Finite Group Databasebeta

← #31816668

Subgroups — #31816668

Order 17792.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581574C211yesmaximal, characteristic, complemented
2#22581433C211yesmaximal, characteristic, complemented
3#22581289C211yesmaximal, characteristic, complemented
4#22581267C211yesmaximal, characteristic, complemented
5#22581249C211yesmaximal, characteristic, complemented
6#22581234C211yesmaximal, characteristic, complemented
7#22581176C211yesmaximal, characteristic, complemented
8#22581169C211yesmaximal, characteristic, complemented
9#22581117C211yesmaximal, characteristic, complemented
10#22581100C211yesmaximal, characteristic
11#22581055C211yesmaximal, characteristic, complemented
12#22581055C211yesmaximal, characteristic, complemented
13C4×Dic556C211yesmaximal, characteristic, complemented
14C4×D1112C211yesmaximal, characteristic, complemented
15#433×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C2×Dic556C2211yescharacteristic
18C2×#14555774C2211yescharacteristic
19C2×#14555774C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21#17984842C2211yescharacteristic
22#17984837—21no—
23#17984830C2211yescharacteristic
24#17984828—21no—
25#17984824—21no—
26#17984821C2211yescharacteristic
27#17984820—21no—
28#17984816C2211yescharacteristic
29C4×Dic278C2211yescharacteristic
30C4×Dic278C2211yescharacteristic
31C4×Dic278C2211yescharacteristic
32C4×D556C2211yescharacteristic
33C4×D556C2211yescharacteristic
34C4×D556C2211yescharacteristic
35(C22⋊D139)⋊C4—21no—
36(C22⋊D139)⋊C4—21no—
37#17984800—21no—
38C2×C4⋊Dic139C2211yescharacteristic
39C4⋊C4×D139—21no—
40#17984776C2211yescharacteristic
41#17984776C2211yescharacteristic
42#17984776C2211yescharacteristic
43#17984776C2211yescharacteristic
44#17984767C2211yescharacteristic
45#17984767C2211yescharacteristic
46#17984767C2211yescharacteristic
47#17984767C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic
52#117×C139C2211yescharacteristic
53C4⋊C8×C139C2211yescharacteristic
54C4⋊C8×C139C2211yescharacteristic
55C22⋊C8×C139C2211yescharacteristic
56C22⋊C8×C139C2211yescharacteristic
57#97×C139C2211yescharacteristic
58C4×C8×C139C2211yescharacteristic
59#14555785—22no—
60#14555785—22no—
61C2×Dic278—21no—
62C2×Dic278C2311yescharacteristic
63C2×Dic278C2311yescharacteristic
64C2×D556C2311yescharacteristic
65C2×D556C2311yescharacteristic
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C22×Dic139—21no—
69C2×C4×D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73Dic556—22no—
74#14555774—22no—
75#14555774—22no—
76D1112—22no—
77C4⋊Dic139—21no—
78C4⋊Dic139—21no—
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87C22⋊Dic139—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94C4×Dic139—21no—
95C4×Dic139—21no—
96C4×Dic139—21no—
97C22×C4×C139C2311yescharacteristic
98C2×C8×C139C2311yescharacteristic
99C2×C8×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C2×C8×C139C2311yescharacteristic
102C4⋊C4×C139D411yescharacteristic
103C4⋊C4×C139D411yescharacteristic
104C22⋊C4×C139D411yescharacteristic
105C22⋊C4×C139D411yescharacteristic
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—21no—
110Dic278—21no—
111Dic278—21no—
112Dic278—21no—
113Dic278—81no—
114Dic278#4112yes—
115D556—21no—
116D556—21no—
117D556—21no—
118D556#4112yes—
119C22⋊D139—24no—
120C22⋊D139—81no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C2×Dic139—21no—
124C2×Dic139—21no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139—81no—
128C4×D139—24no—
129C4×D139—81no—
130C4×D139—81no—
131C4×D139—81no—
132C23×C139C2×D411yescharacteristic
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139C2×D411yescharacteristic
136C2×C4×C139C2×D411yescharacteristic
137C2×C4×C139C2×D411yescharacteristic
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2411yescharacteristic
141C8×C139—21no—
142C8×C139—21no—
143C8×C139—21no—
144C8×C139—21no—
145C22×C139—21no—
146C22×C139—21no—
147C22×C139—21no—
148C22×C139C22×D411yescharacteristic
149C2×D139—22no—
150C2×D139—41no—
151C2×D139—41no—
152C2×D139—41no—
153C2×D139—41no—
154C2×D139—41no—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139C2×#4111yescharacteristic
161C4×C139C2×#4111yescharacteristic
162Dic139—22no—
163Dic139—41no—
164Dic139—41no—
165Dic139—41no—
