Finite Group Databasebeta

← #49094333

Subgroups — #49094333

Order 35968.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31824062C211yesmaximal, characteristic
2#31823781C211yesmaximal, characteristic
3#31823401C211yesmaximal, characteristic, complemented
4#31823200C211yesmaximal, characteristic, complemented
5#31823198C211yesmaximal, characteristic
6#31823188C211yesmaximal, characteristic, complemented
7#484×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582870—21no—
10#22582864—21no—
11#22582863—21no—
12#22582855—21no—
13#22582853C2211yescharacteristic
14#22582839—21no—
15C2×#17985117C2211yescharacteristic
16#22582810—21no—
17#22582799—21no—
18C22⋊#14555886C2211yescharacteristic
19#22582786—21no—
20#22582786—21no—
21#22582786C2211yescharacteristic
22C22⋊Q8×C281C2211yescharacteristic
23C2×C4⋊C4×C281C2211yescharacteristic
24#107×C281—21no—
25#103×C281—21no—
26C22⋊C8×C281C2211yescharacteristic
27C2×D1124D411yescharacteristic
28C2×C22⋊D281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985115—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44C4×Dic281—21no—
45C2×Q8×C281D411yescharacteristic
46C22×C4×C281—21no—
47C22×C4×C281C2311yescharacteristic
48C2×C8×C281—21no—
49C4⋊C4×C281—21no—
50C4⋊C4×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281D411yescharacteristic
53C22⋊C4×C281—21no—
54C22×D281—21no—
55D1124—41no—
56C22⋊D281—41no—
57C22⋊D281—41no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C4×D281—81no—
68#14555886—41no—
69C23×C281C2×D411yescharacteristic
70Q8×C281—41no—
71C2×C4×C281—21no—
72C2×C4×C281—21no—
73C2×C4×C281—41no—
74C2×C4×C281—42no—
75C2×C4×C281—41no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C8×C281—41no—
79C22×C281—21no—
80C22×C281—21no—
81C22×C281#12011yescharacteristic
82C22×C281#13511yescharacteristic
83C22×C281#13711yescharacteristic
84C2×D281—41no—
85C2×D281—41no—
86C2×D281—41no—
87C4×C281—21no—
88C4×C281—21no—
89C4×C281—41no—
90C4×C281—41no—
91C4×C281—81no—
92Dic281—41no—
93Dic281—41no—
94Dic281—41no—
95Dic281—81no—
96C2×C281—21no—
97C2×C281—21no—
98C2×C281#45211yescharacteristic
99C2×C281#45411yescharacteristic
100C2×C281#45811yescharacteristic
101D281—81no—
102C281#161511yescharacteristic, complemented, Sylow
103#1615—2811nomaximal, Sylow
104#539—2811no—
105#484D28111yescharacteristic, complemented
106#481—2811no—
107#400—2811no—
108#328—2811no—
109#327—2811no—
110#324—2811no—
111#126—5621no—
112#125—5621no—
113#123—5621no—
114#123—5621no—
115C22⋊Q8—5621no—
116C22⋊Q8C2×D28111yescharacteristic
117#121—2811no—
118C4×D4—5621no—
119C2×C4⋊C4—2811no—
120C2×C4⋊C4C2×D28111yescharacteristic
121#107—21no—
122#106—5621no—
123#103—21no—
124#102—5621no—
125C22⋊C8—2811no—
126C22⋊C8C2×D28111yescharacteristic
127#95—2811no—
128#95—5621no—
129#95—5621no—
130C2×Q8C22⋊D28111yescharacteristic
131C2×D4—2811no—
132C2×D4—5621no—
133C22×C4—21no—
134C22×C4—2811no—
135C22×C4—2811no—
136C22×C4—5621no—
137C22×C4—5621no—
138C22×C4C22×D28111yescharacteristic
139C2×C8—21no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—2811no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4—5621no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4C22⋊D28111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5621no—
153C22⋊C4—5621no—
154C22⋊C4—5621no—
155C22⋊C4—5621no—
156C42—5621no—
157C23—5621no—
158C23D4×D28111yescharacteristic
159Q8—41no—
160D4—11241no—
161D4—11241no—
162D4—11241no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—5621no—
169C2×C4—5621no—
170C2×C4—5621no—
171C2×C4—5621no—
172C2×C4—5621no—
173C2×C4—11241no—
174C2×C4—11241no—
175C2×C4—11241no—
176C2×C4—11241no—
177C2×C4—22481no—
178C2×C4D4×D28111yescharacteristic
179C2×C4C2×C22⋊D28111yescharacteristic
180C8—41no—
181C8—11241no—
182C22—21no—
183C22—21no—
184C22—11241no—
185C22—11241no—
186C22—11241no—
187C22#2258284711yescharacteristic
188C22#2258290211yescharacteristic
189C22#2258291111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—11241no—
196C4—11241no—
197C4—11241no—
198C4—22481no—
199C2—21no—
200C2—21no—
201C2—22481no—
202C2#3182362411yescharacteristic
203C2#3182363411yescharacteristic
204C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#484×C281C2
socleC22×C281#120
prime radical#22582853C22
hypercenter#484D281
hypocenterC281#1615
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #31823401C2semidirect
4. #31823200C2semidirect
6. #31823188C2semidirect
7. #484×C281C2semidirect
102. C281#1615semidirect
105. #484D281semidirect

Maximal subgroups

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

subgroupindex
#318240622
#318237812
#318234012
#318232002
#318231982
#318231882
#484×C2812
#1615281