Finite Group Databasebeta

← #49096943

Subgroups — #49096943

Order 35968.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#31823971C211yesmaximal, characteristic
2#31823444C211yesmaximal, characteristic, complemented
3#31823435C211yesmaximal, characteristic, complemented
4#31823253C211yesmaximal, characteristic, complemented
5#31823251C211yesmaximal, characteristic, complemented
6#31823249C211yesmaximal, characteristic, complemented
7#352×C281C211yesmaximal, characteristic, complemented
8C2×#17985137C2211yescharacteristic
9C22×C4×D281C411yescharacteristic, complemented
10M16×D281—21no—
11#22582862C411yescharacteristic, complemented
12#22582857—21no—
13#22582852—21no—
14#22582849C411yescharacteristic, complemented
15#22582847C2211yescharacteristic
16#22582841—21no—
17#22582839—21no—
18#22582835—21no—
19#22582835C411yescharacteristic, complemented
20#22582797—21no—
21#22582796C2211yescharacteristic
22#22582794C2211yescharacteristic
23#22582793—21no—
24#123×C281C2211yescharacteristic
25#100×C281C2211yescharacteristic
26#99×C281C2211yescharacteristic
27C23×D281C2×C411yescharacteristic
28#17985137—41no—
29#17985137—41no—
30C2×Dic562D411yescharacteristic
31C2×D1124—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281C2×C411yescharacteristic
34C2×C22⋊D281D411yescharacteristic
35C22×Dic281C2×C411yescharacteristic
36C22×Dic281D411yescharacteristic
37C2×C4×D281—21no—
38C2×C4×D281—21no—
39C2×C4×D281—41no—
40C2×C4×D281—41no—
41C2×C4×D281D411yescharacteristic
42#17985122—21no—
43#17985121—41no—
44C8×D281—41no—
45#17985117—21no—
46#17985117—21no—
47#17985117—41no—
48C22⋊Dic281—21no—
49C22⋊Dic281C2×C411yescharacteristic
50#17985115—21no—
51#17985115—21no—
52#17985115—21no—
53C4×Dic281—21no—
54C4×Dic281—41no—
55C2×D4×C281C2311yescharacteristic
56C22×C4×C281C2×C411yescharacteristic
57M16×C281—21no—
58C4⋊C4×C281—21no—
59C22⋊C4×C281—21no—
60C22⋊C4×C281—21no—
61C22⋊C4×C281C2×C411yescharacteristic
62C22×D281—21no—
63C22×D281—42no—
64C22×D281—41no—
65C22×D281C22⋊C411yescharacteristic
66Dic562—41no—
67D1124—42no—
68C22⋊D281—41no—
69C22⋊D281—41no—
70C22⋊D281—42no—
71C2×Dic281—21no—
72C2×Dic281—21no—
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—41no—
77C2×Dic281C22⋊C411yescharacteristic
78C2×Dic281C22⋊C411yescharacteristic
79C2×Dic281C22⋊C411yescharacteristic
80C4×D281—21no—
81C4×D281—21no—
82C4×D281—42no—
83C4×D281—41no—
84C4×D281—41no—
85#14555886—41no—
86C23×C281C22×C411yescharacteristic
87C23×C281C2×D411yescharacteristic
88D4×C281—41no—
89C2×C4×C281—21no—
90C2×C4×C281—21no—
91C2×C4×C281—41no—
92C2×C4×C281—41no—
93C2×C4×C281C2×D411yescharacteristic
94C8×C281—41no—
95C22×C281—21no—
96C22×C281—21no—
97C22×C281—41no—
98C22×C281—41no—
99C22×C281C2×C22⋊C411yescharacteristic
100C2×D281—22no—
101C2×D281—21no—
102C2×D281—41no—
103C2×D281—42no—
104C2×D281—41no—
105C2×D281—41no—
106C2×D281—42no—
107C4×C281—21no—
108C4×C281—41no—
109C4×C281—41no—
110C4×C281—81no—
111Dic281—21no—
112Dic281—21no—
113Dic281—41no—
114Dic281—81no—
115Dic281#9911yescharacteristic
116Dic281#9911yescharacteristic
