Finite Group Databasebeta

← #49132696

Subgroups — #49132696

Order 36224.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#31827070C211yesmaximal, characteristic, complemented
2#31826765C212yesmaximal, complemented
3#31826762C212yesmaximal, complemented
4#31826716C212yesmaximal, complemented
5#31826699C212yesmaximal, complemented
6#31826660C212yesmaximal, complemented
7#31826657C212yesmaximal, complemented
8#31826492C211yesmaximal, characteristic, complemented
9#540×C283C211yesmaximal, characteristic, complemented
10C2×#17985377C2212yes—
11C2×#17985377C2212yes—
12C2×#17985376C2211yescharacteristic
13C22×C283⋊C8C2211yescharacteristic
14#22583607C2211yescharacteristic
15#22583602C2211yescharacteristic
16#22583595—22no—
17#22583584C2212yes—
18#22583583—22no—
19C4×D1132C2212yes—
20#22583543C2212yes—
21#22583541C2212yes—
22C4⋊(C283⋊C8)C2212yes—
23C4⋊(C283⋊C8)C2212yes—
24#22583531C2212yes—
25#22583531C2212yes—
26#22583530C2212yes—
27#22583530C2212yes—
28#127×C283C2211yescharacteristic
29#125×C283C2211yescharacteristic
30#123×C283—22no—
31#121×C283—22no—
32#121×C283C2212yes—
33C4×D4×C283C2212yes—
34#117×C283C2211yescharacteristic
35C2×D1132—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39#17985377—42no—
40#17985377—42no—
41#17985376—41no—
42C2×C283⋊C8—41no—
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—22no—
47(C2×D283)⋊C4—22no—
48(C2×D283)⋊C4—22no—
49C2×D4×C283—22no—
50C2×D4×C283—22no—
51C2×D4×C283C2312yes—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54C4⋊C4×C283—22no—
55C4⋊C4×C283D412yes—
56C4⋊C4×C283C2312yes—
57C22⋊C4×C283—22no—
58C22⋊C4×C283—22no—
59C22⋊C4×C283D412yes—
60C42×C283C2311yescharacteristic
61C42×C283C2311yescharacteristic
62C22×D283—22no—
63D1132—22no—
64D1132—22no—
65D1132—82no—
66C22⋊D283—82no—
67C2×Dic283—22no—
68C4×D283—82no—
69C283⋊C8—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283C2×D411yescharacteristic
73D4×C283—22no—
74D4×C283—22no—
75D4×C283—82no—
76D4×C283—82no—
77C2×C4×C283—21no—
78C2×C4×C283—21no—
79C2×C4×C283—22no—
80C2×C4×C283—82no—
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D412yes—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2411yescharacteristic
85C22×C283—21no—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—42no—
89C22×C283—42no—
90C22×C283C22×D411yescharacteristic
91C2×D283—42no—
92C2×D283—42no—
93C2×D283—42no—
94C4×C283—21no—
95C4×C283—22no—
96C4×C283—22no—
97C4×C283—42no—
98C4×C283H(5,𝔽2)11yescharacteristic
99C4×C2832−1+411yescharacteristic
100Dic283—42no—
101C2×C283—41no—
102C2×C283—82no—
103C2×C283#53711yescharacteristic
104C2×C283#57612yes—
105D283—82no—
106C283#325911yescharacteristic, complemented, Sylow
107#3259—2831nomaximal, Sylow
108#540—2831no—
109#540D28311yescharacteristic, complemented
110#478—2832no—
111#478—2832no—
112#469—2832no—
113#466—2832no—
114#459—2832no—
115#459—2832no—
116#424—2831no—
117C2×D8—2832no—
118C2×D8—2832no—
119C2×M16—2831no—
120C22×C8—2831no—
121#127—2831no—
122#127C2×D28311yescharacteristic
123#125—2831no—
124#125C2×D28311yescharacteristic
125#123—22no—
126#123—5662no—
127#121—22no—
128#121—2832no—
129#121—5662no—
130#121C2×D28312yes—
131C4×D4—2832no—
132C4×D4C2×D28312yes—
133#117C2×D28311yescharacteristic
134#107—2832no—
135#106—2832no—
136C4⋊C8—2832no—
137C4⋊C8—2832no—
138#102—2832no—
139#102—2832no—
140#102—2832no—
141#102—2832no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—2832no—
145C2×D4—5662no—
146C2×D4—5662no—
147C2×D4C22×D28312yes—
148C22×C4—22no—
149C22×C4—5662no—
150C22×C4C22×D28311yescharacteristic
151D8—11322no—
152D8—11322no—
153M16—11321no—
154C2×C8—2832no—
155C2×C8—2832no—
156C2×C8—11321no—
157C4⋊C4—22no—
158C4⋊C4—2832no—
159C4⋊C4—5662no—
160C4⋊C4C22⋊D28312yes—
161C4⋊C4C22×D28312yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—5662no—
165C22⋊C4—5662no—
166C22⋊C4C22⋊D28312yes—
167C42C22×D28311yescharacteristic
168C42C22×D28311yescharacteristic
169C23—22no—
170C23—5662no—
171C23C2×C22⋊D28311yescharacteristic
172D4—22no—
173D4—22no—
174D4—82no—
175D4—82no—
176D4—5662no—
177D4—5662no—
178D4—22642no—
179D4—22642no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—82no—
184C2×C4—5662no—
185C2×C4—22642no—
186C2×C4C2×C22⋊D28312yes—
187C2×C4C2×C22⋊D28312yes—
188C2×C4C2×C22⋊D28311yescharacteristic
189C2×C4C23×D28311yescharacteristic
190C8—5662no—
191C8—5662no—
192C22—22no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—11322no—
198C22—11322no—
199C22—11322no—
200C22C22×C22⋊D28311yescharacteristic
201C4—22no—
202C4—22no—
203C4—21no—
204C4—42no—
205C4—11322no—
206C4#2258365611yescharacteristic
207C4#2258365711yescharacteristic
208C2—41no—
209C2—82no—
210C2—22642no—
211C2#3182704311yescharacteristic
212C2#3182726812yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#540×C283C2
socleC22×C283C22×D4
hypercenter#540D283
hypocenterC283#3259
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #31827070C2semidirect
2. #31826765C2semidirect
3. #31826762C2semidirect
4. #31826716C2semidirect
5. #31826699C2semidirect
6. #31826660C2semidirect
7. #31826657C2semidirect
8. #31826492C2semidirect
9. #540×C283C2semidirect
106. C283#3259semidirect
109. #540D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318267652
#318267622
#318267162
#318266992
#318266602
#318266572
#318264922
#540×C2832
#3259283