Finite Group Databasebeta

← #31818291

Subgroups — #31818291

Order 17792.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581643C211yesmaximal, characteristic, complemented
2#22581307C211yesmaximal, characteristic, complemented
3#22581291C211yesmaximal, characteristic, complemented
4#22581264C211yesmaximal, characteristic, complemented
5#22581260C211yesmaximal, characteristic, complemented
6#22581192C211yesmaximal, characteristic, complemented
7#22581180C211yesmaximal, characteristic, complemented
8#22581172C211yesmaximal, characteristic, complemented
9#22581115C211yesmaximal, characteristic, complemented
10#22581109C211yesmaximal, characteristic, complemented
11C4×#14555775C211yesmaximal, characteristic, complemented
12D4×C139⋊C8C211yesmaximal, characteristic, complemented
13#22580949C211yesmaximal, characteristic, complemented
14C2×#17984766C211yesmaximal, characteristic, complemented
15#548×C139C211yesmaximal, characteristic
16C2×#14555775C2211yescharacteristic
17C2×#14555775C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C22×C139⋊C8C2211yescharacteristic
20C22×C139⋊C8C2211yescharacteristic
21#17984835—21no—
22#17984834C2211yescharacteristic
23#17984832—21no—
24#17984823—21no—
25#17984821C2211yescharacteristic
26#17984821C2211yescharacteristic
27C4×Dic278C2211yescharacteristic
28#17984801C2211yescharacteristic
29#17984798—21no—
30C2×C4⋊Dic139C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984775C2211yescharacteristic
33#17984773C2211yescharacteristic
34C4⋊(C139⋊C8)C2211yescharacteristic
35#17984766C2211yescharacteristic
36#17984766C2211yescharacteristic
37#17984766C2211yescharacteristic
38#17984766C2211yescharacteristic
39#17984766C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984765C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic
47C4×C139⋊C8C2211yescharacteristic
48C2×#41×C139C2211yescharacteristic
49C22×Q8×C139C2211yescharacteristic
50#124×C139—21no—
51#124×C139C2211yescharacteristic
52C22⋊Q8×C139—21no—
53C22⋊Q8×C139C2211yescharacteristic
54#121×C139—21no—
55#121×C139C2211yescharacteristic
56C4×Q8×C139C2211yescharacteristic
57C4×D4×C139—21no—
58C4×D4×C139C2211yescharacteristic
59C2×Dic278C2311yescharacteristic
60C22×Dic139—21no—
61#14555775—22no—
62#14555775—41no—
63#14555773—41no—
64C2×C139⋊C8—41no—
65C2×C139⋊C8—41no—
66C2×C139⋊C8C2311yescharacteristic
67C2×C139⋊C8C2311yescharacteristic
68C2×C139⋊C8C2311yescharacteristic
69C2×C139⋊C8C2311yescharacteristic
70C4⋊Dic139—21no—
71C4⋊Dic139C2311yescharacteristic
72C4⋊Dic139C2311yescharacteristic
73C4⋊Dic139C2311yescharacteristic
74Dic139⋊C4—21no—
75Dic139⋊C4—21no—
76Dic139⋊C4—21no—
77Dic139⋊C4—21no—
78Dic139⋊C4—21no—
79C22⋊Dic139—21no—
80C22⋊Dic139—21no—
81C22⋊Dic139—21no—
82C4×Dic139—21no—
83C4×Dic139—21no—
84#41×C139—22no—
85#41×C139—41no—
86C2×Q8×C139—21no—
87C2×Q8×C139—22no—
88C2×Q8×C139—41no—
89C2×Q8×C139C2311yescharacteristic
90C2×Q8×C139C2311yescharacteristic
91C2×D4×C139—21no—
92C2×D4×C139—21no—
93C2×D4×C139D411yescharacteristic
94C2×D4×C139C2311yescharacteristic
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139C2311yescharacteristic
98C22×C4×C139C2311yescharacteristic
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139D411yescharacteristic
102C4⋊C4×C139C2311yescharacteristic
103C22⋊C4×C139—21no—
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139D411yescharacteristic
108C22⋊C4×C139D411yescharacteristic
109C42×C139—21no—
110C42×C139C2311yescharacteristic
111Dic278—21no—
112Dic278—21no—
113C2×Dic139—21no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—42no—
118C139⋊C8—21no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C23×C139—21no—
123C23×C139C2×D411yescharacteristic
124C23×C139C2×D411yescharacteristic
125Q8×C139—21no—
126Q8×C139—21no—
127Q8×C139—21no—
128Q8×C139—42no—
129Q8×C139#4112yes—
130D4×C139—22no—
131D4×C139—21no—
132D4×C139—21no—
133D4×C139—42no—
134D4×C139—42no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—42no—
143C2×C4×C139—42no—
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2411yescharacteristic
149C22×C139—21no—
150C22×C139—21no—
151C22×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—41no—
155C22×C139—41no—
156C22×C139—41no—
157C22×C139#13512yes—
158C22×C139C22×D411yescharacteristic
