Finite Group Databasebeta

← #31817907

Subgroups — #31817907

Order 17792.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984874C211yesmaximal, characteristic, complemented
2C22×#14555772C211yesmaximal, characteristic, complemented
3Q8×C22⋊D139C211yesmaximal, characteristic, complemented
4#22581594C211yesmaximal, characteristic
5#22581346C211yesmaximal, characteristic, complemented
6#22581202C211yesmaximal, characteristic, complemented
7#22581192C211yesmaximal, characteristic, complemented
8#22581177C211yesmaximal, characteristic, complemented
9#22581157C211yesmaximal, characteristic, complemented
10#22581114C211yesmaximal, characteristic, complemented
11#22581106C211yesmaximal, characteristic, complemented
12#22581093C211yesmaximal, characteristic, complemented
13#22581056C211yesmaximal, characteristic, complemented
14#22581021C211yesmaximal, characteristic, complemented
15#451×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C2×Q8×D139C2211yescharacteristic, complemented
18C22×D556C2211yescharacteristic
19#17984874—24no—
20C2×#14555775C2211yescharacteristic, complemented
21C2×#14555774C2211yescharacteristic
22C2×#14555774C2211yescharacteristic
23C2×#14555772—24no—
24C2×#14555772C2211yescharacteristic
25C2×#14555772C2211yescharacteristic
26C2×#14555772C2211yescharacteristic
27C2×#14555772C2211yescharacteristic
28C2×#14555768C2211yescharacteristic, complemented
29C22×C139⋊C8C2211yescharacteristic
30#17984840—21no—
31#17984840C2211yescharacteristic, complemented
32#17984831C2211yescharacteristic
33#17984827—21no—
34#17984821—21no—
35#17984821C2211yescharacteristic
36#17984818—21no—
37#17984818C2211yescharacteristic, complemented
38#17984817—21no—
39#17984817C2211yescharacteristic
40#17984812—21no—
41Q8×Dic139C2211yescharacteristic, complemented
42#17984804C2211yescharacteristic
43C4×C22⋊D139—21no—
44C4×C22⋊D139C2211yescharacteristic
45C22⋊C4×D139—21no—
46#17984775C2211yescharacteristic, complemented
47Dic139⋊C8C2211yescharacteristic, complemented
48#17984766C2211yescharacteristic, complemented
49#17984765C2211yescharacteristic, complemented
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic
52(C2×D139)⋊C8C2211yescharacteristic, complemented
53#17984752C2211yescharacteristic, complemented
54C22×Q8×C139C2211yescharacteristic
55C2×Q16×C139C2211yescharacteristic, complemented
56C2×Q16×C139C2211yescharacteristic, complemented
57C22⋊Q8×C139C2211yescharacteristic
58#103×C139C2211yescharacteristic, complemented
59#103×C139C2211yescharacteristic, complemented
60C22⋊C8×C139C2211yescharacteristic
61C23×D139—21no—
62#14555786—22no—
63#14555786—41no—
64C2×Dic278—21no—
65C2×Dic278C2311yescharacteristic
66Q8×D139—22no—
67Q8×D139—41no—
68C2×D556—22no—
69C2×D556—21no—
70C2×D556—21no—
71C2×D556—21no—
72C2×D556—41no—
73C2×D556C2311yescharacteristic
74C2×D556C2311yescharacteristic
75C2×C22⋊D139D411yescharacteristic
