Finite Group Databasebeta

← #31817869

Subgroups — #31817869

Order 17792.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581574C211yesmaximal, characteristic, complemented
2#22581243C211yesmaximal, characteristic, complemented
3#22581240C211yesmaximal, characteristic, complemented
4#22581238C211yesmaximal, characteristic, complemented
5#22581235C211yesmaximal, characteristic, complemented
6#22581209C211yesmaximal, characteristic, complemented
7#22581204C211yesmaximal, characteristic
8#22581184C211yesmaximal, characteristic, complemented
9#22581180C211yesmaximal, characteristic, complemented
10#22581175C211yesmaximal, characteristic, complemented
11#22581172C211yesmaximal, characteristic, complemented
12#22581168C211yesmaximal, characteristic, complemented
13#22581165C211yesmaximal, characteristic, complemented
14#22580980C211yesmaximal, characteristic, complemented
15#542×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555772C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×#14555769C2211yescharacteristic
21C22×C139⋊C8C2211yescharacteristic
22#17984842C2211yescharacteristic
23#17984837—21no—
24#17984830C2211yescharacteristic
25#17984828—21no—
26#17984824—21no—
27#17984821C2211yescharacteristic
28#17984820—21no—
29#17984816C2211yescharacteristic
30C4×Dic278C2211yescharacteristic
31C4×D556C2211yescharacteristic
32#17984773C2211yescharacteristic
33#17984773C2211yescharacteristic
34#17984773C2211yescharacteristic
35#17984773C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39C4⋊(C139⋊C8)C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984766C2211yescharacteristic
42#17984765C2211yescharacteristic
43#17984765C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48C4⋊Q8×C139C2211yescharacteristic
49#126×C139—21no—
50#124×C139—21no—
51#124×C139C2211yescharacteristic
52#123×C139—21no—
53C22⋊Q8×C139—21no—
54C22⋊Q8×C139C2211yescharacteristic
55#121×C139C2211yescharacteristic
56C4×Q8×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58#117×C139C2211yescharacteristic
59C2×Dic278—21no—
60C2×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C4×D139—21no—
64#14555775—41no—
65#14555773—41no—
66#14555772—41no—
67#14555770—41no—
68#14555769—41no—
69C2×C139⋊C8—41no—
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C4⋊Dic139—21no—
75C4⋊Dic139C2311yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77Dic139⋊C4—21no—
78Dic139⋊C4—21no—
79C22⋊Dic139—21no—
80(C2×D139)⋊C4—21no—
81(C2×D139)⋊C4—21no—
82(C2×D139)⋊C4—21no—
83(C2×D139)⋊C4—21no—
84C4×Dic139—21no—
85C2×Q8×C139—21no—
86C2×Q8×C139C2311yescharacteristic
87C2×D4×C139—21no—
88C2×D4×C139C2311yescharacteristic
89C22×C4×C139—21no—
90C22×C4×C139C2311yescharacteristic
91C4⋊C4×C139—21no—
92C4⋊C4×C139—21no—
93C4⋊C4×C139—21no—
94C4⋊C4×C139D411yescharacteristic
95C4⋊C4×C139D411yescharacteristic
96C4⋊C4×C139C2311yescharacteristic
97C4⋊C4×C139C2311yescharacteristic
98C22⋊C4×C139—21no—
99C22⋊C4×C139—21no—
100C22⋊C4×C139—21no—
101C22⋊C4×C139—21no—
102C22⋊C4×C139—21no—
103C22⋊C4×C139D411yescharacteristic
104C22⋊C4×C139D411yescharacteristic
105C42×C139—21no—
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109Dic278—21no—
110Dic278—21no—
111Dic278—81no—
112D556—21no—
113D556—21no—
114C22⋊D139—81no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C4×D139—81no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C139⋊C8—21no—
123C23×C139—21no—
124C23×C139C2×D411yescharacteristic
125Q8×C139—21no—
126Q8×C139—21no—
127Q8×C139—81no—
128D4×C139—21no—
129D4×C139—21no—
130D4×C139—81no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—81no—
137C2×C4×C139C2×D411yescharacteristic
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2411yescharacteristic
143C22×C139—21no—
144C22×C139—21no—
145C22×C139—21no—
146C22×C139—41no—
147C22×C139—41no—
148C22×C139—41no—
149C22×C139C22×D411yescharacteristic
150C2×D139—41no—
151C2×D139—41no—
152C2×D139—41no—
153C4×C139—21no—
154C4×C139—21no—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139H(5,𝔽2)11yescharacteristic
162C4×C1392−1+411yescharacteristic
163Dic139—41no—
164Dic139—41no—
