Finite Group Databasebeta

← #49096321

Subgroups — #49096321

Order 35968.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#22582907C211yesmaximal, characteristic, complemented
2#31824032C211yesmaximal, characteristic, complemented
3C2×#22582876C211yesmaximal, characteristic, complemented
4C2×#22582807C211yesmaximal, characteristic, complemented
5#31823467C211yesmaximal, characteristic, complemented
6C2×#22582795C211yesmaximal, characteristic, complemented
7#339×C281C211yesmaximal, characteristic, complemented
8C2×#17985138C2211yescharacteristic
9C22×D1124—22no—
10C22×D1124C2211yescharacteristic
11C22×D1124C2211yescharacteristic
12#22582907—22no—
13#22582907—22no—
14C2×#17985127—21no—
15C2×D2248—21no—
16C2×#17985122C2211yescharacteristic
17#22582876—22no—
18#22582876—21no—
19#22582876—22no—
20#22582867—21no—
21#22582854—22no—
22#22582849—22no—
23#22582807—22no—
24#22582799—22no—
25#22582795—22no—
26C2×M16×C281C2211yescharacteristic
27#117×C281C2211yescharacteristic
28C2×C42×C281C2211yescharacteristic
29C23×D281—21no—
30C23×D281D412yes—
31#17985138—21no—
32#17985138—21no—
33#17985138—21no—
34#17985138—21no—
35C2×Dic562D411yescharacteristic, complemented
36C2×D1124—28no—
37C2×D1124—24no—
38C2×D1124—21no—
39C2×D1124—21no—
40C2×D1124—21no—
41C2×D1124—21no—
42C2×D1124—21no—
43C2×D1124—21no—
44C2×D1124—21no—
45C2×D1124—21no—
46C2×D1124—21no—
47C2×D1124—21no—
48C2×D1124—21no—
49C2×D1124—48no—
50C2×D1124D411yescharacteristic, complemented
51C2×D1124D412yescomplemented
52C2×C22⋊D281—21no—
53C2×C4×D281—21no—
54#17985127—24no—
55D2248—24no—
56#17985122—21no—
57#17985122—21no—
58C2×#14555886—21no—
59#17985115—24no—
60C22×C4×C281—21no—
61C22×C4×C281C2311yescharacteristic
62M16×C281—21no—
63M16×C281D412yescomplemented
64C2×C8×C281—21no—
65C4⋊C4×C281D412yescomplemented
66C22⋊C4×C281—21no—
67C42×C281—21no—
68C42×C281—21no—
69C42×C281D412yescomplemented
70C22×D281—22no—
71C22×D281—21no—
72C22×D281—22no—
73C22×D281—22no—
74C22×D281—22no—
75C22×D281—44no—
76C22×D281—44no—
77C22×D281—41no—
78C22×D281—41no—
79Dic562—21no—
80Dic562—21no—
81D1124—21no—
82D1124—22no—
83D1124—22no—
84D1124—21no—
85D1124—416no—
86D1124—41no—
87D1124—41no—
88D1124—41no—
89D1124—41no—
90D1124—41no—
91D1124—41no—
92D1124—84no—
93C22⋊D281—41no—
94C22⋊D281—41no—
95C2×Dic281—21no—
96C4×D281—41no—
97C4×D281—41no—
98#14555886—41no—
99C23×C281C2×D411yescharacteristic
100C2×C4×C281—24no—
101C2×C4×C281—22no—
102C2×C4×C281—22no—
103C2×C4×C281C2×D411yescharacteristic
104C2×C4×C281C2×D411yescharacteristic
105C2×C4×C281C2×D411yescharacteristic
106C2×C4×C281C2×D411yescharacteristic
107C2×C4×C281C2×D411yescharacteristic
108C2×C4×C281#4111yescharacteristic
109C8×C281—22no—
110C22×C281—22no—
111C22×C281#12011yescharacteristic
112C22×C281#12011yescharacteristic
113C22×C281#12111yescharacteristic
114C2×D281—44no—
115C2×D281—44no—
116C2×D281—41no—
117C2×D281—42no—
118C2×D281—42no—
119C2×D281—42no—
120C2×D281—44no—
121C2×D281—82no—
122C2×D281—82no—
123C2×D281—82no—
124C4×C281—24no—
125C4×C281—42no—
126C4×C281#12011yescharacteristic
127C4×C281#12111yescharacteristic
128C4×C281#12111yescharacteristic
129C4×C281#12711yescharacteristic
130Dic281—41no—
131C2×C281—21no—
132C2×C281—21no—
133C2×C281#39211yescharacteristic
134C2×C281#45312yes—
135D281—81no—
136D281—82no—
137D281—82no—
138C281#200211yescharacteristic, complemented, Sylow
139#2002—2811nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2811no—
