Finite Group Databasebeta

← #31816666

Subgroups — #31816666

Order 17792.

384 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#22581574C211yesmaximal, characteristic, complemented
2#22581288C211yesmaximal, characteristic, complemented
3#22581266C211yesmaximal, characteristic, complemented
4#22581248C211yesmaximal, characteristic, complemented
5#22581233C211yesmaximal, characteristic, complemented
6#22581175C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581115C211yesmaximal, characteristic, complemented
9#22581098C211yesmaximal, characteristic
10#22581053C211yesmaximal, characteristic, complemented
11#22581051C211yesmaximal, characteristic, complemented
12C4×#14555775C211yesmaximal, characteristic, complemented
13C4×#14555770C211yesmaximal, characteristic, complemented
14#22581014C211yesmaximal, characteristic, complemented
15#520×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555772C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984842C2211yescharacteristic
21#17984837—21no—
22#17984830C2211yescharacteristic
23#17984828—21no—
24#17984824—21no—
25#17984821C2211yescharacteristic
26#17984820—21no—
27#17984816C2211yescharacteristic
28C4×Dic278C2211yescharacteristic
29C4×D556C2211yescharacteristic
30#17984775C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984775C2211yescharacteristic
33#17984775C2211yescharacteristic
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
47C4×C139⋊C8C2211yescharacteristic
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×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139C2211yescharacteristic
59C2×Dic278—21no—
60C2×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C4×D139—21no—
64#14555775—22no—
65#14555773—22no—
66#14555772—22no—
67#14555770—22no—
68C2×C139⋊C8C2311yescharacteristic
69C2×C139⋊C8C2311yescharacteristic
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C4⋊Dic139—21no—
73C4⋊Dic139C2311yescharacteristic
74C4⋊Dic139C2311yescharacteristic
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×C139—21no—
92C22×C4×C139C2311yescharacteristic
93C4⋊C4×C139—21no—
94C4⋊C4×C139—21no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139D411yescharacteristic
97C4⋊C4×C139D411yescharacteristic
98C4⋊C4×C139C2311yescharacteristic
99C4⋊C4×C139C2311yescharacteristic
100C22⋊C4×C139—21no—
101C22⋊C4×C139—21no—
102C22⋊C4×C139D411yescharacteristic
103C22⋊C4×C139D411yescharacteristic
104C42×C139—21no—
105C42×C139—21no—
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109Dic278—21no—
110Dic278—21no—
111Dic278—81no—
112D556—21no—
113D556—21no—
114C22⋊D139—81no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C4×D139—81no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C139⋊C8—21no—
123C23×C139—21no—
124C23×C139C2×D411yescharacteristic
125Q8×C139—21no—
126Q8×C139#4112yes—
127D4×C139—24no—
128D4×C139—21no—
129D4×C139#4112yes—
130C2×C4×C139—24no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—81no—
137C2×C4×C139—81no—
138C2×C4×C139—81no—
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#57611yescharacteristic
172C2×C139#57811yescharacteristic
173D139—81no—
174C139#312411yescharacteristic, complemented, Sylow
175#3124—1391nomaximal, Sylow
176#542—1391no—
177#520D13911yescharacteristic, complemented
178#484—1391no—
179#480—1391no—
180#477—1391no—
181#474—1391no—
182#464—1391no—
183#463—1391no—
184#452—1391no—
185#449—1391no—
186#440—1391no—
187#440—1391no—
188C4×Q16—1391no—
189C4×D8—1391no—
190#433—1391no—
191C2×#41C2×D13911yescharacteristic
192C2×Q16—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×D8—1391no—
196C4⋊Q8—1391no—
197#126—2781no—
198#124—2781no—
199#124—1391no—
200#123—2781no—
201C22⋊Q8—2781no—
202C22⋊Q8—1391no—
203#121—1391no—
204C4×Q8—1391no—
205C4×Q8C2×D13911yescharacteristic
206C4×Q8C2×D13911yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—1391no—
210C4×D4C2×D13911yescharacteristic
211C4×D4C2×D13911yescharacteristic
212#117—21no—
213#117C2×D13911yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D13911yescharacteristic
216#107—1391no—
217#107—1391no—
218#107—1391no—
219#107—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—
233C4×C8—1391no—
234#41—22no—
235#41—22no—
236C2×Q8—2781no—
237C2×Q8—1391no—
238C2×Q8C22×D13911yescharacteristic
239C2×D4—21no—
240C2×D4—2781no—
241C2×D4—1391no—
242C2×D4C22×D13911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2781no—
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—21no—
260C4⋊C4—2781no—
261C4⋊C4—2781no—
262C4⋊C4—2781no—
263C4⋊C4—1391no—
264C4⋊C4—1391no—
265C4⋊C4C22⋊D13911yescharacteristic
266C4⋊C4C22⋊D13911yescharacteristic
267C4⋊C4C22×D13911yescharacteristic
268C4⋊C4C22×D13911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C22⋊C4C22⋊D13911yescharacteristic
277C22⋊C4C22⋊D13911yescharacteristic
278C42—21no—
279C42—21no—
280C42—2781no—
281C42C22×D13911yescharacteristic
282C42C22×D13911yescharacteristic
283C23—21no—
284C23—2781no—
285C23C2×C22⋊D13911yescharacteristic
286Q8—21no—
287Q8—2781no—
288Q8—2781no—
289Q8—11121no—
290Q8#1455578512yes—
291D4—24no—
292D4—21no—
293D4—2781no—
294D4—2781no—
295D4—11121no—
296D4#1455578512yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—2781no—
307C2×C4—2781no—
308C2×C4—2781no—
309C2×C4—11121no—
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—21no—
322C22—22no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—5561no—
327C22—5561no—
328C22—5561no—
329C22C22×C22⋊D13911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
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#2258175611yescharacteristic
348C2#2258176811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#520×C139C2
socleC22×C139C22×D4
prime radical#22581098C2
hypercenter#520D139
hypocenterC139#3124
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581288C2semidirect
3. #22581266C2semidirect
4. #22581248C2semidirect
5. #22581233C2semidirect
6. #22581175C2semidirect
7. #22581168C2semidirect
8. #22581115C2semidirect
10. #22581053C2semidirect
11. #22581051C2semidirect
12. C4×#14555775C2semidirect
13. C4×#14555770C2semidirect
14. #22581014C2semidirect
15. #520×C139C2semidirect
174. C139#3124semidirect
177. #520D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225812882
#225812662
#225812482
#225812332
#225811752
#225811682
#225811152
#225810982
#225810532
#225810512
C4×#145557752
C4×#145557702
#225810142
#520×C1392
#3124139