Finite Group Databasebeta

← #31818252

Subgroups — #31818252

Order 17792.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581651C211yesmaximal, characteristic, complemented
2#22581594C211yesmaximal, characteristic, complemented
3#22581309C211yesmaximal, characteristic, complemented
4#22581280C211yesmaximal, characteristic, complemented
5#22581256C211yesmaximal, characteristic, complemented
6#22581190C211yesmaximal, characteristic, complemented
7#22581184C211yesmaximal, characteristic, complemented
8#22581171C211yesmaximal, characteristic, complemented
9#22581101C211yesmaximal, characteristic, complemented
10#22581089C211yesmaximal, characteristic, complemented
11#22581035C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13#22580948C211yesmaximal, characteristic, complemented
14C2×#17984762C211yesmaximal, characteristic, complemented
15#484×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C22×D556C2211yescharacteristic
18C2×#14555772C2211yescharacteristic, complemented
19C2×D1112C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21C22×C139⋊C8C2211yescharacteristic
22C2×C8×D139C2211yescharacteristic, complemented
23#17984837—21no—
24#17984833C2211yescharacteristic, complemented
25#17984831C2211yescharacteristic
26#17984827—21no—
27#17984827—21no—
28#17984817—21no—
29#17984817C2211yescharacteristic
30#17984817C2211yescharacteristic, complemented
31#17984816—21no—
32#17984816C2211yescharacteristic
33#17984812—21no—
34#17984804C2211yescharacteristic
35#17984804C2211yescharacteristic, complemented
36C4×C22⋊D139—21no—
37C4×C22⋊D139C2211yescharacteristic
38#17984800C2211yescharacteristic, complemented
39C22⋊C4×D139—21no—
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42#17984766C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic
44#17984764C2211yescharacteristic
45#17984762C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic
49#17984762C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22⋊Q8×C139C2211yescharacteristic
53C2×C4⋊C4×C139C2211yescharacteristic
54#107×C139C2211yescharacteristic, complemented
55#107×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58C22⋊C8×C139C2211yescharacteristic
59C23×D139—21no—
60#14555786—22no—
61#14555786—41no—
62C2×D556—22no—
63C2×D556—21no—
64C2×D556—21no—
65C2×D556—21no—
66C2×D556—21no—
67C2×D556—41no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×D556C2311yescharacteristic
71C2×C22⋊D139—21no—
72C2×C22⋊D139D411yescharacteristic
73C2×C4×D139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76C2×C4×D139C2311yescharacteristic
77#14555772—41no—
78D1112—22no—
79D1112—41no—
80C2×C139⋊C8—41no—
81C2×C139⋊C8C2311yescharacteristic
82C2×C139⋊C8C2311yescharacteristic
83C8×D139—41no—
84C4⋊Dic139—21no—
85C4⋊Dic139C2311yescharacteristic
86Dic139⋊C4—21no—
87Dic139⋊C4D411yescharacteristic
88C22⋊Dic139D411yescharacteristic
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4—21no—
97(C2×D139)⋊C4D411yescharacteristic
98C4×Dic139—21no—
99C4×Dic139C2311yescharacteristic
100C2×Q8×C139C2311yescharacteristic
101C22×C4×C139—21no—
102C22×C4×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C2×C8×C139C2311yescharacteristic
105C4⋊C4×C139—21no—
106C4⋊C4×C139—21no—
107C4⋊C4×C139C2311yescharacteristic