166Dic139—41no—
167Dic139—41no—
168C2×C139—41no—
169C2×C139#52511yescharacteristic
170C2×C139#57611yescharacteristic
171C2×C139#57811yescharacteristic
172D139—42no—
173D139—81no—
174C139#312411yescharacteristic, complemented, Sylow
175#3124—1391nomaximal, Sylow
176#542—1391no—
177#520—1391no—
178#484—1391no—
179#480—1391no—
180#477—1391no—
181#474—1391no—
182#464—1391no—
183#463—1391no—
184#452—1391no—
185#449—1391no—
186#440—1391no—
187#440—1391no—
188C4×Q16—1391no—
189C4×D8—1391no—
190#433D13911yescharacteristic, complemented
191C2×#41—1391no—
192C2×Q16—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×D8—1391no—
196C4⋊Q8—1391no—
197#126—2781no—
198#124—2781no—
199#124—1391no—
200#123—2781no—
201C22⋊Q8—2781no—
202C22⋊Q8—1391no—
203#121—1391no—
204C4×Q8—1391no—
205C4×Q8—1391no—
206C4×Q8—1391no—
207C4×D4—2781no—
208C4×D4—2781no—
209C4×D4—1391no—
210C4×D4—1391no—
211C4×D4—1391no—
212#117—2781no—
213#117C2×D13911yescharacteristic
214C2×C4⋊C4—2781no—
215C2×C4⋊C4—1391no—
216#107—1391no—
217#107—1391no—
218#107—1391no—
219#107—1391no—
220C4⋊C8C2×D13911yescharacteristic
221C4⋊C8C2×D13911yescharacteristic
222#103—1391no—
223#103—1391no—
224#103—1391no—
225#103—1391no—
226#102—1391no—
227#102—1391no—
228#102—1391no—
229#102—1391no—
230C22⋊C8C2×D13911yescharacteristic
231C22⋊C8C2×D13911yescharacteristic
232#97C2×D13911yescharacteristic
233C4×C8C2×D13911yescharacteristic
234#41—2782no—
235#41—2782no—
236C2×Q8—2781no—
237C2×Q8—1391no—
238C2×Q8—1391no—
239C2×D4—2781no—
240C2×D4—2781no—
241C2×D4—1391no—
242C2×D4—1391no—
243C22×C4—2781no—
244C22×C4—2781no—
245C22×C4—2781no—
246C22×C4—2781no—
247C22×C4—2781no—
248C22×C4C22×D13911yescharacteristic
249Q16—2782no—
250SD16—2782no—
251SD16—2782no—
252D8—2782no—
253C2×C8C22×D13911yescharacteristic
254C2×C8C22×D13911yescharacteristic
255C2×C8C22×D13911yescharacteristic
256C2×C8C22×D13911yescharacteristic
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—2781no—
262C4⋊C4—2781no—
263C4⋊C4—1391no—
264C4⋊C4—1391no—
265C4⋊C4—1391no—
266C4⋊C4—1391no—
267C4⋊C4D55611yescharacteristic
268C4⋊C4D55611yescharacteristic
269C22⋊C4—2781no—
270C22⋊C4—2781no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C22⋊C4D55611yescharacteristic
277C22⋊C4D55611yescharacteristic
278C42—2781no—
279C42—2781no—
280C42—2781no—
281C42C22×D13911yescharacteristic
282C42C22×D13911yescharacteristic
283C23—2781no—
284C23—2781no—
285C23C2×D55611yescharacteristic
286Q8—2781no—
287Q8—2781no—
288Q8—2781no—
289Q8—11121no—
290Q8—1392no—
291D4—2784no—
292D4—2781no—
293D4—2781no—
294D4—2781no—
295D4—11121no—
296D4—1392no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2784no—
300C2×C4—2781no—
301C2×C4—2781no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—2781no—
306C2×C4—11121no—
307C2×C4—11121no—
308C2×C4—11121no—
309C2×C4—11121no—
310C2×C4C2×D55611yescharacteristic
311C2×C4C2×D55611yescharacteristic
312C2×C4C2×D55611yescharacteristic
313C2×C4C2×D55611yescharacteristic
314C2×C4C2×D55611yescharacteristic
315C2×C4C23×D13911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—2782no—
324C22—5561no—
325C22—5561no—
326C22—5561no—
327C22—5561no—
328C22—5561no—
329C22C22×D55611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—2782no—
336C4—5561no—
337C4—5561no—
338C4—5561no—
339C4—5561no—
340C4—5561no—
341C4#41×D13911yescharacteristic
342C4#41×D13911yescharacteristic
343C2—41no—
344C2—5562no—
345C2—11121no—
346C2#2258146511yescharacteristic
347C2#2258175811yescharacteristic
348C2#2258177011yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#433×C139C2
socleC22×C139C22×D4
prime radical#22581100C2
hypercenter#433D139
hypocenterC139#3124
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581433C2semidirect
3. #22581289C2semidirect
4. #22581267C2semidirect
5. #22581249C2semidirect
6. #22581234C2semidirect
7. #22581176C2semidirect
8. #22581169C2semidirect
9. #22581117C2semidirect
11. #22581055C2semidirect
12. #22581055C2semidirect
13. C4×Dic556C2semidirect
14. C4×D1112C2semidirect
15. #433×C139C2semidirect
174. C139#3124semidirect
190. #433D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225814332
#225812892
#225812672
#225812492
#225812342
#225811762
#225811692
#225811172
#225811002
#225810552
C4×Dic5562
C4×D11122
#433×C1392
#3124139