Finite Group Databasebeta

← #49094346

Subgroups — #49094346

Order 35968.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824092C211yesmaximal, characteristic
2#31823799C211yesmaximal, characteristic
3#31823796C211yesmaximal, characteristic
4#31823403C211yesmaximal, characteristic
5#31823199C211yesmaximal, characteristic
6#31823188C211yesmaximal, characteristic
7#328×C281C211yesmaximal, characteristic
8#22582878—21no—
9#22582877—21no—
10#22582869—21no—
11#22582869—21no—
12#22582858C2211yescharacteristic
13#22582856—21no—
14#22582835—21no—
15C2×C4⋊Dic281C2211yescharacteristic
16C2×#17985117C2211yescharacteristic
17#22582813—21no—
18#22582812—21no—
19#22582804—21no—
20#22582803—21no—
21C22⋊#14555886C2211yescharacteristic
22#22582786—21no—
23#22582786—21no—
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
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—
42#17985117—21no—
43#17985117—21no—
44C22⋊Dic281—21no—
45C4×Dic281—21no—
46C4×Dic281—21no—
47C2×Q8×C281D411yescharacteristic
48C22×C4×C281—21no—
49C22×C4×C281C2311yescharacteristic
50C2×C8×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281D411yescharacteristic
53C22⋊C4×C281—21no—
54Dic562—41no—
55Dic562—81no—
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×Dic281Q1612yes—
65#14555886—41no—
66C23×C281C2×D411yescharacteristic
67Q8×C281—41no—
68C2×C4×C281—21no—
69C2×C4×C281—21no—
70C2×C4×C281—41no—
71C2×C4×C281—41no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C8×C281—41no—
77C22×C281—21no—
78C22×C281—21no—
79C22×C281#12011yescharacteristic
80C22×C281C2×Q1611yescharacteristic
81C22×C281#13711yescharacteristic
82C4×C281—21no—
83C4×C281—21no—
84C4×C281—41no—
85C4×C281—41no—
86C4×C281—81no—
87Dic281—22no—
88Dic281—41no—
89Dic281—41no—
90Dic281—41no—
91Dic281—81no—
92C2×C281—21no—
93C2×C281—21no—
94C2×C281#45111yescharacteristic
95C2×C281#45411yescharacteristic
96C2×C281#45811yescharacteristic
97C281#161711yescharacteristic, complemented, Sylow
98#1617—2811nomaximal, Sylow
99#544—2811no—
100#484—2811no—
101#484—2811no—
102#400—2811no—
103#328—2811no—
104#328D28111yescharacteristic
105#324—2811no—
106C4⋊Q8—5621no—
107C4⋊Q8—5621no—
108#125—5621no—
109#125—5621no—
110C22⋊Q8—2811no—
111C22⋊Q8—5621no—
112C22⋊Q8C2×D28111yescharacteristic
113#117—5621no—
114C2×C4⋊C4—2811no—
115C2×C4⋊C4—2811no—
116#107—5621no—
117#107—5621no—
118#103—5621no—
119#103—5621no—
120C22⋊C8—2811no—
121C22⋊C8C2×D28111yescharacteristic
122#95—5621no—
123#95—5621no—
124#95C2×D28111yescharacteristic
125C2×Q8—2811no—
126C2×Q8—5621no—
127C2×Q8D112411yescharacteristic
128C22×C4—21no—
129C22×C4—2811no—
130C22×C4—2811no—
131C22×C4—5621no—
132C22×C4C22×D28111yescharacteristic
133C2×C8—21no—
134C2×C8—5621no—
135C4⋊C4—21no—
136C4⋊C4—2811no—
137C4⋊C4—5621no—
138C4⋊C4—5621no—
139C4⋊C4—5621no—
140C4⋊C4—5621no—
141C4⋊C4—5621no—
142C4⋊C4—5621no—
143C4⋊C4—5621no—
144C4⋊C4—5621no—
145C4⋊C4—5621no—
146C4⋊C4—5621no—
147C4⋊C4D112411yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5621no—
150C42—5621no—
151C42—5621no—
152C23D4×D28111yescharacteristic
153Q8—41no—
154Q8—11241no—
155Q8—22481no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2812no—
163C2×C4—5621no—
164C2×C4—5621no—
165C2×C4—5621no—
166C2×C4—5621no—
167C2×C4—5621no—
168C2×C4—11241no—
169C2×C4—11242no—
170C2×C4—11241no—
171C2×C4D4×D28111yescharacteristic
172C2×C4C2×D112411yescharacteristic
173C8—41no—
174C8—11241no—
175C22—21no—
176C22—21no—
177C22#2258284911yescharacteristic
178C22Q16×D28111yescharacteristic
179C22#2258290811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—5622no—
186C4—11241no—
187C4—11241no—
188C4—11241no—
189C4—22481no—
190C2—21no—
191C2—21no—
192C2#3182362011yescharacteristic
193C2#3182363711yescharacteristic
194C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#328D281
hypocenterC281#1617
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C281#1617semidirect

Maximal subgroups

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

subgroupindex
#318240922
#318237992
#318237962
#318234032
#318231992
#318231882
#328×C2812
#1617281