Finite Group Databasebeta

← #31818223

Subgroups — #31818223

Order 17792.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581661C211yesmaximal, characteristic, complemented
2#22581587C211yesmaximal, characteristic
3#22581298C211yesmaximal, characteristic, complemented
4#22581273C211yesmaximal, characteristic, complemented
5#22581269C211yesmaximal, characteristic, complemented
6#22581242C211yesmaximal, characteristic, complemented
7#22581185C211yesmaximal, characteristic, complemented
8#22581151C211yesmaximal, characteristic, complemented
9#22581103C211yesmaximal, characteristic, complemented
10#22581102C211yesmaximal, characteristic, complemented
11#22581038C211yesmaximal, characteristic, complemented
12C8×C22⋊D139C211yesmaximal, characteristic, complemented
13C2×#17984764C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#465×C139C211yesmaximal, characteristic, complemented
16C22×D556C2211yescharacteristic
17C2×D4×D139—21no—
18C2×D4×D139C2211yescharacteristic
19C2×#14555772C2211yescharacteristic
20C2×#14555772C2211yescharacteristic, complemented
21C2×C8×D139C2211yescharacteristic, complemented
22#17984841C2211yescharacteristic, complemented
23#17984838C2211yescharacteristic
24#17984832—21no—
25#17984822—21no—
26#17984819—21no—
27#17984818C2211yescharacteristic, complemented
28#17984817C2211yescharacteristic
29#17984815—21no—
30#17984812—21no—
31#17984810—21no—
32Q8×Dic139C2211yescharacteristic, complemented
33#17984804C2211yescharacteristic
34C4×C22⋊D139C2211yescharacteristic
35(C22⋊D139)⋊C4—21no—
36C2×C4⋊Dic139C2211yescharacteristic, complemented
37C4⋊C4×D139C2211yescharacteristic, complemented
38#17984773C2211yescharacteristic, complemented
39#17984773C2211yescharacteristic, complemented
40Dic139⋊C8C2211yescharacteristic, complemented
41#17984764C2211yescharacteristic
42#17984764C2211yescharacteristic
43#17984764C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic, complemented
46#17984763C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic, complemented
49C22⋊(C139⋊C8)C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic, complemented
53C22×C8×C139C2211yescharacteristic, complemented
54C22⋊Q8×C139C2211yescharacteristic, complemented
55#121×C139C2211yescharacteristic
56#106×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C23×D139—21no—
61C2×Dic278—21no—
62C2×D556—22no—
63C2×D556—21no—
64C2×D556—21no—
65C2×D556—41no—
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139D411yescharacteristic
72D4×D139—22no—
73D4×D139—41no—
74D4×D139—44no—
75C22×Dic139—21no—
76C2×C4×D139—21no—
77C2×C4×D139—21no—
78C2×C4×D139C2311yescharacteristic
79#14555772—22no—
80#14555772—41no—
81C2×C139⋊C8C2311yescharacteristic
82C2×C139⋊C8C2311yescharacteristic
83C8×D139—41no—
84C4⋊Dic139—21no—
85C4⋊Dic139—21no—
86C4⋊Dic139C2311yescharacteristic
87C4⋊Dic139C2311yescharacteristic
88Dic139⋊C4—21no—
89Dic139⋊C4—21no—
90Dic139⋊C4—21no—
91Dic139⋊C4D411yescharacteristic
92C22⋊Dic139D411yescharacteristic
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4D411yescharacteristic
97C4×Dic139—21no—
98C4×Dic139C2311yescharacteristic
99C2×Q8×C139C2311yescharacteristic
100C2×D4×C139—21no—
101C2×D4×C139C2311yescharacteristic
102C22×C4×C139C2311yescharacteristic
103SD16×C139—41no—
104C2×C8×C139—41no—
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139—21no—
108C4⋊C4×C139C2311yescharacteristic
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C22⋊C4×C139—21no—
112C22×D139—21no—
113C22×D139—21no—
114C22×D139—42no—
