Finite Group Databasebeta

← #352×D281 #49096937

Subgroups — #352×D281 #49096937

Order 35968.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#123×D281C211yesmaximal, characteristic
2#100×D281C211yesmaximal, characteristic
3#99×D281C211yesmaximal, characteristic
4#31823254C211yesmaximal, characteristic, complemented
5#31823253C211yesmaximal, characteristic, complemented
6#31823252C211yesmaximal, characteristic, complemented
7#352×C281C211yesmaximal, characteristic, complemented
8C2×D4×D281C2211yescharacteristic
9C22×C4×D281C411yescharacteristic, complemented
10M16×D281—21no—
11#22582864—21no—
12#22582863C411yescharacteristic, complemented
13#22582862C411yescharacteristic, complemented
14#22582861—21no—
15#22582860C2211yescharacteristic
16C4⋊C4×D281—21no—
17C22⋊C4×D281—21no—
18C22⋊C4×D281—21no—
19C22⋊C4×D281C411yescharacteristic, complemented
20#22582796C2211yescharacteristic
21#22582795—21no—
22#22582794C2211yescharacteristic
23#22582793—21no—
24#123×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27C23×D281C2×C411yescharacteristic
28C23×D281D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C22⋊D281C2×C411yescharacteristic
31C2×C22⋊D281D411yescharacteristic
32D4×D281—41no—
33D4×D281—41no—
34C22×Dic281C2×C411yescharacteristic, complemented
35C2×C4×D281—21no—
36C2×C4×D281—21no—
37C2×C4×D281—21no—
38C2×C4×D281—41no—
39C2×C4×D281—41no—
40C2×C4×D281—41no—
41C2×C4×D281D411yescharacteristic
42#17985122—21no—
43#17985121—41no—
44C8×D281—41no—
45C4⋊Dic281—21no—
46#17985117—21no—
47#17985117—21no—
48C22⋊Dic281—21no—
49C22⋊Dic281—21no—
50C22⋊Dic281C2×C411yescharacteristic, complemented
51#17985115—21no—
52#17985115—21no—
53#17985115—21no—
54#17985115—41no—
55C2×D4×C281C2311yescharacteristic
56C22×C4×C281C2×C411yescharacteristic, complemented
57M16×C281—21no—
58C4⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281C2×C411yescharacteristic, complemented
62C22×D281—21no—
63C22×D281—21no—
64C22×D281—21no—
65C22×D281—21no—
66C22×D281—42no—
67C22×D281—42no—
68C22×D281C22⋊C411yescharacteristic
69C22×D281C22⋊C411yescharacteristic
70C22×D281C22⋊C411yescharacteristic
71D1124—41no—
72C22⋊D281—41no—
73C22⋊D281—41no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—41no—
77C2×Dic281—41no—
78C2×Dic281C22⋊C411yescharacteristic
79C4×D281—21no—
80C4×D281—21no—
81C4×D281—42no—
82C4×D281—42no—
83C4×D281—41no—
84C4×D281—41no—
85C4×D281—82no—
86#14555886—41no—
87C23×C281C22×C411yescharacteristic
88C23×C281C2×D411yescharacteristic
89D4×C281—41no—
90C2×C4×C281—21no—
91C2×C4×C281—21no—
92C2×C4×C281—41no—
93C2×C4×C281—41no—
94C2×C4×C281C2×D411yescharacteristic
95C8×C281—41no—
96C22×C281—21no—
97C22×C281—21no—
98C22×C281—41no—
99C22×C281—41no—
100C22×C281C2×C22⋊C411yescharacteristic
101C2×D281—22no—
102C2×D281—21no—
103C2×D281—21no—
104C2×D281—42no—
105C2×D281—42no—
106C2×D281—42no—
107C2×D281—41no—
108C2×D281—41no—
109C2×D281—81no—
110C2×D281#9911yescharacteristic
111C2×D281#9911yescharacteristic
112C4×C281—21no—
113C4×C281—41no—
114C4×C281—41no—
115C4×C281—81no—
116Dic281—21no—
117Dic281—41no—
118Dic281—41no—
119Dic281—81no—
120C2×C281—21no—
121C2×C281—41no—
122C2×C281—41no—
123C2×C281C2×#9911yescharacteristic
124D281—21no—
125D281—41no—
126D281—41no—
