Finite Group Databasebeta

← #31818308

Subgroups — #31818308

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#22581612C211yesmaximal, characteristic, complemented
3#22581308C211yesmaximal, characteristic, complemented
4#22581295C211yesmaximal, characteristic, complemented
5#22581272C211yesmaximal, characteristic, complemented
6#22581261C211yesmaximal, characteristic, complemented
7#22581189C211yesmaximal, characteristic, complemented
8#22581182C211yesmaximal, characteristic, complemented
9#22581169C211yesmaximal, characteristic, complemented
10#22581100C211yesmaximal, characteristic, complemented
11#22581094C211yesmaximal, characteristic, complemented
12C4×#14555774C211yesmaximal, characteristic, complemented
13#22580950C211yesmaximal, characteristic, complemented
14C2×#17984767C211yesmaximal, characteristic, complemented
15C8×D4×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C22×Dic278C2211yescharacteristic
18C2×#14555774C2211yescharacteristic
19C2×#14555774C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21#17984837—21no—
22#17984834C2211yescharacteristic
23#17984830C2211yescharacteristic
24#17984828—21no—
25#17984824—21no—
26#17984821C2211yescharacteristic
27#17984820—21no—
28#17984816C2211yescharacteristic
29#17984816C2211yescharacteristic
30#17984816C2211yescharacteristic
31#17984814—21no—
32#17984814—21no—
33C4×Dic278C2211yescharacteristic
34C4×D556C2211yescharacteristic
35(C22⋊D139)⋊C4—21no—
36(C22⋊D139)⋊C4—21no—
37#17984801C2211yescharacteristic
38C2×C4⋊Dic139C2211yescharacteristic
39#17984776C2211yescharacteristic
40#17984774C2211yescharacteristic
41#17984774C2211yescharacteristic
42#17984767C2211yescharacteristic
43#17984767C2211yescharacteristic
44#17984767C2211yescharacteristic
45#17984767C2211yescharacteristic
46#17984767C2211yescharacteristic
47#17984767C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic
52C22×C8×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic
54C4×D4×C139C2211yescharacteristic
55C4⋊C8×C139C2211yescharacteristic
56C22⋊C8×C139C2211yescharacteristic
57C22⋊C8×C139C2211yescharacteristic
58C4×C8×C139C2211yescharacteristic
59#14555785—22no—
60#14555785—41no—
61C2×Dic278—22no—
62C2×Dic278—21no—
63C2×Dic278—41no—
64C2×Dic278C2311yescharacteristic
65C2×Dic278C2311yescharacteristic
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C22×Dic139—21no—
73C22×Dic139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76#14555774—22no—
77#14555774—41no—
78D1112—41no—
79C4⋊Dic139—21no—
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83C4⋊Dic139C2311yescharacteristic
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96C4×Dic139—21no—
97C4×Dic139—21no—
98C2×D4×C139D411yescharacteristic
99C22×C4×C139C2311yescharacteristic
100C22×C4×C139C2311yescharacteristic
101C2×C8×C139—41no—
102C2×C8×C139—41no—
103C2×C8×C139C2311yescharacteristic
104C2×C8×C139C2311yescharacteristic
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139D411yescharacteristic
108C22⋊C4×C139D411yescharacteristic
109C22⋊C4×C139D411yescharacteristic
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—21no—
113Dic278—21no—
114Dic278—21no—
115Dic278—21no—
116Dic278—42no—
117Dic278#4112yes—
118D556—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122C22⋊D139—42no—
123C22⋊D139—42no—
124C22⋊D139—42no—
125C22⋊D139—81no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—21no—
129C2×Dic139—21no—
130C2×Dic139—21no—
131C2×Dic139—21no—
132C2×Dic139—42no—
133C2×Dic139—81no—
134C4×D139—42no—
135C4×D139—81no—
136C23×C139C2×D411yescharacteristic
137C23×C139C2×D411yescharacteristic
138D4×C139—22no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2411yescharacteristic
148C8×C139—21no—
149C8×C139—21no—
150C8×C139—21no—
151C8×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—21no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139#13512yes—
158C22×C139C22×D411yescharacteristic
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—41no—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—21no—
168C4×C139—21no—
169C4×C139C2×#4111yescharacteristic
170C4×C139H(5,𝔽2)11yescharacteristic
