yesmaximal, complemented
8#427×C283C211yesmaximal, characteristic, complemented
9C2×#17985392C2212yes—
10C22×C4×D283C2211yescharacteristic
11#22583632—24no—
12C2×Dic1132C2211yescharacteristic, complemented
13C2×#17985381C2212yescomplemented
14C2×D2264C2211yescharacteristic, complemented
15C22×C283⋊C8C2211yescharacteristic
16C2×C8×D283—24no—
17C2×C8×D283C2212yes—
18C2×C8×D283C2212yes—
19#22583594—22no—
20#22583590C2214yes—
21#22583585C2214yes—
22#22583580—22no—
23C4×D1132—24no—
24#22583533C2214yescomplemented
25#22583530C2214yescomplemented
26C22×C8×C283C2211yescharacteristic
27#117×C283C2212yes—
28#107×C283C2212yescomplemented
29#106×C283C2212yescomplemented
30C23×D283D411yescharacteristic
31#17985392—24no—
32#17985392—24no—
33C2×Dic566C2312yes—
34C2×D1132—24no—
35C2×D1132C2312yes—
36C2×C22⋊D283—22no—
37C22×Dic283D411yescharacteristic
38C2×C4×D283—22no—
39C2×C4×D283—22no—
40C2×C4×D283—22no—
41C2×C4×D283D412yes—
42C2×C4×D283C2312yes—
43Dic1132—22no—
44#17985381—24no—
45D2264—22no—
46C2×C283⋊C8—22no—
47C2×C283⋊C8C2312yes—
48C8×D283—24no—
49C8×D283—24no—
50C4⋊Dic283—24no—
51(C2×D283)⋊C4—24no—
52(C2×D283)⋊C4—24no—
53C22×C4×C283C2311yescharacteristic
54C2×C8×C283D414yescomplemented
55C2×C8×C283C2311yescharacteristic
56C2×C8×C283C2311yescharacteristic
57C4⋊C4×C283C2314yes—
58C22⋊C4×C283—22no—
59C42×C283—22no—
60C22×D283—22no—
61C22×D283—24no—
62C22×D283—22no—
63C22×D283C2×D412yes—
64Dic566—22no—
65Dic566—22no—
66D1132—22no—
67D1132—22no—
68D1132—48no—
69C22⋊D283—44no—
70C2×Dic283—22no—
71C2×Dic283—22no—
72C2×Dic283C2×D412yes—
73C4×D283—24no—
74C4×D283—22no—
75C4×D283—22no—
76C4×D283—44no—
77C283⋊C8—22no—
78C23×C283C2×D411yescharacteristic
79C2×C4×C283—24no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283C2×D412yes—
85C8×C283C2×D412yes—
86C22×C283—22no—
87C22×C283#12112yes—
88C22×C283C22×D411yescharacteristic
89C2×D283—28no—
90C2×D283—22no—
91C2×D283—22no—
92C2×D283—42no—
93C2×D283—44no—
94C2×D283#13514yescomplemented
95C4×C283—44no—
96C4×C283#12112yes—
97C4×C283C22×D411yescharacteristic
98C4×C283C2×#4111yescharacteristic
99Dic283—22no—
100Dic283—42no—
101C2×C283—22no—
102C2×C283C2×#12111yescharacteristic
103C2×C283C2×#13512yes—
104D283—24no—
105D283—82no—
106C283#305011yescharacteristic, complemented, Sylow
107#3050—2831nomaximal, Sylow
108C2×#135—2831no—
109C23×C8—2831no—
110#525—2832no—
111#467—2832no—
112#466—2832no—
113#465—2834no—
114#427D28311yescharacteristic, complemented
115#416—2832no—
116C2×#41—2832no—
117C23×C4—2831no—
118#135—5664no—
119C2×Q16—2831no—
120C2×SD16—2832no—
121C2×D8—2831no—
122C22×C8—2831no—
123C22×C8—2832no—
124C22×C8—2832no—
125C22×C8—5664no—
126C22×C8C2×D28311yescharacteristic
127#123—5662no—
128C22⋊Q8—2834no—
129#121—2834no—
130#120—5662no—
131C4×D4—5664no—
132#117C2×D28312yes—
133#107C2×D28312yescomplemented
134#106C2×D28312yescomplemented
135#103—2834no—
136#102—2834no—
137C24—2831no—
138#41—5664no—
139#41—5664no—
140C2×Q8—2832no—
141C2×D4—2832no—
142C2×D4—5664no—
143C2×D4—5662no—
144C22×C4—2831no—
145C22×C4—2832no—
146C22×C4—2832no—
147C22×C4—5662no—
148C22×C4—5662no—
149C22×C4—5662no—
150C22×C4C22×D28311yescharacteristic
151Q16—5662no—
152SD16—5664no—
153D8—5662no—
154C2×C8—2832no—
155C2×C8—5662no—
156C2×C8—5664no—
157C2×C8—5664no—
158C2×C8D113214yescomplemented
159C2×C8C22×D28311yescharacteristic
160C2×C8C22×D28311yescharacteristic
161C4⋊C4—5664no—
162C4⋊C4C22×D28314yes—
163C22⋊C4—22no—
164C22⋊C4—5664no—
165C22⋊C4—5664no—
166C42—22no—
167C23—2832no—
168C23—5664no—
169C23—5662no—
170C23—5662no—
171C23D4×D28311yescharacteristic
172Q8—5662no—
173Q8—5662no—
174D4—5662no—
175D4—5662no—
176D4—11328no—
177D4—11324no—
178C2×C4—24no—
179C2×C4—2832no—
180C2×C4—5662no—
181C2×C4—5664no—
182C2×C4—5662no—
183C2×C4—5662no—
184C2×C4—5662no—
185C2×C4—11324no—
186C2×C4D4×D28311yescharacteristic
187C2×C4C2×D113212yes—
188C2×C4#1798539312yes—
189C2×C4C23×D28311yescharacteristic
190C8—5662no—
191C8C2×D113212yes—
192C8C2×D113212yes—
193C22—22no—
194C22—2834no—
195C22—5668no—
196C22—5662no—
197C22—5662no—
198C22—11322no—
199C22—11324no—
200C22#2258358512yes—
201C22C2×D4×D28311yescharacteristic
202C4—44no—
203C4—5662no—
204C4—11322no—
205C4#2258358512yes—
206C4C22×D113211yescharacteristic
207C4C2×#1798539311yescharacteristic
208C2—22no—
209C2—5664no—
210C2—22642no—
211C2C2×#2258358511yescharacteristic
212C2#135×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#427×C283C2
socleC22×C283C22×D4
hypercenter#427D283
hypocenterC283#3050
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C2×#22583632C2semidirect
2. C22×C8×D283C2semidirect
3. #31826977C2semidirect
4. #31826707C2semidirect
5. #31826702C2semidirect
6. #31826695C2semidirect
7. #31826459C2semidirect
8. #427×C283C2semidirect
12. C2×Dic1132C22semidirect
13. C2×#17985381C22semidirect
14. C2×D2264C22semidirect
24. #22583533C22semidirect
25. #22583530C22semidirect
28. #107×C283C22semidirect
29. #106×C283C22semidirect
54. C2×C8×C283D4semidirect
94. C2×D283#135semidirect
106. C283#3050semidirect
114. #427D283semidirect
133. #107C2×D283semidirect
134. #106C2×D283semidirect
158. C2×C8D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836322
C22×C8×D2832
#318269772
#318267072
#318267022
#318266952
#318264592
#427×C2832
#3050283