Finite Group Databasebeta

← #31818224

Subgroups — #31818224

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#22581658C211yesmaximal, characteristic, complemented
2D4×C22⋊D139C211yesmaximal, characteristic
3#22581298C211yesmaximal, characteristic, complemented
4#22581271C211yesmaximal, characteristic, complemented
5#22581270C211yesmaximal, characteristic, complemented
6#22581241C211yesmaximal, characteristic, complemented
7#22581182C211yesmaximal, characteristic, complemented
8#22581181C211yesmaximal, characteristic, complemented
9#22581152C211yesmaximal, characteristic, complemented
10#22581105C211yesmaximal, characteristic, complemented
11#22581104C211yesmaximal, characteristic, complemented
12#22581044C211yesmaximal, characteristic, complemented
13C8×C22⋊D139C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15C2×#102×C139C211yesmaximal, characteristic, complemented
16C22×C22⋊D139—21no—
17C2×D4×D139C2211yescharacteristic
18C2×#14555774C2211yescharacteristic, complemented
19C2×#14555773C2211yescharacteristic
20C2×#14555773C2211yescharacteristic, complemented
21C2×C8×D139C2211yescharacteristic, complemented
22#17984841C2211yescharacteristic, complemented
23#17984838C2211yescharacteristic
24#17984832—21no—
25#17984822C2211yescharacteristic, complemented
26#17984821—21no—
27#17984821C2211yescharacteristic, complemented
28#17984820—21no—
29#17984816C2211yescharacteristic
30#17984814—21no—
31#17984813C2211yescharacteristic
32#17984811—21no—
33#17984810—21no—
34#17984807C2211yescharacteristic, complemented
35D4×Dic139C2211yescharacteristic
36C4×C22⋊D139—21no—
37C4×C22⋊D139C2211yescharacteristic
38C4⋊C4×D139C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41#17984773C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic, complemented
48#17984762C2211yescharacteristic, complemented
49C22⋊(C139⋊C8)C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22×D4×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic, complemented
54C2×C4⋊C4×C139C2211yescharacteristic, complemented
55#102×C139C2211yescharacteristic
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×Dic278—21no—
61C2×Dic278C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C2×C22⋊D139—44no—
69C2×C22⋊D139D411yescharacteristic
70D4×D139—22no—
71D4×D139—41no—
72C22×Dic139—21no—
73C2×C4×D139—21no—
74C2×C4×D139C2311yescharacteristic
75#14555774—41no—
76#14555773—22no—
77#14555773—41no—
78C2×C139⋊C8C2311yescharacteristic
79C2×C139⋊C8C2311yescharacteristic
80C8×D139—41no—
81C4⋊Dic139—21no—
82C4⋊Dic139C2311yescharacteristic
83C4⋊Dic139C2311yescharacteristic
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
88Dic139⋊C4D411yescharacteristic
89C22⋊Dic139—21no—
90C22⋊Dic139—21no—
91C22⋊Dic139—21no—
92C22⋊Dic139D411yescharacteristic
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4D411yescharacteristic
96C4×Dic139—21no—
97C4×Dic139C2311yescharacteristic
98C24×C139—21no—
99C2×D4×C139—22no—
100C2×D4×C139—21no—
101C2×D4×C139—41no—
102C2×D4×C139C2311yescharacteristic
103C2×D4×C139C2311yescharacteristic
104C22×C4×C139—21no—
105C22×C4×C139C2311yescharacteristic
106C2×C8×C139—41no—
107C2×C8×C139C2311yescharacteristic
108C2×C8×C139C2311yescharacteristic
109C4⋊C4×C139—21no—
110C4⋊C4×C139C2311yescharacteristic
111C4⋊C4×C139C2311yescharacteristic
112C22×D139—21no—
113C22×D139—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117Dic278—21no—
118Dic278—21no—
119Dic278—81no—
120D556—21no—
121D556—21no—
122C22⋊D139—42no—
123C22⋊D139—42no—
124C22⋊D139—42no—
125C22⋊D139—42no—
126C22⋊D139—81no—
127C22⋊D139SD1614yescomplemented
128C2×Dic139—21no—
129C2×Dic139—21no—
130C2×Dic139—21no—
131C2×Dic139—42no—
132C2×Dic139C2×D411yescharacteristic
133C2×Dic139C2×D411yescharacteristic
134C2×Dic139C2×D411yescharacteristic
135C4×D139—21no—
136C4×D139—21no—
137C4×D139—81no—
138C139⋊C8—21no—
139C139⋊C8—21no—
140C23×C139—21no—
141C23×C139—21no—
142C23×C139—42no—
143C23×C139—42no—
144C23×C139—81no—
145C23×C139C2×D411yescharacteristic
146D4×C139—21no—
147D4×C139—21no—
148D4×C139—21no—
149D4×C139—42no—
150D4×C139#4112yes—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—81no—
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2411yescharacteristic
158C8×C139—21no—
159C8×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—22no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—41no—
167C22×C139—41no—
168C22×C139—84no—
169C22×C139C2×SD1612yes—
170C22×C139C22×D411yescharacteristic
171C2×D139—21no—
172C2×D139—21no—
173C2×D139—41no—
174C2×D139—41no—
175C2×D139—41no—
176C2×D139—84no—
177C2×D139C2×SD1612yes—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—41no—
181C4×C139C2×#4111yescharacteristic
182C4×C139H(5,𝔽2)11yescharacteristic
