Finite Group Databasebeta

← #31816603

Subgroups — #31816603

Order 17792.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581558C211yesmaximal, characteristic, complemented
2#22581271C211yesmaximal, characteristic, complemented
3#22581266C211yesmaximal, characteristic, complemented
4#22581260C211yesmaximal, characteristic, complemented
5#22581253C211yesmaximal, characteristic, complemented
6#22581153C211yesmaximal, characteristic, complemented
7#22581148C211yesmaximal, characteristic, complemented
8#22581098C211yesmaximal, characteristic, complemented
9#22581098C211yesmaximal, characteristic, complemented
10#22581063C211yesmaximal, characteristic, complemented
11#22581051C211yesmaximal, characteristic, complemented
12C4×#14555772C211yesmaximal, characteristic, complemented
13C4×#14555770C211yesmaximal, characteristic, complemented
14#22581014C211yesmaximal, characteristic, complemented
15#520×C139C211yesmaximal, characteristic, complemented
16C2×#14555772C2211yescharacteristic
17C2×#14555772C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984839C2211yescharacteristic
21#17984834C2211yescharacteristic
22#17984827—21no—
23#17984827—21no—
24#17984816C2211yescharacteristic
25#17984816C2211yescharacteristic
26#17984815—21no—
27#17984815—21no—
28C4×D556C2211yescharacteristic
29C4×D556C2211yescharacteristic
30#17984775C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984773C2211yescharacteristic
33#17984773C2211yescharacteristic
34C4⋊(C139⋊C8)C2211yescharacteristic
35C4⋊(C139⋊C8)C2211yescharacteristic
36#17984766C2211yescharacteristic
37#17984766C2211yescharacteristic
38#17984763C2211yescharacteristic
39#17984763C2211yescharacteristic
40#17984762C2211yescharacteristic
41#17984762C2211yescharacteristic
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×D556—21no—
60C2×D556—21no—
61C2×D556C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C4×D139—21no—
66C2×C4×D139—21no—
67#14555772—22no—
68#14555772—22no—
69#14555770—22no—
70#14555770—22no—
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C2×C139⋊C8C2311yescharacteristic
75C4⋊Dic139C2311yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77Dic139⋊C4—21no—
78Dic139⋊C4—21no—
79(C2×D139)⋊C4—21no—
80(C2×D139)⋊C4—21no—
81(C2×D139)⋊C4—21no—
82(C2×D139)⋊C4—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—
109C22×D139—21no—
110D556—21no—
111D556—21no—
112D556—21no—
113D556—21no—
114D556—81no—
115D556—81no—
116C22⋊D139—81no—
117C22⋊D139—81no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C4×D139—81no—
121C4×D139—81no—
122C139⋊C8—21no—
123C139⋊C8—21no—
124C139⋊C8—21no—
125C139⋊C8—21no—
126C23×C139—21no—
127C23×C139C2×D411yescharacteristic
128Q8×C139—21no—
129Q8×C139#4112yes—
130D4×C139—24no—
131D4×C139—21no—
132D4×C139#4112yes—
133C2×C4×C139—24no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—81no—
140C2×C4×C139—81no—
141C2×C4×C139—81no—
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2411yescharacteristic
148C22×C139—21no—
149C22×C139—22no—
150C22×C139—21no—
151C22×C139—21no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139C22×D411yescharacteristic
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C2×D139—41no—
160C2×D139—41no—
161C4×C139—21no—
162C4×C139—22no—
163C4×C139—21no—
164C4×C139—21no—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139C2×#4111yescharacteristic
170C4×C139C2×#4111yescharacteristic
171Dic139—41no—
172Dic139—41no—
173C2×C139—41no—
174C2×C139—42no—
175C2×C139#52511yescharacteristic
176C2×C139#57611yescharacteristic
177C2×C139#57711yescharacteristic
178D139—81no—
179D139—81no—
180C139#311911yescharacteristic, complemented, Sylow
181#3119—1391nomaximal, Sylow
182#540—1391no—
183#520D13911yescharacteristic, complemented
184#481—1391no—
185#480—1391no—
186#479—1391no—
187#478—1391no—
188#460—1391no—
189#459—1391no—
