Finite Group Databasebeta

← #49094312

Subgroups — #49094312

Order 35968.

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

normal subgroups only

This group has 210 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#31823794C211yesmaximal, characteristic
3#31823791C211yesmaximal, characteristic
4#31823395C211yesmaximal, 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⋊Dic281—21no—
16C2×C4⋊Dic281C2211yescharacteristic
17C2×#17985117C2211yescharacteristic
18#22582811—21no—
19#22582810—21no—
20#22582804—21no—
21#22582803—21no—
22C22⋊#14555886C2211yescharacteristic
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⋊Dic281—42no—
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42#17985117—21no—
43#17985117—21no—
44#17985117—21no—
45C22⋊Dic281—21no—
46C4×Dic281—21no—
47C4×Dic281—21no—
48C2×Q8×C281D411yescharacteristic
49C22×C4×C281—21no—
50C22×C4×C281C2311yescharacteristic
51C2×C8×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281D411yescharacteristic
54C22⋊C4×C281—21no—
55Dic562—41no—
56Dic562—81no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281SD1612yes—
67#14555886—41no—
68C23×C281C2×D411yescharacteristic
69Q8×C281—41no—
70C2×C4×C281—22no—
71C2×C4×C281—21no—
72C2×C4×C281—21no—
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#12011yescharacteristic
82C22×C281C2×SD1611yescharacteristic
83C22×C281#13711yescharacteristic
84C4×C281—21no—
85C4×C281—21no—
86C4×C281—42no—
87C4×C281—41no—
88C4×C281—41no—
89Dic281—22no—
90Dic281—41no—
91Dic281—41no—
92Dic281—41no—
93Dic281—81no—
94C2×C281—21no—
95C2×C281—21no—
96C2×C281#44811yescharacteristic
97C2×C281#45611yescharacteristic
98C2×C281#45811yescharacteristic
99C281#161111yescharacteristic, complemented, Sylow
100#1611—2811nomaximal, Sylow
101#544—2811no—
102#483—2811no—
103#483—2811no—
104#398—2811no—
105#328—2811no—
106#328D28111yescharacteristic
107#324—2811no—
108C4⋊Q8—5621no—
109C4⋊Q8—5621no—
110#125—5621no—
111#125—5621no—
112C22⋊Q8—2811no—
113C22⋊Q8—5621no—
114C22⋊Q8C2×D28111yescharacteristic
115#117—5621no—
116C2×C4⋊C4—2811no—
117C2×C4⋊C4—2811no—
118C2×C4⋊C4—5621no—
119#106—5621no—
120#106—5621no—
121#103—5621no—
122#103—5621no—
123C22⋊C8—2811no—
124C22⋊C8C2×D28111yescharacteristic
125#95—5621no—
126#95C2×D28111yescharacteristic
127C2×Q8—2811no—
128C2×Q8—5621no—
129C2×Q8D112411yescharacteristic
130C22×C4—21no—
131C22×C4—2811no—
132C22×C4—2811no—
133C22×C4—5621no—
134C22×C4C22×D28111yescharacteristic
135C2×C8—21no—
136C2×C8—5621no—
137C4⋊C4—21no—
138C4⋊C4—2811no—
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⋊C4—5621no—
148C4⋊C4—5621no—
149C4⋊C4—11242no—
150C4⋊C4D112411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5621no—
153C42—5621no—
154C42—5621no—
155C23D4×D28111yescharacteristic
156Q8—41no—
157Q8—11241no—
158Q8—22481no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2812no—
166C2×C4—5621no—
167C2×C4—5621no—
168C2×C4—5621no—
169C2×C4—5621no—
170C2×C4—5621no—
171C2×C4—11241no—
172C2×C4—11241no—
173C2×C4—11241no—
174C2×C4—11241no—
175C2×C4D4×D28111yescharacteristic
176C2×C4C2×D112411yescharacteristic
177C8—41no—
178C8—11241no—
179C22—21no—
180C22—21no—
181C22#2258284911yescharacteristic
182C22SD16×D28111yescharacteristic
183C22#2258291111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—5622no—
190C4—11241no—
191C4—11241no—
192C4—11241no—
193C4—22481no—
194C2—21no—
195C2—21no—
196C2#3182360311yescharacteristic
197C2#3182364711yescharacteristic
198C2#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#1611
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
99. C281#1611semidirect

Maximal subgroups

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

subgroupindex
#318240922
#318237942
#318237912
#318233952
#318231992
#318231882
#328×C2812
#1611281