Finite Group Databasebeta

← #31817948

Subgroups — #31817948

Order 17792.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984866C211yesmaximal, characteristic, complemented
2C2×#17984862C211yesmaximal, characteristic, complemented
3#22581621C211yesmaximal, characteristic, complemented
4#22581591C211yesmaximal, characteristic, complemented
5#22581339C211yesmaximal, characteristic, complemented
6#22581202C211yesmaximal, characteristic, complemented
7#22581187C211yesmaximal, characteristic, complemented
8#22581178C211yesmaximal, characteristic, complemented
9#22581146C211yesmaximal, characteristic, complemented
10#22581112C211yesmaximal, characteristic, complemented
11#22581100C211yesmaximal, characteristic, complemented
12#22581088C211yesmaximal, characteristic, complemented
13#22581050C211yesmaximal, characteristic, complemented
14#22581021C211yesmaximal, characteristic, complemented
15#449×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic, complemented
17C2×#14555784C2211yescharacteristic
18C2×D4×D139C2211yescharacteristic
19#17984866—24no—
20#17984862—24no—
21C2×#14555775C2211yescharacteristic, complemented
22C2×#14555774C2211yescharacteristic
23C2×#14555773C2211yescharacteristic
24C2×#14555772C2211yescharacteristic, complemented
25C2×D1112C2211yescharacteristic
26C2×#14555770C2211yescharacteristic
27C2×#14555770C2211yescharacteristic
28C2×#14555768C2211yescharacteristic
29C22×C139⋊C8C2211yescharacteristic, complemented
30#17984838—21no—
31#17984838C2211yescharacteristic, complemented
32#17984831C2211yescharacteristic
33#17984825—21no—
34#17984818C2211yescharacteristic
35#17984817C2211yescharacteristic
36#17984816C2211yescharacteristic
37#17984815—21no—
38#17984814—21no—
39#17984814—21no—
40#17984810—21no—
41#17984807C2211yescharacteristic, complemented
42D4×Dic139C2211yescharacteristic
43C4×C22⋊D139C2211yescharacteristic
44(C22⋊D139)⋊C4—21no—
45C2×(C2×D139)⋊C4—21no—
46#17984775C2211yescharacteristic, complemented
47Dic139⋊C8C2211yescharacteristic, complemented
48#17984767C2211yescharacteristic, complemented
49#17984764C2211yescharacteristic, complemented
50#17984763C2211yescharacteristic, complemented
51#17984762C2211yescharacteristic
52(C2×D139)⋊C8C2211yescharacteristic
53#17984752C2211yescharacteristic, complemented
54C2×#41×C139C2211yescharacteristic
55C2×SD16×C139C2211yescharacteristic, complemented
56C2×D8×C139C2211yescharacteristic
57#121×C139C2211yescharacteristic, complemented
58#103×C139C2211yescharacteristic, complemented
59#102×C139C2211yescharacteristic
60C22⋊C8×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62#14555785—22no—
63#14555785—41no—
64#14555784—22no—
65#14555784—41no—
66C2×Dic278C2311yescharacteristic
67C2×D556—21no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C2×C22⋊D139—21no—
73C2×C22⋊D139—21no—
74C2×C22⋊D139—21no—
75C2×C22⋊D139—21no—
76C2×C22⋊D139D411yescharacteristic
77D4×D139—22no—
78D4×D139—41no—
79C22×Dic139—21no—
80C22×Dic139—21no—
81C2×C4×D139—21no—
82C2×C4×D139C2311yescharacteristic
83#14555775—22no—
84#14555774—22no—
85#14555773D414yescomplemented
86#14555772—22no—
87D1112—41no—
88#14555770—22no—
89#14555770—22no—
90#14555768—22no—
91C2×C139⋊C8—22no—
92C2×C139⋊C8C2311yescharacteristic
93C2×C139⋊C8C2311yescharacteristic
94C4⋊Dic139C2311yescharacteristic
95Dic139⋊C4—21no—
96Dic139⋊C4—21no—
97Dic139⋊C4D411yescharacteristic
98C22⋊Dic139—21no—
99C22⋊Dic139D411yescharacteristic
100(C2×D139)⋊C4—21no—
101(C2×D139)⋊C4—21no—
102(C2×D139)⋊C4—21no—
103(C2×D139)⋊C4—21no—
104(C2×D139)⋊C4—21no—
105(C2×D139)⋊C4D411yescharacteristic
106C4×Dic139—21no—
107C4×Dic139C2311yescharacteristic
108#41×C139—22no—
109#41×C139—41no—
110C2×Q8×C139C2311yescharacteristic
111C2×D4×C139—21no—
