Finite Group Databasebeta

← #31815759

Subgroups — #31815759

Order 17792.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#17984888C211yesmaximal, characteristic, complemented
2#22581751C211yesmaximal, characteristic, complemented
3#22581517C211yesmaximal, characteristic, complemented
4#22581129C214yesmaximal, complemented
5#22581119C214yesmaximal, complemented
6#22580970C211yesmaximal, characteristic, complemented
7#22580969C211yesmaximal, characteristic, complemented
8C2×#17984758C211yesmaximal, characteristic, complemented
9#575×C139C211yesmaximal, characteristic, complemented
10#17984888—22no—
11#17984888—22no—
12#17984888—22no—
13#17984888C2214yes—
14C2×#14555786—21no—
15C2×#14555785—21no—
16C2×#14555785C2211yescharacteristic
17C22×D556—21no—
18C22×D556C2211yescharacteristic
19C2×D4×D139—22no—
20C2×D4×D139—21no—
21#17984873C2212yescomplemented
22#17984872—21no—
23#17984868C2212yescomplemented
24#17984867—21no—
25#17984862—22no—
26C2×#14555769C2211yescharacteristic, complemented
27#17984838C2212yescomplemented
28#17984831C2212yescomplemented
29#17984816—22no—
30#17984810—22no—
31#17984801C2211yescharacteristic, complemented
32#17984769C2214yescomplemented
33#17984768C2214yescomplemented
34#17984758C2214yescomplemented
35C2×#41×C139C2211yescharacteristic
36C2×#41×C139C2211yescharacteristic, complemented
37#137×C139—21no—
38#137×C139C2212yescomplemented
39AGL(1,ℤ/8)×C139—21no—
40AGL(1,ℤ/8)×C139C2212yescomplemented
41#135×C139—22no—
42C2×M16×C139C2211yescharacteristic, complemented
43C23×D139—22no—
44C23×D139D412yes—
45#14555786—24no—
46#14555786—24no—
47#14555785—24no—
48#14555785—24no—
49#14555785—21no—
50#14555785—21no—
51#14555785D412yescomplemented
52#14555785C2312yes—
53C2×Dic278D411yescharacteristic, complemented
54C2×D556—22no—
55C2×D556—24no—
56C2×D556—24no—
57C2×D556—21no—
58C2×D556—21no—
59C2×D556—21no—
60C2×D556—21no—
61C2×D556D412yes—
62C2×D556D411yescharacteristic, complemented
63C2×D556C2312yes—
64C2×C22⋊D139—22no—
65C2×C22⋊D139—24no—
66C2×C22⋊D139—21no—
67D4×D139—28no—
68D4×D139—24no—
69D4×D139—28no—
70D4×D139—24no—
71C2×C4×D139—22no—
72C2×C4×D139—21no—
73#14555775—22no—
74#14555773—22no—
75#14555772—22no—
76#14555770—22no—
77#14555769—21no—
78#14555769C2312yescomplemented
79C2×C139⋊C8—21no—
80C4⋊Dic139—21no—
81C22⋊Dic139—21no—
82(C2×D139)⋊C4—24no—
83C4×Dic139C2312yescomplemented
84#41×C139—21no—
85#41×C139—21no—
86#41×C139—21no—
87#41×C139—21no—
88#41×C139—21no—
89#41×C139—21no—
90#41×C139D412yescomplemented
91#41×C139C2312yes—
92C2×Q8×C139D411yescharacteristic, complemented
93C2×Q8×C139C2311yescharacteristic, complemented
94C2×D4×C139—21no—
95C2×D4×C139—21no—
96C2×D4×C139D411yescharacteristic, complemented
97C2×D4×C139C2311yescharacteristic, complemented
98C22×C4×C139—21no—
99C22×C4×C139—21no—
100C22×C4×C139C2311yescharacteristic
101Q16×C139—22no—
102SD16×C139—22no—
103SD16×C139—22no—
104D8×C139—22no—
105M16×C139—21no—
106M16×C139C2312yescomplemented
107C2×C8×C139—21no—
108C22×D139—22no—
109C22×D139—21no—
110C22×D139—28no—
111C22×D139—22no—
112C22×D139—82no—
113C22×D139—84no—
114C22×D139C2×D414yes—
115Dic278—21no—
116Dic278C2×D412yes—
117D556—28no—
118D556—22no—
119D556—22no—
120D556—21no—
121D556—22no—
122D556—22no—
123D556C2×D412yes—
124C22⋊D139—28no—
125C22⋊D139—22no—
126C22⋊D139—22no—
