Finite Group Databasebeta

← #31816655

Subgroups — #31816655

Order 17792.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581561C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic
3#22581296C211yesmaximal, characteristic, complemented
4#22581293C211yesmaximal, characteristic, complemented
5#22581256C211yesmaximal, characteristic, complemented
6#22581251C211yesmaximal, characteristic, complemented
7#22581157C211yesmaximal, characteristic, complemented
8#22581156C211yesmaximal, characteristic, complemented
9#22581105C211yesmaximal, characteristic
10#22581102C211yesmaximal, characteristic
11#22581055C211yesmaximal, characteristic, complemented
12C4×#14555772C211yesmaximal, characteristic, complemented
13C4×#14555773C211yesmaximal, characteristic, complemented
14#22581015C211yesmaximal, characteristic, complemented
15#440×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×#14555774C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C2×#14555772C2211yescharacteristic
20#17984840C2211yescharacteristic, complemented
21#17984837—21no—
22#17984836—21no—
23#17984834—21no—
24#17984833C2211yescharacteristic, complemented
25#17984832—21no—
26#17984822C2211yescharacteristic
27#17984818C2211yescharacteristic
28C4×Dic278C2211yescharacteristic, complemented
29C4×D556C2211yescharacteristic
30D4×Dic139C2211yescharacteristic
31#17984804C2211yescharacteristic
32C4×C22⋊D139—21no—
33(C22⋊D139)⋊C4—21no—
34#17984800C2211yescharacteristic
35#17984799C2211yescharacteristic
36C2×(C2×D139)⋊C4—21no—
37C22⋊C4×D139—21no—
38#17984776C2211yescharacteristic, complemented
39#17984773C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984766C2211yescharacteristic, complemented
45#17984765C2211yescharacteristic, complemented
46#17984764C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984762C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51C4×C139⋊C8C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic
53C4×Q8×C139C2211yescharacteristic, complemented
54C4×D4×C139C2211yescharacteristic
55#107×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic
58#97×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63D4×D139—22no—
64D4×D139—22no—
65C22×Dic139—21no—
66C2×C4×D139—21no—
67C2×C4×D139—21no—
68C2×C4×D139C2311yescharacteristic
69#14555774—22no—
70#14555773—22no—
71#14555772—22no—
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C4⋊Dic139—21no—
75C4⋊Dic139—21no—
76C4⋊Dic139C2311yescharacteristic
77C4⋊Dic139C2311yescharacteristic
78Dic139⋊C4—21no—
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84Dic139⋊C4D411yescharacteristic
85C22⋊Dic139—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4D411yescharacteristic
92(C2×D139)⋊C4D411yescharacteristic
93C4×Dic139—21no—
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C2×Q8×C139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C22×C4×C139—21no—
99SD16×C139—22no—
100C2×C8×C139C2311yescharacteristic
101C2×C8×C139C2311yescharacteristic
102C4⋊C4×C139—21no—
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C22⋊C4×C139—21no—
106C42×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—81no—
111C22×D139—81no—
112C22×D139C2×D411yescharacteristic
113Dic278—21no—
114Dic278—21no—
115D556—21no—
116D556#4112yes—
117C22⋊D139—24no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—81no—
122C2×Dic139C2×D411yescharacteristic
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C4×D139—21no—
126C4×D139—21no—
127C4×D139—81no—
128C4×D139—81no—
129C139⋊C8—21no—
130C139⋊C8—21no—
131C23×C139—21no—
132Q8×C139—21no—
133Q8×C139—21no—
134D4×C139—21no—
135D4×C139#4112yes—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—81no—
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2411yescharacteristic
143C8×C139—21no—
144C8×C139—21no—
145C22×C139—22no—
146C22×C139—41no—
147C22×C139—41no—
148C22×C139C22×D411yescharacteristic
149C2×D139—21no—
150C2×D139—22no—
151C2×D139—21no—
152C2×D139—21no—
153C2×D139—41no—
154C2×D139—41no—
155C2×D139—84no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139C2×#4111yescharacteristic
162C4×C139C2×#4111yescharacteristic
163Dic139—21no—
164Dic139—21no—
165Dic139—21no—
166Dic139—41no—
167Dic139—41no—
168Dic139—41no—
169C2×C139—42no—
170C2×C139#52511yescharacteristic
171C2×C139#57711yescharacteristic
172C2×C139#57711yescharacteristic
173D139—41no—
174D139—42no—
175C139#312311yescharacteristic, complemented, Sylow
