Finite Group Databasebeta

← #49121663

Subgroups — #49121663

Order 36224.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22583598C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826471C211yesmaximal, characteristic
4#31826469C211yesmaximal, characteristic
5C2×#22583528C211yesmaximal, characteristic, complemented
6#31826225C211yesmaximal, characteristic, complemented
7#339×C283C211yesmaximal, characteristic, complemented
8C22×Dic566C2211yescharacteristic
9C22×D1132C2211yescharacteristic
10C2×#17985376C2211yescharacteristic
11#22583598—22no—
12#22583598C414yescomplemented
13C4×Dic566—22no—
14#22583575—22no—
15#22583569C2211yescharacteristic
16#22583566—22no—
17C2×(C2×D283)⋊C4—22no—
18#22583532—22no—
19#22583530—22no—
20#22583528—22no—
21C2×M16×C283C2211yescharacteristic
22#117×C283C2211yescharacteristic
23C2×C42×C283C2211yescharacteristic
24C23×D283—21no—
25C2×Dic566—21no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566C2×C412yes—
30C2×Dic566D412yes—
31C2×D1132—21no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132—21no—
36C2×D1132C2×C412yes—
37C22×Dic283D412yes—
38#17985376—21no—
39#17985376—21no—
40C2×C283⋊C8—21no—
41C4⋊Dic283D412yes—
42Dic283⋊C4—24no—
43C22⋊Dic283—21no—
44(C2×D283)⋊C4—28no—
45C4×Dic283—24no—
46C4×Dic283—21no—
47C22×C4×C283—21no—
48C22×C4×C283C2311yescharacteristic
49M16×C283—21no—
50M16×C283—21no—
51C2×C8×C283—21no—
52C4⋊C4×C283D412yes—
53C22⋊C4×C283—21no—
54C42×C283—21no—
55C42×C283—21no—
56C42×C283C2×C412yes—
57C22×D283—22no—
58C22×D283—44no—
59C22×D283—41no—
60C22×D283—41no—
61Dic566—22no—
62Dic566—22no—
63Dic566—22no—
64Dic566—22no—
65D1132—22no—
66D1132—22no—
67D1132—41no—
68D1132—41no—
69C2×Dic283—22no—
70C2×Dic283—22no—
71C2×Dic283—22no—
72C2×Dic283C22⋊C414yes—
73C283⋊C8—41no—
74C23×C283C2×D411yescharacteristic
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283—42no—
78C2×C4×C283C22×C411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283#4111yescharacteristic
83C2×C4×C283#4111yescharacteristic
84C8×C283—41no—
85C22×C283—22no—
86C22×C283C2×C22⋊C411yescharacteristic
87C22×C283#12011yescharacteristic
88C22×C283#12311yescharacteristic
89C2×D283—44no—
90C2×D283—42no—
91C2×D283—82no—
92C2×D283—82no—
93C4×C283—42no—
94C4×C283—42no—
95C4×C283C4×D411yescharacteristic
96C4×C283C4×D411yescharacteristic
97C4×C283#12111yescharacteristic
98C4×C283#12111yescharacteristic
99Dic283—24no—
100Dic283—42no—
101C2×C283—21no—
102C2×C283—21no—
103C2×C283#38611yescharacteristic
104C2×C283#45412yes—
105D283—82no—
106C283#188811yescharacteristic, complemented, Sylow
107#1888—2831nomaximal, Sylow
108C2×#124—2831no—
109#519—2831no—
110#418—2831no—
111#418—2831no—
112C2×#101—2831no—
113#339—2831no—
114#339D28311yescharacteristic, complemented
115C22×Q8—2831no—
116C22×D4—2831no—
117C2×M16—2831no—
118C2×M16C2×D28311yescharacteristic
119#124—2834no—
120#124—5662no—
121C4×Q8—5662no—
122C4×Q8—5662no—
123#117—2831no—
124#117—5662no—
125#117C2×D28311yescharacteristic
126C2×C22⋊C4—5662no—
127C2×C42C2×D28311yescharacteristic
128#102—5662no—
129#102—5662no—
130#101—5662no—
131C24—5661no—
132C2×Q8—2832no—
133C2×Q8—2832no—
134C2×Q8—5661no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C2×Q8—5661no—
138C2×D4—2832no—
139C2×D4—5661no—
140C2×D4—5661no—
141C2×D4—5661no—
142C2×D4—5661no—
143C2×D4—5661no—
144C22×C4—21no—
145C22×C4—2832no—
146C22×C4C22×D28311yescharacteristic
147M16—21no—
148M16—21no—
149M16—5661no—
150M16—5661no—
151C2×C8—21no—
152C2×C8—5661no—
153C4⋊C4—2832no—
154C4⋊C4—5664no—
155C4⋊C4D113212yes—
156C22⋊C4—21no—
157C22⋊C4—5668no—
158C22⋊C4—5661no—
159C42—21no—
160C42—21no—
161C42—5664no—
162C42—5661no—
163C42C4×D28312yes—
164C23—5662no—
165C23—11324no—
166C23—11321no—
167C23—11321no—
168C23D4×D28311yescharacteristic
169Q8—5662no—
170Q8—5662no—
171Q8—5662no—
172Q8—5662no—
173D4—5662no—
174D4—5662no—
175D4—11321no—
176D4—11321no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2834no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—5662no—
184C2×C4C2×C4×D28311yescharacteristic
185C2×C4D4×D28311yescharacteristic
186C2×C4D4×D28311yescharacteristic
187C2×C4C2×D113211yescharacteristic
188C2×C4#1798539211yescharacteristic
189C2×C4#1798539311yescharacteristic
190C8—41no—
191C8—11321no—
192C22—22no—
193C22—11324no—
194C22—11322no—
195C22—22642no—
196C22—22642no—
197C22C22⋊C4×D28311yescharacteristic
198C22#2258358011yescharacteristic
199C22#2258359511yescharacteristic
200C4—42no—
201C4—42no—
202C4—5664no—
203C4—11322no—
204C4#2258357211yescharacteristic
205C4C4×D113211yescharacteristic
206C4#2258358311yescharacteristic
207C4#2258358511yescharacteristic
208C2—21no—
209C2—21no—
210C2—22642no—
211C2#3182634311yescharacteristic
212C2#3182663912yes—
subgroupG/H
centerC22#22583580
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#339×C283C2
socleC22×C283#120
prime radicalC22×D1132C22
cosocleC22×C4×C283C23
hypercenter#339D283
hypocenterC283#1888
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
5. C2×#22583528C2semidirect
6. #31826225C2semidirect
7. #339×C283C2semidirect
12. #22583598C4semidirect
106. C283#1888semidirect
114. #339D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835982
#318269422
#318264712
#318264692
C2×#225835282
#318262252
#339×C2832
#1888283