Finite Group Databasebeta

← #49132722

Subgroups — #49132722

Order 36224.

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

normal subgroups only

This group has 346 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#31827086C212yesmaximal, complemented
2#31826761C212yesmaximal, complemented
3#31826746C212yesmaximal, complemented
4#31826711C212yesmaximal, complemented
5#31826706C211yesmaximal, characteristic, complemented
6#31826701C211yesmaximal, characteristic
7#31826688C212yesmaximal, complemented
8#31826681C212yesmaximal, complemented
9#424×C283C211yesmaximal, characteristic, complemented
10C2×Dic1132C2211yescharacteristic
11C2×#17985381C2212yes—
12C2×D2264C2211yescharacteristic
13#22583610C2212yes—
14#22583605—22no—
15#22583598C2212yes—
16#22583596—22no—
17#22583592—22no—
18#22583589C2212yes—
19#22583588—22no—
20#22583584C2212yes—
21C4×Dic566C2212yes—
22C4×D1132C2212yes—
23#22583544C2211yescharacteristic
24#22583544C2211yescharacteristic
25#22583544C2212yes—
26#22583535C2212yes—
27#22583535C2212yes—
28#22583532C2212yes—
29#22583532C2212yes—
30C2×M16×C283C2211yescharacteristic
31C22×C8×C283C2211yescharacteristic
32#117×C283C2211yescharacteristic
33C4⋊C8×C283C2212yes—
34C4⋊C8×C283C2212yes—
35C2×Dic566—22no—
36C2×Dic566C2312yes—
37C2×D1132C2312yes—
38C2×C22⋊D283—22no—
39C2×C4×D283—22no—
40Dic1132—41no—
41#17985381—42no—
42D2264—41no—
43C4⋊Dic283—22no—
44C4⋊Dic283C2312yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—22no—
47Dic283⋊C4—22no—
48C22⋊Dic283—22no—
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—22no—
54C22×C4×C283C2311yescharacteristic
55M16×C283—41no—
56C2×C8×C283—41no—
57C2×C8×C283C2311yescharacteristic
58C2×C8×C283C2312yes—
59C2×C8×C283C2311yescharacteristic
60C4⋊C4×C283D411yescharacteristic
61C4⋊C4×C283D411yescharacteristic
62C22⋊C4×C283D412yes—
63C42×C283C2312yes—
64C22×D283—22no—
65Dic566—22no—
66Dic566—22no—
67Dic566—82no—
68D1132—22no—
69D1132—22no—
70C22⋊D283—82no—
71C2×Dic283—22no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C4×D283—82no—
75C23×C283C2×D411yescharacteristic
76C2×C4×C283—21no—
77C2×C4×C283—21no—
78C2×C4×C283C2×D412yes—
79C2×C4×C283C2×D412yes—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2411yescharacteristic
82C8×C283—21no—
83C8×C283—21no—
84C8×C283—22no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283C22×D411yescharacteristic
89C2×D283—42no—
90C2×D283—42no—
91C2×D283—42no—
92C4×C283—21no—
93C4×C283—22no—
94C4×C283—22no—
95C4×C283H(5,𝔽2)11yescharacteristic
96C4×C2832−1+411yescharacteristic
97Dic283—42no—
98Dic283—42no—
99Dic283—42no—
100C2×C283—41no—
101C2×C283#53711yescharacteristic
102C2×C283#57611yescharacteristic
103C2×C283#57811yescharacteristic
104D283—82no—
105C283#326211yescharacteristic, complemented, Sylow
106#3262—2831nomaximal, Sylow
107#542—2832no—
108#477—2832no—
109#474—2832no—
110#468—2832no—
111#467—2831no—
112#466—2831no—
113#464—2832no—
114#463—2832no—
115#424D28311yescharacteristic, complemented
116C2×Q16—2831no—
117C2×SD16—2832no—
118C2×D8—2831no—
119C2×M16C2×D28311yescharacteristic
120C22×C8C2×D28311yescharacteristic
121C4⋊Q8—2832no—
122#126—5662no—
123#124—2832no—
124#124—5662no—
125#123—5662no—
126C22⋊Q8—2832no—
127C22⋊Q8—5662no—
128#121—2832no—
129C4×Q8—2832no—
130C4×D4—2832no—
131#117C2×D28311yescharacteristic
132#107—2831no—
133#107—2831no—
134#107—2832no—
135C4⋊C8C2×D28312yes—
136C4⋊C8C2×D28312yes—
137#103—2832no—
138#103—2832no—
139#102—2832no—
140#102—2832no—
141C2×Q8—2832no—
142C2×Q8—5662no—
143C2×D4—2832no—
144C2×D4—5662no—
145C22×C4—5662no—
146C22×C4C22×D28311yescharacteristic
147Q16—11321no—
148SD16—11322no—
149D8—11321no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D28311yescharacteristic
153C2×C8C22×D28312yes—
154C2×C8C22×D28311yescharacteristic
155C4⋊C4—2832no—
156C4⋊C4—2832no—
157C4⋊C4—5662no—
158C4⋊C4—5662no—
159C4⋊C4—5662no—
160C4⋊C4D113211yescharacteristic
161C4⋊C4D113211yescharacteristic
162C22⋊C4—5662no—
163C22⋊C4—5662no—
164C22⋊C4—5662no—
165C22⋊C4—5662no—
166C22⋊C4—5662no—
167C22⋊C4D113212yes—
168C42—5662no—
169C42C22×D28312yes—
170C23—5662no—
171C23C2×D113211yescharacteristic
172Q8—5662no—
173Q8—5662no—
174Q8—22642no—
175D4—5662no—
176D4—5662no—
177D4—22642no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—5662no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—22642no—
184C2×C4C2×D113212yes—
185C2×C4C2×D113212yes—
186C2×C4C2×D113211yescharacteristic
187C2×C4C23×D28311yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—11322no—
195C22—11322no—
196C22—11322no—
197C22C22×D113211yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—11322no—
202C4—11322no—
203C4—11322no—
204C4#2258365511yescharacteristic
205C4#2258365811yescharacteristic
206C2—41no—
207C2—22642no—
208C2#3182704611yescharacteristic
209C2#3182727011yescharacteristic
210C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#424×C283C2
socleC22×C283C22×D4
prime radical#31826701C2
hypercenter#424D283
hypocenterC283#3262
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31826761C2semidirect
3. #31826746C2semidirect
4. #31826711C2semidirect
5. #31826706C2semidirect
7. #31826688C2semidirect
8. #31826681C2semidirect
9. #424×C283C2semidirect
105. C283#3262semidirect
115. #424D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318267612
#318267462
#318267112
#318267062
#318267012
#318266882
#318266812
#424×C2832
#3262283