Finite Group Databasebeta

← #49097313

Subgroups — #49097313

Order 35968.

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

normal subgroups only

This group has 260 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#31824200C211yesmaximal, characteristic, complemented
2#31823654C211yesmaximal, characteristic, complemented
3#31823651C211yesmaximal, characteristic, complemented
4#31823630C211yesmaximal, characteristic, complemented
5#31823252C211yesmaximal, characteristic, complemented
6#31823249C211yesmaximal, characteristic, complemented
7#353×C281C211yesmaximal, characteristic, complemented
8#22582924C2211yescharacteristic
9#22582905—21no—
10#22582873—21no—
11#22582863—21no—
12#22582860—21no—
13#22582860C2211yescharacteristic
14#22582851—21no—
15#22582851—21no—
16#22582851—21no—
17#22582849—21no—
18#22582847—21no—
19#22582847C2211yescharacteristic
20#22582807—21no—
21#22582796C2211yescharacteristic
22#22582793—21no—
23#22582793—21no—
24#127×C281C2211yescharacteristic
25#99×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28#17985138—21no—
29#17985137—41no—
30C2×D1124—41no—
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C2×C22⋊D281—21no—
35C2×C22⋊D281—21no—
36D4×D281—41no—
37C22×Dic281—21no—
38C22×Dic281D411yescharacteristic, complemented
39#17985126—41no—
40#17985123—41no—
41#17985122—21no—
42C4⋊Dic281—41no—
43#17985117—21no—
44#17985117—21no—
45#17985117—21no—
46C22⋊Dic281—21no—
47C22⋊Dic281—21no—
48C22⋊Dic281D411yescharacteristic
49C22⋊Dic281D411yescharacteristic, complemented
50#17985115—21no—
51#17985115—21no—
52#17985115—21no—
53#17985115—41no—
54#17985115—41no—
55C2×D4×C281—21no—
56C2×D4×C281—21no—
57C2×D4×C281D411yescharacteristic, complemented
58C2×D4×C281C2311yescharacteristic
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C42×C281D411yescharacteristic, complemented
62C22×D281—21no—
63C22×D281—21no—
64C22×D281—21no—
65C22×D281—41no—
66C22×D281—81no—
67Dic562—21no—
68D1124—21no—
69D1124—82no—
70C22⋊D281—41no—
71C22⋊D281—41no—
72C22⋊D281—41no—
73C22⋊D281—81no—
74C22⋊D281—81no—
75C22⋊D281—81no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—21no—
79C2×Dic281—21no—
80C2×Dic281—21no—
81C2×Dic281—41no—
82C2×Dic281—81no—
83C4×D281—41no—
84#14555886—41no—
85C23×C281—21no—
86C23×C281C2×D411yescharacteristic
87C23×C281C2×D411yescharacteristic
88D4×C281—41no—
89D4×C281—41no—
90D4×C281—81no—
91D4×C281—81no—
92C2×C4×C281—21no—
93C2×C4×C281—41no—
94C2×C4×C281—41no—
95C2×C4×C281C2×D411yescharacteristic
96C22×C281—21no—
97C22×C281—21no—
98C22×C281—41no—
99C22×C281—41no—
100C22×C281—41no—
101C22×C281—41no—
102C22×C281—41no—
103C22×C281#12011yescharacteristic
104C2×D281—41no—
105C2×D281—41no—
106C2×D281—42no—
107C2×D281—41no—
108C2×D281—41no—
109C2×D281—81no—
110C2×D281—81no—
111C2×D281—81no—
112C4×C281—21no—
113C4×C281—41no—
114C4×C281—81no—
115C4×C281—81no—
116Dic281—41no—
117Dic281—41no—
118Dic281—41no—
119Dic281—41no—
120C2×C281—21no—
121C2×C281—41no—
122C2×C281—41no—
123C2×C281—81no—
124C2×C281B(4,𝔽2)11yescharacteristic
125D281—81no—
126D281—81no—
127C281#220011yescharacteristic, complemented, Sylow
128#2200—2811nomaximal, Sylow
129#560—2811no—
130#458—2811no—
131B(4,𝔽2)—2811no—
132#453—2811no—
133#353D28111yescharacteristic, complemented
134#352—2811no—
135AΣL(1,𝔽16)—2811no—
136H(5,𝔽2)—2811no—
137AGL(1,ℤ/8)—5621no—
138#127C2×D28111yescharacteristic
139#126—5621no—
140#123—2811no—
141#123—5621no—
142#123—5621no—
143#121—5621no—
144#121—5621no—
145#121—5621no—
146#120—2811no—
147#120—5621no—
148#120—5621no—
149#104—5621no—
150#100—2811no—
151#99—5621no—
152#99—5621no—
153#99C2×D28111yescharacteristic
154#99C2×D28111yescharacteristic
155C24—2811no—
156#41—5621no—
157#41—11241no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—5621no—
161C2×D4—5621no—
162C2×D4—5621no—
163C2×D4—5621no—
164C2×D4—5621no—
165C2×D4—11241no—
166C2×D4—11241no—
167C2×D4D112411yescharacteristic, complemented
168C2×D4C22×D28111yescharacteristic
169C22×C4—2811no—
170C22×C4—5621no—
171SD16—11241no—
172D8—11241no—
173M16—5621no—
174C4⋊C4—5621no—
175C4⋊C4—5621no—
176C4⋊C4—5621no—
177C4⋊C4—11241no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—2811no—
181C22⋊C4—2811no—
182C22⋊C4—5621no—
183C22⋊C4—5621no—
184C22⋊C4—5621no—
185C22⋊C4—5621no—
186C22⋊C4—5621no—
187C22⋊C4—11241no—
188C22⋊C4—11241no—
189C42D112411yescharacteristic, complemented
190C23—21no—
191C23—5621no—
192C23—5621no—
193C23—5621no—
194C23—11241no—
195C23—22481no—
196C23D4×D28111yescharacteristic
197C23D4×D28111yescharacteristic
198Q8—5621no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—5621no—
204D4—11241no—
205D4—11241no—
206D4—11241no—
207D4—22482no—
208D4—22481no—
209D4—22481no—
210D4—22481no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—5621no—
215C2×C4—5621no—
216C2×C4—5621no—
217C2×C4—5621no—
218C2×C4—5621no—
219C2×C4—11241no—
220C2×C4—11241no—
221C2×C4—22481no—
222C2×C4C2×D112411yescharacteristic
223C8—11241no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—11241no—
232C22—11241no—
233C22—11242no—
234C22—11241no—
235C22—11241no—
236C22—22481no—
237C22—22481no—
238C22—22481no—
239C22#2258284911yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—81no—
244C4—11241no—
245C4—11241no—
246C4—11241no—
247C4—11241no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—22481no—
253C2—22481no—
254C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#353×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#353D281
hypocenterC281#2200
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #31824200C2semidirect
2. #31823654C2semidirect
3. #31823651C2semidirect
4. #31823630C2semidirect
5. #31823252C2semidirect
6. #31823249C2semidirect
7. #353×C281C2semidirect
38. C22×Dic281D4semidirect
49. C22⋊Dic281D4semidirect
57. C2×D4×C281D4semidirect
61. C42×C281D4semidirect
127. C281#2200semidirect
133. #353D281semidirect
167. C2×D4D1124semidirect
189. C42D1124semidirect

Maximal subgroups

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

subgroupindex
#318242002
#318236542
#318236512
#318236302
#318232522
#318232492
#353×C2812
#2200281