Finite Group Databasebeta

← #31817809

Subgroups — #31817809

Order 17792.

358 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#22581574C211yesmaximal, characteristic, complemented
2#22581257C211yesmaximal, characteristic, complemented
3#22581250C211yesmaximal, characteristic, complemented
4#22581243C211yesmaximal, characteristic, complemented
5#22581233C211yesmaximal, characteristic, complemented
6#22581204C211yesmaximal, characteristic, complemented
7#22581197C211yesmaximal, characteristic, complemented
8#22581187C211yesmaximal, characteristic, complemented
9#22581180C211yesmaximal, characteristic, complemented
10#22581168C211yesmaximal, characteristic, complemented
11#22581168C211yesmaximal, characteristic, complemented
12#22581150C211yesmaximal, characteristic, complemented
13#22581145C211yesmaximal, characteristic, complemented
14#22580980C211yesmaximal, characteristic, complemented
15#540×C139C211yesmaximal, characteristic, complemented
16C2×#14555773C2211yescharacteristic
17C2×#14555773C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
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#17984775C2211yescharacteristic
33#17984775C2211yescharacteristic
34#17984773C2211yescharacteristic
35#17984773C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39C4⋊(C139⋊C8)C2211yescharacteristic
40#17984765C2211yescharacteristic
41#17984765C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48#127×C139C2211yescharacteristic
49#125×C139C2211yescharacteristic
50#123×C139—21no—
51#123×C139—21no—
52#121×C139—21no—
53#121×C139—21no—
54#121×C139C2211yescharacteristic
55#121×C139C2211yescharacteristic
56C4×D4×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58#117×C139C2211yescharacteristic
59C2×Dic278—21no—
60C2×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C4×D139—21no—
64#14555773—41no—
65#14555773—41no—
66#14555770—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×D4×C139—21no—
86C2×D4×C139—21no—
87C2×D4×C139—21no—
88C2×D4×C139—21no—
89C2×D4×C139C2311yescharacteristic
90C2×D4×C139C2311yescharacteristic
91C22×C4×C139—21no—
92C22×C4×C139—21no—
93C22×C4×C139C2311yescharacteristic
94C4⋊C4×C139—21no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139D411yescharacteristic
97C4⋊C4×C139D411yescharacteristic
98C4⋊C4×C139C2311yescharacteristic
99C4⋊C4×C139C2311yescharacteristic
100C22⋊C4×C139—21no—
101C22⋊C4×C139—21no—
102C22⋊C4×C139—21no—
103C22⋊C4×C139—21no—
104C22⋊C4×C139D411yescharacteristic
105C22⋊C4×C139D411yescharacteristic
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×C139—21no—
125C23×C139C2×D411yescharacteristic
126D4×C139—21no—
127D4×C139—21no—
128D4×C139—21no—
129D4×C139—21no—
130D4×C139—81no—
131D4×C139—81no—
132D4×C139—81no—
133D4×C139—81no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—81no—
139C2×C4×C139—81no—
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2411yescharacteristic
146C22×C139—21no—
147C22×C139—21no—
148C22×C139—21no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139—41no—
155C22×C139C22×D411yescharacteristic
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—21no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—41no—
165C4×C139—41no—
166C4×C139H(5,𝔽2)11yescharacteristic
167C4×C1392−1+411yescharacteristic
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171C2×C139—41no—
172C2×C139—81no—
173C2×C139—81no—
174C2×C139#53711yescharacteristic
175C2×C139#57611yescharacteristic
176C2×C139#57711yescharacteristic
177D139—81no—
178C139#325711yescharacteristic, complemented, Sylow
179#3257—1391nomaximal, Sylow
180#542—1391no—
181#540D13911yescharacteristic, complemented
182#479—1391no—
183#478—1391no—
184#476—1391no—
