Finite Group Databasebeta

← #31819004

Subgroups — #31819004

Order 17792.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581649C211yesmaximal, characteristic, complemented
2#22581352C211yesmaximal, characteristic, complemented
3#22581277C211yesmaximal, characteristic, complemented
4#22581274C211yesmaximal, characteristic, complemented
5#22581266C211yesmaximal, characteristic, complemented
6#22581264C211yesmaximal, characteristic, complemented
7#22581253C211yesmaximal, characteristic, complemented
8#22581250C211yesmaximal, characteristic, complemented
9#22581204C211yesmaximal, characteristic, complemented
10#22581204C211yesmaximal, characteristic, complemented
11C4×#14555770C211yesmaximal, characteristic, complemented
12#22581031C211yesmaximal, characteristic, complemented
13#22580996C211yesmaximal, characteristic, complemented
14#22580993C211yesmaximal, characteristic, complemented
15#553×C139C211yesmaximal, characteristic, complemented
16C2×#14555770C2211yescharacteristic
17C2×#14555769C2211yescharacteristic
18C2×#14555769C2211yescharacteristic
19#17984837—21no—
20#17984834C2211yescharacteristic
21#17984824—21no—
22#17984816C2211yescharacteristic
23#17984816C2211yescharacteristic
24#17984814—21no—
25C4×D556C2211yescharacteristic
26(C22⋊D139)⋊C4—21no—
27#17984801C2211yescharacteristic
28C2×C4⋊Dic139C2211yescharacteristic
29#17984775C2211yescharacteristic
30#17984775C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984775C2211yescharacteristic
33#17984775C2211yescharacteristic
34#17984773C2211yescharacteristic
35#17984773C2211yescharacteristic
36#17984773C2211yescharacteristic
37#17984773C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39#17984763C2211yescharacteristic
40#17984763C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984762C2211yescharacteristic
43#17984762C2211yescharacteristic
44#17984762C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic
47C4×C139⋊C8C2211yescharacteristic
48#126×C139—21no—
49#125×C139C2211yescharacteristic
50#123×C139—21no—
51#121×C139—21no—
52#121×C139C2211yescharacteristic
53#121×C139C2211yescharacteristic
54C4×D4×C139—21no—
55C4×D4×C139C2211yescharacteristic
56C4×D4×C139C2211yescharacteristic
57#117×C139C2211yescharacteristic
58C2×C4⋊C4×C139C2211yescharacteristic
59C2×D556C2311yescharacteristic
60C2×C22⋊D139—21no—
61C2×C22⋊D139—21no—
62C22×Dic139—21no—
63C2×C4×D139—21no—
64#14555770—22no—
65#14555769—22no—
66#14555769—22no—
67C2×C139⋊C8C2311yescharacteristic
68C2×C139⋊C8C2311yescharacteristic
69C2×C139⋊C8C2311yescharacteristic
70C2×C139⋊C8C2311yescharacteristic
71C4⋊Dic139—21no—
72C4⋊Dic139C2311yescharacteristic
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—
81C4×Dic139—21no—
82C2×D4×C139—21no—
83C2×D4×C139—21no—
84C2×D4×C139D411yescharacteristic
85C2×D4×C139C2311yescharacteristic
86C22×C4×C139—21no—
87C22×C4×C139—21no—
88C22×C4×C139C2311yescharacteristic
89C22×C4×C139C2311yescharacteristic
90C4⋊C4×C139—21no—
91C4⋊C4×C139—21no—
92C4⋊C4×C139—21no—
93C4⋊C4×C139D411yescharacteristic
94C4⋊C4×C139C2311yescharacteristic
95C4⋊C4×C139C2311yescharacteristic
96C4⋊C4×C139C2311yescharacteristic
97C22⋊C4×C139—21no—
98C22⋊C4×C139—21no—
99C22⋊C4×C139—21no—
100C22⋊C4×C139—21no—
101C22⋊C4×C139D411yescharacteristic
102C22⋊C4×C139D411yescharacteristic
103C42×C139—21no—
104C42×C139C2311yescharacteristic
105C22×D139—21no—
106D556—21no—
107D556—21no—
108C22⋊D139—42no—
109C22⋊D139—81no—
110C2×Dic139—21no—
111C2×Dic139—21no—
112C2×Dic139—21no—
113C2×Dic139—81no—
114C4×D139—81no—
115C139⋊C8—21no—
116C139⋊C8—21no—
117C139⋊C8—21no—
118C139⋊C8#4112yes—
119C23×C139—21no—
120C23×C139C2×D411yescharacteristic
121C23×C139C2×D411yescharacteristic
122D4×C139—21no—
123D4×C139—21no—
124D4×C139—41no—
125D4×C139—42no—
126D4×C139—81no—
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—81no—
135C2×C4×C139—81no—
136C2×C4×C139C2×D411yescharacteristic
137C2×C4×C139C2×D411yescharacteristic
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2411yescharacteristic
141C22×C139—21no—
142C22×C139—21no—
143C22×C139—21no—
144C22×C139—21no—
145C22×C139—21no—
146C22×C139—21no—
147C22×C139—41no—
148C22×C139—41no—
149C22×C139—41no—
150C22×C139C22×D411yescharacteristic
151C2×D139—41no—
152C2×D139—41no—
153C2×D139—41no—
