Finite Group Databasebeta

← #31818256

Subgroups — #31818256

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#22581649C211yesmaximal, characteristic, complemented
2#22581599C211yesmaximal, characteristic, complemented
3#22581308C211yesmaximal, characteristic, complemented
4#22581289C211yesmaximal, characteristic, complemented
5#22581278C211yesmaximal, characteristic, complemented
6#22581254C211yesmaximal, characteristic, complemented
7#22581189C211yesmaximal, characteristic, complemented
8#22581182C211yesmaximal, characteristic, complemented
9#22581169C211yesmaximal, characteristic, complemented
10#22581100C211yesmaximal, characteristic, complemented
11#22581089C211yesmaximal, characteristic, complemented
12C4×D1112C211yesmaximal, characteristic, complemented
13#22580950C211yesmaximal, characteristic, complemented
14C2×#17984764C211yesmaximal, characteristic, complemented
15C8×D4×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C22×D556C2211yescharacteristic
18C2×#14555774C2211yescharacteristic, complemented
19C2×D1112C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21#17984837—21no—
22#17984834C2211yescharacteristic, complemented
23#17984830C2211yescharacteristic
24#17984827—21no—
25#17984824—21no—
26#17984821C2211yescharacteristic
27#17984816C2211yescharacteristic
28#17984816C2211yescharacteristic
29#17984816C2211yescharacteristic, complemented
30#17984815—21no—
31#17984814—21no—
32#17984810—21no—
33C4×D556C2211yescharacteristic
34C4×D556C2211yescharacteristic, complemented
35(C22⋊D139)⋊C4—21no—
36#17984801C2211yescharacteristic, complemented
37C2×C4⋊Dic139C2211yescharacteristic
38C22⋊C4×D139—21no—
39#17984776C2211yescharacteristic, complemented
40#17984776C2211yescharacteristic, complemented
41#17984774C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984767C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984764C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic, complemented
52C22×C8×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic, complemented
54C4×D4×C139C2211yescharacteristic
55C4⋊C8×C139C2211yescharacteristic, complemented
56C22⋊C8×C139C2211yescharacteristic
57C22⋊C8×C139C2211yescharacteristic, complemented
58C4×C8×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555785—22no—
61#14555785—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556—22no—
64C2×D556—21no—
65C2×D556—41no—
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×D556C2311yescharacteristic
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C2×C22⋊D139—21no—
73C22×Dic139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76C2×C4×D139—21no—
77#14555774—41no—
78D1112—22no—
79D1112—41no—
80C4⋊Dic139—21no—
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83C4⋊Dic139C2311yescharacteristic
84C4⋊Dic139C2311yescharacteristic
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139—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—
97C4×Dic139—21no—
98C2×D4×C139D411yescharacteristic
99C22×C4×C139C2311yescharacteristic
100C22×C4×C139C2311yescharacteristic
101C2×C8×C139—41no—
102C2×C8×C139—41no—
103C2×C8×C139C2311yescharacteristic
104C2×C8×C139C2311yescharacteristic
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139D411yescharacteristic
108C22⋊C4×C139D411yescharacteristic
109C22⋊C4×C139D411yescharacteristic
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—21no—
113C22×D139—21no—
114C22×D139—42no—
115C22×D139—42no—
116C22×D139—81no—
117Dic278—21no—
118Dic278—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122D556—21no—
123D556—21no—
124D556—42no—
125D556#4112yes—
126C22⋊D139—42no—
127C22⋊D139—42no—
128C22⋊D139—81no—
129C22⋊D139—81no—
130C2×Dic139—21no—
131C2×Dic139—21no—
132C2×Dic139—21no—
133C2×Dic139—21no—
134C2×Dic139—21no—
135C2×Dic139—81no—
136C4×D139—42no—
137C4×D139—81no—
138C4×D139—81no—
139C23×C139C2×D411yescharacteristic
140C23×C139C2×D411yescharacteristic
141D4×C139—22no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2411yescharacteristic
151C8×C139—21no—
152C8×C139—21no—
153C8×C139—21no—
154C8×C139—21no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139—21no—
158C22×C139—21no—
159C22×C139—21no—
160C22×C139#13512yes—
161C22×C139C22×D411yescharacteristic
162C2×D139—22no—
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—21no—
174C4×C139—21no—
175C4×C139—21no—
176C4×C139C2×#4111yescharacteristic
177C4×C139H(5,𝔽2)11yescharacteristic
178Dic139—41no—
179Dic139—41no—
180Dic139—41no—
181Dic139—41no—
182Dic139—41no—
183C2×C139—22no—
184C2×C139—41no—
185C2×C139#54611yescharacteristic
