Finite Group Databasebeta

← #49094335

Subgroups — #49094335

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#31824058C211yesmaximal, characteristic
2#31823799C211yesmaximal, characteristic, complemented
3#31823779C211yesmaximal, characteristic
4#31823403C211yesmaximal, characteristic, complemented
5#31823199C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic
8#22582872—21no—
9#22582869—21no—
10#22582860—21no—
11#22582860—21no—
12#22582858C2211yescharacteristic
13#22582856—21no—
14D4×Dic281—21no—
15C2×C4⋊Dic281C2211yescharacteristic
16C2×#17985117C2211yescharacteristic
17#22582813—21no—
18#22582810—21no—
19#22582804—21no—
20#22582800—21no—
21C22⋊#14555886C2211yescharacteristic
22#22582786—21no—
23#22582786—21no—
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C22×Dic281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42C22⋊Dic281—21no—
43C22⋊Dic281—21no—
44C22⋊Dic281—21no—
45C22⋊Dic281—21no—
46C4×Dic281—21no—
47C2×D4×C281—21no—
48C2×D4×C281D411yescharacteristic
49C22×C4×C281—21no—
50C22×C4×C281C2311yescharacteristic
51C2×C8×C281—21no—
52C4⋊C4×C281D411yescharacteristic
53C22⋊C4×C281—21no—
54Dic562—41no—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—41no—
62C2×Dic281—42no—
63C2×Dic281—41no—
64C2×Dic281—81no—
65#14555886—41no—
66C23×C281—21no—
67C23×C281C2×D411yescharacteristic
68D4×C281—41no—
69D4×C281—41no—
70D4×C281—41no—
71C2×C4×C281—21no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C8×C281—41no—
79C22×C281—21no—
80C22×C281—21no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281—41no—
84C22×C281#12011yescharacteristic
85C22×C281#13511yescharacteristic
86C22×C281#13711yescharacteristic
87C4×C281—21no—
88C4×C281—21no—
89C4×C281—41no—
90C4×C281—81no—
91Dic281—41no—
92Dic281—41no—
93Dic281—41no—
94Dic281—41no—
95Dic281—81no—
96C2×C281—21no—
97C2×C281—21no—
98C2×C281—81no—
99C2×C281#45211yescharacteristic
100C2×C281#45411yescharacteristic
101C2×C281#45811yescharacteristic
102C281#161511yescharacteristic, complemented, Sylow
103#1615—2811nomaximal, Sylow
104#539—2811no—
105#484—2811no—
106#481—2811no—
107#400—2811no—
108#328—2811no—
109#327D28111yescharacteristic
110#324—2811no—
111#126—5621no—
112#125—5621no—
113#123—5621no—
114#123—5621no—
115C22⋊Q8—2811no—
116C22⋊Q8—5621no—
117#121C2×D28111yescharacteristic
118C4×D4—5621no—
119C2×C4⋊C4—2811no—
120C2×C4⋊C4—2811no—
121#107—5621no—
122#106—5621no—
123#103—5621no—
124#102—5621no—
125C22⋊C8—2811no—
126C22⋊C8C2×D28111yescharacteristic
127#95—5621no—
128#95—5621no—
129#95C2×D28111yescharacteristic
130C2×Q8—2811no—
131C2×D4—21no—
132C2×D4D112411yescharacteristic
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—2811no—
142C4⋊C4—5621no—
143C4⋊C4—5621no—
144C4⋊C4—5621no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4—5621no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4D112411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5621no—
153C22⋊C4—5621no—
154C22⋊C4—5621no—
155C22⋊C4—5621no—
156C42—5621no—
157C23—21no—
158C23D4×D28111yescharacteristic
159Q8—11241no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—5621no—
169C2×C4—5621no—
170C2×C4—5621no—
171C2×C4—5621no—
172C2×C4—5621no—
173C2×C4—5621no—
174C2×C4—11241no—
175C2×C4—11242no—
176C2×C4—11241no—
177C2×C4—22481no—
178C2×C4D4×D28111yescharacteristic
179C2×C4C2×D112411yescharacteristic
180C8—41no—
181C8—11241no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#2258284911yescharacteristic
188C22#2258289811yescharacteristic
189C22#2258290811yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—11241no—
195C4—11241no—
196C4—11241no—
197C4—11241no—
198C4—22481no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#3182362611yescharacteristic
203C2#3182363711yescharacteristic
204C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#121×C281C22
hypercenter#327D281
hypocenterC281#1615
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31823799C2semidirect
4. #31823403C2semidirect
5. #31823199C2semidirect
6. #31823188C2semidirect
102. C281#1615semidirect

Maximal subgroups

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

subgroupindex
#318240582
#318237992
#318237792
#318234032
#318231992
#318231882
#327×C2812
#1615281