Finite Group Databasebeta

← #31816881

Subgroups — #31816881

Order 17792.

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

normal subgroups only

This group has 564 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×#17984872C211yesmaximal, characteristic, complemented
2C2×#17984867C211yesmaximal, characteristic, complemented
3C22×#14555774C211yesmaximal, characteristic, complemented
4#22581524C211yesmaximal, characteristic, complemented
5#22581517C211yesmaximal, characteristic, complemented
6#22581346C212yesmaximal, complemented
7#22581341C212yesmaximal, complemented
8#22581334C212yesmaximal, complemented
9#22581324C212yesmaximal, complemented
10#22580908C211yesmaximal, characteristic, complemented
11C2×#135×C139C211yesmaximal, characteristic, complemented
12C22×Dic278C2211yescharacteristic
13C22×D556C2211yescharacteristic
14#17984872—24no—
15#17984867—24no—
16C2×#14555775C2212yescomplemented
17C2×#14555774—24no—
18C2×#14555774C2212yes—
19C2×#14555774C2212yes—
20C2×#14555773C2212yescomplemented
21C2×#14555772C2212yes—
22C2×#14555770C2212yes—
23C2×#14555769C2211yescharacteristic
24#17984840C2212yescomplemented
25#17984838C2212yes—
26#17984831C2212yes—
27#17984829C2212yescomplemented
28#17984823—22no—
29#17984821—22no—
30#17984816—22no—
31#17984810—22no—
32#17984801C2211yescharacteristic
33#17984752C2212yescomplemented
34C8×Dic139C2212yescomplemented
35C2×#41×C139C2211yescharacteristic
36C2×#41×C139C2211yescharacteristic
37#135×C139—24no—
38C2×Q16×C139C2211yescharacteristic, complemented
39C2×SD16×C139C2211yescharacteristic, complemented
40C2×SD16×C139C2211yescharacteristic, complemented
41C2×D8×C139C2211yescharacteristic, complemented
42C22×C8×C139C2211yescharacteristic
43C23×D139—21no—
44C2×Dic278—21no—
45C2×Dic278—22no—
46C2×Dic278—22no—
47C2×Dic278C2312yes—
48C2×D556—22no—
49C2×D556—22no—
50C2×D556—21no—
51C2×D556C2312yes—
52C2×C22⋊D139—24no—
53C22×Dic139—21no—
54#14555775—24no—
55#14555774—24no—
56#14555774—24no—
57#14555773—24no—
58#14555772—24no—
59#14555770—24no—
60#14555769D414yescomplemented
61C2×C139⋊C8C2312yes—
62C4⋊Dic139D412yes—
63Dic139⋊C4—24no—
64C22⋊Dic139—24no—
65C22⋊Dic139D412yes—
66(C2×D139)⋊C4—24no—
67C4×Dic139C2312yes—
68#41×C139—22no—
69#41×C139—22no—
70#41×C139—22no—
71#41×C139—22no—
72C2×Q8×C139C2311yescharacteristic
73C2×Q8×C139C2311yescharacteristic
74C2×D4×C139—21no—
75C2×D4×C139—21no—
76C2×D4×C139C2311yescharacteristic
77C2×D4×C139C2311yescharacteristic
78C22×C4×C139—21no—
79C22×C4×C139—21no—
80C22×C4×C139C2311yescharacteristic
81Q16×C139—22no—
82SD16×C139—22no—
83SD16×C139—22no—
84D8×C139—22no—
85C2×C8×C139D414yescomplemented
86C2×C8×C139C2311yescharacteristic
87C2×C8×C139C2311yescharacteristic
88C22×D139—22no—
89C22×D139—42no—
90C22×D139—82no—
91Dic278—22no—
92Dic278—22no—
93Dic278—42no—
94D556—22no—
95D556—22no—
96D556—42no—
97C22⋊D139—84no—
98C2×Dic139—22no—
99C2×Dic139—42no—
100C2×Dic139C2×D414yes—
101C139⋊C8C2×D414yes—
102C23×C139—21no—
103C23×C139—21no—
104C23×C139C2×D411yescharacteristic
105Q8×C139—21no—
106Q8×C139—21no—
107Q8×C139—21no—
108Q8×C139—21no—
109D4×C139—21no—
110D4×C139—21no—
111D4×C139—21no—
112D4×C139—21no—
113D4×C139—42no—
114D4×C139—42no—
115C2×C4×C139—21no—
116C2×C4×C139—21no—
117C2×C4×C139—42no—
118C2×C4×C139—42no—
119C2×C4×C139C2×D411yescharacteristic
120C2×C4×C139C2×D412yes—
121C2×C4×C139C2×D412yes—
122C2×C4×C139C2411yescharacteristic
123C8×C139C2×D412yes—
124C8×C139C2×D412yes—
125C22×C139—22no—
126C22×C139—41no—
127C22×C139—41no—
128C22×C139—42no—
129C22×C139—42no—
130C22×C139#12712yes—
131C22×C139C22×D411yescharacteristic
132C2×D139—42no—
133C2×D139—44no—
134C2×D139—84no—
135C4×C139—41no—
136C4×C139—41no—
137C4×C139#12712yes—
138C4×C139C22×D411yescharacteristic
139C4×C139C22×D411yescharacteristic
140Dic139—24no—
141Dic139—42no—
142C2×C139—22no—
143C2×C139—81no—
144C2×C139—81no—
145C2×C139C2×#12711yescharacteristic
146C2×C139#57712yes—
147D139—82no—
148C139#315411yescharacteristic, complemented, Sylow
