Finite Group Databasebeta

← #31818287

Subgroups — #31818287

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#22581638C211yesmaximal, characteristic, complemented
2#22581614C211yesmaximal, characteristic
3#22581309C211yesmaximal, characteristic, complemented
4#22581292C211yesmaximal, characteristic, complemented
5#22581266C211yesmaximal, characteristic, complemented
6#22581258C211yesmaximal, characteristic, complemented
7#22581193C211yesmaximal, characteristic, complemented
8#22581182C211yesmaximal, characteristic, complemented
9#22581178C211yesmaximal, characteristic, complemented
10#22581118C211yesmaximal, characteristic, complemented
11#22581109C211yesmaximal, characteristic, complemented
12#22581045C211yesmaximal, characteristic, complemented
13C8×C22⋊D139C211yesmaximal, characteristic, complemented
14#22580948C211yesmaximal, characteristic, complemented
15C2×#103×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C2×#14555775C2211yescharacteristic
18C2×#14555775C2211yescharacteristic
19C2×#14555774C2211yescharacteristic
20C2×C8×D139C2211yescharacteristic
21#17984837—21no—
22#17984833C2211yescharacteristic
23#17984832—21no—
24#17984831—21no—
25#17984831C2211yescharacteristic
26#17984825—21no—
27#17984822C2211yescharacteristic
28#17984821C2211yescharacteristic
29#17984818—21no—
30#17984818C2211yescharacteristic
31#17984816—21no—
32#17984816C2211yescharacteristic
33Q8×Dic139C2211yescharacteristic
34#17984807C2211yescharacteristic
35C4×C22⋊D139—21no—
36C4×C22⋊D139C2211yescharacteristic
37#17984801—21no—
38#17984800C2211yescharacteristic
39#17984775C2211yescharacteristic
40#17984775C2211yescharacteristic
41#17984774C2211yescharacteristic
42Dic139⋊C8C2211yescharacteristic
43#17984767C2211yescharacteristic
44#17984766C2211yescharacteristic
45#17984766C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic
49C22⋊(C139⋊C8)C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51C8×Dic139C2211yescharacteristic
52C22×Q8×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic
54C2×C4⋊C4×C139C2211yescharacteristic
55#103×C139C2211yescharacteristic
56#103×C139C2211yescharacteristic
57#103×C139C2211yescharacteristic
58#103×C139C2211yescharacteristic
59#14555786—22no—
60#14555786—41no—
61C2×Dic278C2311yescharacteristic
62C2×D556—21no—
63C2×D556C2311yescharacteristic
64C2×C22⋊D139—21no—
65C2×C22⋊D139D411yescharacteristic
66C2×C4×D139—21no—
67C2×C4×D139C2311yescharacteristic
68#14555775—22no—
69#14555775—41no—
70#14555774—41no—
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C8×D139—41no—
74C4⋊Dic139—21no—
75C4⋊Dic139—21no—
76C4⋊Dic139—21no—
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84C22⋊Dic139—21no—
85C22⋊Dic139D411yescharacteristic
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4D411yescharacteristic
93C4×Dic139—21no—
94C4×Dic139—21no—
95C4×Dic139—21no—
96C4×Dic139C2311yescharacteristic
97C2×Q8×C139—21no—
98C2×Q8×C139—22no—
99C2×Q8×C139—41no—
100C2×Q8×C139C2311yescharacteristic
101C2×Q8×C139C2311yescharacteristic
102C22×C4×C139—21no—
103C22×C4×C139—21no—
104C22×C4×C139C2311yescharacteristic
105C2×C8×C139—41no—
106C2×C8×C139C2311yescharacteristic
107C2×C8×C139C2311yescharacteristic
108C4⋊C4×C139—21no—
109C4⋊C4×C139C2311yescharacteristic
110C4⋊C4×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139C2×D411yescharacteristic
113Dic278—21no—
114Dic278—21no—
115D556—21no—
116D556—21no—
117D556—42no—
118C22⋊D139—22no—
119C22⋊D139—42no—
120C2×Dic139—21no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C4×D139—21no—
127C4×D139—21no—
128C4×D139—42no—
129C139⋊C8—21no—
130C139⋊C8—21no—
131C23×C139C2×D411yescharacteristic
132Q8×C139—21no—
133Q8×C139—21no—
134Q8×C139—21no—
135Q8×C139—42no—
136Q8×C139#4112yes—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—42no—
144C2×C4×C139—42no—
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2411yescharacteristic
147C8×C139—21no—
148C8×C139—21no—
149C22×C139—21no—
150C22×C139—21no—
151C22×C139#13512yes—
152C22×C139C22×D411yescharacteristic
153C2×D139—21no—
154C2×D139—21no—
155C2×D139—21no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C4×C139—21no—
