Finite Group Databasebeta

← #31815983

Subgroups — #31815983

Order 17792.

520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17984861C211yesmaximal, characteristic, complemented
2C22×C8×D139C211yesmaximal, characteristic, complemented
3#22581463C212yesmaximal, complemented
4#22581195C211yesmaximal, characteristic, complemented
5#22581194C211yesmaximal, characteristic, complemented
6#22581186C211yesmaximal, characteristic, complemented
7#22581181C212yesmaximal, complemented
8#22581180C212yesmaximal, complemented
9#22580990C211yesmaximal, characteristic, complemented
10#22580946C212yesmaximal, complemented
11#466×C139C211yesmaximal, characteristic, complemented
12C2×#14555784C2212yes—
13C22×C4×D139C2211yescharacteristic
14#17984861—24no—
15C2×Dic556C2211yescharacteristic, complemented
16C2×#14555773C2212yescomplemented
17C22×C139⋊C8C2211yescharacteristic
18C2×C8×D139—24no—
19C2×C8×D139C2211yescharacteristic
20C2×C8×D139C2211yescharacteristic
21C2×C8×D139C2211yescharacteristic
22C2×C8×D139C2211yescharacteristic
23#17984824—22no—
24#17984822C2212yes—
25#17984821C2212yes—
26#17984813C2212yes—
27#17984810—22no—
28D4×Dic139—22no—
29(C22⋊D139)⋊C4—22no—
30#17984800C2212yes—
31#17984776C2211yescharacteristic, complemented
32#17984773C2212yescomplemented
33#17984767C2212yescomplemented
34#17984765C2212yescomplemented
35#17984763C2212yescomplemented
36C2×D8×C139C2211yescharacteristic, complemented
37C22×C8×C139C2211yescharacteristic
38#121×C139C2212yes—
39#107×C139C2211yescharacteristic, complemented
40#102×C139C2212yescomplemented
41C23×D139D411yescharacteristic
42#14555784—24no—
43#14555784—24no—
44C2×Dic278C2312yes—
45C2×C22⋊D139—22no—
46C2×C22⋊D139—22no—
47C22×Dic139—22no—
48C22×Dic139D411yescharacteristic
49C2×C4×D139—22no—
50C2×C4×D139—22no—
51C2×C4×D139D411yescharacteristic
52C2×C4×D139D411yescharacteristic
53C2×C4×D139C2311yescharacteristic
54C2×C4×D139C2311yescharacteristic
55Dic556—22no—
56#14555773—24no—
57C2×C139⋊C8—22no—
58C2×C139⋊C8C2311yescharacteristic
59C2×C139⋊C8C2311yescharacteristic
60C8×D139—22no—
61C8×D139—22no—
62C8×D139—22no—
63C8×D139D414yescomplemented
64C4⋊Dic139—22no—
65C4⋊Dic139C2312yes—
66Dic139⋊C4—22no—
67C22⋊Dic139—22no—
68C22⋊Dic139—22no—
69(C2×D139)⋊C4—22no—
70(C2×D139)⋊C4—22no—
71C4×Dic139—22no—
72C2×D4×C139—22no—
73C2×D4×C139C2312yes—
74C22×C4×C139C2311yescharacteristic
75D8×C139—22no—
76C2×C8×C139—22no—
77C2×C8×C139C2311yescharacteristic
78C2×C8×C139C2311yescharacteristic
79C4⋊C4×C139C2312yes—
80C22⋊C4×C139—22no—
81C22×D139—22no—
82C22×D139—22no—
83C22×D139—22no—
84C22×D139C2×D411yescharacteristic
85C22×D139C2×D411yescharacteristic
86Dic278—22no—
87Dic278—22no—
88C22⋊D139—44no—
89C22⋊D139—44no—
90C2×Dic139—22no—
91C2×Dic139—22no—
92C2×Dic139—22no—
93C2×Dic139—44no—
94C2×Dic139C2×D411yescharacteristic
95C2×Dic139C2×D411yescharacteristic
96C4×D139—22no—
97C4×D139—21no—
98C4×D139—21no—
99C4×D139—22no—
100C4×D139C2×D412yes—
101C4×D139#4112yes—
102C139⋊C8—21no—
103C139⋊C8C2×D412yes—
104C23×C139—22no—
105C23×C139C2×D411yescharacteristic
106D4×C139—22no—
107D4×C139—22no—
108D4×C139—44no—
109C2×C4×C139—21no—
110C2×C4×C139—21no—
111C2×C4×C139—22no—
112C2×C4×C139C2×D411yescharacteristic
113C2×C4×C139C2411yescharacteristic
114C8×C139—21no—
115C8×C139C2×D412yes—
116C22×C139—21no—
117C22×C139—21no—
118C22×C139—42no—
119C22×C139—42no—
120C22×C139—42no—
121C22×C139#13512yescomplemented
122C22×C139C22×D411yescharacteristic
123C2×D139—28no—
124C2×D139—21no—
125C2×D139—21no—
126C2×D139—21no—
127C2×D139—21no—
128C2×D139#12112yes—
129C2×D139#13512yescomplemented
130C4×C139—21no—
131C4×C139—42no—
132C4×C139C22×D411yescharacteristic
133C4×C139C2×#4111yescharacteristic
134Dic139—21no—
135Dic139—42no—
136Dic139—42no—
137Dic139#12112yes—
138C2×C139—22no—
139C2×C139—82no—
140C2×C139C2×#12111yescharacteristic
141C2×C139C2×#13511yescharacteristic
142C2×C139C2×#13511yescharacteristic
143D139—22no—
144D139—22no—
