Finite Group Databasebeta

← #31819488

Subgroups — #31819488

Order 17792.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581688C211yesmaximal, characteristic, complemented
2#22581343C211yesmaximal, characteristic, complemented
3#22581340C211yesmaximal, characteristic, complemented
4#22581335C211yesmaximal, characteristic, complemented
5#22581175C211yesmaximal, characteristic, complemented
6#22581172C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581165C211yesmaximal, characteristic, complemented
9#22581148C211yesmaximal, characteristic, complemented
10#22581145C211yesmaximal, characteristic, complemented
11#22581084C211yesmaximal, characteristic, complemented
12#22581053C211yesmaximal, characteristic, complemented
13#22581051C211yesmaximal, characteristic, complemented
14C4×#14555770C211yesmaximal, characteristic, complemented
15#559×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C2×#14555772C2211yescharacteristic
20C2×#14555772C2211yescharacteristic
21C2×#14555770C2211yescharacteristic
22C2×#14555770C2211yescharacteristic
23C2×#14555770C2211yescharacteristic
24C2×#14555770C2211yescharacteristic
25#17984839C2211yescharacteristic
26#17984831—21no—
27#17984830C2211yescharacteristic
28#17984830C2211yescharacteristic
29#17984827—21no—
30#17984827—21no—
31C4×Dic278C2211yescharacteristic
32C4×D556C2211yescharacteristic
33C4×D556C2211yescharacteristic
34#17984804—21no—
35#17984775C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39#17984766C2211yescharacteristic
40#17984765C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984762C2211yescharacteristic
44#17984762C2211yescharacteristic
45#17984753C2211yescharacteristic
46#17984753C2211yescharacteristic
47C4×C139⋊C8C2211yescharacteristic
48#127×C139C2211yescharacteristic
49#124×C139—21no—
50#124×C139C2211yescharacteristic
51#124×C139C2211yescharacteristic
52#123×C139—21no—
53#123×C139—21no—
54C4×Q8×C139C2211yescharacteristic
55C4×Q8×C139C2211yescharacteristic
56C4×D4×C139—21no—
57C4×D4×C139C2211yescharacteristic
58C4×D4×C139C2211yescharacteristic
59C2×Dic278C2311yescharacteristic
60C2×D556—21no—
61C2×D556—21no—
62C2×D556C2311yescharacteristic
63C2×D556C2311yescharacteristic
64C2×C4×D139—21no—
65C2×C4×D139—21no—
66#14555775—41no—
67#14555773—22no—
68#14555773—41no—
69#14555772—22no—
70#14555772—41no—
71#14555770—22no—
72#14555770—41no—
73#14555770—41no—
74#14555770—41no—
75C2×C139⋊C8C2311yescharacteristic
76C2×C139⋊C8C2311yescharacteristic
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80Dic139⋊C4—21no—
81(C2×D139)⋊C4—21no—
82(C2×D139)⋊C4—21no—
83(C2×D139)⋊C4—21no—
84(C2×D139)⋊C4—21no—
85(C2×D139)⋊C4—21no—
86(C2×D139)⋊C4—21no—
87C4×Dic139—21no—
88C2×Q8×C139D411yescharacteristic
89C2×Q8×C139C2311yescharacteristic
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139C2311yescharacteristic
93C2×D4×C139C2311yescharacteristic
94C22×C4×C139—21no—
95C22×C4×C139—21no—
96C4⋊C4×C139—21no—
97C4⋊C4×C139D411yescharacteristic
98C4⋊C4×C139D411yescharacteristic
99C4⋊C4×C139D411yescharacteristic
100C4⋊C4×C139C2311yescharacteristic
101C22⋊C4×C139—21no—
102C22⋊C4×C139—21no—
103C22⋊C4×C139—21no—
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C42×C139—21no—
108C42×C139C2311yescharacteristic
109C42×C139C2311yescharacteristic
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—21no—
113Dic278—21no—
114Dic278—21no—
115D556—21no—
116D556—21no—
117D556—21no—
118D556—21no—
119D556—42no—
120D556—81no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C4×D139—81no—
124C4×D139—81no—
125C139⋊C8—21no—
126C139⋊C8—21no—
127C139⋊C8—21no—
128C139⋊C8#4112yes—
129C23×C139—21no—
130C23×C139—21no—
131Q8×C139—21no—
132Q8×C139—21no—
133Q8×C139—41no—
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×C139—81no—
143C2×C4×C139—81no—
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2411yescharacteristic
151C22×C139—41no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139—41no—
155C22×C139—41no—
156C22×C139—41no—
157C22×C139C22×D411yescharacteristic
158C2×D139—41no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C4×C139—21no—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—21no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—41no—
171C4×C139—41no—
172C4×C139C2×#4111yescharacteristic
173C4×C139H(5,𝔽2)11yescharacteristic