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—22no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—41no—
165C4×C139—41no—
166C4×C139C2×#4111yescharacteristic
167C4×C139H(5,𝔽2)11yescharacteristic
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171Dic139—41no—
172C2×C139—22no—
173C2×C139—41no—
174C2×C139—81no—
175C2×C139#54611yescharacteristic
176C2×C139C2×#13511yescharacteristic
177C2×C139#57811yescharacteristic
178C139#330011yescharacteristic, complemented, Sylow
179#3300—1391nomaximal, Sylow
180#552—1391no—
181#548D13911yescharacteristic
182#488—1391no—
183#485—1391no—
184#480—1391no—
185#479—1391no—
186#467—1391no—
187#465—1391no—
188#464—1391no—
189#452—1391no—
190#451—1391no—
191C4×Q16—1391no—
192C8×D4—1391no—
193#416—1391no—
194C2×#103—1391no—
195C2×#41C2×D13911yescharacteristic
196C22×Q8C2×D13911yescharacteristic
197C2×Q16—1391no—
198C2×Q16—1391no—
199C2×SD16—1391no—
200C22×C8—1391no—
201C22×C8—1391no—
202#126—2781no—
203#125—2781no—
204#125—1391no—
205#124—21no—
206#124C2×D13911yescharacteristic
207#123—2781no—
208C22⋊Q8—21no—
209C22⋊Q8—1391no—
210C22⋊Q8—1391no—
211C22⋊Q8C2×D13911yescharacteristic
212#121—21no—
213#121C2×D13911yescharacteristic
214C4×Q8—1391no—
215C4×Q8C2×D13911yescharacteristic
216C4×D4—21no—
217C4×D4C2×D13911yescharacteristic
218#117—2781no—
219#117—1391no—
220C2×C4⋊C4—1391no—
221#107—1391no—
222#107—1391no—
223#106—1391no—
224C4⋊C8—1391no—
225#103—1391no—
226#103—1391no—
227#103—1391no—
228#103—1391no—
229#103—1391no—
230#103—1391no—
231#103—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235C22⋊C8—1391no—
236C22⋊C8—1391no—
237C4×C8—1391no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—1391no—
244C2×Q8C22×D13911yescharacteristic
245C2×Q8C22×D13911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D13911yescharacteristic
249C2×D4C22×D13911yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—2781no—
253C22×C4C22×D13911yescharacteristic
254C22×C4C22×D13911yescharacteristic
255Q16—2782no—
256Q16—5561no—
257SD16—5561no—
258C2×C8—5561no—
259C2×C8—5561no—
260C2×C8—1391no—
261C2×C8—1391no—
262C2×C8—1391no—
263C2×C8—1391no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2781no—
267C4⋊C4—2781no—
268C4⋊C4—2781no—
269C4⋊C4—2781no—
270C4⋊C4—2781no—
271C4⋊C4—2781no—
272C4⋊C4—1391no—
273C4⋊C4—1391no—
274C4⋊C4—1391no—
275C4⋊C4C22⋊D13911yescharacteristic
276C4⋊C4C22×D13911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C22⋊C4—2781no—
284C22⋊C4C22⋊D13911yescharacteristic
285C22⋊C4C22⋊D13911yescharacteristic
286C42—21no—
287C42—2781no—
288C42—2781no—
289C42C22×D13911yescharacteristic
290C23—21no—
291C23C2×C22⋊D13911yescharacteristic
292C23C2×C22⋊D13911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—2781no—
298Q8—2781no—
299Q8#1455578412yes—
300D4—22no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—5562no—
319C2×C4C2×C22⋊D13911yescharacteristic
320C2×C4C2×C22⋊D13911yescharacteristic
321C2×C4C2×C22⋊D13911yescharacteristic
322C2×C4C2×C22⋊D13911yescharacteristic
323C2×C4C23×D13911yescharacteristic
324C8—2781no—
325C8—2781no—
326C8—2781no—
327C8—2781no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1798486212yes—
337C22C22×C22⋊D13911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—5561no—
346C4—5561no—
347C4—5561no—
348C4—5561no—
349C4C2×#1455578411yescharacteristic
350C4#1798488711yescharacteristic
351C2—22no—
352C2—41no—
353C2—81no—
354C2#2258159711yescharacteristic
355C2C2×#1798486211yescharacteristic
356C2#2258176811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting, prime radical#548×C139C2
socleC22×C139C22×D4
hypercenter#548D139
hypocenterC139#3300
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #22581643C2semidirect
2. #22581307C2semidirect
3. #22581291C2semidirect
4. #22581264C2semidirect
5. #22581260C2semidirect
6. #22581192C2semidirect
7. #22581180C2semidirect
8. #22581172C2semidirect
9. #22581115C2semidirect
10. #22581109C2semidirect
11. C4×#14555775C2semidirect
12. D4×C139⋊C8C2semidirect
13. #22580949C2semidirect
14. C2×#17984766C2semidirect
178. C139#3300semidirect

Maximal subgroups

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

subgroupindex
#225816432
#225813072
#225812912
#225812642
#225812602
#225811922
#225811802
#225811722
#225811152
#225811092
C4×#145557752
D4×C139⋊C82
#225809492
C2×#179847662
#548×C1392
#3300139