115C22×D139—42no—
116C22×D139—42no—
117C22×D139—42no—
118C22×D139—81no—
119C22×D139—81no—
120C22×D139C2×D411yescharacteristic
121Dic278—81no—
122D556—21no—
123D556—21no—
124D556—21no—
125D556—42no—
126D556—42no—
127D556#4112yes—
128C22⋊D139—42no—
129C22⋊D139—42no—
130C22⋊D139—81no—
131C22⋊D139SD1614yescomplemented
132C2×Dic139—21no—
133C2×Dic139—21no—
134C2×Dic139—81no—
135C2×Dic139C2×D411yescharacteristic
136C2×Dic139C2×D411yescharacteristic
137C2×Dic139C2×D411yescharacteristic
138C4×D139—21no—
139C4×D139—21no—
140C4×D139—42no—
141C4×D139—81no—
142C139⋊C8—21no—
143C139⋊C8—21no—
144C23×C139—21no—
145C23×C139C2×D411yescharacteristic
146Q8×C139—21no—
147Q8×C139—21no—
148D4×C139—21no—
149D4×C139—21no—
150D4×C139—42no—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2411yescharacteristic
158C8×C139—21no—
159C8×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—41no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139C2×SD1612yes—
166C22×C139C22×D411yescharacteristic
167C2×D139—21no—
168C2×D139—21no—
169C2×D139—22no—
170C2×D139—41no—
171C2×D139—41no—
172C2×D139—41no—
173C2×D139—41no—
174C2×D139—41no—
175C2×D139—84no—
176C2×D139—84no—
177C2×D139C2×SD1612yes—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—41no—
181C4×C139—41no—
182C4×C139C2×#4111yescharacteristic
183C4×C139H(5,𝔽2)11yescharacteristic
184Dic139—21no—
185Dic139—21no—
186Dic139—41no—
187Dic139—41no—
188Dic139C2×SD1612yes—
189C2×C139—22no—
190C2×C139—81no—
191C2×C139#54611yescharacteristic
192C2×C139C22×SD1611yescharacteristic
193C2×C139#57611yescharacteristic
194D139—22no—
195D139—42no—
196D139—81no—
197C139#329511yescharacteristic, complemented, Sylow
198#3295—1391nomaximal, Sylow
199#554—1391no—
200D42—1391no—
201#486—1391no—
202#481—1391no—
203#481—1391no—
204#476—1391no—
205#465—1391no—
206#465D13911yescharacteristic, complemented
207#460—1391no—
208#450—1391no—
209#450—1391no—
210C4×SD16—1391no—
211C8×D4—1391no—
212C2×#102—1391no—
213C2×#102—1391no—
214C22×D4—2781no—
215C22×D4—1391no—
216C22×D4—1391no—
217C2×SD16—1391no—
218C2×SD16—1391no—
219C2×SD16C2×D13911yescharacteristic, complemented
220C22×C8—1391no—
221C22×C8C2×D13911yescharacteristic, complemented
222C4⋊Q8—1391no—
223#127—1391no—
224#125—2781no—
225C22⋊Q8—2781no—
226C22⋊Q8—2781no—
227C22⋊Q8—1391no—
228C22⋊Q8C2×D13911yescharacteristic, complemented
229#121—2781no—
230#121—1391no—
231#121C2×D13911yescharacteristic
232#120—2781no—
233#120—2781no—
234C4×Q8—1391no—
235C4×D4—2781no—
236C4×D4—1391no—
237C4×D4—1391no—
238C2×C4⋊C4—1391no—
239C2×C4⋊C4—1391no—
240#106—1391no—
241#106—1391no—
242#106C2×D13911yescharacteristic, complemented
243C4⋊C8—1391no—
244#103C2×D13911yescharacteristic, complemented
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102—1391no—
250#102—1391no—
251#102—1391no—
252#102—1391no—
253#102C2×D13911yescharacteristic, complemented
254C22⋊C8—1391no—
255C22⋊C8—1391no—
256C4×C8—1391no—
257C24—2781no—
258C24—2781no—
259C2×Q8—2781no—
260C2×Q8C22×D13911yescharacteristic
261C2×D4—21no—
262C2×D4—2782no—
263C2×D4—2781no—
264C2×D4—2782no—
265C2×D4—2781no—
266C2×D4—2781no—
267C2×D4—2781no—
268C2×D4—2781no—
269C2×D4—5561no—
270C2×D4—5561no—
271C2×D4—5564no—
272C2×D4—1391no—
273C2×D4—1391no—
274C2×D4—1391no—
275C2×D4C22×D13911yescharacteristic
276C22×C4—2781no—
277C22×C4—2781no—
278C22×C4—2781no—
279C22×C4—1391no—
280C22×C4C22×D13911yescharacteristic
281SD16—41no—
282SD16—2782no—
283SD16—5561no—
284C2×C8—41no—
285C2×C8—5561no—
286C2×C8—1391no—
287C2×C8—1391no—
