Finite Group Databasebeta

← #49094230

Subgroups — #49094230

Order 35968.

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

normal subgroups only

This group has 272 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#31824060C211yesmaximal, characteristic, complemented
2#31823614C211yesmaximal, characteristic, complemented
3#31823597C211yesmaximal, characteristic
4#31823199C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823189C211yesmaximal, characteristic, complemented
7#394×C281C211yesmaximal, characteristic, complemented
8C2×#17985126—21no—
9C2×#17985123—21no—
10#22582874—21no—
11#22582869—21no—
12#22582864—21no—
13#22582862—21no—
14#22582858C2211yescharacteristic
15#22582857—21no—
16#22582853C2211yescharacteristic
17C4×C22⋊D281—21no—
18#22582800—21no—
19#22582800—21no—
20C22⋊#14555886C2211yescharacteristic
21C22⋊#14555886C2211yescharacteristic
22C22×D4×C281C2211yescharacteristic
23C2×C4⋊C4×C281C2211yescharacteristic
24C2×C22⋊C4×C281—21no—
25C2×C22⋊C4×C281—21no—
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C4×D281—21no—
31#17985126—42no—
32#17985123—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41C22⋊Dic281—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46C4×Dic281—21no—
47C24×C281—21no—
48C2×D4×C281—21no—
49C2×D4×C281—21no—
50C2×D4×C281—42no—
51C22×C4×C281—21no—
52C22×C4×C281D411yescharacteristic
53C22×C4×C281D411yescharacteristic
54C22×C4×C281C2311yescharacteristic
55C4⋊C4×C281—21no—
56C4⋊C4×C281—21no—
57C22⋊C4×C281—42no—
58C22⋊C4×C281—42no—
59C22×D281—21no—
60Dic562—41no—
61D1124—41no—
62C22⋊D281—41no—
63C22⋊D281—41no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C4×D281—81no—
68#14555886—41no—
69#14555886—41no—
70C23×C281—22no—
71C23×C281—41no—
72C23×C281—41no—
73C23×C281—41no—
74C23×C281—41no—
75C23×C281—41no—
76C23×C281—41no—
77C23×C281C2×D411yescharacteristic
78D4×C281—22no—
79D4×C281—22no—
80D4×C281—41no—
81D4×C281—41no—
82C2×C4×C281—21no—
83C2×C4×C281—21no—
84C2×C4×C281—21no—
85C2×C4×C281—21no—
86C2×C4×C281—41no—
87C2×C4×C281—41no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281—41no—
91C2×C4×C281C2×D411yescharacteristic
92C2×C4×C281C2×D411yescharacteristic
93C22×C281—21no—
94C22×C281—21no—
95C22×C281—42no—
96C22×C281—42no—
97C22×C281—42no—
98C22×C281—81no—
99C22×C281—81no—
100C22×C281—81no—
101C22×C281—81no—
102C22×C281#12011yescharacteristic
103C22×C281#13511yescharacteristic
104C22×C281AGL(1,ℤ/8)11yescharacteristic
105C2×D281—41no—
106C2×D281—41no—
107C2×D281—41no—
108C4×C281—21no—
109C4×C281—21no—
110C4×C281—41no—
111C4×C281—41no—
112C4×C281—81no—
113Dic281—41no—
114Dic281—41no—
115Dic281—41no—
116C2×C281—21no—
117C2×C281—21no—
118C2×C281—82no—
119C2×C281#44911yescharacteristic
120C2×C281#45411yescharacteristic
121C2×C281B(4,𝔽2)11yescharacteristic
122D281—81no—
123C281#159711yescharacteristic, complemented, Sylow
124#1597—2811nomaximal, Sylow
125#539—2811no—
126#450—2811no—
127#447—2811no—
128#394D28111yescharacteristic, complemented
129#328—2811no—
130#327—2811no—
131#324—2811no—
132C22×D4C2×D28111yescharacteristic
133C2×SD16—5621no—
134C2×D8—5621no—
135#126—5621no—
136#125—5621no—
137#123—5621no—
138#123—5621no—
139C22⋊Q8—2811no—
140C22⋊Q8—5621no—
141#121—2811no—
142C4×D4—5621no—
143C2×C4⋊C4C2×D28111yescharacteristic
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146#102—5621no—
147#102—5621no—
148C22⋊C8—2811no—
149C22⋊C8—2811no—
150#95C2×D28111yescharacteristic
151C24—21no—
152C2×Q8—2811no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—2811no—
157C2×D4—5621no—
158C22×C4—21no—
159C22×C4—5621no—
160C22×C4C22⋊D28111yescharacteristic
161C22×C4C22⋊D28111yescharacteristic
162C22×C4C22×D28111yescharacteristic
163SD16—11242no—
164D8—11242no—
165C2×C8—5621no—
166C2×C8—5621no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—2811no—
170C4⋊C4—2811no—
171C4⋊C4—5621no—
172C4⋊C4—5621no—
173C4⋊C4—5621no—
174C4⋊C4—5621no—
175C22⋊C4—42no—
176C22⋊C4—42no—
177C22⋊C4—5621no—
178C22⋊C4—5621no—
179C22⋊C4—5621no—
180C22⋊C4—5621no—
181C22⋊C4—5621no—
182C42—5621no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—5621no—
191C23C2×C22⋊D28111yescharacteristic
192Q8—11241no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—11241no—
198D4—11241no—
199D4—11241no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—5621no—
210C2×C4—5621no—
211C2×C4—5621no—
212C2×C4—22481no—
213C2×C4D4×D28111yescharacteristic
214C2×C4D4×D28111yescharacteristic
215C8—11241no—
216C8—11241no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—11241no—
227C22—11241no—
228C22—11241no—
229C22#2258284711yescharacteristic
230C22#2258289911yescharacteristic
231C22#2258290511yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—11241no—
238C4—11241no—
239C4—11241no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—22481no—
244C2#3182360611yescharacteristic
245C2#3182363511yescharacteristic
246C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#394×C281C2
socleC22×C281#120
prime radical#31823597C2
hypercenter#394D281
hypocenterC281#1597
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #31824060C2semidirect
2. #31823614C2semidirect
4. #31823199C2semidirect
5. #31823196C2semidirect
6. #31823189C2semidirect
7. #394×C281C2semidirect
123. C281#1597semidirect
128. #394D281semidirect

Maximal subgroups

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

subgroupindex
#318240602
#318236142
#318235972
#318231992
#318231962
#318231892
#394×C2812
#1597281