Finite Group Databasebeta

← #31818237

Subgroups — #31818237

Order 17792.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581638C211yesmaximal, characteristic, complemented
2#22581594C211yesmaximal, characteristic
3#22581309C211yesmaximal, characteristic, complemented
4#22581279C211yesmaximal, characteristic, complemented
5#22581252C211yesmaximal, characteristic, complemented
6#22581192C211yesmaximal, characteristic, complemented
7#22581183C211yesmaximal, characteristic, complemented
8#22581178C211yesmaximal, characteristic, complemented
9#22581118C211yesmaximal, characteristic, complemented
10#22581106C211yesmaximal, characteristic, complemented
11#22581040C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13#22580948C211yesmaximal, characteristic, complemented
14C2×#17984762C211yesmaximal, characteristic, complemented
15#483×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C22×D556C2211yescharacteristic
18C2×#14555775C2211yescharacteristic, complemented
19C2×#14555774C2211yescharacteristic
20C2×#14555774C2211yescharacteristic
21C22×C139⋊C8C2211yescharacteristic
22C2×C8×D139C2211yescharacteristic, complemented
23#17984837—21no—
24#17984833C2211yescharacteristic, complemented
25#17984832—21no—
26#17984831C2211yescharacteristic
27#17984827—21no—
28#17984825—21no—
29#17984822C2211yescharacteristic, complemented
30#17984821C2211yescharacteristic
31#17984817—21no—
32#17984817C2211yescharacteristic
33#17984812—21no—
34#17984807C2211yescharacteristic, complemented
35#17984804C2211yescharacteristic
36C4×C22⋊D139C2211yescharacteristic
37#17984801—21no—
38#17984800C2211yescharacteristic, complemented
39C22⋊C4×D139—21no—
40#17984775C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42#17984766C2211yescharacteristic, complemented
43#17984765C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic
45#17984764C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic
49#17984762C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22⋊Q8×C139C2211yescharacteristic
53C2×C4⋊C4×C139C2211yescharacteristic
54#106×C139C2211yescharacteristic, complemented
55#106×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58C22⋊C8×C139C2211yescharacteristic
59C23×D139—21no—
60#14555786—22no—
61#14555786—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556—22no—
64C2×D556—21no—
65C2×D556—21no—
66C2×D556—21no—
67C2×D556—41no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×C22⋊D139D411yescharacteristic
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139C2311yescharacteristic
74#14555775—41no—
75#14555774—22no—
76#14555774—41no—
77C2×C139⋊C8—41no—
78C2×C139⋊C8C2311yescharacteristic
79C2×C139⋊C8C2311yescharacteristic
80C8×D139—41no—
81C4⋊Dic139—21no—
82C4⋊Dic139—21no—
83C4⋊Dic139C2311yescharacteristic
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4D411yescharacteristic
88C22⋊Dic139—21no—
89C22⋊Dic139D411yescharacteristic
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)⋊C4D411yescharacteristic
97C4×Dic139—21no—
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—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117Dic278—21no—
118Dic278—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122D556—42no—
123D556—42no—
124D556—81no—
125D556#4112yes—
126C22⋊D139—22no—
127C2×Dic139—21no—
128C2×Dic139—21no—
129C2×Dic139C2×D411yescharacteristic
130C2×Dic139C2×D411yescharacteristic
131C2×Dic139C2×D411yescharacteristic
132C4×D139—21no—
133C4×D139—21no—
134C4×D139—42no—
135C4×D139—81no—
136C139⋊C8—21no—
137C139⋊C8—21no—
138C23×C139C2×D411yescharacteristic
139Q8×C139—21no—
140Q8×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—42no—
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2411yescharacteristic
150C8×C139—21no—
151C8×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139#13512yes—
155C22×C139C22×D411yescharacteristic
156C2×D139—21no—
157C2×D139—22no—
158C2×D139—21no—
159C2×D139—21no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—41no—
165C2×D139—84no—
166C4×C139—21no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139—41no—
170C4×C139—41no—
171C4×C139C2×#4111yescharacteristic
172C4×C139H(5,𝔽2)11yescharacteristic
173Dic139—21no—
174Dic139—21no—
175Dic139—21no—
176Dic139—41no—
177Dic139—41no—
178C2×C139—22no—
179C2×C139#54611yescharacteristic
180C2×C139C2×#13511yescharacteristic
181C2×C139#57711yescharacteristic
182D139—41no—
183D139—42no—
184D139—81no—
185C139#329611yescharacteristic, complemented, Sylow
186#3296—1391nomaximal, Sylow
187#552—1391no—
188#546—1391no—
