Finite Group Databasebeta

← #31816513

Subgroups — #31816513

Order 17792.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581487C211yesmaximal, characteristic, complemented
2#22581294C211yesmaximal, characteristic, complemented
3#22581277C211yesmaximal, characteristic, complemented
4#22581260C211yesmaximal, characteristic, complemented
5#22581253C211yesmaximal, characteristic, complemented
6#22581175C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581115C211yesmaximal, characteristic, complemented
9#22581098C211yesmaximal, characteristic
10#22581063C211yesmaximal, characteristic, complemented
11#22581058C211yesmaximal, characteristic, complemented
12#22581053C211yesmaximal, characteristic, complemented
13#22581051C211yesmaximal, characteristic, complemented
14#22581010C211yesmaximal, characteristic, complemented
15C4×#41×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555772C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984836—21no—
21#17984834C2211yescharacteristic
22#17984830C2211yescharacteristic
23#17984825—21no—
24#17984821C2211yescharacteristic
25#17984816C2211yescharacteristic
26C4×Dic278C2211yescharacteristic
27C4×D556C2211yescharacteristic
28C4×C22⋊D139—21no—
29#17984799—21no—
30#17984775C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984773C2211yescharacteristic
33#17984773C2211yescharacteristic
34C4⋊(C139⋊C8)C2211yescharacteristic
35C4⋊(C139⋊C8)C2211yescharacteristic
36#17984766C2211yescharacteristic
37#17984766C2211yescharacteristic
38#17984765C2211yescharacteristic
39#17984765C2211yescharacteristic
40#17984763C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984762C2211yescharacteristic
43#17984762C2211yescharacteristic
44C22⋊(C139⋊C8)C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46#17984753C2211yescharacteristic
47#17984753C2211yescharacteristic
48C2×#41×C139C2211yescharacteristic
49C4×Q8×C139C2211yescharacteristic
50C4×Q8×C139C2211yescharacteristic
51C4×D4×C139—21no—
52C4×D4×C139—21no—
53C4×D4×C139C2211yescharacteristic
54C4×D4×C139C2211yescharacteristic
55#117×C139—21no—
56#117×C139C2211yescharacteristic
57C2×C42×C139—21no—
58C2×C42×C139C2211yescharacteristic
59C2×Dic278C2311yescharacteristic
60C2×D556C2311yescharacteristic
61C2×C22⋊D139—21no—
62C2×C4×D139—21no—
63#14555775—22no—
64#14555773—22no—
65#14555772—22no—
66#14555770—22no—
67C2×C139⋊C8C2311yescharacteristic
68C2×C139⋊C8C2311yescharacteristic
69C2×C139⋊C8C2311yescharacteristic
70C2×C139⋊C8C2311yescharacteristic
71C4⋊Dic139C2311yescharacteristic
72C4⋊Dic139C2311yescharacteristic
73Dic139⋊C4—21no—
74Dic139⋊C4—21no—
75Dic139⋊C4—21no—
76Dic139⋊C4—21no—
77C22⋊Dic139—21no—
78(C2×D139)⋊C4—21no—
79(C2×D139)⋊C4—21no—
80(C2×D139)⋊C4—21no—
81(C2×D139)⋊C4—21no—
82C4×Dic139—21no—
83#41×C139—22no—
84#41×C139—22no—
85C2×Q8×C139C2311yescharacteristic
86C2×D4×C139—21no—
87C2×D4×C139C2311yescharacteristic
88C22×C4×C139—21no—
89C22×C4×C139—21no—
90C22×C4×C139—21no—
91C22×C4×C139D411yescharacteristic
92C22×C4×C139D411yescharacteristic
93C22×C4×C139C2311yescharacteristic
94C4⋊C4×C139—21no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139C2311yescharacteristic
97C4⋊C4×C139C2311yescharacteristic
98C22⋊C4×C139—21no—
99C22⋊C4×C139—21no—
100C22⋊C4×C139—21no—
101C42×C139—21no—
102C42×C139—21no—
103C42×C139—21no—
104C42×C139D411yescharacteristic
105C42×C139D411yescharacteristic
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109Dic278—21no—
110Dic278—21no—
111D556—21no—
112D556—21no—
113C22⋊D139—42no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C4×D139—42no—
118C139⋊C8—21no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C23×C139—21no—
123C23×C139C2×D411yescharacteristic
124Q8×C139—21no—
125Q8×C139#4112yes—
126D4×C139—24no—
127D4×C139—21no—
128D4×C139#4112yes—
129C2×C4×C139—24no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—41no—
136C2×C4×C139—41no—
137C2×C4×C139—42no—
138C2×C4×C139—42no—
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2411yescharacteristic
145C22×C139—21no—
146C22×C139—22no—
147C22×C139—21no—
148C22×C139—21no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139C22×D411yescharacteristic
152C2×D139—41no—
153C2×D139—41no—
154C2×D139—41no—
155C4×C139—21no—
156C4×C139—22no—