127C22⋊D139—84no—
128C2×Dic139—21no—
129C2×Dic139—22no—
130C4×D139—28no—
131C4×D139—22no—
132C4×D139—22no—
133C139⋊C8—22no—
134C23×C139—21no—
135C23×C139—21no—
136C23×C139C2×D411yescharacteristic
137Q8×C139—21no—
138Q8×C139—21no—
139Q8×C139—21no—
140Q8×C139C2×D412yes—
141D4×C139—22no—
142D4×C139—22no—
143D4×C139—21no—
144D4×C139—21no—
145D4×C139—21no—
146D4×C139—41no—
147D4×C139—41no—
148D4×C139C2×D412yes—
149C2×C4×C139—21no—
150C2×C4×C139—22no—
151C2×C4×C139—22no—
152C2×C4×C139—21no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139C2×D411yescharacteristic
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2×D411yescharacteristic
158C2×C4×C139C2×D411yescharacteristic
159C2×C4×C139C2×D411yescharacteristic
160C2×C4×C139C2411yescharacteristic
161C8×C139—22no—
162C22×C139—22no—
163C22×C139—41no—
164C22×C139—42no—
165C22×C139—42no—
166C22×C139—41no—
167C22×C139#12011yescharacteristic
168C22×C139#12011yescharacteristic
169C22×C139C22×D411yescharacteristic
170C2×D139—24no—
171C2×D139—22no—
172C2×D139—44no—
173C2×D139—42no—
174C2×D139—44no—
175C2×D139—82no—
176C2×D139—88no—
177C4×C139—22no—
178C4×C139—41no—
179C4×C139#12011yescharacteristic
180C4×C139#12011yescharacteristic
181C4×C139C22×D411yescharacteristic
182C4×C139C22×D411yescharacteristic
183Dic139—22no—
184Dic139—42no—
185C2×C139—21no—
186C2×C139—21no—
187C2×C139—21no—
188C2×C139—42no—
189C2×C139—81no—
190C2×C139C2×#12011yescharacteristic
191D139—44no—
192D139—42no—
193C139#301911yescharacteristic, complemented, Sylow
194#3019—1391nomaximal, Sylow
195C2×H(5,𝔽2)—1391no—
196#575—1391no—
197#575D13911yescharacteristic, complemented
198#535—1391no—
199#455—1394no—
200#453—1394no—
201#421—1391no—
202#421—1391no—
203C2×#100—1391no—
204H(5,𝔽2)—2782no—
205H(5,𝔽2)—2782no—
206H(5,𝔽2)—2782no—
207H(5,𝔽2)—1394no—
208C2×#41—2781no—
209C2×#41—2781no—
210C2×#41—1391no—
211C2×#41C2×D13911yescharacteristic
212C2×#41C2×D13911yescharacteristic, complemented
213C22×D4—2781no—
214C22×D4—2782no—
215C22×D4—2781no—
216C22×D4—1391no—
217#137—21no—
218#137—2781no—
219#137—1392no—
220#137C2×D13912yescomplemented
221AGL(1,ℤ/8)—21no—
222AGL(1,ℤ/8)—2781no—
223AGL(1,ℤ/8)—1392no—
224AGL(1,ℤ/8)C2×D13912yescomplemented
225#135—22no—
226#135—2782no—
227C2×M16—1391no—
228C2×M16C2×D13911yescharacteristic, complemented
229#127—1392no—
230#124—1392no—
231#121—2782no—
232#120—2782no—
233#117—1391no—
234#104—1394no—
235#104—1394no—
236#100—1394no—
237C24—2782no—
238C24—1392no—
239#41—21no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—2784no—
246#41—2784no—
247#41—2784no—
248#41—2784no—
249#41—2781no—
250#41—2781no—
251#41—1392no—
252#41—1392no—
253#41C22⋊D13912yescomplemented
254#41C22×D13912yes—
255C2×Q8—1391no—
256C2×Q8C22⋊D13911yescharacteristic, complemented
257C2×Q8C22×D13911yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—2782no—
261C2×D4—2784no—
262C2×D4—2784no—
263C2×D4—2788no—
264C2×D4—2784no—
265C2×D4—2788no—
266C2×D4—2782no—
267C2×D4—2781no—
268C2×D4—2784no—
269C2×D4—2784no—
270C2×D4—2781no—
271C2×D4—2781no—
272C2×D4—2781no—
273C2×D4—2781no—
274C2×D4—1392no—
275C2×D4—1391no—
276C2×D4—1392no—
277C2×D4C22⋊D13911yescharacteristic, complemented
278C2×D4C22×D13911yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—2782no—
282C22×C4—2781no—
283C22×C4C22×D13911yescharacteristic
