Finite Group Databasebeta

← #31818306

Subgroups — #31818306

Order 17792.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581649C211yesmaximal, characteristic, complemented
2#22581307C211yesmaximal, characteristic, complemented
3#22581291C211yesmaximal, characteristic, complemented
4#22581269C211yesmaximal, characteristic, complemented
5#22581260C211yesmaximal, characteristic, complemented
6#22581187C211yesmaximal, characteristic, complemented
7#22581184C211yesmaximal, characteristic, complemented
8#22581165C211yesmaximal, characteristic, complemented
9#22581098C211yesmaximal, characteristic, complemented
10#22581092C211yesmaximal, characteristic, complemented
11C4×#14555772C211yesmaximal, characteristic, complemented
12D4×C139⋊C8C211yesmaximal, characteristic, complemented
13#22580949C211yesmaximal, characteristic, complemented
14C2×#17984766C211yesmaximal, characteristic, complemented
15#548×C139C211yesmaximal, characteristic, complemented
16C2×#14555772C2211yescharacteristic
17C2×#14555772C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19C22×C139⋊C8C2211yescharacteristic
20C22×C139⋊C8C2211yescharacteristic
21#17984837—21no—
22#17984834C2211yescharacteristic
23#17984824—21no—
24#17984816C2211yescharacteristic
25#17984816C2211yescharacteristic
26#17984814—21no—
27C4×D556C2211yescharacteristic
28(C22⋊D139)⋊C4—21no—
29#17984801C2211yescharacteristic
30C2×C4⋊Dic139C2211yescharacteristic
31#17984775C2211yescharacteristic
32#17984773C2211yescharacteristic
33#17984773C2211yescharacteristic
34C4⋊(C139⋊C8)C2211yescharacteristic
35#17984766C2211yescharacteristic
36#17984766C2211yescharacteristic
37#17984766C2211yescharacteristic
38#17984766C2211yescharacteristic
39#17984766C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984762C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic
47C4×C139⋊C8C2211yescharacteristic
48C2×#41×C139C2211yescharacteristic
49C22×Q8×C139C2211yescharacteristic
50#124×C139—21no—
51#124×C139C2211yescharacteristic
52C22⋊Q8×C139—21no—
53C22⋊Q8×C139C2211yescharacteristic
54#121×C139—21no—
55#121×C139C2211yescharacteristic
56C4×Q8×C139C2211yescharacteristic
57C4×D4×C139—21no—
58C4×D4×C139C2211yescharacteristic
59C2×D556C2311yescharacteristic
60C2×C22⋊D139—21no—
61C2×C22⋊D139—21no—
62C22×Dic139—21no—
63C2×C4×D139—21no—
64#14555772—22no—
65#14555772—41no—
66#14555770—41no—
67C2×C139⋊C8—41no—
68C2×C139⋊C8—41no—
69C2×C139⋊C8C2311yescharacteristic
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C4⋊Dic139—21no—
74C4⋊Dic139C2311yescharacteristic
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—
83C4×Dic139—21no—
84#41×C139—22no—
85#41×C139—41no—
86C2×Q8×C139—21no—
87C2×Q8×C139—22no—
88C2×Q8×C139—41no—
89C2×Q8×C139C2311yescharacteristic
90C2×Q8×C139C2311yescharacteristic
91C2×D4×C139—21no—
92C2×D4×C139—21no—
93C2×D4×C139D411yescharacteristic
94C2×D4×C139C2311yescharacteristic
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139C2311yescharacteristic
98C22×C4×C139C2311yescharacteristic
99C4⋊C4×C139—21no—
100C4⋊C4×C139—21no—
101C4⋊C4×C139D411yescharacteristic
102C4⋊C4×C139C2311yescharacteristic
103C22⋊C4×C139—21no—
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139D411yescharacteristic
108C22⋊C4×C139D411yescharacteristic
109C42×C139—21no—
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112D556—21no—
113D556—21no—
114C22⋊D139—42no—
115C22⋊D139—81no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139—81no—
120C4×D139—81no—
121C139⋊C8—21no—
122C139⋊C8—21no—
123C139⋊C8—21no—
124C139⋊C8—21no—
125C23×C139—21no—
126C23×C139C2×D411yescharacteristic
127C23×C139C2×D411yescharacteristic
128Q8×C139—21no—
129Q8×C139—21no—
130Q8×C139—21no—
131Q8×C139—42no—
132Q8×C139#4112yes—
133D4×C139—22no—
134D4×C139—21no—
135D4×C139—21no—
136D4×C139—42no—
137D4×C139—42no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—42no—
146C2×C4×C139—42no—
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2×D411yescharacteristic
151C2×C4×C139C2411yescharacteristic
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—21no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139—41no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139#13512yes—
161C22×C139C22×D411yescharacteristic
