Finite Group Databasebeta

← #49094266

Subgroups — #49094266

Order 35968.

244 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 53 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#31823618C211yesmaximal, characteristic, complemented
2#31823601C211yesmaximal, characteristic
3#31823383C211yesmaximal, characteristic, complemented
4#31823200C211yesmaximal, characteristic, complemented
5#31823197C211yesmaximal, characteristic
6#31823189C211yesmaximal, characteristic, complemented
7#539×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C2×#17985128—21no—
10C2×#17985126—21no—
11C2×#17985117—21no—
12#22582802—21no—
13#22582802—21no—
14C22⋊#14555886C2211yescharacteristic
15C22⋊#14555886C2211yescharacteristic
16#22582786—21no—
17#22582786C2211yescharacteristic
18#126×C281—21no—
19#125×C281—21no—
20#123×C281—21no—
21#123×C281—21no—
22C22⋊Q8×C281—21no—
23C22⋊Q8×C281C2211yescharacteristic
24#121×C281C2211yescharacteristic
25C4×D4×C281—21no—
26C2×C4⋊C4×C281C2211yescharacteristic
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—42no—
30C22×Dic281—21no—
31C22×Dic281—21no—
32#17985128—42no—
33#17985126—42no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36#17985117—42no—
37C2×Q8×C281D411yescharacteristic
38C2×D4×C281—21no—
39C2×D4×C281D411yescharacteristic
40C22×C4×C281—21no—
41C22×C4×C281D411yescharacteristic
42C22×C4×C281D411yescharacteristic
43C22×C4×C281C2311yescharacteristic
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281—21no—
49C4⋊C4×C281—21no—
50C4⋊C4×C281D411yescharacteristic
51C4⋊C4×C281D411yescharacteristic
52C22⋊C4×C281—21no—
53C22⋊C4×C281—21no—
54C22⋊C4×C281—21no—
55C22⋊C4×C281—21no—
56C22⋊C4×C281—21no—
57C42×C281—21no—
58Dic562—22no—
59Dic562—22no—
60Dic562—41no—
61Dic562—41no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68#14555886—41no—
69#14555886—41no—
70C23×C281—21no—
71C23×C281C2×D411yescharacteristic
72Q8×C281—41no—
73D4×C281—41no—
74D4×C281—41no—
75D4×C281—41no—
76C2×C4×C281—21no—
77C2×C4×C281—21no—
78C2×C4×C281—21no—
79C2×C4×C281—21no—
80C2×C4×C281—21no—
81C2×C4×C281—21no—
82C2×C4×C281—21no—
83C2×C4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281—81no—
86C2×C4×C281C2×D411yescharacteristic
87C2×C4×C281C2×D411yescharacteristic
88C22×C281—21no—
89C22×C281—21no—
90C22×C281—41no—
91C22×C281—41no—
92C22×C281—41no—
93C22×C281#12011yescharacteristic
94C22×C281#13511yescharacteristic
95C22×C281#13711yescharacteristic
96C4×C281—21no—
97C4×C281—21no—
98C4×C281—41no—
99C4×C281—41no—
100C4×C281—41no—
101C4×C281—41no—
102C4×C281—41no—
103Dic281—42no—
104Dic281—42no—
105C2×C281—21no—
106C2×C281—21no—
107C2×C281—81no—
108C2×C281#45211yescharacteristic
109C2×C281#45611yescharacteristic
110C2×C281B(4,𝔽2)11yescharacteristic
111C281#160311yescharacteristic, complemented, Sylow
112#1603—2811nomaximal, Sylow
113#539D28111yescharacteristic
114#451—2811no—
115#448—2811no—
116#395—2811no—
117#328—2811no—
118#327—2811no—
119#324—2811no—
120C22×Q8—2811no—
121C2×Q16—5621no—
122C2×SD16—5621no—
123#126—21no—
124#125—21no—
125#123—21no—
126#123—21no—
127C22⋊Q8—21no—
128C22⋊Q8C2×D28111yescharacteristic
129#121C2×D28111yescharacteristic
130C4×D4—21no—
131C2×C4⋊C4—5621no—
132C2×C4⋊C4C2×D28111yescharacteristic
133#103—5621no—
134#103—5621no—
135C22⋊C8—2811no—
136C22⋊C8—2811no—
137#95—2811no—
138#95—5621no—
139C2×Q8—5621no—
140C2×Q8—5621no—
141C2×Q8—11242no—
142C2×Q8C22⋊D28111yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D28111yescharacteristic
145C22×C4—21no—
146C22×C4—5621no—
147C22×C4—5621no—
148C22×C4C22⋊D28111yescharacteristic
149C22×C4C22⋊D28111yescharacteristic
150C22×C4C22×D28111yescharacteristic
151Q16—11242no—
152SD16—11242no—
153C2×C8—5621no—
154C2×C8—5621no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—11242no—
162C4⋊C4C22⋊D28111yescharacteristic
163C4⋊C4C22⋊D28111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C42—21no—
170C23—21no—
171C23C2×C22⋊D28111yescharacteristic
172Q8—41no—
173Q8—5622no—
174Q8—5622no—
175Q8—11241no—
176Q8—11241no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—5622no—
191C2×C4—5622no—
192C2×C4—11241no—
193C2×C4—11241no—
194C2×C4—11241no—
195C2×C4—11241no—
196C2×C4C2×C22⋊D28111yescharacteristic
197C2×C4C2×C22⋊D28111yescharacteristic
198C8—11241no—
199C8—11241no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#2258284811yescharacteristic
206C22#2258289911yescharacteristic
207C22#2258290911yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—11242no—
216C4—11242no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#3182362511yescharacteristic
221C2#3182364611yescharacteristic
222C2#3182365011yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#539×C281C2
socleC22×C281#120
prime radical#121×C281C22
hypercenter#539D281
hypocenterC281#1603
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #31823618C2semidirect
3. #31823383C2semidirect
4. #31823200C2semidirect
6. #31823189C2semidirect
111. C281#1603semidirect

Maximal subgroups

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

subgroupindex
#318236182
#318236012
#318233832
#318232002
#318231972
#318231892
#539×C2812
#1603281