284Q16—22no—
285Q16—2782no—
286SD16—22no—
287SD16—22no—
288SD16—2782no—
289SD16—2782no—
290D8—22no—
291D8—2782no—
292M16—21no—
293M16—2781no—
294M16—1392no—
295M16C22×D13912yescomplemented
296C2×C8—21no—
297C2×C8—2781no—
298C4⋊C4—2781no—
299C22⋊C4—2784no—
300C22⋊C4—2781no—
301C42—1392no—
302C23—21no—
303C23—21no—
304C23—2788no—
305C23—2782no—
306C23—2781no—
307C23—2782no—
308C23—11122no—
309C23—11124no—
310C23—1394no—
311C23D4×D13911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—2781no—
316Q8—1392no—
317Q8C2×C22⋊D13912yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—2788no—
326D4—2788no—
327D4—2782no—
328D4—2782no—
329D4—2782no—
330D4—2781no—
331D4—2782no—
332D4—2782no—
333D4—2782no—
334D4—11124no—
335D4—1392no—
336D4C2×C22⋊D13912yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—2788no—
344C2×C4—2781no—
345C2×C4—2782no—
346C2×C4—2782no—
347C2×C4—2782no—
348C2×C4D4×D13911yescharacteristic
349C2×C4D4×D13911yescharacteristic
350C2×C4D4×D13911yescharacteristic
351C2×C4C2×C22⋊D13911yescharacteristic
352C2×C4C2×C22⋊D13911yescharacteristic
353C2×C4C23×D13911yescharacteristic
354C8—22no—
355C8—2782no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—2784no—
362C22—2782no—
363C22—5564no—
364C22—5564no—
365C22—5562no—
366C22—11122no—
367C22—11128no—
368C22#1798481011yescharacteristic
369C22#1798481011yescharacteristic
370C22C2×D4×D13911yescharacteristic
371C4—22no—
372C4—41no—
373C4—2782no—
374C4—5562no—
375C4#1798481011yescharacteristic
376C4#1798481011yescharacteristic
377C4C2×D4×D13911yescharacteristic
378C4C22×C22⋊D13911yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—81no—
384C2—5564no—
385C2—5562no—
386C2C2×#1798481011yescharacteristic
subgroupG/H
centerC2C2×#17984810
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#575×C139C2
socleC2×C139C2×#120
hypercenter#575D139
hypocenterC139#3019
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#17984888C2semidirect
2. #22581751C2semidirect
3. #22581517C2semidirect
4. #22581129C2semidirect
5. #22581119C2semidirect
6. #22580970C2semidirect
7. #22580969C2semidirect
8. C2×#17984758C2semidirect
9. #575×C139C2semidirect
21. #17984873C22semidirect
23. #17984868C22semidirect
26. C2×#14555769C22semidirect
27. #17984838C22semidirect
28. #17984831C22semidirect
31. #17984801C22semidirect
32. #17984769C22semidirect
33. #17984768C22semidirect
34. #17984758C22semidirect
36. C2×#41×C139C22semidirect
38. #137×C139C22semidirect
40. AGL(1,ℤ/8)×C139C22semidirect
42. C2×M16×C139C22semidirect
51. #14555785D4semidirect
53. C2×Dic278D4semidirect
62. C2×D556D4semidirect
78. #14555769C23semidirect
83. C4×Dic139C23semidirect
90. #41×C139D4semidirect
92. C2×Q8×C139D4semidirect
93. C2×Q8×C139C23semidirect
96. C2×D4×C139D4semidirect
97. C2×D4×C139C23semidirect
106. M16×C139C23semidirect
193. C139#3019semidirect
197. #575D139semidirect
212. C2×#41C2×D139semidirect
220. #137C2×D139semidirect
224. AGL(1,ℤ/8)C2×D139semidirect
228. C2×M16C2×D139semidirect
253. #41C22⋊D139semidirect
256. C2×Q8C22⋊D139semidirect
257. C2×Q8C22×D139semidirect
277. C2×D4C22⋊D139semidirect
278. C2×D4C22×D139semidirect
295. M16C22×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848882
#225817512
#225815172
#225811292
#225811192
#225809702
#225809692
C2×#179847582
#575×C1392
#3019139