Finite Group Databasebeta

← #31819108

Subgroups — #31819108

Order 17792.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581659C211yesmaximal, characteristic, complemented
2#22581623C211yesmaximal, characteristic, complemented
3#22581316C211yesmaximal, characteristic, complemented
4#22581298C211yesmaximal, characteristic, complemented
5#22581255C211yesmaximal, characteristic, complemented
6#22581250C211yesmaximal, characteristic, complemented
7#22581241C211yesmaximal, characteristic, complemented
8#22581147C211yesmaximal, characteristic, complemented
9#22581147C211yesmaximal, characteristic, complemented
10#22581145C211yesmaximal, characteristic, complemented
11#22581081C211yesmaximal, characteristic, complemented
12#22581066C211yesmaximal, characteristic, complemented
13#22581062C211yesmaximal, characteristic, complemented
14#22581033C211yesmaximal, characteristic, complemented
15#490×C139C211yesmaximal, characteristic, complemented
16C2×#14555784—21no—
17C2×D1112C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984841C2211yescharacteristic
21#17984838C2211yescharacteristic
22#17984838C2211yescharacteristic
23#17984833C2211yescharacteristic
24#17984822—21no—
25#17984820—21no—
26#17984820—21no—
27#17984814—21no—
28#17984814—21no—
29#17984813—21no—
30C4×Dic278C2211yescharacteristic
31C4×D556C2211yescharacteristic
32C4×D556C2211yescharacteristic
33D4×Dic139C2211yescharacteristic
34D4×Dic139C2211yescharacteristic
35#17984804C2211yescharacteristic
36#17984804C2211yescharacteristic
37C4⋊C4×D139—21no—
38#17984775C2211yescharacteristic
39#17984774C2211yescharacteristic
40#17984773C2211yescharacteristic
41C4⋊(C139⋊C8)C2211yescharacteristic
42Dic139⋊C8C2211yescharacteristic
43Dic139⋊C8C2211yescharacteristic
44#17984764C2211yescharacteristic
45#17984764C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984762C2211yescharacteristic
49#17984762C2211yescharacteristic
50#17984752C2211yescharacteristic
51C8×Dic139C2211yescharacteristic
52#127×C139C2211yescharacteristic
53#125×C139C2211yescharacteristic
54#102×C139C2211yescharacteristic
55#102×C139C2211yescharacteristic
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic
58#97×C139C2211yescharacteristic
59#14555784—44no—
60C2×Dic278—21no—
61C2×Dic278D411yescharacteristic
62C2×D556C2311yescharacteristic
63C2×D556C2311yescharacteristic
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C22×Dic139—21no—
69C22×Dic139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139—21no—
74D1112—22no—
75#14555770—22no—
76#14555770—22no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C4⋊Dic139—21no—
80C4⋊Dic139D411yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4D411yescharacteristic
86Dic139⋊C4D411yescharacteristic
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93C4×Dic139C2311yescharacteristic
94C4×Dic139C2311yescharacteristic
95C2×D4×C139—21no—
96C2×D4×C139—21no—
97C2×D4×C139C2311yescharacteristic
98C2×D4×C139C2311yescharacteristic
99C2×C8×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C4⋊C4×C139—21no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C42×C139C2311yescharacteristic
106C22×D139—21no—
107C22×D139—21no—
108Dic278—22no—
109Dic278—81no—
110D556—21no—
111D556—21no—
112D556—21no—
113D556#4112yescomplemented
114C22⋊D139—42no—
115C22⋊D139—42no—
116C22⋊D139—81no—
117C22⋊D139—81no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—42no—
121C2×Dic139—42no—
122C2×Dic139C2×D411yescharacteristic
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C4×D139—42no—
127C4×D139—42no—
128C4×D139—81no—
129C4×D139—81no—
130C139⋊C8—21no—
131C139⋊C8—21no—
132C23×C139—21no—
133C23×C139—21no—
134D4×C139—21no—
135D4×C139—21no—
136D4×C139—21no—
137D4×C139—21no—
138D4×C139—42no—
139D4×C139—81no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2411yescharacteristic
145C8×C139—21no—
146C8×C139—21no—
147C22×C139—41no—
148C22×C139—41no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139C22×D411yescharacteristic
154C2×D139—22no—
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C2×D139—41no—
160C4×C139—21no—
161C4×C139—21no—
162C4×C139—41no—
163C4×C139—41no—
164C4×C139C2×#4111yescharacteristic
165C4×C1392−1+411yescharacteristic
166Dic139—21no—
167Dic139—21no—
168Dic139—21no—
169Dic139—41no—
170Dic139—41no—
171Dic139AGL(1,ℤ/8)12yes—
