Finite Group Databasebeta

← #31817800

Subgroups — #31817800

Order 17792.

354 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#22581487C211yesmaximal, characteristic, complemented
2#22581260C211yesmaximal, characteristic, complemented
3#22581257C211yesmaximal, characteristic, complemented
4#22581253C211yesmaximal, characteristic, complemented
5#22581250C211yesmaximal, characteristic, complemented
6#22581209C211yesmaximal, characteristic, complemented
7#22581204C211yesmaximal, characteristic
8#22581201C211yesmaximal, characteristic, complemented
9#22581197C211yesmaximal, characteristic, complemented
10#22581175C211yesmaximal, characteristic, complemented
11#22581172C211yesmaximal, characteristic, complemented
12#22581168C211yesmaximal, characteristic, complemented
13#22581165C211yesmaximal, characteristic, complemented
14#22580977C211yesmaximal, characteristic, complemented
15#529×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555772C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×#14555769C2211yescharacteristic
21C2×#14555769C2211yescharacteristic
22#17984836—21no—
23#17984834C2211yescharacteristic
24#17984830C2211yescharacteristic
25#17984825—21no—
26#17984821C2211yescharacteristic
27#17984816C2211yescharacteristic
28C4×Dic278C2211yescharacteristic
29C4×D556C2211yescharacteristic
30C4×C22⋊D139—21no—
31#17984799—21no—
32#17984775C2211yescharacteristic
33#17984775C2211yescharacteristic
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
48#126×C139—21no—
49#125×C139C2211yescharacteristic
50#124×C139C2211yescharacteristic
51#123×C139—21no—
52C22⋊Q8×C139C2211yescharacteristic
53#121×C139C2211yescharacteristic
54C4×Q8×C139C2211yescharacteristic
55C4×D4×C139—21no—
56C4×D4×C139C2211yescharacteristic
57#117×C139—21no—
58C2×C42×C139C2211yescharacteristic
59C2×Dic278C2311yescharacteristic
60C2×D556C2311yescharacteristic
61C2×C22⋊D139—21no—
62C2×C4×D139—21no—
63#14555775—41no—
64#14555773—41no—
65#14555772—41no—
66#14555770—41no—
67#14555769—41no—
68#14555769—41no—
69C2×C139⋊C8C2311yescharacteristic
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C4⋊Dic139C2311yescharacteristic
74C4⋊Dic139C2311yescharacteristic
75Dic139⋊C4—21no—
76Dic139⋊C4—21no—
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×C139C2311yescharacteristic
86C2×D4×C139—21no—
87C2×D4×C139C2311yescharacteristic
88C22×C4×C139—21no—
89C22×C4×C139D411yescharacteristic
90C22×C4×C139D411yescharacteristic
91C22×C4×C139C2311yescharacteristic
92C4⋊C4×C139—21no—
93C4⋊C4×C139—21no—
94C4⋊C4×C139—21no—
95C4⋊C4×C139—21no—
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—
103C42×C139—21no—
104C42×C139D411yescharacteristic
105C42×C139D411yescharacteristic
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109Dic278—21no—
110Dic278—21no—
111D556—21no—
112D556—21no—
113C22⋊D139—42no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C4×D139—42no—
118C139⋊C8—21no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C23×C139—21no—
123C23×C139C2×D411yescharacteristic
124Q8×C139—21no—
125Q8×C139—21no—
126D4×C139—21no—
127D4×C139—21no—
128D4×C139—42no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—41no—
135C2×C4×C139—41no—
136C2×C4×C139—42no—
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#57511yescharacteristic
170C2×C139#57511yescharacteristic
171D139—81no—
172C139#325611yescharacteristic, complemented, Sylow
173#3256—1391nomaximal, Sylow
174#529—1391no—
175#529D13911yescharacteristic, complemented
176#479—1391no—
177#479—1391no—
178#478—1391no—
179#478—1391no—
180#470—1391no—
181#469—1391no—
182#468—1391no—
183#468—1391no—
184#464—1391no—
185#464—1391no—
186#463—1391no—
187#463—1391no—
188#423—1391no—
189C2×Q16—1391no—
190C2×SD16—1391no—
191C2×SD16—1391no—
192C2×D8—1391no—
193C2×M16—1391no—
194C2×M16—1391no—
195#126—21no—
196#126—2781no—
197#125—1391no—
198#125C2×D13911yescharacteristic
199#124—1391no—
200#124C2×D13911yescharacteristic
201#123—21no—
202#123—2781no—
203C22⋊Q8—1391no—
204C22⋊Q8C2×D13911yescharacteristic
205#121—1391no—
206#121C2×D13911yescharacteristic
207C4×Q8—1391no—
208C4×Q8C2×D13911yescharacteristic
209C4×D4—21no—
210C4×D4—2781no—
211C4×D4—1391no—
212C4×D4C2×D13911yescharacteristic
213#117—21no—
214#117—2781no—
215C2×C42C2×D13911yescharacteristic
216#107—1391no—
217#107—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—1391no—
233C2×Q8C22×D13911yescharacteristic
234C2×D4—21no—
235C2×D4—2781no—
236C2×D4—1391no—
237C2×D4C22×D13911yescharacteristic
238C22×C4—21no—
239C22×C4—2781no—
240C22×C4C22⋊D13911yescharacteristic
241C22×C4C22⋊D13911yescharacteristic
242C22×C4C22×D13911yescharacteristic
243Q16—5561no—
244SD16—5561no—
245SD16—5561no—
246D8—5561no—
247M16—5561no—
248M16—5561no—
249C2×C8—1391no—
250C2×C8—1391no—
251C2×C8—1391no—
252C2×C8—1391no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—1391no—
262C4⋊C4—1391no—
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—
275C42—21no—
276C42—2781no—
277C42C22⋊D13911yescharacteristic
278C42C22⋊D13911yescharacteristic
279C42C22×D13911yescharacteristic
280C42C22×D13911yescharacteristic
281C23—21no—
282C23—2781no—
283C23C2×C22⋊D13911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—2781no—
287Q8—2781no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—2781no—
292D4—2781no—
293D4—5562no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—5562no—
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#2258175111yescharacteristic
344C2#2258175111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#529×C139C2
socleC22×C139C22×D4
prime radical#22581204C2
hypercenter#529D139
hypocenterC139#3256
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #22581487C2semidirect
2. #22581260C2semidirect
3. #22581257C2semidirect
4. #22581253C2semidirect
5. #22581250C2semidirect
6. #22581209C2semidirect
8. #22581201C2semidirect
9. #22581197C2semidirect
10. #22581175C2semidirect
11. #22581172C2semidirect
12. #22581168C2semidirect
13. #22581165C2semidirect
14. #22580977C2semidirect
15. #529×C139C2semidirect
172. C139#3256semidirect
175. #529D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225812602
#225812572
#225812532
#225812502
#225812092
#225812042
#225812012
#225811972
#225811752
#225811722
#225811682
#225811652
#225809772
#529×C1392
#3256139