Finite Group Databasebeta

← #31816755

Subgroups — #31816755

Order 17792.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581580C211yesmaximal, characteristic, complemented
2#22581521C211yesmaximal, characteristic
3#22581318C211yesmaximal, characteristic, complemented
4#22581316C211yesmaximal, characteristic, complemented
5#22581314C211yesmaximal, characteristic, complemented
6#22581309C211yesmaximal, characteristic, complemented
7#22581307C211yesmaximal, characteristic, complemented
8#22581301C211yesmaximal, characteristic, complemented
9#22581298C211yesmaximal, characteristic, complemented
10#22580956C211yesmaximal, characteristic, complemented
11#22580953C211yesmaximal, characteristic, complemented
12#22580948C211yesmaximal, characteristic, complemented
13#102×D139C211yesmaximal, characteristic, complemented
14#22580910C211yesmaximal, characteristic, complemented
15#489×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18C2×#14555768C2211yescharacteristic
19C2×C8×D139C2211yescharacteristic
20#17984841C2211yescharacteristic, complemented
21#17984840—21no—
22#17984839C2211yescharacteristic
23#17984838C2211yescharacteristic
24#17984834C2211yescharacteristic, complemented
25#17984833C2211yescharacteristic, complemented
26#17984832—21no—
27#17984831C2211yescharacteristic
28#17984820—21no—
29#17984818—21no—
30#17984815—21no—
31#17984815—21no—
32#17984812—21no—
33#17984812—21no—
34#17984800C2211yescharacteristic
35#17984799C2211yescharacteristic
36C4⋊C4×D139C2211yescharacteristic
37#17984766C2211yescharacteristic, complemented
38#17984766C2211yescharacteristic, complemented
39#17984764C2211yescharacteristic
40#17984764C2211yescharacteristic
41#17984764C2211yescharacteristic, complemented
42#17984764C2211yescharacteristic, complemented
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984762C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic, complemented
48#17984762C2211yescharacteristic, complemented
49#17984752C2211yescharacteristic, complemented
50C4×C139⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C4⋊Q8×C139C2211yescharacteristic, complemented
53#124×C139C2211yescharacteristic
54#103×C139C2211yescharacteristic, complemented
55#103×C139C2211yescharacteristic, complemented
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic
58#97×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555786—22no—
61#14555786—22no—
62C2×Dic278—21no—
63C2×D556—21no—
64C2×D556—21no—
65C2×D556—21no—
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71D4×D139—22no—
72D4×D139—22no—
73C2×C4×D139—21no—
74C2×C4×D139—21no—
75C2×C4×D139C2311yescharacteristic
76#14555768—22no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C8×D139—22no—
80C4⋊Dic139—21no—
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
88Dic139⋊C4D411yescharacteristic
89Dic139⋊C4D411yescharacteristic
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4D411yescharacteristic
94(C2×D139)⋊C4D411yescharacteristic
95C4×Dic139—21no—
96C4×Dic139C2311yescharacteristic
97C2×Q8×C139—21no—
98C2×Q8×C139C2311yescharacteristic
99C2×D4×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C2×C8×C139C2311yescharacteristic
102C4⋊C4×C139—21no—
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—21no—
110C22×D139—42no—
111C22×D139—81no—
112C22×D139—81no—
113C22×D139C2×D411yescharacteristic
114Dic278—81no—
115D556—21no—
116D556—21no—
117D556—21no—
118D556—21no—
119D556—42no—
120D556—81no—
121D556—81no—
122C22⋊D139—42no—
123C22⋊D139—81no—
124C22⋊D139—81no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139C2×D411yescharacteristic
128C2×Dic139C2×D411yescharacteristic
129C2×Dic139C2×D411yescharacteristic
130C4×D139—42no—
131C4×D139—81no—
132C4×D139#4112yes—
133C4×D139#4112yes—
134C139⋊C8—21no—
135C139⋊C8—21no—
136C23×C139—21no—
137Q8×C139—21no—
138Q8×C139—21no—
139Q8×C139—81no—
140D4×C139—21no—
141D4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2411yescharacteristic
148C8×C139—21no—
149C8×C139—21no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139C22×D411yescharacteristic
154C2×D139—21no—
155C2×D139—21no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—84no—
163C2×D139#12412yes—
164C4×C139—21no—
165C4×C139—21no—
166C4×C139—41no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139C2×#4111yescharacteristic
170C4×C139C2×#4111yescharacteristic
171Dic139—21no—
172Dic139—21no—
173Dic139—41no—
174Dic139—41no—
175Dic139#12412yes—
176C2×C139—81no—
177C2×C139C2×#12411yescharacteristic
178C2×C139#57611yescharacteristic
179C2×C139#57711yescharacteristic
180D139—22no—
181D139—81no—
182D139—81no—
183C139#313611yescharacteristic, complemented, Sylow