172C2×C139—81no—
173C2×C139—81no—
174C2×C139#54811yescharacteristic
175C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C139#57611yescharacteristic
177D139—42no—
178D139—81no—
179C139#336611yescharacteristic, complemented, Sylow
180#3366—1391nomaximal, Sylow
181#554—1391no—
182#550—1391no—
183#490—1391no—
184#490D13911yescharacteristic, complemented
185#486—1391no—
186#478—1391no—
187#478—1391no—
188#476—1391no—
189#459—1391no—
190#459—1391no—
191#459—1391no—
192#446—1391no—
193#442—1391no—
194#442—1391no—
195C4×D8—1391no—
196C2×#41—2781no—
197C2×D8—1391no—
198C2×D8—1391no—
199C2×D8—1391no—
200C4⋊Q8—1391no—
201#127—1391no—
202#127—1391no—
203#127C2×D13911yescharacteristic
204#125—1391no—
205#125C2×D13911yescharacteristic
206C22⋊Q8—2781no—
207C22⋊Q8—2781no—
208C22⋊Q8—2781no—
209#121—2781no—
210#121—2781no—
211#121—2781no—
212C4×Q8—1391no—
213C4×D4—1391no—
214C4×D4—1391no—
215C4×D4—1391no—
216C4×D4—1391no—
217C4×D4—1391no—
218C4×D4—1391no—
219C2×C4⋊C4—2781no—
220#107—1391no—
221#106—1391no—
222#106—1391no—
223C4⋊C8—1391no—
224C4⋊C8—1391no—
225C4⋊C8—1391no—
226#102—1391no—
227#102—1391no—
228#102—1391no—
229#102—1391no—
230#102—1391no—
231#102—1391no—
232#102C2×D13911yescharacteristic
233#102C2×D13911yescharacteristic
234#102C2×D13911yescharacteristic
235#102C2×D13911yescharacteristic
236#97—1391no—
237#97C2×D13911yescharacteristic
238C4×C8—1391no—
239#41—5564no—
240C2×Q8—2781no—
241C2×Q8—1391no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2781no—
245C2×D4—2781no—
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4—1391no—
250C2×D4C22×D13911yescharacteristic
251C2×D4C22×D13911yescharacteristic
252C22×C4—2781no—
253C22×C4—2781no—
254C22×C4—2781no—
255C22×C4—2781no—
256C22×C4—2781no—
257C22×C4—2781no—
258D8—2782no—
259D8—2782no—
260D8—2782no—
261C2×C8—1391no—
262C2×C8—1391no—
263C2×C8C22×D13911yescharacteristic
264C2×C8C22×D13911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—2781no—
268C4⋊C4—2781no—
269C4⋊C4—2781no—
270C4⋊C4—1391no—
271C4⋊C4—1391no—
272C4⋊C4—1391no—
273C4⋊C4—1391no—
274C4⋊C4—1391no—
275C4⋊C4C22×D13911yescharacteristic
276C4⋊C4C22×D13911yescharacteristic
277C22⋊C4—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C42—1391no—
284C42—1391no—
285C42C22×D13911yescharacteristic
286C23—21no—
287C23—21no—
288C23—2781no—
289C23—2781no—
290Q8—2782no—
291Q8—11121no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—2781no—
299D4—2781no—
300D4—2781no—
301D4—5562no—
302D4—5562no—
303D4—11121no—
304D4—11121no—
305D4—1392no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2781no—
309C2×C4—2781no—
310C2×C4—5562no—
311C2×C4—5562no—
312C2×C4—5562no—
313C2×C4—5562no—
314C2×C4—11121no—
315C2×C4—11121no—
316C2×C4—1391no—
317C2×C4—1391no—
318C2×C4—1391no—
319C2×C4—1391no—
320C2×C4D4×D13911yescharacteristic
321C2×C4D4×D13911yescharacteristic
322C2×C4C23×D13911yescharacteristic
323C8—21no—
324C8—21no—
325C8—2781no—
326C8—2781no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2782no—
334C22—5561no—
335C22—5561no—
336C22—5561no—
337C22—5561no—
338C22—5561no—
339C22C2×D4×D13911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—2781no—
345C4—2781no—
346C4—2781no—
347C4—5561no—
348C4—5561no—
349C4—1392no—
350C4#41×D13911yescharacteristic
351C4#1798488911yescharacteristic
352C2—81no—
353C2—81no—
354C2—5562no—
355C2—11121no—
356C2#2258161111yescharacteristic
357C2AGL(1,ℤ/8)×D13911yescharacteristic
358C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#490×C139C2
socleC22×C139C22×D4
hypercenter#490D139
hypocenterC139#3366
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #22581659C2semidirect
2. #22581623C2semidirect
3. #22581316C2semidirect
4. #22581298C2semidirect
5. #22581255C2semidirect
6. #22581250C2semidirect
7. #22581241C2semidirect
8. #22581147C2semidirect
9. #22581147C2semidirect
10. #22581145C2semidirect
11. #22581081C2semidirect
12. #22581066C2semidirect
13. #22581062C2semidirect
14. #22581033C2semidirect
15. #490×C139C2semidirect
113. D556#41semidirect
179. C139#3366semidirect
184. #490D139semidirect

Maximal subgroups

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

subgroupindex
#225816592
#225816232
#225813162
#225812982
#225812552
#225812502
#225812412
#225811472
#225811452
#225810812
#225810662
#225810622
#225810332
#490×C1392
#3366139