Finite Group Databasebeta

← #31818213

Subgroups — #31818213

Order 17792.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581604C211yesmaximal, characteristic, complemented
2D4×C22⋊D139C211yesmaximal, characteristic, complemented
3#22581298C211yesmaximal, characteristic, complemented
4#22581266C211yesmaximal, characteristic, complemented
5#22581265C211yesmaximal, characteristic, complemented
6#22581231C211yesmaximal, characteristic, complemented
7#22581189C211yesmaximal, characteristic, complemented
8#22581188C211yesmaximal, characteristic, complemented
9#22581147C211yesmaximal, characteristic, complemented
10#22581088C211yesmaximal, characteristic, complemented
11#22581087C211yesmaximal, characteristic, complemented
12#22581033C211yesmaximal, characteristic, complemented
13C8×C22⋊D139C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15C2×#102×C139C211yesmaximal, characteristic, complemented
16C2×#14555785—21no—
17C22×C22⋊D139—21no—
18C2×D4×D139C2211yescharacteristic
19C2×D1112C2211yescharacteristic, complemented
20C2×#14555770C2211yescharacteristic
21C2×#14555770C2211yescharacteristic, complemented
22C2×C8×D139C2211yescharacteristic, complemented
23#17984841C2211yescharacteristic, complemented
24#17984838C2211yescharacteristic
25#17984827—21no—
26#17984825—21no—
27#17984820—21no—
28#17984817C2211yescharacteristic, complemented
29#17984816C2211yescharacteristic
30#17984816C2211yescharacteristic, complemented
31#17984814—21no—
32#17984813C2211yescharacteristic
33#17984811—21no—
34#17984810—21no—
35D4×Dic139C2211yescharacteristic
36#17984804C2211yescharacteristic, complemented
37C4×C22⋊D139C2211yescharacteristic
38C4⋊C4×D139C2211yescharacteristic, complemented
39#17984776C2211yescharacteristic, complemented
40#17984775C2211yescharacteristic, complemented
41#17984775C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic, 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—
60#14555785—44no—
61C2×Dic278—21no—
62C2×D556—21no—
63C2×D556C2311yescharacteristic
64C2×D556C2311yescharacteristic
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139—44no—
72C2×C22⋊D139D411yescharacteristic
73D4×D139—22no—
74D4×D139—41no—
75C22×Dic139—21no—
76C2×C4×D139—21no—
77C2×C4×D139—21no—
78C2×C4×D139C2311yescharacteristic
79D1112—41no—
80#14555770—22no—
81#14555770—41no—
82C2×C139⋊C8C2311yescharacteristic
83C2×C139⋊C8C2311yescharacteristic
84C8×D139—41no—
85C4⋊Dic139C2311yescharacteristic
86C4⋊Dic139C2311yescharacteristic
87Dic139⋊C4—21no—
88Dic139⋊C4—21no—
89Dic139⋊C4D411yescharacteristic
90C22⋊Dic139—21no—
91C22⋊Dic139—21no—
92C22⋊Dic139D411yescharacteristic
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×Dic139C2311yescharacteristic
99C24×C139—21no—
100C2×D4×C139—22no—
101C2×D4×C139—21no—
102C2×D4×C139—41no—
103C2×D4×C139C2311yescharacteristic
104C2×D4×C139C2311yescharacteristic
105C22×C4×C139—21no—
106C22×C4×C139C2311yescharacteristic
107C2×C8×C139—41no—
108C2×C8×C139C2311yescharacteristic
109C2×C8×C139C2311yescharacteristic
110C4⋊C4×C139—21no—
111C4⋊C4×C139C2311yescharacteristic
112C4⋊C4×C139C2311yescharacteristic
113C22×D139—21no—
114C22×D139—21no—
115C22×D139—42no—
116C22×D139—42no—
117C22×D139—81no—
118C22×D139C2×D411yescharacteristic
119Dic278—42no—
120D556—21no—
121D556—21no—
122D556—21no—
123D556—21no—
124D556—42no—
125C22⋊D139—42no—
126C22⋊D139—42no—
127C22⋊D139—42no—
128C22⋊D139—42no—
