Finite Group Databasebeta

← #49121474

Subgroups — #49121474

Order 36224.

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

normal subgroups only

This group has 272 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
1#31826942C211yesmaximal, characteristic
2#31826505C211yesmaximal, characteristic
3C2×#22583528C211yesmaximal, characteristic
4#31826370C211yesmaximal, characteristic
5#31826226C211yesmaximal, characteristic
6#31826224C211yesmaximal, characteristic
7#428×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10C4×Dic566—21no—
11C4×Dic566—21no—
12#22583575—21no—
13#22583575—21no—
14#22583569C2211yescharacteristic
15#22583566—22no—
16C2×C4×Dic283C2211yescharacteristic
17#22583543—21no—
18#22583541—21no—
19#22583528C414yescomplemented
20C283⋊#95—22no—
21C2×M16×C283C2211yescharacteristic
22#117×C283C2211yescharacteristic
23C2×C4⋊C4×C283C2211yescharacteristic
24#107×C283—21no—
25#106×C283—21no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566—21no—
30C2×Dic566C2×C412yes—
31C2×Dic566Q812yes—
32C22×Dic283—21no—
33C22×Dic283D412yes—
34#17985376—21no—
35#17985376C2×C412yes—
36C2×C283⋊C8—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D411yescharacteristic
39Dic283⋊C4—22no—
40Dic283⋊C4—22no—
41C22⋊Dic283—21no—
42C4×Dic283—22no—
43C4×Dic283—22no—
44C4×Dic283—21no—
45C4×Dic283—21no—
46C4×Dic283—21no—
47C22×C4×C283—21no—
48C22×C4×C283C2311yescharacteristic
49M16×C283—21no—
50M16×C283C2×C412yes—
51C2×C8×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283—21no—
54C4⋊C4×C283D411yescharacteristic
55C4⋊C4×C283D411yescharacteristic
56C22⋊C4×C283—21no—
57C42×C283—21no—
58Dic566—22no—
59Dic566—22no—
60Dic566—22no—
61Dic566—22no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—21no—
66C2×Dic283—21no—
67C2×Dic283—41no—
68C2×Dic283—41no—
69C2×Dic283C4⋊C414yes—
70C283⋊C8—22no—
71C23×C283C2×D411yescharacteristic
72C2×C4×C283—21no—
73C2×C4×C283—21no—
74C2×C4×C283—42no—
75C2×C4×C283—41no—
76C2×C4×C283C22×C411yescharacteristic
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2×Q811yescharacteristic
80C2×C4×C283#4111yescharacteristic
81C2×C4×C283#4111yescharacteristic
82C8×C283—22no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283C2×C4⋊C411yescharacteristic
86C22×C283#12011yescharacteristic
87C22×C283#12311yescharacteristic
88C4×C283—41no—
89C4×C283—41no—
90C4×C283—81no—
91C4×C283C4×D411yescharacteristic
92C4×C283C4×D411yescharacteristic
93C4×C283C22⋊Q811yescharacteristic
94C4×C283C22⋊Q811yescharacteristic
95Dic283—24no—
96Dic283—42no—
97Dic283—41no—
98Dic283—41no—
99C2×C283—21no—
100C2×C283—21no—
101C2×C283#38511yescharacteristic
102C2×C283#45411yescharacteristic
103C2×C283#45611yescharacteristic
104C283#185711yescharacteristic, complemented, Sylow
105#1857—2831nomaximal, Sylow
106#519—2831no—
107#428—2831no—
108#428D28311yescharacteristic
109C2×#101—2831no—
110#391—2831no—
111#339—2831no—
112#339—2831no—
113C22×Q8—2831no—
114C2×M16—2831no—
115C2×M16C2×D28311yescharacteristic
116C4×Q8—5661no—
117C4×Q8—5661no—
118C4×Q8—5661no—
119C4×Q8—5661no—
120#117—2831no—
121#117—5662no—
122#117C2×D28311yescharacteristic
123C2×C4⋊C4C2×D28311yescharacteristic
124C2×C42—2831no—
125#107—21no—
126#107—5661no—
127#106—21no—
128#106—5661no—
129#101—2834no—
130#95—5662no—
131C2×Q8—2832no—
132C2×Q8—2832no—
133C2×Q8—5661no—
134C2×Q8—5661no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C22×C4—21no—
138C22×C4—2832no—
139C22×C4—5661no—
140C22×C4C22×D28311yescharacteristic
141M16—21no—
142M16—2832no—
143M16—5661no—
144M16C4×D28312yes—
145C2×C8—21no—
146C2×C8—5661no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—2831no—
150C4⋊C4—2831no—
151C4⋊C4—5662no—
152C4⋊C4—5662no—
153C4⋊C4C22⋊D28311yescharacteristic
154C4⋊C4C22⋊D28311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5661no—
157C42—21no—
158C42—5662no—
159C42—5662no—
160C42—5661no—
161C42—5661no—
162C42—5661no—
163C23D4×D28311yescharacteristic
164Q8—5662no—
165Q8—5662no—
166Q8—5662no—
167Q8—5662no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—2834no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—5661no—
177C2×C4—5661no—
178C2×C4—11321no—
179C2×C4—11321no—
180C2×C4C2×C4×D28311yescharacteristic
181C2×C4D4×D28311yescharacteristic
182C2×C4C2×C22⋊D28311yescharacteristic
183C2×C4Q8×D28311yescharacteristic
184C2×C4#1798539211yescharacteristic
185C2×C4#1798539311yescharacteristic
186C8—22no—
187C8—5662no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D28311yescharacteristic
191C22#2258357811yescharacteristic
192C22#2258359511yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—5664no—
197C4—11322no—
198C4—11321no—
199C4—11321no—
200C4C4×C22⋊D28311yescharacteristic
201C4#2258357211yescharacteristic
202C4#2258358611yescharacteristic
203C4#2258358811yescharacteristic
204C2—21no—
205C2—21no—
206C2#3182633611yescharacteristic
207C2#3182663611yescharacteristic
208C2#3182664611yescharacteristic
subgroupG/H
centerC22#22583578
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#428×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
cosocleC22×C4×C283C23
hypercenter#428D283
hypocenterC283#1857
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
19. #22583528C4semidirect
104. C283#1857semidirect

Maximal subgroups

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

subgroupindex
#318269422
#318265052
C2×#225835282
#318263702
#318262262
#318262242
#428×C2832
#1857283