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—41no—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—22no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—41no—
171C4×C139—41no—
172C4×C139C2×#4111yescharacteristic
173C4×C139H(5,𝔽2)11yescharacteristic
174Dic139—41no—
175Dic139—41no—
176Dic139—41no—
177C2×C139—22no—
178C2×C139—41no—
179C2×C139—81no—
180C2×C139#54611yescharacteristic
181C2×C139C2×#13511yescharacteristic
182C2×C139#57711yescharacteristic
183D139—81no—
184C139#330111yescharacteristic, complemented, Sylow
185#3301—1391nomaximal, Sylow
186#553—1391no—
187#548D13911yescharacteristic, complemented
188#488—1391no—
189#485—1391no—
190#481—1391no—
191#479—1391no—
192#466—1391no—
193#465—1391no—
194#463—1391no—
195#449—1391no—
196#448—1391no—
197C4×SD16—1391no—
198C8×D4—1391no—
199#416—1391no—
200C2×#103—1391no—
201C2×#41C2×D13911yescharacteristic
202C22×Q8C2×D13911yescharacteristic
203C2×SD16—1391no—
204C2×SD16—1391no—
205C2×D8—1391no—
206C22×C8—1391no—
207C22×C8—1391no—
208#126—2781no—
209#125—1391no—
210#124—21no—
211#124C2×D13911yescharacteristic
212#123—2781no—
213C22⋊Q8—21no—
214C22⋊Q8C2×D13911yescharacteristic
215#121—21no—
216#121—2781no—
217#121—1391no—
218#121—1391no—
219#121C2×D13911yescharacteristic
220C4×Q8C2×D13911yescharacteristic
221C4×D4—21no—
222C4×D4—2781no—
223C4×D4—1391no—
224C4×D4C2×D13911yescharacteristic
225#117—1391no—
226C2×C4⋊C4—1391no—
227#107—1391no—
228#106—1391no—
229#106—1391no—
230C4⋊C8—1391no—
231#103—1391no—
232#103—1391no—
233#103—1391no—
234#103—1391no—
235#103—1391no—
236#103—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241C22⋊C8—1391no—
242C22⋊C8—1391no—
243C4×C8—1391no—
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D13911yescharacteristic
250C2×Q8C22×D13911yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4C22⋊D13911yescharacteristic
257C2×D4C22×D13911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4C22×D13911yescharacteristic
263C22×C4C22×D13911yescharacteristic
264SD16—2782no—
265SD16—5561no—
266D8—5561no—
267C2×C8—5561no—
268C2×C8—5561no—
269C2×C8—1391no—
270C2×C8—1391no—
271C2×C8—1391no—
272C2×C8—1391no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—1391no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4C22⋊D13911yescharacteristic
282C4⋊C4C22×D13911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4C22⋊D13911yescharacteristic
292C22⋊C4C22⋊D13911yescharacteristic
293C42—21no—
294C42—2781no—
295C42C22×D13911yescharacteristic
296C23—21no—
297C23—2781no—
298C23C2×C22⋊D13911yescharacteristic
299C23C2×C22⋊D13911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1455578412yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—2781no—
311D4—2781no—
312D4—5562no—
313D4—11121no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—11121no—
327C2×C4—11121no—
328C2×C4C2×C22⋊D13911yescharacteristic
329C2×C4C2×C22⋊D13911yescharacteristic
330C2×C4C2×C22⋊D13911yescharacteristic
331C2×C4C2×C22⋊D13911yescharacteristic
332C2×C4C23×D13911yescharacteristic
333C8—2781no—
334C8—2781no—
335C8—2781no—
336C8—2781no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5561no—
346C22—5561no—
347C22—5561no—
348C22#1798486212yes—
349C22C22×C22⋊D13911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—5561no—
358C4—5561no—
359C4—5561no—
360C4C2×#1455578411yescharacteristic
361C4#1798488711yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—11121no—
366C2#2258159711yescharacteristic
367C2C2×#1798486211yescharacteristic
368C2#2258176111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#548×C139C2
socleC22×C139C22×D4
hypercenter#548D139
hypocenterC139#3301
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #22581649C2semidirect
2. #22581307C2semidirect
3. #22581291C2semidirect
4. #22581269C2semidirect
5. #22581260C2semidirect
6. #22581187C2semidirect
7. #22581184C2semidirect
8. #22581165C2semidirect
9. #22581098C2semidirect
10. #22581092C2semidirect
11. C4×#14555772C2semidirect
12. D4×C139⋊C8C2semidirect
13. #22580949C2semidirect
14. C2×#17984766C2semidirect
15. #548×C139C2semidirect
184. C139#3301semidirect
187. #548D139semidirect

Maximal subgroups

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

subgroupindex
#225816492
#225813072
#225812912
#225812692
#225812602
#225811872
#225811842
#225811652
#225810982
#225810922
C4×#145557722
D4×C139⋊C82
#225809492
C2×#179847662
#548×C1392
#3301139