145C139#305011yescharacteristic, complemented, Sylow
146#3050—1391nomaximal, Sylow
147C2×#135—1391no—
148C23×C8—1391no—
149#525—1392no—
150#467—1391no—
151#467—1391no—
152#466—1391no—
153#466D13911yescharacteristic, complemented
154#465—1392no—
155#465—1392no—
156#427—1391no—
157#416—1392no—
158C2×#41—1392no—
159C23×C4—1391no—
160#135—2784no—
161C2×Q16—1391no—
162C2×SD16—1392no—
163C2×D8C2×D13911yescharacteristic, complemented
164C22×C8—2784no—
165C22×C8—1391no—
166C22×C8—1391no—
167C22×C8—1391no—
168C22×C8—1391no—
169C22×C8—1391no—
170C22×C8C2×D13911yescharacteristic
171#123—2782no—
172C22⋊Q8—1392no—
173C22⋊Q8—1392no—
174#121—1392no—
175#121C2×D13912yes—
176#120—2782no—
177C4×D4—2782no—
178C4×D4—2782no—
179#117—1392no—
180#107—1391no—
181#107C2×D13911yescharacteristic, complemented
182#106—1392no—
183#103—1392no—
184#103—1392no—
185#102—1392no—
186#102C2×D13912yescomplemented
187C24—1391no—
188#41—2784no—
189#41—2784no—
190C2×Q8—1392no—
191C2×D4—22no—
192C2×D4—2782no—
193C2×D4—2782no—
194C2×D4C22×D13912yes—
195C22×C4—2782no—
196C22×C4—2782no—
197C22×C4—2782no—
198C22×C4—1391no—
199C22×C4—1391no—
200C22×C4—1391no—
201C22×C4—1391no—
202C22×C4—1391no—
203C22×C4C22×D13911yescharacteristic
204Q16—2782no—
205SD16—2784no—
206D8—22no—
207C2×C8—22no—
208C2×C8—2782no—
209C2×C8—2782no—
210C2×C8—2782no—
211C2×C8—2782no—
212C2×C8—1391no—
213C2×C8—1391no—
214C2×C8—1394no—
215C2×C8C22×D13911yescharacteristic
216C2×C8C22×D13911yescharacteristic
217C4⋊C4—2782no—
218C4⋊C4—2782no—
219C4⋊C4—1392no—
220C4⋊C4C22×D13912yes—
221C22⋊C4—22no—
222C22⋊C4—2782no—
223C22⋊C4—2782no—
224C22⋊C4—2782no—
225C22⋊C4—2782no—
226C42—2782no—
227C23—22no—
228C23—2782no—
229C23—2782no—
230C23—2782no—
231C23—1391no—
232C23—1391no—
233C23D4×D13911yescharacteristic
234Q8—2782no—
235Q8—2782no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—5564no—
240D4—5564no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—2782no—
245C2×C4—2782no—
246C2×C4—2782no—
247C2×C4—2781no—
248C2×C4—2781no—
249C2×C4—2782no—
250C2×C4—2782no—
251C2×C4—5564no—
252C2×C4—1391no—
253C2×C4—1391no—
254C2×C4—1392no—
255C2×C4—1392no—
256C2×C4D4×D13911yescharacteristic
257C2×C4C23×D13911yescharacteristic
258C8—21no—
259C8—2781no—
260C8—1392no—
261C8D4×D13912yes—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—2788no—
268C22—2781no—
269C22—2781no—
270C22—2781no—
271C22—2781no—
272C22—1392no—
273C22—1392no—
274C22#1798486112yescomplemented
275C22C2×D4×D13911yescharacteristic
276C4—21no—
277C4—42no—
278C4—2781no—
279C4—5562no—
280C4—5562no—
281C4—1392no—
282C4C2×D4×D13911yescharacteristic
283C4#41×D13911yescharacteristic
284C2—22no—
285C2—82no—
286C2—2782no—
287C2—2782no—
288C2#121×D13911yescharacteristic
289C2#135×D13911yescharacteristic
290C2C2×#1798486111yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#466×C139C2
socleC22×C139C22×D4
hypercenter#466D139
hypocenterC139#3050
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#17984861C2semidirect
2. C22×C8×D139C2semidirect
3. #22581463C2semidirect
4. #22581195C2semidirect
5. #22581194C2semidirect
6. #22581186C2semidirect
7. #22581181C2semidirect
8. #22581180C2semidirect
9. #22580990C2semidirect
10. #22580946C2semidirect
11. #466×C139C2semidirect
15. C2×Dic556C22semidirect
16. C2×#14555773C22semidirect
31. #17984776C22semidirect
32. #17984773C22semidirect
33. #17984767C22semidirect
34. #17984765C22semidirect
35. #17984763C22semidirect
36. C2×D8×C139C22semidirect
39. #107×C139C22semidirect
40. #102×C139C22semidirect
63. C8×D139D4semidirect
121. C22×C139#135semidirect
129. C2×D139#135semidirect
145. C139#3050semidirect
153. #466D139semidirect
163. C2×D8C2×D139semidirect
181. #107C2×D139semidirect
186. #102C2×D139semidirect
274. C22#17984861semidirect

Maximal subgroups

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

subgroupindex
C2×#179848612
C22×C8×D1392
#225814632
#225811952
#225811942
#225811862
#225811812
#225811802
#225809902
#225809462
#466×C1392
#3050139