141#535—2811no—
142C2×#127—2811no—
143C2×#104—2811no—
144#418—2811no—
145C2×#100—2811no—
146#339D28111yescharacteristic, complemented
147C2×#41—2811no—
148C22×D4—2811no—
149C22×D4—2811no—
150C22×D4—5622no—
151AGL(1,ℤ/8)—5622no—
152AGL(1,ℤ/8)—5622no—
153C2×SD16—5621no—
154C2×D8—5621no—
155C2×M16—2811no—
156C2×M16C2×D28111yescharacteristic
157#127—5622no—
158#127—5621no—
159#127—5622no—
160#124—5621no—
161#121—5622no—
162#120—5622no—
163#117C2×D28111yescharacteristic
164C2×C42C2×D28111yescharacteristic
165#104—5622no—
166#102—5622no—
167#100—5622no—
168C24—2812no—
169C24—5621no—
170#41—5621no—
171#41—5621no—
172#41—5621no—
173#41—5621no—
174C2×Q8—2811no—
175C2×D4—2811no—
176C2×D4—2812no—
177C2×D4—5628no—
178C2×D4—5624no—
179C2×D4—5621no—
180C2×D4—5621no—
181C2×D4—5621no—
182C2×D4—5621no—
183C2×D4—5621no—
184C2×D4—5621no—
185C2×D4—5621no—
186C2×D4—5621no—
187C2×D4—5621no—
188C2×D4—5621no—
189C2×D4—5621no—
190C2×D4—5621no—
191C2×D4—11248no—
192C22×C4—21no—
193C22×C4—5621no—
194C22×C4C22×D28111yescharacteristic
195SD16—5624no—
196D8—5624no—
197M16—21no—
198M16—5621no—
199M16—5621no—
200M16D112412yescomplemented
201C2×C8—21no—
202C2×C8—5621no—
203C4⋊C4D112412yescomplemented
204C22⋊C4—21no—
205C22⋊C4—5624no—
206C42—21no—
207C42—21no—
208C42D112412yescomplemented
209C23—5622no—
210C23—5622no—
211C23—5622no—
212C23—5621no—
213C23—5622no—
214C23—11244no—
215C23—11244no—
216C23—11241no—
217C23—11241no—
218C23D4×D28111yescharacteristic
219Q8—5621no—
220Q8—5621no—
221D4—5621no—
222D4—5622no—
223D4—5622no—
224D4—5621no—
225D4—112416no—
226D4—11241no—
227D4—11241no—
228D4—11241no—
229D4—11241no—
230D4—11241no—
231D4—11241no—
232D4—11241no—
233D4—11241no—
234D4—22484no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—5621no—
239C2×C4—11241no—
240C2×C4—11241no—
241C2×C4D4×D28111yescharacteristic
242C2×C4D4×D28111yescharacteristic
243C2×C4C2×D112411yescharacteristic
244C2×C4C2×D112411yescharacteristic
245C2×C4C2×D112411yescharacteristic
246C2×C4#1798513911yescharacteristic
247C8—22no—
248C8—11241no—
249C22—22no—
250C22—11244no—
251C22—11244no—
252C22—11241no—
253C22—11242no—
254C22—11242no—
255C22—11242no—
256C22—11244no—
257C22—22482no—
258C22—22482no—
259C22—22482no—
260C22#2258284911yescharacteristic
261C22#2258284911yescharacteristic
262C22#2258285411yescharacteristic
263C4—24no—
264C4—42no—
265C4—11241no—
266C4#2258284911yescharacteristic
267C4#2258285411yescharacteristic
268C4#2258285411yescharacteristic
269C4#2258287611yescharacteristic
270C2—21no—
271C2—21no—
272C2—22482no—
273C2—22482no—
274C2—22481no—
275C2#3182337311yescharacteristic
276C2#3182363212yes—
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#339×C281C2
socleC22×C281#120
hypercenter#339D281
hypocenterC281#2002
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#22582907C2semidirect
2. #31824032C2semidirect
3. C2×#22582876C2semidirect
4. C2×#22582807C2semidirect
5. #31823467C2semidirect
6. C2×#22582795C2semidirect
7. #339×C281C2semidirect
35. C2×Dic562D4semidirect
50. C2×D1124D4semidirect
51. C2×D1124D4semidirect
63. M16×C281D4semidirect
65. C4⋊C4×C281D4semidirect
69. C42×C281D4semidirect
138. C281#2002semidirect
146. #339D281semidirect
200. M16D1124semidirect
203. C4⋊C4D1124semidirect
208. C42D1124semidirect

Maximal subgroups

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

subgroupindex
C2×#225829072
#318240322
C2×#225828762
C2×#225828072
#318234672
C2×#225827952
#339×C2812
#2002281