108C4⋊C4×C139C2311yescharacteristic
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C22×D139—21no—
112C22×D139—21no—
113C22×D139—21no—
114C22×D139—42no—
115C22×D139—42no—
116C22×D139—81no—
117C22×D139C2×D411yescharacteristic
118D556—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122D556—21no—
123D556—42no—
124D556—42no—
125D556—81no—
126D556—81no—
127D556#4112yes—
128C22⋊D139—22no—
129C22⋊D139—42no—
130C2×Dic139—21no—
131C2×Dic139C2×D411yescharacteristic
132C2×Dic139C2×D411yescharacteristic
133C2×Dic139C2×D411yescharacteristic
134C4×D139—21no—
135C4×D139—21no—
136C4×D139—42no—
137C4×D139—81no—
138C4×D139—81no—
139C139⋊C8—21no—
140C139⋊C8—21no—
141C23×C139C2×D411yescharacteristic
142Q8×C139—21no—
143Q8×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—81no—
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2411yescharacteristic
153C8×C139—21no—
154C8×C139—21no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139#13512yes—
158C22×C139C22×D411yescharacteristic
159C2×D139—21no—
160C2×D139—22no—
161C2×D139—21no—
162C2×D139—21no—
163C2×D139—41no—
164C2×D139—41no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—41no—
168C2×D139—41no—
169C2×D139—41no—
170C2×D139—41no—
171C2×D139—84no—
172C4×C139—21no—
173C4×C139—41no—
174C4×C139—41no—
175C4×C139—41no—
176C4×C139—41no—
177C4×C139C2×#4111yescharacteristic
178C4×C139H(5,𝔽2)11yescharacteristic
179Dic139—21no—
180Dic139—21no—
181Dic139—21no—
182Dic139—41no—
183C2×C139—22no—
184C2×C139#54611yescharacteristic
185C2×C139C2×#13511yescharacteristic
186C2×C139#57611yescharacteristic
187D139—41no—
188D139—42no—
189D139—81no—
190D139—81no—
191C139#329711yescharacteristic, complemented, Sylow
192#3297—1391nomaximal, Sylow
193#553—1391no—
194#546—1391no—
195#488—1391no—
196#484D13911yescharacteristic, complemented
197#482—1391no—
198#478—1391no—
199#466—1391no—
200#465—1391no—
201#463—1391no—
202#449—1391no—
203#447—1391no—
204C4×D8—1391no—
205C8×D4—1391no—
206#416—1391no—
207C2×#102—1391no—
208C2×#41—1391no—
209C22×D4—1391no—
210C2×SD16—1391no—
211C2×D8—1391no—
212C2×D8—1391no—
213C22×C8—1391no—
214C22×C8—1391no—
215#126—2781no—
216#125—1391no—
217#124—1391no—
218#123—2781no—
219#123—2781no—
220C22⋊Q8C2×D13911yescharacteristic
221#121—2781no—
222#121—2781no—
223#121—1391no—
224#121—1391no—
225#121—1391no—
226#120—2781no—
227C4×D4—2781no—
228C4×D4—1391no—
229C4×D4—1391no—
230C4×D4—1391no—
231#117—1391no—
232C2×C4⋊C4C2×D13911yescharacteristic
233C2×C22⋊C4—2781no—
234#107C2×D13911yescharacteristic, complemented
235#107C2×D13911yescharacteristic, complemented
236#106—1391no—
237C4⋊C8—1391no—
238#103—1391no—
239#103C2×D13911yescharacteristic, complemented
240#103C2×D13911yescharacteristic, complemented
241#102—1391no—
242#102—1391no—
243#102—1391no—
244#102—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248C22⋊C8—1391no—
249C22⋊C8C2×D13911yescharacteristic
250C4×C8—1391no—
251C24—2781no—
252#41—2782no—
253#41—5561no—
254C2×Q8C22×D13911yescharacteristic
255C2×D4—2782no—
256C2×D4—2781no—
257C2×D4—2781no—
258C2×D4—2781no—
259C2×D4—2781no—
260C2×D4—2781no—
261C2×D4—5561no—
262C2×D4—1391no—
263C2×D4—1391no—
264C2×D4—1391no—
265C2×D4—1391no—
266C22×C4—21no—
267C22×C4—2781no—
268C22×C4—2781no—
269C22×C4—2781no—