174Dic139—41no—
175Dic139—41no—
176C2×C139—81no—
177C2×C139—81no—
178C2×C139#55011yescharacteristic
179C2×C139#57511yescharacteristic
180C2×C139#57611yescharacteristic
181D139—81no—
182D139—81no—
183C139#340311yescharacteristic, complemented, Sylow
184#3403—1391nomaximal, Sylow
185#559—1391no—
186#559D13911yescharacteristic, complemented
187#496—1391no—
188#496—1391no—
189#495—1391no—
190#464—1391no—
191#464—1391no—
192#463—1391no—
193#463—1391no—
194#459—1391no—
195#459—1391no—
196#446—1391no—
197#440—1391no—
198#440—1391no—
199C4×D8—1391no—
200C2×Q16—1391no—
201C2×SD16—1391no—
202C2×SD16—1391no—
203C2×SD16—1391no—
204C2×SD16—1391no—
205C2×D8—1391no—
206C2×D8—1391no—
207C2×D8—1391no—
208C2×D8—1391no—
209#127—1391no—
210#127C2×D13911yescharacteristic
211#124—21no—
212#124—2781no—
213#124—1391no—
214#124—1391no—
215#124C2×D13911yescharacteristic
216#124C2×D13911yescharacteristic
217#123—21no—
218#123—21no—
219#123—2781no—
220#123—2781no—
221C4×Q8—1391no—
222C4×Q8C2×D13911yescharacteristic
223C4×Q8C2×D13911yescharacteristic
224C4×D4—21no—
225C4×D4—2781no—
226C4×D4—1391no—
227C4×D4—1391no—
228C4×D4C2×D13911yescharacteristic
229C4×D4C2×D13911yescharacteristic
230#107—1391no—
231C4⋊C8—1391no—
232C4⋊C8—1391no—
233C4⋊C8—1391no—
234#103—1391no—
235#103—1391no—
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#97—1391no—
241#97—1391no—
242C4×C8—1391no—
243C2×Q8—1391no—
244C2×Q8C22⋊D13911yescharacteristic
245C2×Q8C22×D13911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—2781no—
249C2×D4—2781no—
250C2×D4—1391no—
251C2×D4—1391no—
252C2×D4C22×D13911yescharacteristic
253C2×D4C22×D13911yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—2781no—
257C22×C4—2781no—
258Q16—5561no—
259SD16—2782no—
260SD16—2782no—
261SD16—5561no—
262SD16—5561no—
263D8—2782no—
264D8—5561no—
265D8—5561no—
266D8—5561no—
267C2×C8—1391no—
268C2×C8—1391no—
269C2×C8—1391no—
270C2×C8—1391no—
271C4⋊C4—21no—
272C4⋊C4—2781no—
273C4⋊C4—1391no—
274C4⋊C4C22⋊D13911yescharacteristic
275C4⋊C4C22⋊D13911yescharacteristic
276C4⋊C4C22⋊D13911yescharacteristic
277C4⋊C4C22×D13911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C42—21no—
291C42—2781no—
292C42C22×D13911yescharacteristic
293C42C22×D13911yescharacteristic
294C42C22×D13911yescharacteristic
295C23—21no—
296C23—21no—
297C23—2781no—
298C23—2781no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—2781no—
303Q8—2781no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—2781no—
311D4—2781no—
312D4—2781no—
313D4—2781no—
314D4—5562no—
315D4—11121no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—2781no—
321C2×C4—2781no—
322C2×C4—11121no—
323C2×C4—11121no—
324C2×C4C2×C22⋊D13911yescharacteristic
325C2×C4C2×C22⋊D13911yescharacteristic
326C2×C4C2×C22⋊D13911yescharacteristic
327C2×C4C2×C22⋊D13911yescharacteristic
328C2×C4C2×C22⋊D13911yescharacteristic
329C2×C4C2×C22⋊D13911yescharacteristic
330C2×C4C23×D13911yescharacteristic
331C8—2781no—
332C8—2781no—
333C8—2781no—
334C8—1392no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5561no—
342C22—5561no—
343C22—5561no—
344C22—5561no—
345C22—5561no—
346C22—5561no—
347C22C22×C22⋊D13911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—5561no—
357C4—5561no—
358C4#41×D13911yescharacteristic
359C4#1798488811yescharacteristic
360C2—81no—
361C2—81no—
362C2—11121no—
363C2—11121no—
364C2#2258162211yescharacteristic
365C2#2258175111yescharacteristic
366C2#2258175611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#559×C139C2
socleC22×C139C22×D4
hypercenter#559D139
hypocenterC139#3403
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #22581688C2semidirect
2. #22581343C2semidirect
3. #22581340C2semidirect
4. #22581335C2semidirect
5. #22581175C2semidirect
6. #22581172C2semidirect
7. #22581168C2semidirect
8. #22581165C2semidirect
9. #22581148C2semidirect
10. #22581145C2semidirect
11. #22581084C2semidirect
12. #22581053C2semidirect
13. #22581051C2semidirect
14. C4×#14555770C2semidirect
15. #559×C139C2semidirect
183. C139#3403semidirect
186. #559D139semidirect

Maximal subgroups

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

subgroupindex
#225816882
#225813432
#225813402
#225813352
#225811752
#225811722
#225811682
#225811652
#225811482
#225811452
#225810842
#225810532
#225810512
C4×#145557702
#559×C1392
#3403139