127D281#35212yesdirect product factor
128C281C2×#35211yescharacteristic, complemented, Sylow
129C2×#352—2811nomaximal, Sylow
130C2×#123—2811no—
131C2×#100—2811no—
132C2×#99—2811no—
133#352—2811no—
134#352—2811no—
135#352—2811no—
136#352D28111yescharacteristic, direct product factor
137C22×D4—2811no—
138C23×C4—2811no—
139C2×M16—5621no—
140#123—2811no—
141#123—2811no—
142#123—2811no—
143#123—5621no—
144#123—5621no—
145#123C2×D28111yescharacteristic
146C2×C4⋊C4—5621no—
147C2×C22⋊C4—2811no—
148C2×C22⋊C4—5621no—
149C2×C22⋊C4—5621no—
150#100—2811no—
151#100—5621no—
152#100C2×D28111yescharacteristic
153#99—2811no—
154#99—5621no—
155#99C2×D28111yescharacteristic
156C24—2811no—
157C24—2811no—
158C2×D4—2811no—
159C2×D4—2811no—
160C2×D4—2811no—
161C2×D4—11241no—
162C2×D4—11241no—
163C2×D4C22×D28111yescharacteristic
164C22×C4—2811no—
165C22×C4—2811no—
166C22×C4—5621no—
167C22×C4—5621no—
168C22×C4—5621no—
169C22×C4—11241no—
170C22×C4—11241no—
171C22×C4—11241no—
172C22×C4C4×D28111yescharacteristic, complemented
173M16—21no—
174M16—5621no—
175M16—11241no—
176C2×C8—11241no—
177C4⋊C4—21no—
178C4⋊C4—5621no—
179C4⋊C4—5621no—
180C4⋊C4—5621no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—2811no—
184C22⋊C4—5621no—
185C22⋊C4—5621no—
186C22⋊C4—5621no—
187C22⋊C4—5621no—
188C22⋊C4—5621no—
189C22⋊C4—11241no—
190C22⋊C4C4×D28111yescharacteristic, complemented
191C23—2811no—
192C23—2811no—
193C23—2811no—
194C23—5621no—
195C23—5621no—
196C23—5621no—
197C23—5621no—
198C23—11242no—
199C23—11242no—
200C23C2×C4×D28111yescharacteristic
201C23D4×D28111yescharacteristic
202D4—41no—
203D4—11241no—
204D4—11241no—
205D4—11241no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—2811no—
211C2×C4—5621no—
212C2×C4—5621no—
213C2×C4—5621no—
214C2×C4—5621no—
215C2×C4—11241no—
216C2×C4—11241no—
217C2×C4—11242no—
218C2×C4—11242no—
219C2×C4—11241no—
220C2×C4—11241no—
221C2×C4—22482no—
222C2×C4D4×D28111yescharacteristic
223C8—41no—
224C8—11241no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—2811no—
230C22—2811no—
231C22—5622no—
232C22—5621no—
233C22—5621no—
234C22—11241no—
235C22—11241no—
236C22—11242no—
237C22—11242no—
238C22—11242no—
239C22—22481no—
240C22C22⋊C4×D28111yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—5621no—
246C4—11241no—
247C4—11241no—
248C4—22481no—
249C2—21no—
250C2—41no—
251C2—41no—
252C2—2812no—
253C2—5621no—
254C2—11241no—
255C2—11241no—
256C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#352×C281C2
socleC2×C281C2×#99
prime radicalC2×D4×D281C22
cosocleC2×D4×C281C23
hypercenter#352D281
hypocenterC281C2×#352
LCSG ▷ C23×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
4. #31823254C2semidirect
5. #31823253C2semidirect
6. #31823252C2semidirect
7. #352×C281C2semidirect
9. C22×C4×D281C4semidirect
12. #22582863C4semidirect
13. #22582862C4semidirect
19. C22⋊C4×D281C4semidirect
34. C22×Dic281C2×C4semidirect
50. C22⋊Dic281C2×C4semidirect
56. C22×C4×C281C2×C4semidirect
61. C22⋊C4×C281C2×C4semidirect
127. D281#352direct (N × H)
128. C281C2×#352semidirect
136. #352D281direct (N × H)
172. C22×C4C4×D281semidirect
190. C22⋊C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
#123×D2812
#100×D2812
#99×D2812
#318232542
#318232532
#318232522
#352×C2812
C2×#352281