270C22×C4—1391no—
271C22×C4C22×D13911yescharacteristic
272SD16—5561no—
273D8—2782no—
274D8—5561no—
275C2×C8—5561no—
276C2×C8—5561no—
277C2×C8—1391no—
278C2×C8—1391no—
279C2×C8C22×D13911yescharacteristic
280C2×C8C22×D13911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2781no—
284C4⋊C4—2781no—
285C4⋊C4—1391no—
286C4⋊C4—1391no—
287C4⋊C4C22×D13911yescharacteristic
288C4⋊C4C22×D13911yescharacteristic
289C4⋊C4C22×D13911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2781no—
292C22⋊C4—2781no—
293C22⋊C4—2781no—
294C22⋊C4—2781no—
295C22⋊C4—2781no—
296C22⋊C4—2781no—
297C22⋊C4—2781no—
298C22⋊C4—2781no—
299C22⋊C4—1391no—
300C22⋊C4—1391no—
301C42—2781no—
302C42—1391no—
303C23—2781no—
304C23—2781no—
305C23—2781no—
306C23—5562no—
307C23—5562no—
308C23—11121no—
309C23—1391no—
310C23D4×D13911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—2782no—
314D4—2781no—
315D4—2781no—
316D4—2781no—
317D4—2781no—
318D4—2781no—
319D4—5562no—
320D4—5562no—
321D4—5562no—
322D4—11121no—
323D4—11121no—
324D4—1392no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—2781no—
335C2×C4—5562no—
336C2×C4—11121no—
337C2×C4—11121no—
338C2×C4—1391no—
339C2×C4—1391no—
340C2×C4—1391no—
341C2×C4D4×D13911yescharacteristic
342C2×C4C23×D13911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2781no—
346C8—2781no—
347C22—21no—
348C22—21no—
349C22—2781no—
350C22—2782no—
351C22—2781no—
352C22—2781no—
353C22—5561no—
354C22—5561no—
355C22—5561no—
356C22—5561no—
357C22—5561no—
358C22—5561no—
359C22—5561no—
360C22—5561no—
361C22—11124no—
362C22#1798486512yes—
363C22C2×D4×D13911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2781no—
370C4—2781no—
371C4—2781no—
372C4—5561no—
373C4#41×D13911yescharacteristic
374C4#1798488811yescharacteristic
375C2—22no—
376C2—5561no—
377C2—5562no—
378C2—11121no—
379C2—11121no—
380C2#2258159511yescharacteristic
381C2C2×#1798486511yescharacteristic
382C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#484×C139C2
socleC22×C139C22×D4
hypercenter#484D139
hypocenterC139#3297
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #22581651C2semidirect
2. #22581594C2semidirect
3. #22581309C2semidirect
4. #22581280C2semidirect
5. #22581256C2semidirect
6. #22581190C2semidirect
7. #22581184C2semidirect
8. #22581171C2semidirect
9. #22581101C2semidirect
10. #22581089C2semidirect
11. #22581035C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. #22580948C2semidirect
14. C2×#17984762C2semidirect
15. #484×C139C2semidirect
18. C2×#14555772C22semidirect
22. C2×C8×D139C22semidirect
24. #17984833C22semidirect
30. #17984817C22semidirect
35. #17984804C22semidirect
38. #17984800C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. #17984766C22semidirect
49. #17984762C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
54. #107×C139C22semidirect
55. #107×C139C22semidirect
56. #103×C139C22semidirect
57. #103×C139C22semidirect
191. C139#3297semidirect
196. #484D139semidirect
234. #107C2×D139semidirect
235. #107C2×D139semidirect
239. #103C2×D139semidirect
240. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816512
#225815942
#225813092
#225812802
#225812562
#225811902
#225811842
#225811712
#225811012
#225810892
#225810352
(C22⋊D139)⋊C82
#225809482
C2×#179847622
#484×C1392
#3297139