Finite Group Databasebeta

← #31818295

Subgroups — #31818295

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#22581645C211yesmaximal, characteristic, complemented
2#22581614C211yesmaximal, characteristic
3#22581309C211yesmaximal, characteristic, complemented
4#22581293C211yesmaximal, characteristic, complemented
5#22581267C211yesmaximal, characteristic, complemented
6#22581262C211yesmaximal, characteristic, complemented
7#22581191C211yesmaximal, characteristic, complemented
8#22581184C211yesmaximal, characteristic, complemented
9#22581177C211yesmaximal, characteristic, complemented
10#22581114C211yesmaximal, characteristic, complemented
11Q16×Dic139C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13#22580948C211yesmaximal, characteristic, complemented
14C2×#17984766C211yesmaximal, characteristic, complemented
15#451×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C2×#14555772C2211yescharacteristic
18C22×C139⋊C8C2211yescharacteristic
19C2×C8×D139C2211yescharacteristic
20#17984837—21no—
21#17984833—21no—
22#17984833C2211yescharacteristic
23#17984831—21no—
24#17984831C2211yescharacteristic
25#17984826—21no—
26#17984818—21no—
27#17984818C2211yescharacteristic
28#17984818C2211yescharacteristic
29#17984816—21no—
30#17984816C2211yescharacteristic
31Q8×Dic139C2211yescharacteristic
32Q8×Dic139C2211yescharacteristic
33C4×C22⋊D139—21no—
34C4×C22⋊D139C2211yescharacteristic
35#17984800C2211yescharacteristic
36#17984798—21no—
37C2×C4⋊Dic139C2211yescharacteristic
38#17984776C2211yescharacteristic
39#17984776C2211yescharacteristic
40#17984773C2211yescharacteristic
41Dic139⋊C8C2211yescharacteristic
42#17984766C2211yescharacteristic
43#17984766C2211yescharacteristic
44#17984766C2211yescharacteristic
45#17984766C2211yescharacteristic
46#17984766C2211yescharacteristic
47#17984764C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984762C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51C8×Dic139C2211yescharacteristic
52C22×Q8×C139C2211yescharacteristic
53C2×Q16×C139C2211yescharacteristic
54C2×Q16×C139C2211yescharacteristic
55C22⋊Q8×C139C2211yescharacteristic
56#103×C139C2211yescharacteristic
57#103×C139C2211yescharacteristic
58C22⋊C8×C139C2211yescharacteristic
59#14555786—22no—
60#14555786—41no—
61C2×D556—21no—
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139D411yescharacteristic
65C22×Dic139—21no—
66C2×C4×D139—21no—
67C2×C4×D139C2311yescharacteristic
68#14555772—41no—
69C2×C139⋊C8—41no—
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C8×D139—41no—
73C4⋊Dic139—21no—
74C4⋊Dic139—21no—
75C4⋊Dic139—21no—
76C4⋊Dic139—21no—
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80Dic139⋊C4—21no—
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84C22⋊Dic139D411yescharacteristic
85(C2×D139)⋊C4—21no—
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)⋊C4D411yescharacteristic
92C4×Dic139—21no—
93C4×Dic139—21no—
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C2×Q8×C139—21no—
97C2×Q8×C139—22no—
98C2×Q8×C139—41no—
99C2×Q8×C139C2311yescharacteristic
100C2×Q8×C139C2311yescharacteristic
101C2×Q8×C139C2311yescharacteristic
102C22×C4×C139—21no—
103C22×C4×C139C2311yescharacteristic
104Q16×C139—22no—
105Q16×C139—41no—
106C2×C8×C139C2311yescharacteristic
107C2×C8×C139C2311yescharacteristic
108C4⋊C4×C139—21no—
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C22×D139—21no—
112C22×D139C2×D411yescharacteristic
113D556—21no—
114D556—21no—
115D556—42no—
116C22⋊D139—22no—
117C22⋊D139—42no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—42no—
122C2×Dic139C2×D411yescharacteristic
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C4×D139—21no—
126C4×D139—21no—
127C4×D139—42no—
128C139⋊C8—21no—
129C139⋊C8—21no—
130C23×C139C2×D411yescharacteristic
131Q8×C139—21no—
132Q8×C139—21no—
133Q8×C139—21no—
134Q8×C139—21no—
135Q8×C139—21no—
136Q8×C139—42no—
137Q8×C139#4112yes—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
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#451D13911yescharacteristic, complemented
191C4×Q16—1391no—
192C8×D4—1391no—
193#416—1391no—
194C2×#103—1391no—
195C2×#41—1391no—
196C22×Q8C2×D13911yescharacteristic
197C2×Q16C2×D13911yescharacteristic
198C2×Q16C2×D13911yescharacteristic
199C2×SD16—1391no—
200C22×C8—1391no—
201C22×C8—1391no—
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⋊Q8C2×D13911yescharacteristic
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⋊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#103C2×D13911yescharacteristic
231#103C2×D13911yescharacteristic
232#102—1391no—
233#102—1391no—
234#102—1391no—
235C22⋊C8—1391no—
236C22⋊C8C2×D13911yescharacteristic
237C4×C8—1391no—
238#41—2782no—
239#41—5561no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C22×D13911yescharacteristic
244C2×Q8C22×D13911yescharacteristic
245C2×Q8C22×D13911yescharacteristic
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4—1391no—
250C22×C4—21no—
251C22×C4—2781no—
252C22×C4—2781no—
253C22×C4—1391no—
254C22×C4C22×D13911yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—5561no—
258C2×C8—5561no—
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⋊C4—1391no—
276C4⋊C4C22×D13911yescharacteristic
277C22⋊C4—21no—
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—21no—
297Q8—21no—
298Q8—42no—
299Q8#1455578412yes—
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—2781no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—5562no—
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#1798486512yes—
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×#1455578411yescharacteristic
350C4#1798488711yescharacteristic
351C2—22no—
352C2—5561no—
353C2—11121no—
354C2#2258159011yescharacteristic
355C2C2×#1798486511yescharacteristic
356C2#2258176911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#451×C139C2
socleC22×C139C22×D4
prime radical#22581614C2
hypercenter#451D139
hypocenterC139#3300
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #22581645C2semidirect
3. #22581309C2semidirect
4. #22581293C2semidirect
5. #22581267C2semidirect
6. #22581262C2semidirect
7. #22581191C2semidirect
8. #22581184C2semidirect
9. #22581177C2semidirect
10. #22581114C2semidirect
11. Q16×Dic139C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. #22580948C2semidirect
14. C2×#17984766C2semidirect
15. #451×C139C2semidirect
178. C139#3300semidirect
190. #451D139semidirect

Maximal subgroups

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

subgroupindex
#225816452
#225816142
#225813092
#225812932
#225812672
#225812622
#225811912
#225811842
#225811772
#225811142
Q16×Dic1392
(C22⋊D139)⋊C82
#225809482
C2×#179847662
#451×C1392
#3300139