154C4×C139—21no—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139C2×#4111yescharacteristic
162C4×C1392−1+411yescharacteristic
163Dic139—41no—
164Dic139—41no—
165Dic139—41no—
166C2×C139—41no—
167C2×C139—41no—
168C2×C139—81no—
169C2×C139#54711yescharacteristic
170C2×C139#57511yescharacteristic
171C2×C139#57611yescharacteristic
172D139—81no—
173C139#335511yescharacteristic, complemented, Sylow
174#3355—1391nomaximal, Sylow
175#553—1391no—
176#553D13911yescharacteristic, complemented
177#499—1391no—
178#482—1391no—
179#482—1391no—
180#480—1391no—
181#480—1391no—
182#478—1391no—
183#478—1391no—
184#469—1391no—
185#469—1391no—
186C4×D8—1391no—
187#436—1391no—
188#428—1391no—
189#428—1391no—
190C2×D8—1391no—
191C2×M16—1391no—
192C2×M16—1391no—
193#126—21no—
194#126—2781no—
195#125—1391no—
196#125C2×D13911yescharacteristic
197#123—21no—
198#123—2781no—
199#121—21no—
200#121—2781no—
201#121—1391no—
202#121—1391no—
203#121C2×D13911yescharacteristic
204#121C2×D13911yescharacteristic
205C4×D4—21no—
206C4×D4—2781no—
207C4×D4—1391no—
208C4×D4C2×D13911yescharacteristic
209C4×D4C2×D13911yescharacteristic
210#117—1391no—
211#117C2×D13911yescharacteristic
212C2×C4⋊C4—1391no—
213C2×C4⋊C4C2×D13911yescharacteristic
214#107—1391no—
215#107—1391no—
216#107—1391no—
217#107—1391no—
218#107—1391no—
219#106—1391no—
220#106—1391no—
221#106—1391no—
222#106—1391no—
223C4⋊C8—1391no—
224#102—1391no—
225#102—1391no—
226#102—1391no—
227#102—1391no—
228#102—1391no—
229#102—1391no—
230C22⋊C8—1391no—
231C22⋊C8—1391no—
232C4×C8—1391no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—2781no—
236C2×D4—2781no—
237C2×D4—1391no—
238C2×D4C22⋊D13911yescharacteristic
239C2×D4C22×D13911yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—2781no—
243C22×C4—2781no—
244C22×C4C22×D13911yescharacteristic
245C22×C4C22×D13911yescharacteristic
246D8—2782no—
247M16—2782no—
248M16—2782no—
249C2×C8—1391no—
250C2×C8—1391no—
251C2×C8—1391no—
252C2×C8—1391no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2781no—
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—1391no—
260C4⋊C4—1391no—
261C4⋊C4—1391no—
262C4⋊C4C22⋊D13911yescharacteristic
263C4⋊C4C22×D13911yescharacteristic
264C4⋊C4C22×D13911yescharacteristic
265C4⋊C4C22×D13911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2781no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4C22⋊D13911yescharacteristic
275C22⋊C4C22⋊D13911yescharacteristic
276C42—21no—
277C42—2781no—
278C42C22×D13911yescharacteristic
279C23—21no—
280C23—2781no—
281C23C2×C22⋊D13911yescharacteristic
282C23C2×C22⋊D13911yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—2781no—
289D4—2781no—
290D4—5562no—
291D4—11121no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—2781no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—11121no—
305C2×C4—11121no—
306C2×C4C2×C22⋊D13911yescharacteristic
307C2×C4C2×C22⋊D13911yescharacteristic
308C2×C4C2×C22⋊D13911yescharacteristic
309C2×C4C2×C22⋊D13911yescharacteristic
310C2×C4C23×D13911yescharacteristic
311C8—2781no—
312C8—2781no—
313C8—2781no—
314C8—1392no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—5561no—
325C22—5561no—
326C22—5561no—
327C22C22×C22⋊D13911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5561no—
336C4—5561no—
337C4—5561no—
338C4#41×D13911yescharacteristic
339C4#1798488911yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—11121no—
344C2#2258160211yescharacteristic
345C2#2258175111yescharacteristic
346C2#2258175611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#553×C139C2
socleC22×C139C22×D4
hypercenter#553D139
hypocenterC139#3355
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #22581649C2semidirect
2. #22581352C2semidirect
3. #22581277C2semidirect
4. #22581274C2semidirect
5. #22581266C2semidirect
6. #22581264C2semidirect
7. #22581253C2semidirect
8. #22581250C2semidirect
9. #22581204C2semidirect
10. #22581204C2semidirect
11. C4×#14555770C2semidirect
12. #22581031C2semidirect
13. #22580996C2semidirect
14. #22580993C2semidirect
15. #553×C139C2semidirect
173. C139#3355semidirect
176. #553D139semidirect

Maximal subgroups

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

subgroupindex
#225816492
#225813522
#225812772
#225812742
#225812662
#225812642
#225812532
#225812502
#225812042
C4×#145557702
#225810312
#225809962
#225809932
#553×C1392
#3355139