112C2×D4×C139—21no—
113C2×D4×C139C2311yescharacteristic
114C2×D4×C139C2311yescharacteristic
115C22×C4×C139—21no—
116C22×C4×C139C2311yescharacteristic
117SD16×C139—41no—
118D8×C139—22no—
119C2×C8×C139C2311yescharacteristic
120C2×C8×C139C2311yescharacteristic
121C4⋊C4×C139C2311yescharacteristic
122C22⋊C4×C139—21no—
123C22×D139—21no—
124C22×D139—21no—
125C22×D139—42no—
126C22×D139—42no—
127C22×D139—81no—
128C22×D139C2×D411yescharacteristic
129Dic278—21no—
130Dic278C2×D412yes—
131D556—21no—
132D556—21no—
133D556—21no—
134D556—21no—
135D556—81no—
136C22⋊D139—41no—
137C22⋊D139—42no—
138C22⋊D139—42no—
139C22⋊D139—42no—
140C22⋊D139—42no—
141C22⋊D139—81no—
142C22⋊D139—81no—
143C2×Dic139—21no—
144C2×Dic139—21no—
145C2×Dic139—42no—
146C2×Dic139—81no—
147C2×Dic139C2×D411yescharacteristic
148C2×Dic139C2×D411yescharacteristic
149C2×Dic139C2×D411yescharacteristic
150C4×D139—21no—
151C4×D139—21no—
152C4×D139—42no—
153C139⋊C8—21no—
154C139⋊C8C2×D412yes—
155C23×C139—21no—
156C23×C139—21no—
157C23×C139C2×D411yescharacteristic
158Q8×C139—21no—
159Q8×C139—21no—
160D4×C139—21no—
161D4×C139—21no—
162D4×C139—21no—
163D4×C139—42no—
164D4×C139—81no—
165D4×C139C2×D412yes—
166C2×C4×C139—21no—
167C2×C4×C139—21no—
168C2×C4×C139—21no—
169C2×C4×C139—21no—
170C2×C4×C139—42no—
171C2×C4×C139C2×D411yescharacteristic
172C2×C4×C139C2411yescharacteristic
173C8×C139—21no—
174C8×C139—21no—
175C22×C139—21no—
176C22×C139—22no—
177C22×C139—21no—
178C22×C139—21no—
179C22×C139—41no—
180C22×C139—41no—
181C22×C139—41no—
182C22×C139—41no—
183C22×C139—41no—
184C22×C139C22×D411yescharacteristic
185C2×D139—21no—
186C2×D139—21no—
187C2×D139—21no—
188C2×D139—41no—
189C2×D139—41no—
190C2×D139—41no—
191C2×D139—41no—
192C2×D139—41no—
193C2×D139—41no—
194C2×D139—84no—
195C4×C139—21no—
196C4×C139—41no—
197C4×C139—41no—
198C4×C139C22×D411yescharacteristic
199C4×C139H(5,𝔽2)11yescharacteristic
200Dic139—21no—
201Dic139—22no—
202Dic139—21no—
203Dic139—21no—
204Dic139—41no—
205C2×C139—42no—
206C2×C139—41no—
207C2×C139—81no—
208C2×C139D4211yescharacteristic
209C2×C139#57511yescharacteristic
210C2×C139#57611yescharacteristic
211D139—41no—
212D139—81no—
213D139—81no—
214C139#326811yescharacteristic, complemented, Sylow
215#3268—1391nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1391no—
217C2×#135—1391no—
218#550—1391no—
219#546—1391no—
220#496—1391no—
221#468—1391no—
222#466—1391no—
223#464—1391no—
224#459—1391no—
225#452—1391no—
226#449—1391no—
227#449D13911yescharacteristic, complemented
228#447—1391no—
229#440—1391no—
230#435—1391no—
231C2×#41—1391no—
232C2×#41—1391no—
233C2×#41C2×D13911yescharacteristic
234C22×D4—1391no—
235AGL(1,ℤ/8)—2784no—
236#135—2784no—
237C2×Q16—1391no—
238C2×SD16—1391no—
239C2×SD16—1391no—
240C2×SD16—1391no—
241C2×SD16C2×D13911yescharacteristic, complemented
242C2×D8—1391no—
243C2×D8—1391no—
244C2×D8—1391no—
245C2×D8C2×D13911yescharacteristic
246C2×M16—1391no—
247C22×C8—1391no—
248#127—2781no—
249#127—1391no—
250#124—1391no—
251#123—2781no—
252C22⋊Q8—1391no—
253#121—2781no—
254#121—2781no—
255#121—2781no—
256#121—1391no—
257#121—1391no—
258#121C2×D13911yescharacteristic, complemented
259#120—2781no—
260C4×Q8—1391no—
261C4×D4—2781no—
262C4×D4—1391no—
263C4×D4—1391no—
264C2×C22⋊C4—2781no—
265#107—1391no—
266C4⋊C8—1391no—
267#103—1391no—
268#103C2×D13911yescharacteristic, complemented
269#102—1391no—
270#102—1391no—
271#102—1391no—
272#102C2×D13911yescharacteristic
273C22⋊C8—1391no—
274C22⋊C8C2×D13911yescharacteristic, complemented
275#97—1391no—
276C24—2781no—
277#41—22no—
278#41—41no—
279#41—2782no—
280#41—2782no—
281#41—5561no—
282#41—5561no—
283C2×Q8—1391no—
284C2×Q8C22×D13911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2781no—
288C2×D4—2782no—