157C4×C139—21no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—41no—
162C4×C139—41no—
163C4×C139C2×#4111yescharacteristic
164C4×C139C2×#4111yescharacteristic
165Dic139—41no—
166Dic139—41no—
167Dic139—41no—
168C2×C139—41no—
169C2×C139—42no—
170C2×C139#52511yescharacteristic
171C2×C139#57511yescharacteristic
172C2×C139#57511yescharacteristic
173D139—81no—
174C139#311111yescharacteristic, complemented, Sylow
175#3111—1391nomaximal, Sylow
176#529—1391no—
177C4×#41D13911yescharacteristic, complemented
178#485—1391no—
179#482—1391no—
180#479—1391no—
181#478—1391no—
182#464—1391no—
183#463—1391no—
184#452—1391no—
185#449—1391no—
186#442—1391no—
187#441—1391no—
188#440—1391no—
189#440—1391no—
190#432—1391no—
191C2×#41C2×D13911yescharacteristic
192C2×Q16—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×D8—1391no—
196#126—2781no—
197#125—1391no—
198#124—1391no—
199#123—2781no—
200C22⋊Q8—1391no—
201#121—1391no—
202C4×Q8—1391no—
203C4×Q8C2×D13911yescharacteristic
204C4×Q8C2×D13911yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—2781no—
208C4×D4—1391no—
209C4×D4C2×D13911yescharacteristic
210C4×D4C2×D13911yescharacteristic
211#117—21no—
212#117—2781no—
213#117C2×D13911yescharacteristic
214C2×C42—21no—
215C2×C42C2×D13911yescharacteristic
216#107—1391no—
217#107—1391no—
218#106—1391no—
219#106—1391no—
220C4⋊C8—1391no—
221C4⋊C8—1391no—
222#103—1391no—
223#103—1391no—
224#103—1391no—
225#103—1391no—
226#102—1391no—
227#102—1391no—
228#102—1391no—
229#102—1391no—
230C22⋊C8—1391no—
231C22⋊C8—1391no—
232#97—1391no—
233#97—1391no—
234#41—22no—
235#41—22no—
236C2×Q8—1391no—
237C2×Q8C22×D13911yescharacteristic
238C2×D4—21no—
239C2×D4—2781no—
240C2×D4—1391no—
241C2×D4C22×D13911yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—2781no—
246C22×C4C22⋊D13911yescharacteristic
247C22×C4C22⋊D13911yescharacteristic
248C22×C4C22×D13911yescharacteristic
249Q16—2782no—
250SD16—2782no—
251SD16—2782no—
252D8—2782no—
253C2×C8—1391no—
254C2×C8—1391no—
255C2×C8—1391no—
256C2×C8—1391no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—2781no—
262C4⋊C4—2781no—
263C4⋊C4—1391no—
264C4⋊C4—1391no—
265C4⋊C4C22×D13911yescharacteristic
266C4⋊C4C22×D13911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2781no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—2781no—
279C42C22⋊D13911yescharacteristic
280C42C22⋊D13911yescharacteristic
281C42C22×D13911yescharacteristic
282C42C22×D13911yescharacteristic
283C23—21no—
284C23—2781no—
285C23C2×C22⋊D13911yescharacteristic
286Q8—21no—
287Q8—2781no—
288Q8—2781no—
289Q8#1455578512yes—
290D4—24no—
291D4—21no—
292D4—2781no—
293D4—2781no—
294D4—5562no—
295D4#1455578512yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—2781no—
307C2×C4—2781no—
308C2×C4—2781no—
309C2×C4—5562no—
310C2×C4C2×C22⋊D13911yescharacteristic
311C2×C4C2×C22⋊D13911yescharacteristic
312C2×C4C2×C22⋊D13911yescharacteristic
313C2×C4C2×C22⋊D13911yescharacteristic
314C2×C4C2×C22⋊D13911yescharacteristic
315C2×C4C23×D13911yescharacteristic
316C8—2781no—
317C8—2781no—
318C8—2781no—
319C8—2781no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—5561no—
327C22—5561no—
328C22—5561no—
329C22C22×C22⋊D13911yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—5561no—
339C4—5561no—
340C4—5561no—
341C4C2×#1455578511yescharacteristic
342C4C2×#1455578511yescharacteristic
343C2—41no—
344C2—42no—
345C2—11121no—
346C2#2258146411yescharacteristic
347C2#2258175111yescharacteristic
348C2#2258175111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC4×#41×C139C2
socleC22×C139C22×D4
prime radical#22581098C2
hypercenterC4×#41D139
hypocenterC139#3111
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #22581487C2semidirect
2. #22581294C2semidirect
3. #22581277C2semidirect
4. #22581260C2semidirect
5. #22581253C2semidirect
6. #22581175C2semidirect
7. #22581168C2semidirect
8. #22581115C2semidirect
10. #22581063C2semidirect
11. #22581058C2semidirect
12. #22581053C2semidirect
13. #22581051C2semidirect
14. #22581010C2semidirect
15. C4×#41×C139C2semidirect
174. C139#3111semidirect
177. C4×#41D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225812942
#225812772
#225812602
#225812532
#225811752
#225811682
#225811152
#225810982
#225810632
#225810582
#225810532
#225810512
#225810102
C4×#41×C1392
#3111139