Finite Group Databasebeta

← #31815668

Subgroups — #31815668

Order 17792.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984887C211yesmaximal, characteristic, complemented
2C2×#17984868C211yesmaximal, characteristic, complemented
3#22581520C211yesmaximal, characteristic, complemented
4#22581095C214yesmaximal, complemented
5#22581085C214yesmaximal, complemented
6#22580958C211yesmaximal, characteristic, complemented
7#22580950C211yesmaximal, characteristic, complemented
8#22580919C211yesmaximal, characteristic, complemented
9C22×D8×C139C211yesmaximal, characteristic, complemented
10#17984887—24no—
11#17984887—24no—
12C2×#14555785C2211yescharacteristic
13C2×#14555785C2211yescharacteristic
14C2×#14555784—21no—
15C2×#14555784C2212yescomplemented
16C22×C22⋊D139—22no—
17C2×D4×D139—21no—
18C2×D4×D139C2212yescomplemented
19#17984868—24no—
20C2×#14555773C2212yescomplemented
21C2×#14555770C2212yescomplemented
22C2×#14555769C2211yescharacteristic, complemented
23#17984838—21no—
24#17984829—21no—
25#17984813C2214yescomplemented
26#17984811—22no—
27#17984801C2211yescharacteristic, complemented
28#17984767C2212yescomplemented
29#17984764C2212yescomplemented
30#17984763C2214yescomplemented
31(C2×D139)⋊C8C2214yescomplemented
32C22×D4×C139C2211yescharacteristic
33C22×D4×C139C2211yescharacteristic, complemented
34C2×D8×C139—24no—
35C2×D8×C139C2214yescomplemented
36C22×C8×C139C2211yescharacteristic, complemented
37C23×D139—22no—
38#14555785—22no—
39#14555785—22no—
40#14555785—22no—
41#14555785D414yescomplemented
42#14555784—28no—
43#14555784—24no—
44#14555784—24no—
45C2×Dic278D411yescharacteristic
46C2×Dic278C2311yescharacteristic
47C2×D556D411yescharacteristic
48C2×D556C2311yescharacteristic
49C2×C22⋊D139—216no—
50C2×C22⋊D139—22no—
51C2×C22⋊D139—24no—
52C2×C22⋊D139—22no—
53C2×C22⋊D139—21no—
54C2×C22⋊D139D412yes—
55D4×D139—28no—
56D4×D139—24no—
57D4×D139—24no—
58C22×Dic139—22no—
59C2×C4×D139—21no—
60C2×C4×D139C2312yes—
61#14555773—24no—
62#14555770—24no—
63#14555769—22no—
64C2×C139⋊C8C2312yes—
65C4⋊Dic139C2312yes—
66C22⋊Dic139—24no—
67C22⋊Dic139—21no—
68C4×Dic139—21no—
69C24×C139—21no—
70C24×C139—21no—
71C2×D4×C139—21no—
72C2×D4×C139—22no—
73C2×D4×C139—22no—
74C2×D4×C139—22no—
75C2×D4×C139—21no—
76C2×D4×C139D414yescomplemented
77C2×D4×C139C2312yes—
78C2×D4×C139C2312yes—
79C22×C4×C139C2311yescharacteristic
80D8×C139—28no—
81C2×C8×C139—22no—
82C2×C8×C139C2312yes—
83C22×D139—21no—
84C22×D139—28no—
85C22×D139—84no—
86C22×D139C2×D412yes—
87Dic278—22no—
88Dic278—21no—
89Dic278C2×D412yes—
90D556—22no—
91D556—21no—
92D556C2×D412yes—
93C22⋊D139—28no—
94C22⋊D139—28no—
95C22⋊D139—24no—
96C22⋊D139—24no—
97C22⋊D139—84no—
98C2×Dic139—28no—
99C2×Dic139—21no—
100C2×Dic139—22no—
101C2×Dic139C2×D412yes—
102C4×D139—24no—
103C4×D139—22no—
104C4×D139—22no—
105C139⋊C8—22no—
106C23×C139—22no—
107C23×C139—24no—
108C23×C139—22no—
109C23×C139—42no—
110C23×C139—82no—
111C23×C139—82no—
112C23×C139C2×D411yescharacteristic
113D4×C139—24no—
114D4×C139—22no—
115D4×C139—22no—
116D4×C139—22no—
117D4×C139—42no—
118D4×C139C2×D414yes—
119C2×C4×C139C2×D411yescharacteristic
120C2×C4×C139C2×D412yes—
121C2×C4×C139C2×D412yes—
122C2×C4×C139C2411yescharacteristic
123C8×C139—22no—
124C22×C139—22no—
125C22×C139—24no—
126C22×C139—44no—
127C22×C139—42no—
128C22×C139—44no—
129C22×C139—84no—
130C22×C139—84no—
131C22×C139#12012yes—
132C22×C139C22×D411yescharacteristic
133C2×D139—22no—
134C2×D139—22no—
135C2×D139—24no—
136C2×D139—42no—
137C2×D139—88no—
138C4×C139#12012yes—
139C4×C139C22×D411yescharacteristic
140C4×C139C22×D411yescharacteristic
141Dic139—22no—
142Dic139—22no—
143Dic139—42no—
144C2×C139—22no—
145C2×C139—44no—
146C2×C139—82no—
147C2×C139C2×#12011yescharacteristic
148C2×C139#57612yes—
149D139—42no—
150D139—42no—
151C139#300811yescharacteristic, complemented, Sylow