186C2×C139C2×#13511yescharacteristic
187C2×C139#57611yescharacteristic
188D139—42no—
189D139—81no—
190D139—81no—
191C139#329711yescharacteristic, complemented, Sylow
192#3297—1391nomaximal, Sylow
193#553—1391no—
194#546—1391no—
195#488—1391no—
196#484—1391no—
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×D4D13911yescharacteristic, complemented
206#416—1391no—
207C2×#102—1391no—
208C2×#41—1391no—
209C22×D4—1391no—
210C2×SD16—1391no—
211C2×D8—1391no—
212C2×D8—1391no—
213C22×C8C2×D13911yescharacteristic
214C22×C8C2×D13911yescharacteristic, complemented
215#126—2781no—
216#125—1391no—
217#124—1391no—
218#123—2781no—
219#123—2781no—
220C22⋊Q8—1391no—
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×D4C2×D13911yescharacteristic
231#117—1391no—
232C2×C4⋊C4—1391no—
233C2×C22⋊C4—2781no—
234#107—1391no—
235#107—1391no—
236#106—1391no—
237C4⋊C8C2×D13911yescharacteristic, complemented
238#103—1391no—
239#103—1391no—
240#103—1391no—
241#102—1391no—
242#102—1391no—
243#102—1391no—
244#102—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248C22⋊C8C2×D13911yescharacteristic
249C22⋊C8C2×D13911yescharacteristic, complemented
250C4×C8C2×D13911yescharacteristic, complemented
251C24—2781no—
252#41—2782no—
253#41—5561no—
254C2×Q8—1391no—
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×D4D55611yescharacteristic
266C22×C4—2781no—
267C22×C4—2781no—
268C22×C4—2781no—
269C22×C4—2781no—
270C22×C4C22×D13911yescharacteristic
271C22×C4C22×D13911yescharacteristic
272SD16—5561no—
273D8—2782no—
274D8—5561no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D13911yescharacteristic
278C2×C8C22×D13911yescharacteristic
279C2×C8C22×D13911yescharacteristic
280C2×C8C22×D13911yescharacteristic
281C4⋊C4—2781no—
282C4⋊C4—2781no—
283C4⋊C4—2781no—
284C4⋊C4—2781no—
285C4⋊C4—1391no—
286C4⋊C4—1391no—
287C4⋊C4—1391no—
288C4⋊C4—1391no—
289C4⋊C4D55611yescharacteristic
290C22⋊C4—2781no—
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⋊C4D55611yescharacteristic
300C22⋊C4D55611yescharacteristic
301C42—2781no—
302C42C22×D13911yescharacteristic
303C23—2781no—
304C23—2781no—
305C23—2781no—
306C23—5562no—
307C23—5562no—
308C23—11121no—
309C23C2×D55611yescharacteristic
310C23C2×D55611yescharacteristic
311Q8—2781no—
312Q8—2781no—
313D4—22no—
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—2781no—
330C2×C4—2781no—
331C2×C4—2781no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—5562no—
335C2×C4—11121no—
336C2×C4—11121no—
337C2×C4—11121no—
338C2×C4C2×D55611yescharacteristic
339C2×C4C2×D55611yescharacteristic
340C2×C4C2×D55611yescharacteristic
341C2×C4C2×D55611yescharacteristic
342C2×C4C23×D13911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2782no—
353C22—5561no—
354C22—5561no—
355C22—5561no—
356C22—5561no—
357C22—5561no—
358C22—5561no—
359C22—5561no—
360C22—5561no—
361C22—11124no—
362C22#1798486412yes—
363C22C22×D55611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—5561no—
369C4—5561no—
370C4—5561no—
371C4—5561no—
372C4—5561no—
373C4#41×D13911yescharacteristic
374C4#1798488711yescharacteristic
375C2—22no—
376C2—41no—
377C2—5562no—
378C2—11121no—
379C2—11121no—
380C2#2258159811yescharacteristic
381C2C2×#1798486411yescharacteristic
382C2#2258175811yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC8×D4×C139C2
socleC22×C139C22×D4
hypercenterC8×D4D139
hypocenterC139#3297
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #22581649C2semidirect
2. #22581599C2semidirect
3. #22581308C2semidirect
4. #22581289C2semidirect
5. #22581278C2semidirect
6. #22581254C2semidirect
7. #22581189C2semidirect
8. #22581182C2semidirect
9. #22581169C2semidirect
10. #22581100C2semidirect
11. #22581089C2semidirect
12. C4×D1112C2semidirect
13. #22580950C2semidirect
14. C2×#17984764C2semidirect
15. C8×D4×C139C2semidirect
18. C2×#14555774C22semidirect
22. #17984834C22semidirect
29. #17984816C22semidirect
34. C4×D556C22semidirect
36. #17984801C22semidirect
39. #17984776C22semidirect
40. #17984776C22semidirect
41. #17984774C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984767C22semidirect
51. #17984764C22semidirect
53. C22×C8×C139C22semidirect
55. C4⋊C8×C139C22semidirect
57. C22⋊C8×C139C22semidirect
58. C4×C8×C139C22semidirect
191. C139#3297semidirect
205. C8×D4D139semidirect
214. C22×C8C2×D139semidirect
237. C4⋊C8C2×D139semidirect
249. C22⋊C8C2×D139semidirect
250. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816492
#225815992
#225813082
#225812892
#225812782
#225812542
#225811892
#225811822
#225811692
#225811002
#225810892
C4×D11122
#225809502
C2×#179847642
C8×D4×C1392
#3297139