176#3123—1391nomaximal, Sylow
177#541—1391no—
178#518—1391no—
179#485—1391no—
180#485—1391no—
181#478—1391no—
182#478—1391no—
183#461—1391no—
184#461—1391no—
185#450—1391no—
186#450—1391no—
187#440—1391no—
188#440D13911yescharacteristic, complemented
189C4×SD16—1391no—
190C4×SD16—1391no—
191#433—1391no—
192C22×D4—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×SD16—1391no—
196C2×SD16C2×D13911yescharacteristic
197C4⋊Q8—1391no—
198#126—2781no—
199#126—2781no—
200#125—2781no—
201#125—2781no—
202#125—1391no—
203C22⋊Q8—1391no—
204C22⋊Q8—1391no—
205C4×Q8—1391no—
206C4×Q8C2×D13911yescharacteristic, complemented
207C4×D4—2781no—
208C4×D4—2781no—
209C4×D4—1391no—
210C4×D4—1391no—
211C4×D4—1391no—
212C4×D4C2×D13911yescharacteristic
213#117—1391no—
214#117—1391no—
215C2×C22⋊C4—2781no—
216C2×C22⋊C4—2781no—
217#107—1391no—
218#107C2×D13911yescharacteristic, complemented
219#106—1391no—
220#106—1391no—
221C4⋊C8—1391no—
222C4⋊C8—1391no—
223#103—1391no—
224#103—1391no—
225#103—1391no—
226#103C2×D13911yescharacteristic, complemented
227#102—1391no—
228#102—1391no—
229#102—1391no—
230#102C2×D13911yescharacteristic
231C22⋊C8—1391no—
232C22⋊C8—1391no—
233#97C2×D13911yescharacteristic, complemented
234C4×C8—1391no—
235C24—2781no—
236C2×Q8—1391no—
237C2×Q8C22×D13911yescharacteristic
238C2×D4—2782no—
239C2×D4—2782no—
240C2×D4—2781no—
241C2×D4—1391no—
242C2×D4C22×D13911yescharacteristic
243C22×C4—21no—
244C22×C4—2781no—
245C22×C4—2781no—
246C22×C4—2781no—
247C22×C4—1391no—
248SD16—22no—
249SD16—2782no—
250SD16—2782no—
251SD16—2782no—
252C2×C8—1391no—
253C2×C8—1391no—
254C2×C8C22×D13911yescharacteristic
255C2×C8C22×D13911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—2781no—
262C4⋊C4—2781no—
263C4⋊C4—2781no—
264C4⋊C4—1391no—
265C4⋊C4—1391no—
266C4⋊C4—1391no—
267C4⋊C4—1391no—
268C4⋊C4C22×D13911yescharacteristic
269C4⋊C4C22×D13911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C22⋊C4—2781no—
277C22⋊C4—1391no—
278C22⋊C4—1391no—
279C42—21no—
280C42—2781no—
281C42—2781no—
282C42—1391no—
283C42C22×D13911yescharacteristic
284C23—21no—
285C23—2784no—
286C23—2781no—
287C23—11121no—
288C23—11121no—
289C23—1391no—
290Q8—21no—
291Q8—21no—
292Q8—2781no—
293Q8—2781no—
294D4—21no—
295D4—2784no—
296D4—2781no—
297D4—1392no—
298D4#1455578512yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—2781no—
306C2×C4—2781no—
307C2×C4—2781no—
308C2×C4—11121no—
309C2×C4—11121no—
310C2×C4—11121no—
311C2×C4—1391no—
312C2×C4—1391no—
313C2×C4—1391no—
314C2×C4D4×D13911yescharacteristic
315C2×C4D4×D13911yescharacteristic
316C2×C4C23×D13911yescharacteristic
317C8—21no—
318C8—21no—
319C8—2781no—
320C8—2781no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2781no—
325C22—2781no—
326C22—2781no—
327C22—2782no—
328C22—5561no—
329C22—5561no—
330C22—11124no—
331C22C2×D4×D13911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2781no—
338C4—2781no—
339C4—2781no—
340C4—5561no—
341C4—5561no—
342C4—5561no—
343C4#41×D13911yescharacteristic
344C4C2×#1455578511yescharacteristic
345C2—42no—
346C2—5561no—
347C2—5562no—
348C2#2258146211yescharacteristic
349C2#2258176211yescharacteristic
350C2#2258176311yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#440×C139C2
socleC22×C139C22×D4
prime radicalC2×D4×D139C22
hypercenter#440D139
hypocenterC139#3123
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #22581561C2semidirect
3. #22581296C2semidirect
4. #22581293C2semidirect
5. #22581256C2semidirect
6. #22581251C2semidirect
7. #22581157C2semidirect
8. #22581156C2semidirect
11. #22581055C2semidirect
12. C4×#14555772C2semidirect
13. C4×#14555773C2semidirect
14. #22581015C2semidirect
15. #440×C139C2semidirect
20. #17984840C22semidirect
24. #17984833C22semidirect
28. C4×Dic278C22semidirect
38. #17984776C22semidirect
39. #17984773C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984767C22semidirect
44. #17984766C22semidirect
45. #17984765C22semidirect
51. C4×C139⋊C8C22semidirect
53. C4×Q8×C139C22semidirect
55. #107×C139C22semidirect
56. #103×C139C22semidirect
58. #97×C139C22semidirect
175. C139#3123semidirect
188. #440D139semidirect
206. C4×Q8C2×D139semidirect
218. #107C2×D139semidirect
226. #103C2×D139semidirect
233. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815612
#225814252
#225812962
#225812932
#225812562
#225812512
#225811572
#225811562
#225811052
#225811022
#225810552
C4×#145557722
C4×#145557732
#225810152
#440×C1392
#3123139