149#3154—1391nomaximal, Sylow
150C2×#137—1391no—
151C2×AGL(1,ℤ/8)—1391no—
152C2×#135D13911yescharacteristic, complemented
153C22×SD16—1391no—
154#536—1391no—
155#535—1391no—
156#497—1392no—
157#496—1392no—
158#495—1392no—
159#492—1392no—
160#405—1391no—
161C2×#41C2×D13911yescharacteristic
162C2×#41C2×D13911yescharacteristic
163C22×Q8—1391no—
164C22×D4—1391no—
165#137—2784no—
166AGL(1,ℤ/8)—2784no—
167#135—24no—
168C2×Q16—1392no—
169C2×Q16C2×D13911yescharacteristic, complemented
170C2×SD16—2784no—
171C2×SD16—1392no—
172C2×SD16—1392no—
173C2×SD16—1392no—
174C2×SD16—1392no—
175C2×SD16C2×D13911yescharacteristic, complemented
176C2×SD16C2×D13911yescharacteristic, complemented
177C2×D8—1392no—
178C2×D8C2×D13911yescharacteristic, complemented
179C2×M16—1391no—
180C22×C8C2×D13911yescharacteristic
181C4⋊Q8—1392no—
182#127—1392no—
183#124—1392no—
184#124—1392no—
185#123—2782no—
186C22⋊Q8—2782no—
187#121—2782no—
188#120—2782no—
189#117—1391no—
190#97—1392no—
191C4×C8—1392no—
192C24—2781no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—2781no—
198C2×Q8—2782no—
199C2×Q8—2782no—
200C2×Q8—1392no—
201C2×Q8C22×D13911yescharacteristic
202C2×Q8C22×D13911yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—2784no—
206C2×D4—2782no—
207C2×D4—2781no—
208C2×D4—2782no—
209C2×D4—1392no—
210C2×D4C22×D13911yescharacteristic
211C2×D4C22×D13911yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—2781no—
215C22×C4C22×D13911yescharacteristic
216Q16—22no—
217Q16—2784no—
218SD16—22no—
219SD16—22no—
220SD16—2784no—
221SD16—2784no—
222SD16—2784no—
223SD16—2784no—
224D8—22no—
225D8—2784no—
226M16—1394no—
227C2×C8—1392no—
228C2×C8C22⋊D13914yescomplemented
229C2×C8C22×D13911yescharacteristic
230C2×C8C22×D13911yescharacteristic
231C4⋊C4—2784no—
232C4⋊C4—1392no—
233C22⋊C4—2784no—
234C22⋊C4—2784no—
235C22⋊C4—1392no—
236C42—1392no—
237C23—21no—
238C23—21no—
239C23—2782no—
240C23—5562no—
241C23—11122no—
242C23D4×D13911yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—2782no—
248Q8—2782no—
249Q8—5562no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—2782no—
257D4—2782no—
258D4—5562no—
259D4—11124no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—2782no—
265C2×C4—5562no—
266C2×C4—1394no—
267C2×C4D4×D13911yescharacteristic
268C2×C4D4×D13912yes—
269C2×C4C2×C22⋊D13912yes—
270C2×C4C23×D13911yescharacteristic
271C8—1394no—
272C8C2×C22⋊D13912yes—
273C8C2×C22⋊D13912yes—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—5564no—
280C22—5562no—
281C22—11124no—
282C22#1798483812yes—
283C22C2×D4×D13911yescharacteristic
284C4—41no—
285C4—41no—
286C4—2784no—
287C4—5562no—
288C4#1798483812yes—
289C4C2×D4×D13911yescharacteristic
290C4C22×C22⋊D13911yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—11122no—
295C2C2×#1798483811yescharacteristic
296C2#2258176012yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#135×C139C2
socleC22×C139C22×D4
hypercenterC2×#135D139
hypocenterC139#3154
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#17984872C2semidirect
2. C2×#17984867C2semidirect
3. C22×#14555774C2semidirect
4. #22581524C2semidirect
5. #22581517C2semidirect
6. #22581346C2semidirect
7. #22581341C2semidirect
8. #22581334C2semidirect
9. #22581324C2semidirect
10. #22580908C2semidirect
11. C2×#135×C139C2semidirect
16. C2×#14555775C22semidirect
20. C2×#14555773C22semidirect
24. #17984840C22semidirect
27. #17984829C22semidirect
33. #17984752C22semidirect
34. C8×Dic139C22semidirect
38. C2×Q16×C139C22semidirect
39. C2×SD16×C139C22semidirect
40. C2×SD16×C139C22semidirect
41. C2×D8×C139C22semidirect
60. #14555769D4semidirect
85. C2×C8×C139D4semidirect
148. C139#3154semidirect
152. C2×#135D139semidirect
169. C2×Q16C2×D139semidirect
175. C2×SD16C2×D139semidirect
176. C2×SD16C2×D139semidirect
178. C2×D8C2×D139semidirect
228. C2×C8C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848722
C2×#179848672
C22×#145557742
#225815242
#225815172
#225813462
#225813412
#225813342
#225813242
#225809082
C2×#135×C1392
#3154139