Finite Group Databasebeta

← #31818359

Subgroups — #31818359

Order 17792.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581599C211yesmaximal, characteristic, complemented
2#22581315C211yesmaximal, characteristic, complemented
3#22581283C211yesmaximal, characteristic, complemented
4#22581271C211yesmaximal, characteristic, complemented
5#22581240C211yesmaximal, characteristic, complemented
6#22581204C211yesmaximal, characteristic, complemented
7#22581180C211yesmaximal, characteristic, complemented
8#22581168C211yesmaximal, characteristic, complemented
9#22581096C211yesmaximal, characteristic, complemented
10#22581086C211yesmaximal, characteristic, complemented
11#22581063C211yesmaximal, characteristic, complemented
12#22581025C211yesmaximal, characteristic, complemented
13#22580952C211yesmaximal, characteristic, complemented
14C2×#17984762C211yesmaximal, characteristic, complemented
15#547×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C22×D556C2211yescharacteristic
18C2×#14555773C2211yescharacteristic, complemented
19C2×#14555770C2211yescharacteristic
20C2×#14555770C2211yescharacteristic
21C2×#14555769C2211yescharacteristic, complemented
22C22×C139⋊C8C2211yescharacteristic
23#17984830C2211yescharacteristic
24#17984827—21no—
25#17984821C2211yescharacteristic
26#17984816C2211yescharacteristic
27#17984815—21no—
28#17984810—21no—
29C4×D556C2211yescharacteristic
30C22⋊C4×D139—21no—
31#17984773C2211yescharacteristic, complemented
32#17984773C2211yescharacteristic, complemented
33#17984773C2211yescharacteristic, complemented
34C4⋊(C139⋊C8)C2211yescharacteristic, complemented
35#17984765C2211yescharacteristic, complemented
36#17984765C2211yescharacteristic, complemented
37#17984765C2211yescharacteristic, complemented
38#17984763C2211yescharacteristic, complemented
39#17984762C2211yescharacteristic
40#17984762C2211yescharacteristic
41#17984762C2211yescharacteristic
42#17984762C2211yescharacteristic
43#17984762C2211yescharacteristic
44#17984762C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic, complemented
47#17984753C2211yescharacteristic, complemented
48C2×#41×C139—21no—
49C4⋊Q8×C139C2211yescharacteristic, complemented
50#123×C139—21no—
51#123×C139—21no—
52C22⋊Q8×C139—21no—
53#121×C139C2211yescharacteristic
54#121×C139C2211yescharacteristic, complemented
55C4×D4×C139C2211yescharacteristic
56C4×D4×C139C2211yescharacteristic, complemented
57C2×C4⋊C4×C139C2211yescharacteristic
58C2×C4⋊C4×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555785—22no—
61#14555785—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556—22no—
64C2×D556—21no—
65C2×D556—41no—
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72#14555773—41no—
73#14555770—22no—
74#14555770—41no—
75#14555769—41no—
76C2×C139⋊C8—41no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C2×C139⋊C8C2311yescharacteristic
80C2×C139⋊C8C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82Dic139⋊C4—21no—
83C22⋊Dic139—21no—
84(C2×D139)⋊C4—21no—
85(C2×D139)⋊C4—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88#41×C139—44no—
89C2×Q8×C139—21no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139D411yescharacteristic
93C2×D4×C139C2311yescharacteristic
94C22×C4×C139—21no—
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139C2311yescharacteristic
98C22×C4×C139C2311yescharacteristic