165Dic139—41no—
166C2×C139—41no—
167C2×C139—81no—
168C2×C139#53711yescharacteristic
169C2×C139#57711yescharacteristic
170C2×C139#57711yescharacteristic
171D139—81no—
172C139#326311yescharacteristic, complemented, Sylow
173#3263—1391nomaximal, Sylow
174#542—1391no—
175#542D13911yescharacteristic, complemented
176#476—1391no—
177#476—1391no—
178#475—1391no—
179#475—1391no—
180#470—1391no—
181#469—1391no—
182#465—1391no—
183#465—1391no—
184#464—1391no—
185#464—1391no—
186#463—1391no—
187#463—1391no—
188#424—1391no—
189C2×Q16—1391no—
190C2×SD16—1391no—
191C2×SD16—1391no—
192C2×D8—1391no—
193C2×M16—1391no—
194C22×C8—1391no—
195C4⋊Q8—1391no—
196C4⋊Q8C2×D13911yescharacteristic
197#126—21no—
198#126—2781no—
199#124—21no—
200#124—2781no—
201#124—1391no—
202#124C2×D13911yescharacteristic
203#123—21no—
204#123—2781no—
205C22⋊Q8—21no—
206C22⋊Q8—2781no—
207C22⋊Q8—1391no—
208C22⋊Q8C2×D13911yescharacteristic
209#121—1391no—
210#121C2×D13911yescharacteristic
211C4×Q8—1391no—
212C4×Q8C2×D13911yescharacteristic
213C4×D4—1391no—
214C4×D4C2×D13911yescharacteristic
215#117C2×D13911yescharacteristic
216#106—1391no—
217#106—1391no—
218#106—1391no—
219#106—1391no—
220C4⋊C8—1391no—
221C4⋊C8—1391no—
222C4⋊C8—1391no—
223C4⋊C8—1391no—
224#103—1391no—
225#103—1391no—
226#103—1391no—
227#103—1391no—
228#102—1391no—
229#102—1391no—
230#102—1391no—
231#102—1391no—
232C2×Q8—21no—
233C2×Q8—2781no—
234C2×Q8—1391no—
235C2×Q8C22×D13911yescharacteristic
236C2×D4—21no—
237C2×D4—2781no—
238C2×D4—1391no—
239C2×D4C22×D13911yescharacteristic
240C22×C4—21no—
241C22×C4—2781no—
242C22×C4C22×D13911yescharacteristic
243Q16—5561no—
244SD16—5561no—
245SD16—5561no—
246D8—5561no—
247M16—5561no—
248C2×C8—5561no—
249C2×C8—1391no—
250C2×C8—1391no—
251C2×C8—1391no—
252C2×C8—1391no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2781no—
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—1391no—
260C4⋊C4—1391no—
261C4⋊C4C22⋊D13911yescharacteristic
262C4⋊C4C22⋊D13911yescharacteristic
263C4⋊C4C22×D13911yescharacteristic
264C4⋊C4C22×D13911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2781no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4C22⋊D13911yescharacteristic
276C22⋊C4C22⋊D13911yescharacteristic
277C42—21no—
278C42—2781no—
279C42C22×D13911yescharacteristic
280C42C22×D13911yescharacteristic
281C23—21no—
282C23—2781no—
283C23C2×C22⋊D13911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—2781no—
288Q8—2781no—
289Q8—11121no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—2781no—
294D4—2781no—
295D4—11121no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—11121no—
306C2×C4C2×C22⋊D13911yescharacteristic
307C2×C4C2×C22⋊D13911yescharacteristic
308C2×C4C2×C22⋊D13911yescharacteristic
309C2×C4C2×C22⋊D13911yescharacteristic
310C2×C4C2×C22⋊D13911yescharacteristic
311C2×C4C23×D13911yescharacteristic
312C8—2781no—
313C8—2781no—
314C8—2781no—
315C8—2781no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—5561no—
323C22—5561no—
324C22—5561no—
325C22C22×C22⋊D13911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—5561no—
335C4—5561no—
336C4—5561no—
337C4#1798488811yescharacteristic
338C4#1798488911yescharacteristic
339C2—41no—
340C2—81no—
341C2—11121no—
342C2#2258153111yescharacteristic
343C2#2258176111yescharacteristic
344C2#2258176411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#542×C139C2
socleC22×C139C22×D4
prime radical#22581204C2
hypercenter#542D139
hypocenterC139#3263
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581243C2semidirect
3. #22581240C2semidirect
4. #22581238C2semidirect
5. #22581235C2semidirect
6. #22581209C2semidirect
8. #22581184C2semidirect
9. #22581180C2semidirect
10. #22581175C2semidirect
11. #22581172C2semidirect
12. #22581168C2semidirect
13. #22581165C2semidirect
14. #22580980C2semidirect
15. #542×C139C2semidirect
172. C139#3263semidirect
175. #542D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225812432
#225812402
#225812382
#225812352
#225812092
#225812042
#225811842
#225811802
#225811752
#225811722
#225811682
#225811652
#225809802
#542×C1392
#3263139