184#3136—1391nomaximal, Sylow
185#544—1391no—
186#535—1391no—
187#490—1391no—
188#490—1391no—
189#489—1391no—
190#489D13911yescharacteristic, complemented
191#488—1391no—
192#488—1391no—
193#486—1391no—
194#486—1391no—
195#418—1391no—
196#417—1391no—
197#416—1391no—
198C2×#102—1391no—
199#405—1391no—
200C2×#41—1391no—
201C22×D4—1391no—
202C2×M16—1391no—
203C22×C8—1391no—
204C4⋊Q8—2781no—
205C4⋊Q8—1391no—
206C4⋊Q8C2×D13911yescharacteristic, complemented
207#127—1391no—
208#127—1391no—
209#125—2781no—
210#125—1391no—
211#125—1391no—
212#124—1391no—
213#124C2×D13911yescharacteristic
214C22⋊Q8—2781no—
215C22⋊Q8—2781no—
216#121—2781no—
217#121—2781no—
218#120—2781no—
219#120—2781no—
220#117—1391no—
221#117—1391no—
222C2×C4⋊C4—1391no—
223#103—1391no—
224#103—1391no—
225#103C2×D13911yescharacteristic, complemented
226#103C2×D13911yescharacteristic, complemented
227#102—1391no—
228#102—1391no—
229#102—1391no—
230#102—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102—1391no—
236#102—1391no—
237#102C2×D13911yescharacteristic
238#102C2×D13911yescharacteristic
239#97—1391no—
240#97C2×D13911yescharacteristic, complemented
241C4×C8—1391no—
242C4×C8—1391no—
243C24—2781no—
244#41—2782no—
245#41—2782no—
246C2×Q8—21no—
247C2×Q8—2781no—
248C2×Q8C22×D13911yescharacteristic
249C2×D4—2781no—
250C2×D4—2782no—
251C2×D4—2782no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—2781no—
256C2×D4—2781no—
257C2×D4—1391no—
258C2×D4—1391no—
259C2×D4C22×D13911yescharacteristic
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4—1391no—
263M16—2782no—
264C2×C8—2782no—
265C2×C8—1391no—
266C2×C8—1391no—
267C2×C8C22×D13911yescharacteristic
268C2×C8C22×D13911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—2781no—
271C4⋊C4—2781no—
272C4⋊C4—2781no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—1391no—
277C4⋊C4—1391no—
278C4⋊C4—1391no—
279C4⋊C4—1391no—
280C4⋊C4C22×D13911yescharacteristic
281C4⋊C4C22×D13911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—1391no—
288C22⋊C4—1391no—
289C42—2781no—
290C42—1391no—
291C42C22×D13911yescharacteristic
292C23—21no—
293C23—2781no—
294C23—2781no—
295C23—5562no—
296C23—11121no—
297C23—11121no—
298C23—1391no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—11121no—
303D4—21no—
304D4—21no—
305D4—2781no—
306D4—2781no—
307D4—2781no—
308D4—2781no—
309D4—5562no—
310D4—5562no—
311D4—11121no—
312D4—11121no—
313D4—11121no—
314D4—11121no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—5562no—
321C2×C4—11121no—
322C2×C4—1391no—
323C2×C4—1391no—
324C2×C4—1391no—
325C2×C4—1392no—
326C2×C4—1392no—
327C2×C4D4×D13911yescharacteristic
328C2×C4D4×D13911yescharacteristic
329C2×C4C23×D13911yescharacteristic
330C8—21no—
331C8—21no—
332C8—2781no—
333C8—2781no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2781no—
338C22—2781no—
339C22—5561no—
340C22—5561no—
341C22—5561no—
342C22—5561no—
343C22—5561no—
344C22—5561no—
345C22—11124no—
346C22—1392no—
347C22C2×D4×D13911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2781no—
354C4—2781no—
355C4—5561no—
356C4—5561no—
357C4—1392no—
358C4#41×D13911yescharacteristic
359C4#41×D13911yescharacteristic
360C2—81no—
361C2—2782no—
362C2—11121no—
363C2—11121no—
364C2#124×D13911yescharacteristic
365C2#2258175711yescharacteristic
366C2#2258176211yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#489×C139C2
socleC22×C139C22×D4
prime radical#22581521C2
hypercenter#489D139
hypocenterC139#3136
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #22581580C2semidirect
3. #22581318C2semidirect
4. #22581316C2semidirect
5. #22581314C2semidirect
6. #22581309C2semidirect
7. #22581307C2semidirect
8. #22581301C2semidirect
9. #22581298C2semidirect
10. #22580956C2semidirect
11. #22580953C2semidirect
12. #22580948C2semidirect
13. #102×D139C2semidirect
14. #22580910C2semidirect
15. #489×C139C2semidirect
20. #17984841C22semidirect
24. #17984834C22semidirect
25. #17984833C22semidirect
37. #17984766C22semidirect
38. #17984766C22semidirect
41. #17984764C22semidirect
42. #17984764C22semidirect
47. #17984762C22semidirect
48. #17984762C22semidirect
49. #17984752C22semidirect
50. C4×C139⋊C8C22semidirect
51. C8×Dic139C22semidirect
52. C4⋊Q8×C139C22semidirect
54. #103×C139C22semidirect
55. #103×C139C22semidirect
58. #97×C139C22semidirect
183. C139#3136semidirect
190. #489D139semidirect
206. C4⋊Q8C2×D139semidirect
225. #103C2×D139semidirect
226. #103C2×D139semidirect
240. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815802
#225815212
#225813182
#225813162
#225813142
#225813092
#225813072
#225813012
#225812982
#225809562
#225809532
#225809482
#102×D1392
#225809102
#489×C1392
#3136139