129C22⋊D139—42no—
130C22⋊D139—81no—
131C22⋊D139D814yescomplemented
132C2×Dic139—21no—
133C2×Dic139—21no—
134C2×Dic139—42no—
135C2×Dic139C2×D411yescharacteristic
136C2×Dic139C2×D411yescharacteristic
137C2×Dic139C2×D411yescharacteristic
138C4×D139—21no—
139C4×D139—21no—
140C4×D139—42no—
141C4×D139—42no—
142C139⋊C8—21no—
143C139⋊C8—21no—
144C23×C139—21no—
145C23×C139—21no—
146C23×C139—42no—
147C23×C139—42no—
148C23×C139—81no—
149C23×C139C2×D411yescharacteristic
150D4×C139—21no—
151D4×C139—21no—
152D4×C139—21no—
153D4×C139—42no—
154D4×C139#4112yescomplemented
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—21no—
159C2×C4×C139—42no—
160C2×C4×C139C2×D411yescharacteristic
161C2×C4×C139C2411yescharacteristic
162C8×C139—21no—
163C8×C139—21no—
164C22×C139—21no—
165C22×C139—21no—
166C22×C139—22no—
167C22×C139—41no—
168C22×C139—41no—
169C22×C139—41no—
170C22×C139—41no—
171C22×C139—41no—
172C22×C139—84no—
173C22×C139C2×D812yes—
174C22×C139C22×D411yescharacteristic
175C2×D139—21no—
176C2×D139—21no—
177C2×D139—41no—
178C2×D139—41no—
179C2×D139—41no—
180C2×D139—41no—
181C2×D139—41no—
182C2×D139—41no—
183C2×D139—84no—
184C2×D139C2×D812yes—
185C4×C139—21no—
186C4×C139—41no—
187C4×C139—41no—
188C4×C139C2×#4111yescharacteristic
189C4×C139H(5,𝔽2)11yescharacteristic
190Dic139—21no—
191Dic139—21no—
192Dic139—41no—
193Dic139—41no—
194Dic139C2×D812yes—
195C2×C139—22no—
196C2×C139—42no—
197C2×C139—81no—
198C2×C139#54611yescharacteristic
199C2×C139C22×D811yescharacteristic
200C2×C139#57711yescharacteristic
201D139—22no—
202D139—81no—
203D139—81no—
204C139#329411yescharacteristic, complemented, Sylow
205#3294—1391nomaximal, Sylow
206#547—1391no—
207D42—1391no—
208#486—1391no—
209#480—1391no—
210#480—1391no—
211#474—1391no—
212#466—1391no—
213#466—1391no—
214#459—1391no—
215#447—1391no—
216#447—1391no—
217C4×D8—1391no—
218C8×D4—1391no—
219C2×#102—1391no—
220C2×#102D13911yescharacteristic, complemented
221C2×#41—2781no—
222C22×D4—2781no—
223C22×D4—1391no—
224C22×D4C2×D13911yescharacteristic
225C2×D8—1391no—
226C2×D8—1391no—
227C2×D8—1391no—
228C22×C8—1391no—
229C22×C8C2×D13911yescharacteristic, complemented
230C4⋊Q8—1391no—
231#127—1391no—
232#123—2781no—
233#123—2781no—
234C22⋊Q8—2781no—
235#121—2781no—
236#121—1391no—
237#121—1391no—
238#121—1391no—
239#121—1391no—
240#120—2781no—
241#120—2781no—
242C4×D4—1391no—
243C4×D4—1391no—
244C4×D4—1391no—
245C2×C4⋊C4—1391no—
246C2×C4⋊C4C2×D13911yescharacteristic, complemented
247#107—1391no—
248#107—1391no—
249#107—1391no—
250C4⋊C8—1391no—
251#102—1391no—
252#102—1391no—
253#102—1391no—
254#102—1391no—
255#102—1391no—
256#102—1391no—
257#102C2×D13911yescharacteristic
258#102C2×D13911yescharacteristic
259#102C2×D13911yescharacteristic, complemented
260#102C2×D13911yescharacteristic, complemented
261C22⋊C8—1391no—
262C22⋊C8—1391no—
263C4×C8—1391no—
264C24—21no—
265C24—2781no—
266#41—5564no—
267C2×Q8—2781no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—2781no—
272C2×D4—2782no—
273C2×D4—2781no—
274C2×D4—2781no—
275C2×D4—2781no—
276C2×D4—2781no—
277C2×D4—2781no—
278C2×D4—2781no—
279C2×D4—5561no—
280C2×D4—5564no—
281C2×D4—1391no—
282C2×D4—1391no—
283C2×D4—1391no—
284C2×D4C22×D13911yescharacteristic
285C2×D4C22×D13911yescharacteristic
286C22×C4—21no—
287C22×C4—2781no—
288C22×C4—2781no—
289C22×C4—2781no—
290C22×C4—1391no—
291C22×C4C22×D13911yescharacteristic
