Finite Group Databasebeta

← #49132695

Subgroups — #49132695

Order 36224.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#31827068C212yesmaximal, complemented
2#31826768C212yesmaximal, complemented
3#31826763C212yesmaximal, complemented
4#31826716C212yesmaximal, complemented
5#31826701C211yesmaximal, characteristic, complemented
6#31826659C212yesmaximal, complemented
7#31826658C212yesmaximal, complemented
8#31826491C211yesmaximal, characteristic, complemented
9#466×C283C211yesmaximal, characteristic, complemented
10C2×D2264C2211yescharacteristic
11C2×#17985377C2212yes—
12C2×#17985376C2211yescharacteristic
13#22583606C2212yes—
14#22583601C2212yes—
15#22583594—22no—
16#22583592—22no—
17#22583584C2212yes—
18#22583582—22no—
19#22583581—22no—
20D4×Dic283C2212yes—
21#22583572C2212yes—
22#22583569C2211yescharacteristic
23#22583544C2211yescharacteristic
24#22583541C2212yes—
25Dic283⋊C8C2212yes—
26Dic283⋊C8C2212yes—
27#22583532C2212yes—
28#22583531C2212yes—
29#22583530C2212yes—
30C2×D8×C283C2211yescharacteristic
31C22×C8×C283C2211yescharacteristic
32#121×C283C2212yes—
33#107×C283C2211yescharacteristic
34#102×C283C2212yes—
35C2×D1132C2312yes—
36C2×C22⋊D283—22no—
37C2×C22⋊D283—22no—
38C2×C22⋊D283—22no—
39C22×Dic283—22no—
40C2×C4×D283—22no—
41D2264—41no—
42#17985377—42no—
43#17985376—41no—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283—22no—
46C4⋊Dic283D411yescharacteristic
47C4⋊Dic283D411yescharacteristic
48C4⋊Dic283C2312yes—
49Dic283⋊C4—22no—
50C22⋊Dic283—22no—
51C22⋊Dic283D412yes—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54C4×Dic283C2312yes—
55C2×D4×C283—22no—
56C2×D4×C283C2312yes—
57C22×C4×C283C2311yescharacteristic
58D8×C283—41no—
59C2×C8×C283—41no—
60C2×C8×C283C2311yescharacteristic
61C2×C8×C283C2311yescharacteristic
62C4⋊C4×C283C2312yes—
63C22⋊C4×C283—22no—
64C22×D283—22no—
65D1132—22no—
66D1132—22no—
67C22⋊D283—82no—
68C22⋊D283—82no—
69C22⋊D283—82no—
70C2×Dic283—22no—
71C2×Dic283—82no—
72C2×Dic283C2×D412yes—
73C2×Dic283C2×D412yes—
74C4×D283—82no—
75C283⋊C8—22no—
76C23×C283—22no—
77C23×C283C2×D411yescharacteristic
78D4×C283—22no—
79D4×C283—22no—
80D4×C283—82no—
81C2×C4×C283—21no—
82C2×C4×C283—21no—
83C2×C4×C283—22no—
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2411yescharacteristic
86C8×C283—21no—
87C8×C283—21no—
88C22×C283—21no—
89C22×C283—21no—
90C22×C283—21no—
91C22×C283—42no—
92C22×C283—42no—
93C22×C283—42no—
94C22×C283C22×D411yescharacteristic
95C2×D283—42no—
96C2×D283—42no—
97C2×D283—42no—
98C4×C283—21no—
99C4×C283—42no—
100C4×C283H(5,𝔽2)11yescharacteristic
101C4×C2832−1+411yescharacteristic
102Dic283—22no—
103Dic283—22no—
104Dic283—42no—
105C2×C283—41no—
106C2×C283—82no—
107C2×C283#53711yescharacteristic
108C2×C283#57611yescharacteristic
109C2×C283#57611yescharacteristic
110D283—82no—
111C283#325911yescharacteristic, complemented, Sylow
112#3259—2831nomaximal, Sylow
113#540—2832no—
114#478—2832no—
115#478—2832no—
116#469—2832no—
117#466—2831no—
118#466D28311yescharacteristic, complemented
119#459—2832no—
120#459—2832no—
121#424—2831no—
122C2×D8—2832no—
123C2×D8—2831no—
124C2×D8C2×D28311yescharacteristic
125C2×M16—2831no—
126C22×C8C2×D28311yescharacteristic
127#127—2832no—
128#125—2832no—
129#123—5662no—
130#123—5662no—
131#121—2832no—
132#121—5662no—
133#121—5662no—
134#121C2×D28312yes—
135C4×D4—2832no—
136C4×D4—2832no—
137#117—2831no—
138#107—2831no—
139#107C2×D28311yescharacteristic
140#106—2832no—
141C4⋊C8—2832no—
142C4⋊C8—2832no—
143#102—2832no—
144#102—2832no—
145#102—2832no—
146#102C2×D28312yes—
147C2×D4—22no—
148C2×D4—2832no—
149C2×D4—5662no—
150C2×D4—5662no—
151C2×D4—5662no—
152C2×D4C22×D28312yes—
153C22×C4—5662no—
154C22×C4—5662no—
155C22×C4C22×D28311yescharacteristic
156D8—41no—
157D8—11321no—
158D8—11322no—
159M16—11321no—
160C2×C8—41no—
161C2×C8—2832no—
162C2×C8C22×D28311yescharacteristic
163C2×C8C22×D28311yescharacteristic
164C4⋊C4—2831no—
165C4⋊C4—2831no—
166C4⋊C4—2832no—
167C4⋊C4—5662no—
168C4⋊C4—5662no—
169C4⋊C4C22×D28312yes—
170C22⋊C4—22no—
171C22⋊C4—2832no—
172C22⋊C4—5662no—
173C22⋊C4—5662no—
174C22⋊C4—5662no—
175C42—2832no—
176C23—22no—
177C23—5662no—
178C23D4×D28311yescharacteristic
179D4—22no—
180D4—22no—
181D4—82no—
182D4—5662no—
183D4—5662no—
184D4—22642no—
185D4—22642no—
186D4—22642no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—2832no—
191C2×C4—2832no—
192C2×C4—5662no—
193C2×C4—22642no—
194C2×C4—22642no—
195C2×C4D4×D28311yescharacteristic
196C2×C4C23×D28311yescharacteristic
197C8—21no—
198C8—21no—
199C8—5662no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—11322no—
207C22—11322no—
208C22—11322no—
209C22C2×D4×D28311yescharacteristic
210C4—21no—
211C4—42no—
212C4—5662no—
213C4—5662no—
214C4—11322no—
215C4#2258365511yescharacteristic
216C4#2258365711yescharacteristic
217C2—41no—
218C2—82no—
219C2—22642no—
220C2#3182704211yescharacteristic
221C2#3182726611yescharacteristic
222C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#466×C283C2
socleC22×C283C22×D4
hypercenter#466D283
hypocenterC283#3259
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31827068C2semidirect
2. #31826768C2semidirect
3. #31826763C2semidirect
4. #31826716C2semidirect
5. #31826701C2semidirect
6. #31826659C2semidirect
7. #31826658C2semidirect
8. #31826491C2semidirect
9. #466×C283C2semidirect
111. C283#3259semidirect
118. #466D283semidirect

Maximal subgroups

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

subgroupindex
#318270682
#318267682
#318267632
#318267162
#318267012
#318266592
#318266582
#318264912
#466×C2832
#3259283