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139D411yescharacteristic
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C4⋊C4×C139C2311yescharacteristic
106C22⋊C4×C139—21no—
107C22⋊C4×C139—21no—
108C22⋊C4×C139—21no—
109C22⋊C4×C139D411yescharacteristic
110C22⋊C4×C139D411yescharacteristic
111C42×C139C2311yescharacteristic
112C22×D139—21no—
113C22×D139—21no—
114C22×D139—42no—
115C22×D139—42no—
116C22×D139—81no—
117Dic278—21no—
118Dic278—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122D556—42no—
123D556#4112yescomplemented
124C22⋊D139—42no—
125C22⋊D139—81no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C4×D139—42no—
129C4×D139—81no—
130C139⋊C8—21no—
131C139⋊C8—21no—
132C139⋊C8—21no—
133C139⋊C8—21no—
134C23×C139—21no—
135C23×C139C2×D411yescharacteristic
136C23×C139C2×D411yescharacteristic
137Q8×C139—42no—
138D4×C139—22no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—42no—
142D4×C139—42no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—42no—
153C2×C4×C139C2×D411yescharacteristic
154C2×C4×C139C2×D411yescharacteristic
155C2×C4×C139C2×D411yescharacteristic
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2411yescharacteristic
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—21no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139AGL(1,ℤ/8)12yes—
167C22×C139C22×D411yescharacteristic
168C2×D139—22no—
169C2×D139—41no—
170C2×D139—41no—
171C2×D139—41no—
172C2×D139—41no—
173C2×D139—41no—
174C2×D139—84no—
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—41no—
181C4×C139—41no—
182C4×C139C2×#4111yescharacteristic
183C4×C139H(5,𝔽2)11yescharacteristic
184Dic139—41no—
185Dic139—41no—
186C2×C139—22no—
187C2×C139—41no—
188C2×C139—81no—
189C2×C139#54611yescharacteristic
190C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C139#57711yescharacteristic
192D139—42no—
193D139—81no—
194C139#330611yescharacteristic, complemented, Sylow
195#3306—1391nomaximal, Sylow
196#547D13911yescharacteristic, complemented
197#546—1391no—
198#489—1391no—
199#483—1391no—
200#481—1391no—
201#476—1391no—
202#469—1391no—
203#465—1391no—
204#463—1391no—
205#449—1391no—
206#447—1391no—
207#442—1391no—
208#435—1391no—
209#417—1391no—
210C2×#102—1391no—
211C2×#41—21no—
212C2×#41—1391no—
213C22×D4—1391no—
214C2×SD16—1391no—
215C2×D8—1391no—
216C2×D8—1391no—
217C2×M16—1391no—
218C22×C8—1391no—
219C4⋊Q8C2×D13911yescharacteristic, complemented
220#124—1391no—
221#123—21no—
222#123—21no—
223#123—2781no—
224C22⋊Q8—21no—
225C22⋊Q8—1391no—
226#121—2781no—
227#121—1391no—
228#121C2×D13911yescharacteristic
229#121C2×D13911yescharacteristic, complemented
230#120—2781no—
231C4×D4—1391no—
232C4×D4C2×D13911yescharacteristic
233C4×D4C2×D13911yescharacteristic, complemented
234C2×C4⋊C4C2×D13911yescharacteristic
235C2×C4⋊C4C2×D13911yescharacteristic, complemented
236C2×C22⋊C4—2781no—
237#106—1391no—
238#106—1391no—
239#106—1391no—
240C4⋊C8—1391no—
241#103—1391no—
242#103—1391no—
243#103—1391no—
244#102—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102—1391no—
250#102—1391no—
251C22⋊C8—1391no—
252C22⋊C8—1391no—
253#97—1391no—
254C24—2781no—
255#41—44no—
256#41—2782no—
257#41—5561no—
258C2×Q8—21no—
259C2×Q8—1391no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—2782no—
263C2×D4—2781no—
264C2×D4—2781no—
265C2×D4—2781no—
266C2×D4—5561no—
267C2×D4—1391no—
268C2×D4—1391no—
269C2×D4C22⋊D13911yescharacteristic
