Finite Group Databasebeta

← #49134352

Subgroups — #49134352

Order 36224.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#31827197C212yesmaximal, complemented
2#31826851C212yesmaximal, complemented
3#31826689C212yesmaximal, complemented
4#31826677C212yesmaximal, complemented
5#31826658C212yesmaximal, complemented
6#31826595C211yesmaximal, characteristic, complemented
7#31826566C212yesmaximal, complemented
8C4×D2264C211yesmaximal, characteristic, complemented
9#495×C283C211yesmaximal, characteristic, complemented
10C2×#17985379C2212yes—
11C2×D2264C2211yescharacteristic
12C2×#17985377C2212yes—
13#22583606C2212yes—
14#22583599C2212yes—
15#22583596—22no—
16#22583594—22no—
17#22583592—22no—
18Q8×Dic283C2212yes—
19C4×Dic566C2211yescharacteristic
20C4×D1132C2212yes—
21D4×Dic283C2212yes—
22(C22⋊D283)⋊C4—22no—
23#22583544C2211yescharacteristic
24C4⋊(C283⋊C8)C2211yescharacteristic
25Dic283⋊C8C2212yes—
26#22583534C2212yes—
27#22583532C2212yes—
28#22583531C2212yes—
29#22583520C2212yes—
30C2×Q16×C283C2211yescharacteristic
31C2×SD16×C283C2212yes—
32C2×D8×C283C2211yescharacteristic
33#124×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566D411yescharacteristic
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C22⋊D283—22no—
39C22×Dic283—22no—
40C2×C4×D283—22no—
41#17985379—42no—
42D2264—22no—
43#17985377—42no—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283—22no—
46C4⋊Dic283D411yescharacteristic
47C4⋊Dic283C2312yes—
48Dic283⋊C4D412yes—
49C22⋊Dic283—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—22no—
54C4×Dic283C2312yes—
55C2×Q8×C283C2312yes—
56C2×D4×C283C2312yes—
57Q16×C283—41no—
58SD16×C283—24no—
59D8×C283—41no—
60C2×C8×C283C2311yescharacteristic
61C2×C8×C283C2311yescharacteristic
62C22⋊C4×C283—22no—
63C22⋊C4×C283—22no—
64C42×C283C2311yescharacteristic
65C22×D283—22no—
66Dic566—41no—
67D1132—22no—
68D1132—22no—
69C22⋊D283—44no—
70C22⋊D283—82no—
71C2×Dic283—22no—
72C2×Dic283—82no—
73C2×Dic283C2×D412yes—
74C2×Dic283C2×D412yes—
75C4×D283—82no—
76C283⋊C8—22no—
77C23×C283—22no—
78Q8×C283—22no—
79Q8×C283—22no—
80D4×C283—22no—
81D4×C283—22no—
82C2×C4×C283—22no—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2411yescharacteristic
86C8×C283—21no—
87C8×C283#4112yes—
88C22×C283—42no—
89C22×C283—42no—
90C22×C283—42no—
91C22×C283C22×D411yescharacteristic
92C2×D283—42no—
93C2×D283—42no—
94C2×D283—42no—
95C4×C283—21no—
96C4×C283—21no—
97C4×C283—42no—
98C4×C283C2×#4111yescharacteristic
99C4×C283H(5,𝔽2)11yescharacteristic
100Dic283—22no—
101Dic283—22no—
102Dic283—42no—
103C2×C283—82no—
104C2×C283#55011yescharacteristic
105C2×C283#57511yescharacteristic
106C2×C283#57611yescharacteristic
107D283—82no—
108C283#340311yescharacteristic, complemented, Sylow
109#3403—2831nomaximal, Sylow
110#559—2832no—
111#496—2832no—
112#495D28311yescharacteristic, complemented
113#464—2832no—
114#463—2832no—
115#459—2832no—
116#446—2831no—
117#440—2832no—
118C4×D8—2831no—
119C2×Q16C2×D28311yescharacteristic
120C2×SD16—2832no—
121C2×SD16C2×D28312yes—
122C2×D8—2832no—
123C2×D8—2831no—
124C2×D8C2×D28311yescharacteristic
125#127—2832no—
126#124—2832no—
127#124—5662no—
128#124C2×D28312yes—
129#123—5662no—
130#123—5662no—
131C4×Q8—2831no—
132C4×Q8—2832no—
133C4×D4—2832no—
134C4×D4—2832no—
135C4×D4—5662no—
136#107—2831no—
137C4⋊C8—2832no—
138C4⋊C8—2831no—
139#103—2832no—
140#102—2832no—
141#102—2832no—
142#97—2832no—
143C4×C8C2×D28311yescharacteristic
144C2×Q8—2831no—
145C2×Q8C22×D28312yes—
146C2×D4—2832no—
147C2×D4—5662no—
148C2×D4—5662no—
149C2×D4C22×D28312yes—
150C22×C4—5662no—
151C22×C4—5662no—
152Q16—41no—
153SD16—24no—
154SD16—11322no—
155D8—41no—
156D8—5662no—
157D8—11322no—
158C2×C8—2832no—
159C2×C8C22×D28311yescharacteristic
160C2×C8C22×D28311yescharacteristic
161C4⋊C4—2832no—
162C4⋊C4—2831no—
163C4⋊C4—2832no—
164C4⋊C4—5662no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—5662no—
168C22⋊C4—5662no—
169C22⋊C4—5662no—
170C22⋊C4—5662no—
171C42—2832no—
172C42—5662no—
173C42C22×D28311yescharacteristic
174C23—22no—
175C23—5662no—
176Q8—22no—
177Q8—22no—
178Q8—11321no—
179D4—22no—
180D4—22no—
181D4—5662no—
182D4—5662no—
183D4—11324no—
184D4—22642no—
185C2×C4—22no—
186C2×C4—2832no—
187C2×C4—2832no—
188C2×C4—5662no—
189C2×C4—22642no—
190C2×C4—22642no—
191C2×C4D4×D28311yescharacteristic
192C2×C4D4×D28311yescharacteristic
193C2×C4C23×D28311yescharacteristic
194C8—21no—
195C8—5662no—
196C8#1798539112yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—11322no—
201C22—11322no—
202C22—11322no—
203C22C2×D4×D28311yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—5662no—
208C4—5662no—
209C4—11322no—
210C4C2×#1798539111yescharacteristic
211C4#2258365511yescharacteristic
212C2—82no—
213C2—22642no—
214C2#3182713511yescharacteristic
215C2#3182726211yescharacteristic
216C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#495×C283C2
socleC22×C283C22×D4
hypercenter#495D283
hypocenterC283#3403
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #31827197C2semidirect
2. #31826851C2semidirect
3. #31826689C2semidirect
4. #31826677C2semidirect
5. #31826658C2semidirect
6. #31826595C2semidirect
7. #31826566C2semidirect
8. C4×D2264C2semidirect
9. #495×C283C2semidirect
108. C283#3403semidirect
112. #495D283semidirect

Maximal subgroups

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

subgroupindex
#318271972
#318268512
#318266892
#318266772
#318266582
#318265952
#318265662
C4×D22642
#495×C2832
#3403283