117C2×C281—21no—
118C2×C281—41no—
119C2×C281—41no—
120C2×C281C2×#9911yescharacteristic
121D281—41no—
122D281—42no—
123C281#212011yescharacteristic, complemented, Sylow
124#2120—2811nomaximal, Sylow
125#525—2811no—
126#413—2811no—
127#410—2811no—
128#352—2811no—
129#352D28111yescharacteristic, complemented
130AΣL(1,𝔽16)—2811no—
131AΣL(1,𝔽16)—2811no—
132C2×#41—2811no—
133C23×C4—2811no—
134C2×M16—5621no—
135#123—2811no—
136#123C2×D28111yescharacteristic
137C22⋊Q8—5621no—
138#121—5621no—
139#120—2811no—
140#120—2811no—
141C4×D4—5621no—
142C4×D4—5621no—
143#117—2811no—
144#117—5621no—
145#101—5621no—
146#100—2811no—
147#100C2×D28111yescharacteristic
148#99—2811no—
149#99—5621no—
150#99C2×D28111yescharacteristic
151C24—2811no—
152#41—11241no—
153#41—11241no—
154C2×Q8—2811no—
155C2×D4—2811no—
156C2×D4—2811no—
157C2×D4—5621no—
158C2×D4—5621no—
159C2×D4C22×D28111yescharacteristic
160C22×C4—2811no—
161C22×C4—2811no—
162C22×C4—2811no—
163C22×C4—5621no—
164C22×C4—5621no—
165C22×C4—11241no—
166C22×C4—11241no—
167C22×C4C4×D28111yescharacteristic
168M16—21no—
169M16—5621no—
170M16—11241no—
171C2×C8—11241no—
172C4⋊C4—21no—
173C4⋊C4—5621no—
174C4⋊C4—5621no—
175C4⋊C4—11241no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—2811no—
179C22⋊C4—5621no—
180C22⋊C4—5621no—
181C22⋊C4—5621no—
182C22⋊C4—5621no—
183C22⋊C4C4×D28111yescharacteristic
184C42—5621no—
185C42—11241no—
186C23—2811no—
187C23—5621no—
188C23—11241no—
189C23—11242no—
190C23C2×C4×D28111yescharacteristic
191C23D4×D28111yescharacteristic
192Q8—11241no—
193D4—41no—
194D4—11242no—
195D4—11241no—
196D4—11241no—
197D4—11242no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—2811no—
203C2×C4—2811no—
204C2×C4—2811no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—5621no—
209C2×C4—5621no—
210C2×C4—5621no—
211C2×C4—5621no—
212C2×C4—11241no—
213C2×C4—11241no—
214C2×C4—11242no—
215C2×C4—11241no—
216C2×C4D4×D28111yescharacteristic
217C8—41no—
218C8—11241no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—5622no—
224C22—5621no—
225C22—11241no—
226C22—11241no—
227C22—11242no—
228C22—11242no—
229C22—11241no—
230C22C22⋊C4×D28111yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—2811no—
236C4—2811no—
237C4—5621no—
238C4—5621no—
239C4—11241no—
240C4—22481no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—11242no—
245C2—11241no—
246C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#352×C281C2
socleC2×C281C2×#99
prime radical#31823971C2
cosocleC2×D4×C281C23
hypercenter#352D281
hypocenterC281#2120
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
2. #31823444C2semidirect
3. #31823435C2semidirect
4. #31823253C2semidirect
5. #31823251C2semidirect
6. #31823249C2semidirect
7. #352×C281C2semidirect
9. C22×C4×D281C4semidirect
11. #22582862C4semidirect
14. #22582849C4semidirect
19. #22582835C4semidirect
123. C281#2120semidirect
129. #352D281semidirect

Maximal subgroups

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

subgroupindex
#318239712
#318234442
#318234352
#318232532
#318232512
#318232492
#352×C2812
#2120281