185#474—1391no—
186#469—1391no—
187#468—1391no—
188#466—1391no—
189#465—1391no—
190#463—1391no—
191#463—1391no—
192#460—1391no—
193#459—1391no—
194#424—1391no—
195C2×SD16—1391no—
196C2×SD16—1391no—
197C2×D8—1391no—
198C2×D8—1391no—
199C2×M16—1391no—
200C22×C8—1391no—
201C4⋊Q8—1391no—
202#127C2×D13911yescharacteristic
203#126—2781no—
204#125C2×D13911yescharacteristic
205#124—2781no—
206#124—1391no—
207#123—21no—
208#123—21no—
209#123—2781no—
210C22⋊Q8—2781no—
211C22⋊Q8—1391no—
212#121—21no—
213#121—21no—
214#121—1391no—
215#121C2×D13911yescharacteristic
216#121C2×D13911yescharacteristic
217C4×Q8—1391no—
218C4×D4—1391no—
219C4×D4C2×D13911yescharacteristic
220C4×D4C2×D13911yescharacteristic
221#117C2×D13911yescharacteristic
222#107—1391no—
223#107—1391no—
224#106—1391no—
225#106—1391no—
226C4⋊C8—1391no—
227C4⋊C8—1391no—
228C4⋊C8—1391no—
229C4⋊C8—1391no—
230#103—1391no—
231#103—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102—1391no—
236#102—1391no—
237#102—1391no—
238C2×Q8—2781no—
239C2×Q8—1391no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2781no—
245C2×D4—1391no—
246C2×D4C22×D13911yescharacteristic
247C2×D4C22×D13911yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—2781no—
251C22×C4C22×D13911yescharacteristic
252SD16—5561no—
253SD16—5561no—
254D8—5561no—
255D8—5561no—
256M16—5561no—
257C2×C8—5561no—
258C2×C8—1391no—
259C2×C8—1391no—
260C2×C8—1391no—
261C2×C8—1391no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—2781no—
265C4⋊C4—2781no—
266C4⋊C4—2781no—
267C4⋊C4—1391no—
268C4⋊C4—1391no—
269C4⋊C4C22⋊D13911yescharacteristic
270C4⋊C4C22⋊D13911yescharacteristic
271C4⋊C4C22×D13911yescharacteristic
272C4⋊C4C22×D13911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4C22⋊D13911yescharacteristic
283C22⋊C4C22⋊D13911yescharacteristic
284C42—2781no—
285C42C22×D13911yescharacteristic
286C42C22×D13911yescharacteristic
287C23—21no—
288C23—21no—
289C23—2781no—
290C23C2×C22⋊D13911yescharacteristic
291Q8—2781no—
292Q8—2781no—
293Q8—11121no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—2781no—
303D4—2781no—
304D4—11121no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—2781no—
312C2×C4—2781no—
313C2×C4—2781no—
314C2×C4—11121no—
315C2×C4C2×C22⋊D13911yescharacteristic
316C2×C4C2×C22⋊D13911yescharacteristic
317C2×C4C2×C22⋊D13911yescharacteristic
318C2×C4C2×C22⋊D13911yescharacteristic
319C2×C4C2×C22⋊D13911yescharacteristic
320C2×C4C23×D13911yescharacteristic
321C8—2781no—
322C8—2781no—
323C8—2781no—
324C8—2781no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—5561no—
335C22—5561no—
336C22—5561no—
337C22C22×C22⋊D13911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—5561no—
346C4—5561no—
347C4—5561no—
348C4#1798488811yescharacteristic
349C4#1798488911yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—11121no—
354C2#2258153111yescharacteristic
355C2#2258175611yescharacteristic
356C2#2258176411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#540×C139C2
socleC22×C139C22×D4
hypercenter#540D139
hypocenterC139#3257
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581257C2semidirect
3. #22581250C2semidirect
4. #22581243C2semidirect
5. #22581233C2semidirect
6. #22581204C2semidirect
7. #22581197C2semidirect
8. #22581187C2semidirect
9. #22581180C2semidirect
10. #22581168C2semidirect
11. #22581168C2semidirect
12. #22581150C2semidirect
13. #22581145C2semidirect
14. #22580980C2semidirect
15. #540×C139C2semidirect
178. C139#3257semidirect
181. #540D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225812572
#225812502
#225812432
#225812332
#225812042
#225811972
#225811872
#225811802
#225811682
#225811502
#225811452
#225809802
#540×C1392
#3257139