189#488—1391no—
190#483D13911yescharacteristic, complemented
191#482—1391no—
192#478—1391no—
193#467—1391no—
194#465—1391no—
195#464—1391no—
196#452—1391no—
197#450—1391no—
198C4×SD16—1391no—
199C8×D4—1391no—
200#416—1391no—
201C2×#102—1391no—
202C2×#41—1391no—
203C22×D4—1391no—
204C2×Q16—1391no—
205C2×SD16—1391no—
206C2×SD16—1391no—
207C22×C8—1391no—
208C22×C8—1391no—
209#126—2781no—
210#125—2781no—
211#125—1391no—
212#124—1391no—
213#123—2781no—
214#123—2781no—
215C22⋊Q8—1391no—
216C22⋊Q8—1391no—
217C22⋊Q8C2×D13911yescharacteristic
218#121—2781no—
219#121—1391no—
220#120—2781no—
221C4×Q8—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224#117—2781no—
225#117—1391no—
226C2×C4⋊C4C2×D13911yescharacteristic
227C2×C22⋊C4—2781no—
228#107—1391no—
229#106C2×D13911yescharacteristic, complemented
230#106C2×D13911yescharacteristic, complemented
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#103C2×D13911yescharacteristic, complemented
235#103C2×D13911yescharacteristic, complemented
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241#102—1391no—
242C22⋊C8—1391no—
243C22⋊C8C2×D13911yescharacteristic
244C4×C8—1391no—
245C24—2781no—
246#41—2782no—
247#41—5561no—
248C2×Q8—1391no—
249C2×Q8C22×D13911yescharacteristic
250C2×D4—2782no—
251C2×D4—2781no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—5561no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4—1391no—
258C22×C4—21no—
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—1391no—
262C22×C4C22×D13911yescharacteristic
263Q16—5561no—
264SD16—2782no—
265SD16—5561no—
266C2×C8—5561no—
267C2×C8—5561no—
268C2×C8—1391no—
269C2×C8—1391no—
270C2×C8C22×D13911yescharacteristic
271C2×C8C22×D13911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—2781no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4C22×D13911yescharacteristic
282C4⋊C4C22×D13911yescharacteristic
283C4⋊C4C22×D13911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—2781no—
292C22⋊C4—1391no—
293C22⋊C4—1391no—
294C42—2781no—
295C42—2781no—
296C42—1391no—
297C23—2781no—
298C23—2781no—
299C23—5562no—
300C23—5562no—
301C23—11121no—
302C23—1391no—
303C23D4×D13911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2781no—
307Q8—2781no—
308D4—2782no—
309D4—2781no—
310D4—2781no—
311D4—2781no—
312D4—5562no—
313D4—5562no—
314D4—11121no—
315D4—1392no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—2781no—
327C2×C4—5562no—
328C2×C4—11121no—
329C2×C4—1391no—
330C2×C4—1391no—
331C2×C4—1391no—
332C2×C4D4×D13911yescharacteristic
333C2×C4C23×D13911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2781no—
337C8—2781no—
338C22—21no—
339C22—21no—
340C22—2781no—
341C22—2781no—
342C22—2782no—
343C22—2781no—
344C22—5561no—
345C22—5561no—
346C22—5561no—
347C22—5561no—
348C22—5561no—
349C22—11124no—
350C22#1798486312yes—
351C22C2×D4×D13911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2781no—
358C4—2781no—
359C4—2781no—
360C4—5561no—
361C4—5561no—
362C4#41×D13911yescharacteristic
363C4#1798488811yescharacteristic
364C2—22no—
365C2—5561no—
366C2—5562no—
367C2—11121no—
368C2#2258159511yescharacteristic
369C2C2×#1798486311yescharacteristic
370C2#2258176211yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#483×C139C2
socleC22×C139C22×D4
prime radical#22581594C2
hypercenter#483D139
hypocenterC139#3296
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #22581638C2semidirect
3. #22581309C2semidirect
4. #22581279C2semidirect
5. #22581252C2semidirect
6. #22581192C2semidirect
7. #22581183C2semidirect
8. #22581178C2semidirect
9. #22581118C2semidirect
10. #22581106C2semidirect
11. #22581040C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. #22580948C2semidirect
14. C2×#17984762C2semidirect
15. #483×C139C2semidirect
18. C2×#14555775C22semidirect
22. C2×C8×D139C22semidirect
24. #17984833C22semidirect
29. #17984822C22semidirect
34. #17984807C22semidirect
38. #17984800C22semidirect
40. #17984775C22semidirect
41. Dic139⋊C8C22semidirect
42. #17984766C22semidirect
43. #17984765C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
54. #106×C139C22semidirect
55. #106×C139C22semidirect
56. #103×C139C22semidirect
57. #103×C139C22semidirect
185. C139#3296semidirect
190. #483D139semidirect
229. #106C2×D139semidirect
230. #106C2×D139semidirect
234. #103C2×D139semidirect
235. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816382
#225815942
#225813092
#225812792
#225812522
#225811922
#225811832
#225811782
#225811182
#225811062
#225810402
(C22⋊D139)⋊C82
#225809482
C2×#179847622
#483×C1392
#3296139