Finite Group Databasebeta

← #49097294

Subgroups — #49097294

Order 35968.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824141C211yesmaximal, characteristic, complemented
2#31823652C211yesmaximal, characteristic, complemented
3#31823651C211yesmaximal, characteristic
4#31823643C211yesmaximal, characteristic, complemented
5#31823257C211yesmaximal, characteristic, complemented
6#31823251C211yesmaximal, characteristic, complemented
7#352×C281C211yesmaximal, characteristic, complemented
8#22582924C2211yescharacteristic
9#22582912—21no—
10#22582872—21no—
11#22582866C2211yescharacteristic
12#22582862—21no—
13#22582861—21no—
14#22582857—21no—
15#22582849—21no—
16#22582847C2211yescharacteristic
17C4×C22⋊D281—21no—
18#22582837—21no—
19C22⋊C4×D281—21no—
20#22582805—21no—
21#22582794C2211yescharacteristic
22#22582793—21no—
23#22582793—21no—
24#123×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28#17985138—21no—
29#17985137—41no—
30C2×Dic562D411yescharacteristic, complemented
31C2×D1124—41no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C2×C22⋊D281—21no—
35D4×D281—41no—
36C2×C4×D281—21no—
37C2×C4×D281—21no—
38Dic1124—41no—
39#17985127—41no—
40C4⋊Dic281—21no—
41#17985117—21no—
42#17985117—21no—
43#17985117—41no—
44C22⋊Dic281—21no—
45C22⋊Dic281—21no—
46C22⋊Dic281—21no—
47C22⋊Dic281D411yescharacteristic
48#17985115—21no—
49#17985115—21no—
50#17985115—21no—
51#17985115—41no—
52#17985115—41no—
53C4×Dic281—21no—
54C4×Dic281D411yescharacteristic, complemented
55C2×D4×C281C2311yescharacteristic
56C22×C4×C281D411yescharacteristic, complemented
57M16×C281—21no—
58C4⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281D411yescharacteristic, complemented
62C22×D281—21no—
63C22×D281—21no—
64C22×D281—21no—
65C22×D281—42no—
66C22×D281—41no—
67Dic562—21no—
68Dic562—41no—
69D1124—21no—
70D1124—82no—
71C22⋊D281—42no—
72C22⋊D281—41no—
73C22⋊D281—41no—
74C22⋊D281—41no—
75C2×Dic281—21no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—21no—
79C2×Dic281—21no—
80C2×Dic281—41no—
81C4×D281—41no—
82C4×D281—42no—
83C4×D281—81no—
84C23×C281C2×D411yescharacteristic
85C23×C281C2×D411yescharacteristic
86D4×C281—41no—
87C2×C4×C281—21no—
88C2×C4×C281—21no—
89C2×C4×C281—41no—
90C2×C4×C281—41no—
91C2×C4×C281C2×D411yescharacteristic
92C8×C281—41no—
93C22×C281—21no—
94C22×C281—21no—
95C22×C281—41no—
96C22×C281—41no—
97C22×C281#12011yescharacteristic
98C2×D281—22no—
99C2×D281—41no—
100C2×D281—41no—
101C2×D281—42no—
102C2×D281—41no—
103C2×D281—81no—
104C2×D281—81no—
105C2×D281—81no—
106C4×C281—21no—
107C4×C281—41no—
108C4×C281—41no—
109C4×C281—81no—
110Dic281—41no—
111Dic281—41no—
112Dic281—41no—
113Dic281—41no—
114Dic281—81no—
115C2×C281—21no—
116C2×C281—41no—
117C2×C281—41no—
118C2×C281B(4,𝔽2)11yescharacteristic
119D281—42no—
120D281—81no—
121C281#219711yescharacteristic, complemented, Sylow
122#2197—2811nomaximal, Sylow
123#551—2811no—
124#458—2811no—
125B(4,𝔽2)—2811no—
126#455—2811no—
127#354—2811no—
128#352D28111yescharacteristic, complemented
129AΣL(1,𝔽16)—2811no—
130H(5,𝔽2)—2811no—
131#137—5621no—
132#126—5621no—
133#124—2811no—
134#123—5621no—
135#123—5621no—
136#123C2×D28111yescharacteristic
137C22⋊Q8—5621no—
138#120—2811no—
139#120—5621no—
140C4×D4—5621no—
141#117—5621no—
142C2×C22⋊C4—5621no—
143#104—5621no—
144#100C2×D28111yescharacteristic
145#99—2811no—
146#99—5621no—
147#99—5621no—
148#99C2×D28111yescharacteristic
149C24—2811no—
150#41—5621no—
151#41—11241no—
152C2×Q8—2811no—
153C2×D4—5621no—
154C2×D4—5621no—
155C2×D4—5621no—
156C2×D4—11241no—
157C2×D4—11241no—
158C2×D4C22×D28111yescharacteristic
159C22×C4—5621no—
160C22×C4—5621no—
161C22×C4D112411yescharacteristic, complemented
162Q16—11241no—
163SD16—11241no—
164M16—21no—
165C4⋊C4—21no—
166C4⋊C4—5621no—
167C4⋊C4—5621no—
168C4⋊C4—5621no—
169C4⋊C4—11241no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—2811no—
173C22⋊C4—5621no—
174C22⋊C4—5621no—
175C22⋊C4—5621no—
176C22⋊C4—5621no—
177C22⋊C4—5621no—
178C22⋊C4—5621no—
179C22⋊C4—11241no—
180C22⋊C4—11241no—
181C22⋊C4D112411yescharacteristic, complemented
182C42—2811no—
183C42—5621no—
184C23—5621no—
185C23—5621no—
186C23—5621no—
187C23—11241no—
188C23—11242no—
189C23D4×D28111yescharacteristic
190C23C2×D112411yescharacteristic
191Q8—5621no—
192Q8—11241no—
193D4—41no—
194D4—5621no—
195D4—11241no—
196D4—11241no—
197D4—11242no—
198D4—11241no—
199D4—22482no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—5621no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—5621no—
209C2×C4—11241no—
210C2×C4—11242no—
211C2×C4—11241no—
212C2×C4—22481no—
213C2×C4D4×D28111yescharacteristic
214C8—41no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—5622no—
220C22—11241no—
221C22—11242no—
222C22—11241no—
223C22—11241no—
224C22—22481no—
225C22—22481no—
226C22—22481no—
227C22#2258284911yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—11241no—
233C4—11241no—
234C4—11241no—
235C4—11241no—
236C4—22481no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—11242no—
241C2—22481no—
242C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#352×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823651C2
hypercenter#352D281
hypocenterC281#2197
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #31824141C2semidirect
2. #31823652C2semidirect
4. #31823643C2semidirect
5. #31823257C2semidirect
6. #31823251C2semidirect
7. #352×C281C2semidirect
30. C2×Dic562D4semidirect
54. C4×Dic281D4semidirect
56. C22×C4×C281D4semidirect
61. C22⋊C4×C281D4semidirect
121. C281#2197semidirect
128. #352D281semidirect
161. C22×C4D1124semidirect
181. C22⋊C4D1124semidirect

Maximal subgroups

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

subgroupindex
#318241412
#318236522
#318236512
#318236432
#318232572
#318232512
#352×C2812
#2197281