270C2×D4C22×D13911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—2781no—
275C22×C4—2781no—
276C22×C4C22×D13911yescharacteristic
277C22×C4C22×D13911yescharacteristic
278SD16—5561no—
279D8—2782no—
280D8—5561no—
281M16—5561no—
282C2×C8—5561no—
283C2×C8—1391no—
284C2×C8—1391no—
285C2×C8—1391no—
286C2×C8—1391no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—2781no—
291C4⋊C4—1391no—
292C4⋊C4C22⋊D13911yescharacteristic
293C4⋊C4C22×D13911yescharacteristic
294C4⋊C4C22×D13911yescharacteristic
295C4⋊C4C22×D13911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—2781no—
300C22⋊C4—2781no—
301C22⋊C4—2781no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4C22⋊D13911yescharacteristic
305C22⋊C4C22⋊D13911yescharacteristic
306C42C22×D13911yescharacteristic
307C23—21no—
308C23—2781no—
309C23—2781no—
310C23—5562no—
311C23—5562no—
312C23—11121no—
313C23C2×C22⋊D13911yescharacteristic
314C23C2×C22⋊D13911yescharacteristic
315Q8—42no—
316Q8—2781no—
317Q8—2781no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—2781no—
324D4—2781no—
325D4—2781no—
326D4—5562no—
327D4—5562no—
328D4—11121no—
329D4—1392no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—2781no—
341C2×C4—2781no—
342C2×C4—5562no—
343C2×C4—11121no—
344C2×C4C2×C22⋊D13911yescharacteristic
345C2×C4C2×C22⋊D13911yescharacteristic
346C2×C4C2×C22⋊D13911yescharacteristic
347C2×C4C2×C22⋊D13911yescharacteristic
348C2×C4C23×D13911yescharacteristic
349C8—2781no—
350C8—2781no—
351C8—2781no—
352C8—2781no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—2782no—
362C22—5561no—
363C22—5561no—
364C22—5561no—
365C22—5561no—
366C22—5561no—
367C22—11124no—
368C22#1798486812yes—
369C22C22×C22⋊D13911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—5561no—
378C4—5561no—
379C4#41×D13911yescharacteristic
380C4#1798488811yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—5562no—
385C2—11121no—
386C2#2258159111yescharacteristic
387C2C2×#1798486811yescharacteristic
388C2#2258176111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#547×C139C2
socleC22×C139C22×D4
hypercenter#547D139
hypocenterC139#3306
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #22581599C2semidirect
2. #22581315C2semidirect
3. #22581283C2semidirect
4. #22581271C2semidirect
5. #22581240C2semidirect
6. #22581204C2semidirect
7. #22581180C2semidirect
8. #22581168C2semidirect
9. #22581096C2semidirect
10. #22581086C2semidirect
11. #22581063C2semidirect
12. #22581025C2semidirect
13. #22580952C2semidirect
14. C2×#17984762C2semidirect
15. #547×C139C2semidirect
18. C2×#14555773C22semidirect
21. C2×#14555769C22semidirect
31. #17984773C22semidirect
32. #17984773C22semidirect
33. #17984773C22semidirect
34. C4⋊(C139⋊C8)C22semidirect
35. #17984765C22semidirect
36. #17984765C22semidirect
37. #17984765C22semidirect
38. #17984763C22semidirect
46. C22⋊(C139⋊C8)C22semidirect
47. #17984753C22semidirect
49. C4⋊Q8×C139C22semidirect
54. #121×C139C22semidirect
56. C4×D4×C139C22semidirect
58. C2×C4⋊C4×C139C22semidirect
123. D556#41semidirect
194. C139#3306semidirect
196. #547D139semidirect
219. C4⋊Q8C2×D139semidirect
229. #121C2×D139semidirect
233. C4×D4C2×D139semidirect
235. C2×C4⋊C4C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815992
#225813152
#225812832
#225812712
#225812402
#225812042
#225811802
#225811682
#225810962
#225810862
#225810632
#225810252
#225809522
C2×#179847622
#547×C1392
#3306139