160C4×C139—22no—
161C4×C139—41no—
162C4×C139—41no—
163C4×C139—41no—
164C4×C139C2×#4111yescharacteristic
165C4×C139H(5,𝔽2)11yescharacteristic
166Dic139—21no—
167Dic139—21no—
168Dic139—21no—
169Dic139—41no—
170Dic139—41no—
171Dic139—41no—
172C2×C139—22no—
173C2×C139#54611yescharacteristic
174C2×C139C2×#13511yescharacteristic
175C2×C139#57811yescharacteristic
176D139—41no—
177D139—81no—
178C139#330011yescharacteristic, complemented, Sylow
179#3300—1391nomaximal, Sylow
180#552—1391no—
181#548—1391no—
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×#103D13911yescharacteristic, complemented
195C2×#41—1391no—
196C22×Q8C2×D13911yescharacteristic
197C2×Q16—1391no—
198C2×Q16—1391no—
199C2×SD16—1391no—
200C22×C8—1391no—
201C22×C8C2×D13911yescharacteristic
202#126—2781no—
203#125—2781no—
204#125—1391no—
205#124—2781no—
206#124—1391no—
207#123—2781no—
208C22⋊Q8—2781no—
209C22⋊Q8—1391no—
210C22⋊Q8—1391no—
211C22⋊Q8—1391no—
212#121—2781no—
213#121—1391no—
214C4×Q8—1391no—
215C4×Q8—1391no—
216C4×D4—2781no—
217C4×D4—1391no—
218#117—2781no—
219#117—1391no—
220C2×C4⋊C4C2×D13911yescharacteristic
221#107—1391no—
222#107—1391no—
223#106—1391no—
224C4⋊C8—1391no—
225#103—1391no—
226#103—1391no—
227#103—1391no—
228#103C2×D13911yescharacteristic
229#103C2×D13911yescharacteristic
230#103C2×D13911yescharacteristic
231#103C2×D13911yescharacteristic
232#102—1391no—
233#102—1391no—
234#102—1391no—
235C22⋊C8—1391no—
236C22⋊C8—1391no—
237C4×C8—1391no—
238#41—2782no—
239#41—5561no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—1391no—
244C2×Q8C22×D13911yescharacteristic
245C2×Q8C22×D13911yescharacteristic
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4—1391no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—2781no—
253C22×C4—1391no—
254C22×C4C22×D13911yescharacteristic
255Q16—2782no—
256Q16—5561no—
257SD16—5561no—
258C2×C8—41no—
259C2×C8—5561no—
260C2×C8—1391no—
261C2×C8—1391no—
262C2×C8C22×D13911yescharacteristic
263C2×C8C22×D13911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2781no—
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—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C22⋊C4—2781no—
284C22⋊C4—1391no—
285C22⋊C4—1391no—
286C42—2781no—
287C42—2781no—
288C42—2781no—
289C42—1391no—
290C23—2781no—
291C23—1391no—
292C23D4×D13911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—2781no—
298Q8—2781no—
299Q8#1455578512yes—
300D4—2782no—
301D4—2781no—
302D4—2781no—
303D4—5562no—
304D4—5562no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—5562no—
319C2×C4—1391no—
320C2×C4—1391no—
321C2×C4—1391no—
322C2×C4D4×D13911yescharacteristic
323C2×C4C23×D13911yescharacteristic
324C8—21no—
325C8—21no—
326C8—2781no—
327C8—2781no—
328C22—21no—
329C22—21no—
330C22—2781no—
331C22—2781no—
332C22—2781no—
333C22—5561no—
334C22—5561no—
335C22—5561no—
336C22#1798486312yes—
337C22C2×D4×D13911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2781no—
344C4—2781no—
345C4—2781no—
346C4—5561no—
347C4—5561no—
348C4—5561no—
349C4C2×#1455578511yescharacteristic
350C4#1798488711yescharacteristic
351C2—22no—
352C2—5561no—
353C2—11121no—
354C2#2258159311yescharacteristic
355C2C2×#1798486311yescharacteristic
356C2#2258176611yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#103×C139C2
socleC22×C139C22×D4
prime radical#22581614C2
hypercenterC2×#103D139
hypocenterC139#3300
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #22581638C2semidirect
3. #22581309C2semidirect
4. #22581292C2semidirect
5. #22581266C2semidirect
6. #22581258C2semidirect
7. #22581193C2semidirect
8. #22581182C2semidirect
9. #22581178C2semidirect
10. #22581118C2semidirect
11. #22581109C2semidirect
12. #22581045C2semidirect
13. C8×C22⋊D139C2semidirect
14. #22580948C2semidirect
15. C2×#103×C139C2semidirect
178. C139#3300semidirect
194. C2×#103D139semidirect

Maximal subgroups

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

subgroupindex
#225816382
#225816142
#225813092
#225812922
#225812662
#225812582
#225811932
#225811822
#225811782
#225811182
#225811092
#225810452
C8×C22⋊D1392
#225809482
C2×#103×C1392
#3300139