183Dic139—21no—
184Dic139—21no—
185Dic139—41no—
186Dic139—41no—
187Dic139—41no—
188Dic139C2×SD1612yes—
189C2×C139—22no—
190C2×C139—42no—
191C2×C139—81no—
192C2×C139#54611yescharacteristic
193C2×C139C22×SD1611yescharacteristic
194C2×C139#57611yescharacteristic
195D139—22no—
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#465—1391no—
207#460—1391no—
208#450—1391no—
209#450—1391no—
210C4×SD16—1391no—
211C8×D4—1391no—
212C2×#102—1391no—
213C2×#102D13911yescharacteristic, complemented
214C22×D4—2781no—
215C22×D4—1391no—
216C22×D4C2×D13911yescharacteristic
217C2×SD16—1391no—
218C2×SD16—1391no—
219C2×SD16—1391no—
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⋊Q8—1391no—
229#121—2781no—
230#121—1391no—
231#121—1391no—
232#120—2781no—
233#120—2781no—
234C4×Q8—1391no—
235C4×D4—2781no—
236C4×D4—1391no—
237C4×D4—1391no—
238C2×C4⋊C4—1391no—
239C2×C4⋊C4C2×D13911yescharacteristic, complemented
240#106—1391no—
241#106—1391no—
242#106—1391no—
243C4⋊C8—1391no—
244#103—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102—1391no—
250#102C2×D13911yescharacteristic
251#102C2×D13911yescharacteristic
252#102C2×D13911yescharacteristic, complemented
253#102C2×D13911yescharacteristic, complemented
254C22⋊C8—1391no—
255C22⋊C8—1391no—
256C4×C8—1391no—
257C24—21no—
258C24—2781no—
259C2×Q8—2781no—
260C2×Q8—1391no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2782no—
265C2×D4—2781no—
266C2×D4—2781no—
267C2×D4—2781no—
268C2×D4—2781no—
269C2×D4—2781no—
270C2×D4—5561no—
271C2×D4—5564no—
272C2×D4—1391no—
273C2×D4—1391no—
274C2×D4C22×D13911yescharacteristic
275C2×D4C22×D13911yescharacteristic
276C22×C4—21no—
277C22×C4—2781no—
278C22×C4—2781no—
279C22×C4—1391no—
280C22×C4C22×D13911yescharacteristic
281SD16—2782no—
282SD16—5561no—
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—2781no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4—2781no—
305C22⋊C4—2781no—
306C22⋊C4—1391no—
307C22⋊C4—1391no—
308C42—2781no—
309C42—1391no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2781no—
316C23—5562no—
317C23—5562no—
318C23—11121no—
319C23—1391no—
320C23D4×D13911yescharacteristic
321Q8—2781no—
322Q8—2781no—
323Q8—11121no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2781no—
329D4—2781no—
330D4—5562no—
331D4—5562no—
332D4—5562no—
333D4—5562no—
334D4—11121no—
335D4—1394no—
336D4#1455578512yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—2781no—
343C2×C4—2781no—
344C2×C4—2781no—
345C2×C4—2781no—
346C2×C4—2781no—
347C2×C4—5562no—
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—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2781no—
368C22—2781no—
369C22—5561no—
370C22—5561no—
371C22—5561no—
372C22—11124no—
373C22—1392no—
374C22SD16×D13912yes—
375C22C2×D4×D13911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2781no—
380C4—2781no—
381C4—5561no—
382C4—5561no—
383C4—5561no—
384C4—1392no—
385C4C2×#1455578511yescharacteristic
386C4#1798488711yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—2782no—
391C2—11121no—
392C2#2258159311yescharacteristic
393C2C2×SD16×D13911yescharacteristic
394C2#2258175411yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#102×C139C2
socleC22×C139C22×D4
prime radicalD4×C22⋊D139C2
hypercenterC2×#102D139
hypocenterC139#3295
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #22581658C2semidirect
3. #22581298C2semidirect
4. #22581271C2semidirect
5. #22581270C2semidirect
6. #22581241C2semidirect
7. #22581182C2semidirect
8. #22581181C2semidirect
9. #22581152C2semidirect
10. #22581105C2semidirect
11. #22581104C2semidirect
12. #22581044C2semidirect
13. C8×C22⋊D139C2semidirect
14. #102×D139C2semidirect
15. C2×#102×C139C2semidirect
18. C2×#14555774C22semidirect
20. C2×#14555773C22semidirect
21. C2×C8×D139C22semidirect
22. #17984841C22semidirect
25. #17984822C22semidirect
27. #17984821C22semidirect
34. #17984807C22semidirect
38. C4⋊C4×D139C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. #17984773C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984767C22semidirect
44. #17984764C22semidirect
46. #17984763C22semidirect
47. #17984762C22semidirect
48. #17984762C22semidirect
49. C22⋊(C139⋊C8)C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
53. C22×C8×C139C22semidirect
54. C2×C4⋊C4×C139C22semidirect
57. #102×C139C22semidirect
58. #102×C139C22semidirect
127. C22⋊D139SD16semidirect
197. C139#3295semidirect
213. C2×#102D139semidirect
221. C22×C8C2×D139semidirect
239. C2×C4⋊C4C2×D139semidirect
252. #102C2×D139semidirect
253. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816582
D4×C22⋊D1392
#225812982
#225812712
#225812702
#225812412
#225811822
#225811812
#225811522
#225811052
#225811042
#225810442
C8×C22⋊D1392
#102×D1392
C2×#102×C1392
#3295139