292D8—2782no—
293D8—5561no—
294D8—5561no—
295C2×C8—41no—
296C2×C8—5561no—
297C2×C8—1391no—
298C2×C8—1391no—
299C2×C8C22×D13911yescharacteristic
300C2×C8C22×D13911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2781no—
303C4⋊C4—2781no—
304C4⋊C4—1391no—
305C4⋊C4—1391no—
306C4⋊C4—1391no—
307C4⋊C4C22×D13911yescharacteristic
308C4⋊C4C22×D13911yescharacteristic
309C22⋊C4—2781no—
310C22⋊C4—2781no—
311C22⋊C4—2781no—
312C22⋊C4—2781no—
313C22⋊C4—2781no—
314C22⋊C4—2781no—
315C22⋊C4—1391no—
316C22⋊C4—1391no—
317C42—1391no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—2781no—
324C23—2781no—
325C23—5562no—
326C23—5562no—
327C23—11121no—
328C23—1391no—
329C23D4×D13911yescharacteristic
330Q8—5562no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—2781no—
336D4—2781no—
337D4—2781no—
338D4—2781no—
339D4—5562no—
340D4—5562no—
341D4—5562no—
342D4—5562no—
343D4—5562no—
344D4—5562no—
345D4—11121no—
346D4—1394no—
347D4#1455578512yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—2781no—
354C2×C4—2781no—
355C2×C4—2781no—
356C2×C4—2781no—
357C2×C4—5562no—
358C2×C4—5562no—
359C2×C4—5562no—
360C2×C4—1391no—
361C2×C4—1391no—
362C2×C4—1391no—
363C2×C4D4×D13911yescharacteristic
364C2×C4C23×D13911yescharacteristic
365C8—21no—
366C8—21no—
367C8—2781no—
368C8—2781no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—2781no—
379C22—2781no—
380C22—5561no—
381C22—5561no—
382C22—5561no—
383C22—5561no—
384C22—5561no—
385C22—5561no—
386C22—11124no—
387C22—1392no—
388C22D8×D13912yes—
389C22C2×D4×D13911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2781no—
394C4—2781no—
395C4—5561no—
396C4—5561no—
397C4—1392no—
398C4C2×#1455578511yescharacteristic
399C4#1798488711yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—2782no—
404C2—11121no—
405C2—11121no—
406C2#2258159311yescharacteristic
407C2C2×D8×D13911yescharacteristic
408C2#2258175911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#102×C139C2
socleC22×C139C22×D4
hypercenterC2×#102D139
hypocenterC139#3294
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. #22581604C2semidirect
2. D4×C22⋊D139C2semidirect
3. #22581298C2semidirect
4. #22581266C2semidirect
5. #22581265C2semidirect
6. #22581231C2semidirect
7. #22581189C2semidirect
8. #22581188C2semidirect
9. #22581147C2semidirect
10. #22581088C2semidirect
11. #22581087C2semidirect
12. #22581033C2semidirect
13. C8×C22⋊D139C2semidirect
14. #102×D139C2semidirect
15. C2×#102×C139C2semidirect
19. C2×D1112C22semidirect
21. C2×#14555770C22semidirect
22. C2×C8×D139C22semidirect
23. #17984841C22semidirect
28. #17984817C22semidirect
30. #17984816C22semidirect
36. #17984804C22semidirect
38. C4⋊C4×D139C22semidirect
39. #17984776C22semidirect
40. #17984775C22semidirect
41. #17984775C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984764C22semidirect
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
131. C22⋊D139D8semidirect
154. D4×C139#41semidirect
204. C139#3294semidirect
220. C2×#102D139semidirect
229. C22×C8C2×D139semidirect
246. C2×C4⋊C4C2×D139semidirect
259. #102C2×D139semidirect
260. #102C2×D139semidirect
347. D4#14555785semidirect

Maximal subgroups

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

subgroupindex
#225816042
D4×C22⋊D1392
#225812982
#225812662
#225812652
#225812312
#225811892
#225811882
#225811472
#225810882
#225810872
#225810332
C8×C22⋊D1392
#102×D1392
C2×#102×C1392
#3294139