171Dic139—22no—
172Dic139—41no—
173Dic139—41no—
174Dic139—41no—
175Dic139—41no—
176Dic139—41no—
177C2×C139—22no—
178C2×C139—41no—
179C2×C139#54611yescharacteristic
180C2×C139C2×#13511yescharacteristic
181C2×C139#57711yescharacteristic
182D139—81no—
183D139—81no—
184C139#330111yescharacteristic, complemented, Sylow
185#3301—1391nomaximal, Sylow
186#553—1391no—
187#548—1391no—
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×D4D13911yescharacteristic, complemented
199#416—1391no—
200C2×#103—1391no—
201C2×#41—1391no—
202C22×Q8—1391no—
203C2×SD16—1391no—
204C2×SD16—1391no—
205C2×D8—1391no—
206C22×C8C2×D13911yescharacteristic
207C22×C8C2×D13911yescharacteristic
208#126—2781no—
209#125—1391no—
210#124—2781no—
211#124—1391no—
212#123—2781no—
213C22⋊Q8—2781no—
214C22⋊Q8—1391no—
215#121—2781no—
216#121—2781no—
217#121—1391no—
218#121—1391no—
219#121—1391no—
220C4×Q8—1391no—
221C4×D4—2781no—
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⋊C8C2×D13911yescharacteristic
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⋊C8C2×D13911yescharacteristic
242C22⋊C8C2×D13911yescharacteristic
243C4×C8C2×D13911yescharacteristic
244#41—2782no—
245#41—5561no—
246C2×Q8—2782no—
247C2×Q8—2781no—
248C2×Q8—5561no—
249C2×Q8—1391no—
250C2×Q8—1391no—
251C2×D4—2781no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4D55611yescharacteristic
258C22×C4—2781no—
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4C22×D13911yescharacteristic
263C22×C4C22×D13911yescharacteristic
264SD16—2782no—
265SD16—5561no—
266D8—5561no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D13911yescharacteristic
270C2×C8C22×D13911yescharacteristic
271C2×C8C22×D13911yescharacteristic
272C2×C8C22×D13911yescharacteristic
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—1391no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4—1391no—
282C4⋊C4D55611yescharacteristic
283C22⋊C4—2781no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4D55611yescharacteristic
292C22⋊C4D55611yescharacteristic
293C42—2781no—
294C42—2781no—
295C42C22×D13911yescharacteristic
296C23—2781no—
297C23—2781no—
298C23C2×D55611yescharacteristic
299C23C2×D55611yescharacteristic
300Q8—2781no—
301Q8—2781no—
302Q8—2781no—
303Q8—5562no—
304Q8—1392no—
305D4—22no—
306D4—2781no—
307D4—2781no—
308D4—2781no—
309D4—2781no—
310D4—5562no—
311D4—5562no—
312D4—5562no—
313D4—11121no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—2781no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—5562no—
325C2×C4—5562no—
326C2×C4—11121no—
327C2×C4—11121no—
328C2×C4C2×D55611yescharacteristic
329C2×C4C2×D55611yescharacteristic
330C2×C4C2×D55611yescharacteristic
331C2×C4C2×D55611yescharacteristic
332C2×C4C23×D13911yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—5561no—
343C22—5561no—
344C22—5561no—
345C22—5561no—
346C22—5561no—
347C22—5561no—
348C22#1798486412yes—
349C22C22×D55611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—2782no—
355C4—5561no—
356C4—5561no—
357C4—5561no—
358C4—5561no—
359C4—5561no—
360C4#41×D13911yescharacteristic
361C4#1798488711yescharacteristic
362C2—22no—
363C2—41no—
364C2—11121no—
365C2—11121no—
366C2#2258159811yescharacteristic
367C2C2×#1798486411yescharacteristic
368C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC8×D4×C139C2
socleC22×C139C22×D4
hypercenterC8×D4D139
hypocenterC139#3301
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #22581649C2semidirect
2. #22581612C2semidirect
3. #22581308C2semidirect
4. #22581295C2semidirect
5. #22581272C2semidirect
6. #22581261C2semidirect
7. #22581189C2semidirect
8. #22581182C2semidirect
9. #22581169C2semidirect
10. #22581100C2semidirect
11. #22581094C2semidirect
12. C4×#14555774C2semidirect
13. #22580950C2semidirect
14. C2×#17984767C2semidirect
15. C8×D4×C139C2semidirect
184. C139#3301semidirect
198. C8×D4D139semidirect

Maximal subgroups

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

subgroupindex
#225816492
#225816122
#225813082
#225812952
#225812722
#225812612
#225811892
#225811822
#225811692
#225811002
#225810942
C4×#145557742
#225809502
C2×#179847672
C8×D4×C1392
#3301139