289C2×D4—2781no—
290C2×D4—2781no—
291C2×D4—2781no—
292C2×D4—2781no—
293C2×D4—2781no—
294C2×D4—2781no—
295C2×D4—5561no—
296C2×D4—1391no—
297C2×D4—1391no—
298C2×D4—1391no—
299C2×D4C22×D13911yescharacteristic
300C2×D4C22×D13911yescharacteristic
301C22×C4—21no—
302C22×C4—2781no—
303C22×C4—2781no—
304C22×C4—2781no—
305C22×C4—1391no—
306C22×C4C22×D13911yescharacteristic
307Q16—2782no—
308SD16—41no—
309SD16—2782no—
310SD16—2782no—
311SD16—1394no—
312D8—22no—
313D8—2782no—
314D8—2782no—
315D8—5561no—
316M16—2782no—
317C2×C8—2782no—
318C2×C8—1391no—
319C2×C8—1391no—
320C2×C8C22×D13911yescharacteristic
321C2×C8C22×D13911yescharacteristic
322C4⋊C4—2781no—
323C4⋊C4—2781no—
324C4⋊C4—1391no—
325C4⋊C4—1391no—
326C4⋊C4C22×D13911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—2781no—
329C22⋊C4—2781no—
330C22⋊C4—2781no—
331C22⋊C4—2781no—
332C22⋊C4—2781no—
333C22⋊C4—2781no—
334C22⋊C4—1391no—
335C22⋊C4—1391no—
336C42—2781no—
337C42—1391no—
338C23—21no—
339C23—21no—
340C23—2781no—
341C23—2781no—
342C23—5562no—
343C23—5562no—
344C23—11121no—
345C23—1391no—
346C23D4×D13911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—2781no—
350Q8—1392no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—81no—
356D4—2781no—
357D4—2781no—
358D4—2781no—
359D4—2781no—
360D4—5561no—
361D4—5562no—
362D4—5562no—
363D4—5562no—
364D4—5562no—
365D4—11121no—
366D4—11121no—
367D4—11121no—
368D4D4×D13912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—2781no—
375C2×C4—2781no—
376C2×C4—2781no—
377C2×C4—2781no—
378C2×C4—5562no—
379C2×C4—5562no—
380C2×C4—11121no—
381C2×C4—1391no—
382C2×C4—1391no—
383C2×C4—1391no—
384C2×C4D4×D13911yescharacteristic
385C2×C4C23×D13911yescharacteristic
386C8—21no—
387C8—21no—
388C8—2781no—
389C8—1392no—
390C22—21no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2781no—
400C22—2781no—
401C22—2781no—
402C22—5561no—
403C22—5561no—
404C22—5561no—
405C22—5561no—
406C22—5561no—
407C22—5561no—
408C22—11124no—
409C22C2×D4×D13911yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—2781no—
414C4—2782no—
415C4—2781no—
416C4—2781no—
417C4—5561no—
418C4C2×D4×D13911yescharacteristic
419C4#1798488711yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—5561no—
424C2—11121no—
425C2—11121no—
426C2#2258158511yescharacteristic
427C2#2258175011yescharacteristic
428C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#449×C139C2
socleC22×C139C22×D4
hypercenter#449D139
hypocenterC139#3268
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#17984866C2semidirect
2. C2×#17984862C2semidirect
3. #22581621C2semidirect
4. #22581591C2semidirect
5. #22581339C2semidirect
6. #22581202C2semidirect
7. #22581187C2semidirect
8. #22581178C2semidirect
9. #22581146C2semidirect
10. #22581112C2semidirect
11. #22581100C2semidirect
12. #22581088C2semidirect
13. #22581050C2semidirect
14. #22581021C2semidirect
15. #449×C139C2semidirect
16. C2×#14555785C22semidirect
21. C2×#14555775C22semidirect
24. C2×#14555772C22semidirect
29. C22×C139⋊C8C22semidirect
31. #17984838C22semidirect
41. #17984807C22semidirect
46. #17984775C22semidirect
47. Dic139⋊C8C22semidirect
48. #17984767C22semidirect
49. #17984764C22semidirect
50. #17984763C22semidirect
53. #17984752C22semidirect
55. C2×SD16×C139C22semidirect
57. #121×C139C22semidirect
58. #103×C139C22semidirect
60. C22⋊C8×C139C22semidirect
85. #14555773D4semidirect
214. C139#3268semidirect
227. #449D139semidirect
241. C2×SD16C2×D139semidirect
258. #121C2×D139semidirect
268. #103C2×D139semidirect
274. C22⋊C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848662
C2×#179848622
#225816212
#225815912
#225813392
#225812022
#225811872
#225811782
#225811462
#225811122
#225811002
#225810882
#225810502
#225810212
#449×C1392
#3268139