152#3008—1391nomaximal, Sylow
153C2×H(5,𝔽2)—1391no—
154C2×AGL(1,ℤ/8)—1391no—
155C22×D8D13911yescharacteristic, complemented
156#535—1391no—
157#449—1394no—
158#447—1394no—
159#418—1391no—
160#416—1391no—
161#408—1391no—
162H(5,𝔽2)—2784no—
163H(5,𝔽2)—2784no—
164C2×#41—2781no—
165C2×#41—1392no—
166C2×#41—1391no—
167C2×#41—1391no—
168C22×D4—2781no—
169C22×D4—2782no—
170C22×D4—1392no—
171C22×D4C2×D13911yescharacteristic
172C22×D4C2×D13911yescharacteristic, complemented
173AGL(1,ℤ/8)—2784no—
174C2×SD16—1392no—
175C2×D8—24no—
176C2×D8—1392no—
177C2×D8C2×D13914yescomplemented
178C2×M16—1391no—
179C22×C8C2×D13911yescharacteristic, complemented
180#127—2781no—
181#124—2781no—
182#121—1394no—
183#120—2782no—
184#117—1391no—
185#103—1392no—
186#102—1394no—
187#102—1392no—
188C22⋊C8—1394no—
189C24—21no—
190C24—21no—
191C24—2782no—
192#41—2788no—
193#41—2784no—
194#41—2784no—
195#41—2782no—
196#41—2782no—
197#41—2782no—
198#41—1394no—
199C2×Q8—1391no—
200C2×Q8—1391no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—2788no—
207C2×D4—2784no—
208C2×D4—27816no—
209C2×D4—2782no—
210C2×D4—2781no—
211C2×D4—2784no—
212C2×D4—2784no—
213C2×D4—2782no—
214C2×D4—1392no—
215C2×D4—1391no—
216C2×D4—1391no—
217C2×D4C22⋊D13914yescomplemented
218C2×D4C22×D13912yes—
219C2×D4C22×D13912yes—
220C22×C4—2782no—
221C22×C4—2781no—
222C22×C4—1392no—
223C22×C4C22×D13911yescharacteristic
224SD16—2784no—
225D8—28no—
226D8—2784no—
227M16—2782no—
228C2×C8—22no—
229C2×C8—1392no—
230C2×C8C22×D13912yes—
231C4⋊C4—1392no—
232C22⋊C4—2781no—
233C22⋊C4—2784no—
234C42—2781no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—2788no—
242C23—2781no—
243C23—11124no—
244C23—1392no—
245C23D4×D13911yescharacteristic
246Q8—2782no—
247Q8—2781no—
248Q8—1392no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—2788no—
255D4—2788no—
256D4—2784no—
257D4—2784no—
258D4—2782no—
259D4—2781no—
260D4—11124no—
261D4—1392no—
262D4C2×C22⋊D13914yes—
263C2×C4—2788no—
264C2×C4—2781no—
265C2×C4—2784no—
266C2×C4—2782no—
267C2×C4—2782no—
268C2×C4—2782no—
269C2×C4—1392no—
270C2×C4D4×D13911yescharacteristic
271C2×C4D4×D13912yes—
272C2×C4C2×C22⋊D13912yes—
273C2×C4C23×D13911yescharacteristic
274C8—22no—
275C8—2782no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—84no—
283C22—2782no—
284C22—2782no—
285C22—2784no—
286C22—5562no—
287C22—11128no—
288C22#1798481012yes—
289C22C2×D4×D13911yescharacteristic
290C4—2782no—
291C4—2782no—
292C4—5562no—
293C4#1798481012yes—
294C4C2×D4×D13911yescharacteristic
295C4C22×C22⋊D13911yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—5562no—
300C2—5562no—
301C2C2×#1798481011yescharacteristic
302C2#2258175412yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC22×D8×C139C2
socleC22×C139C22×D4
hypercenterC22×D8D139
hypocenterC139#3008
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#17984887C2semidirect
2. C2×#17984868C2semidirect
3. #22581520C2semidirect
4. #22581095C2semidirect
5. #22581085C2semidirect
6. #22580958C2semidirect
7. #22580950C2semidirect
8. #22580919C2semidirect
9. C22×D8×C139C2semidirect
15. C2×#14555784C22semidirect
18. C2×D4×D139C22semidirect
20. C2×#14555773C22semidirect
21. C2×#14555770C22semidirect
22. C2×#14555769C22semidirect
25. #17984813C22semidirect
27. #17984801C22semidirect
28. #17984767C22semidirect
29. #17984764C22semidirect
30. #17984763C22semidirect
31. (C2×D139)⋊C8C22semidirect
33. C22×D4×C139C22semidirect
35. C2×D8×C139C22semidirect
36. C22×C8×C139C22semidirect
41. #14555785D4semidirect
76. C2×D4×C139D4semidirect
151. C139#3008semidirect
155. C22×D8D139semidirect
172. C22×D4C2×D139semidirect
177. C2×D8C2×D139semidirect
179. C22×C8C2×D139semidirect
217. C2×D4C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848872
C2×#179848682
#225815202
#225810952
#225810852
#225809582
#225809502
#225809192
C22×D8×C1392
#3008139