190#449—1391no—
191#449—1391no—
192#442—1391no—
193#440—1391no—
194C4×SD16—1391no—
195C4×D8—1391no—
196#433—1391no—
197C2×#41C2×D13911yescharacteristic
198C2×SD16—1391no—
199C2×SD16—1391no—
200C2×D8—1391no—
201C2×D8—1391no—
202#127—1391no—
203#125—1391no—
204#123—2781no—
205#123—2781no—
206#121—2781no—
207#121—2781no—
208#121—1391no—
209#121—1391no—
210C4×Q8C2×D13911yescharacteristic
211C4×Q8C2×D13911yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1391no—
215C4×D4—1391no—
216C4×D4C2×D13911yescharacteristic
217C4×D4C2×D13911yescharacteristic
218#117—21no—
219#117C2×D13911yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D13911yescharacteristic
222#107—1391no—
223#107—1391no—
224#106—1391no—
225#106—1391no—
226C4⋊C8—1391no—
227C4⋊C8—1391no—
228#103—1391no—
229#103—1391no—
230#102—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102—1391no—
236C22⋊C8—1391no—
237C22⋊C8—1391no—
238#97—1391no—
239C4×C8—1391no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D13911yescharacteristic
243C2×D4—21no—
244C2×D4—2781no—
245C2×D4—2781no—
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4—1391no—
250C2×D4C22×D13911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2781no—
256C22×C4—2781no—
257C22×C4C22×D13911yescharacteristic
258SD16—2782no—
259SD16—2782no—
260D8—2782no—
261D8—2782no—
262C2×C8—1391no—
263C2×C8—1391no—
264C2×C8—1391no—
265C2×C8—1391no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—2781no—
270C4⋊C4—2781no—
271C4⋊C4—1391no—
272C4⋊C4—1391no—
273C4⋊C4C22⋊D13911yescharacteristic
274C4⋊C4C22⋊D13911yescharacteristic
275C4⋊C4C22×D13911yescharacteristic
276C4⋊C4C22×D13911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C22⋊C4C22⋊D13911yescharacteristic
284C22⋊C4C22⋊D13911yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D13911yescharacteristic
288C42C22×D13911yescharacteristic
289C23—21no—
290C23—2781no—
291C23—2781no—
292C23C2×C22⋊D13911yescharacteristic
293Q8—21no—
294Q8#1455578512yes—
295D4—24no—
296D4—21no—
297D4—2781no—
298D4—2781no—
299D4—2781no—
300D4—2781no—
301D4—11121no—
302D4—11121no—
303D4—11121no—
304D4—11121no—
305D4#1455578512yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—11121no—
318C2×C4—11121no—
319C2×C4C2×C22⋊D13911yescharacteristic
320C2×C4C2×C22⋊D13911yescharacteristic
321C2×C4C2×C22⋊D13911yescharacteristic
322C2×C4C2×C22⋊D13911yescharacteristic
323C2×C4C2×C22⋊D13911yescharacteristic
324C2×C4C23×D13911yescharacteristic
325C8—2781no—
326C8—2781no—
327C8—2781no—
328C8—2781no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—5561no—
336C22—5561no—
337C22—5561no—
338C22—5561no—
339C22—5561no—
340C22—5561no—
341C22C22×C22⋊D13911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—5561no—
351C4—5561no—
352C4C2×#1455578511yescharacteristic
353C4C2×#1455578511yescharacteristic
354C2—41no—
355C2—42no—
356C2—11121no—
357C2—11121no—
358C2#2258146411yescharacteristic
359C2#2258175611yescharacteristic
360C2#2258176111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#520×C139C2
socleC22×C139C22×D4
hypercenter#520D139
hypocenterC139#3119
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. #22581558C2semidirect
2. #22581271C2semidirect
3. #22581266C2semidirect
4. #22581260C2semidirect
5. #22581253C2semidirect
6. #22581153C2semidirect
7. #22581148C2semidirect
8. #22581098C2semidirect
9. #22581098C2semidirect
10. #22581063C2semidirect
11. #22581051C2semidirect
12. C4×#14555772C2semidirect
13. C4×#14555770C2semidirect
14. #22581014C2semidirect
15. #520×C139C2semidirect
180. C139#3119semidirect
183. #520D139semidirect

Maximal subgroups

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

subgroupindex
#225815582
#225812712
#225812662
#225812602
#225812532
#225811532
#225811482
#225810982
#225810632
#225810512
C4×#145557722
C4×#145557702
#225810142
#520×C1392
#3119139