288C2×C8C22×D13911yescharacteristic
289C2×C8C22×D13911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2781no—
292C4⋊C4—2781no—
293C4⋊C4—2781no—
294C4⋊C4—2781no—
295C4⋊C4—2781no—
296C4⋊C4—1391no—
297C4⋊C4—1391no—
298C4⋊C4—1391no—
299C4⋊C4C22×D13911yescharacteristic
300C4⋊C4C22×D13911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2781no—
304C22⋊C4—2781no—
305C22⋊C4—2781no—
306C22⋊C4—1391no—
307C22⋊C4—1391no—
308C42—2781no—
309C42—1391no—
310C23—21no—
311C23—2781no—
312C23—2781no—
313C23—5562no—
314C23—5562no—
315C23—5562no—
316C23—5562no—
317C23—11121no—
318C23—11121no—
319C23—1391no—
320C23D4×D13911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—11121no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2781no—
328D4—2781no—
329D4—2781no—
330D4—5562no—
331D4—5562no—
332D4—5562no—
333D4—5562no—
334D4—11121no—
335D4—1394no—
336D4—1392no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2781no—
343C2×C4—2781no—
344C2×C4—2781no—
345C2×C4—2781no—
346C2×C4—5562no—
347C2×C4—11121no—
348C2×C4—11121no—
349C2×C4—1391no—
350C2×C4—1391no—
351C2×C4—1391no—
352C2×C4D4×D13911yescharacteristic
353C2×C4C23×D13911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2781no—
357C8—2781no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2781no—
364C22—2781no—
365C22—2782no—
366C22—5561no—
367C22—5561no—
368C22—5561no—
369C22—5561no—
370C22—5561no—
371C22—11124no—
372C22—11124no—
373C22—1392no—
374C22SD16×D13912yes—
375C22C2×D4×D13911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2781no—
381C4—2781no—
382C4—5561no—
383C4—5561no—
384C4—1392no—
385C4#41×D13911yescharacteristic
386C4#1798488711yescharacteristic
387C2—22no—
388C2—81no—
389C2—2782no—
390C2—5562no—
391C2—11121no—
392C2#2258159211yescharacteristic
393C2C2×SD16×D13911yescharacteristic
394C2#2258175511yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#465×C139C2
socleC22×C139C22×D4
prime radical#22581587C2
hypercenter#465D139
hypocenterC139#3295
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #22581661C2semidirect
3. #22581298C2semidirect
4. #22581273C2semidirect
5. #22581269C2semidirect
6. #22581242C2semidirect
7. #22581185C2semidirect
8. #22581151C2semidirect
9. #22581103C2semidirect
10. #22581102C2semidirect
11. #22581038C2semidirect
12. C8×C22⋊D139C2semidirect
13. C2×#17984764C2semidirect
14. #102×D139C2semidirect
15. #465×C139C2semidirect
20. C2×#14555772C22semidirect
21. C2×C8×D139C22semidirect
22. #17984841C22semidirect
27. #17984818C22semidirect
32. Q8×Dic139C22semidirect
36. C2×C4⋊Dic139C22semidirect
37. C4⋊C4×D139C22semidirect
38. #17984773C22semidirect
39. #17984773C22semidirect
40. Dic139⋊C8C22semidirect
43. #17984764C22semidirect
44. #17984764C22semidirect
45. #17984763C22semidirect
46. #17984763C22semidirect
48. #17984762C22semidirect
49. C22⋊(C139⋊C8)C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
52. C2×SD16×C139C22semidirect
53. C22×C8×C139C22semidirect
54. C22⋊Q8×C139C22semidirect
56. #106×C139C22semidirect
57. #103×C139C22semidirect
58. #102×C139C22semidirect
131. C22⋊D139SD16semidirect
197. C139#3295semidirect
206. #465D139semidirect
219. C2×SD16C2×D139semidirect
221. C22×C8C2×D139semidirect
228. C22⋊Q8C2×D139semidirect
242. #106C2×D139semidirect
244. #103C2×D139semidirect
253. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816612
#225815872
#225812982
#225812732
#225812692
#225812422
#225811852
#225811512
#225811032
#225811022
#225810382
C8×C22⋊D1392
C2×#179847642
#102×D1392
#465×C1392
#3295139