76C2×C4×D139—21no—
77C2×C4×D139—21no—
78C2×C4×D139—21no—
79C2×C4×D139C2311yescharacteristic
80#14555775—22no—
81#14555774—22no—
82#14555774—41no—
83#14555772—22no—
84#14555772—22no—
85#14555772—22no—
86#14555772D414yescomplemented
87#14555768—22no—
88C2×C139⋊C8—22no—
89C2×C139⋊C8C2311yescharacteristic
90C2×C139⋊C8C2311yescharacteristic
91C4⋊Dic139—21no—
92C4⋊Dic139C2311yescharacteristic
93Dic139⋊C4—21no—
94Dic139⋊C4—21no—
95Dic139⋊C4—21no—
96Dic139⋊C4—21no—
97Dic139⋊C4D411yescharacteristic
98C22⋊Dic139—21no—
99C22⋊Dic139D411yescharacteristic
100(C2×D139)⋊C4—21no—
101(C2×D139)⋊C4—21no—
102(C2×D139)⋊C4—21no—
103(C2×D139)⋊C4—21no—
104(C2×D139)⋊C4—21no—
105(C2×D139)⋊C4D411yescharacteristic
106C4×Dic139—21no—
107C4×Dic139C2311yescharacteristic
108C2×Q8×C139—21no—
109C2×Q8×C139—22no—
110C2×Q8×C139—41no—
111C2×Q8×C139C2311yescharacteristic
112C2×Q8×C139C2311yescharacteristic
113C2×Q8×C139C2311yescharacteristic
114C22×C4×C139—21no—
115C22×C4×C139C2311yescharacteristic
116Q16×C139—22no—
117Q16×C139—41no—
118C2×C8×C139C2311yescharacteristic
119C2×C8×C139C2311yescharacteristic
120C4⋊C4×C139—21no—
121C4⋊C4×C139C2311yescharacteristic
122C22⋊C4×C139—21no—
123C22×D139—21no—
124C22×D139—21no—
125C22×D139—42no—
126C22×D139—42no—
127C22×D139—81no—
128C22×D139C2×D411yescharacteristic
129Dic278—21no—
130Dic278—21no—
131Dic278—42no—
132D556—21no—
133D556—21no—
134D556—21no—
135D556—42no—
136D556—42no—
137D556—81no—
138D556C2×D412yes—
139C22⋊D139—22no—
140C2×Dic139—21no—
141C2×Dic139—21no—
142C2×Dic139C2×D411yescharacteristic
143C2×Dic139C2×D411yescharacteristic
144C2×Dic139C2×D411yescharacteristic
145C4×D139—21no—
146C4×D139—21no—
147C4×D139—42no—
148C4×D139—42no—
149C4×D139—81no—
150C139⋊C8—21no—
151C139⋊C8C2×D412yes—
152C23×C139C2×D411yescharacteristic
153Q8×C139—21no—
154Q8×C139—21no—
155Q8×C139—21no—
156Q8×C139—21no—
157Q8×C139—21no—
158Q8×C139—42no—
159Q8×C139C2×D412yes—
160C2×C4×C139—21no—
161C2×C4×C139—21no—
162C2×C4×C139—21no—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—21no—
166C2×C4×C139—42no—
167C2×C4×C139C2×D411yescharacteristic
168C2×C4×C139C2411yescharacteristic
169C8×C139—21no—
170C8×C139—21no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139#13712yescomplemented
174C22×C139C22×D411yescharacteristic
175C2×D139—21no—
176C2×D139—22no—
177C2×D139—21no—
178C2×D139—21no—
179C2×D139—41no—
180C2×D139—41no—
181C2×D139—41no—
182C2×D139—41no—
183C2×D139—41no—
184C2×D139—84no—
185C4×C139—21no—
186C4×C139—22no—
187C4×C139—41no—
188C4×C139—41no—
189C4×C139—41no—
190C4×C139C22×D411yescharacteristic
191C4×C139H(5,𝔽2)11yescharacteristic
192Dic139—21no—
193Dic139—21no—
194Dic139—21no—
195Dic139—41no—
196Dic139—41no—
197C2×C139—22no—
198C2×C139D4211yescharacteristic
199C2×C139C2×#13711yescharacteristic
200C2×C139#57711yescharacteristic
201D139—41no—
202D139—42no—
203D139—81no—
204C139#326611yescharacteristic, complemented, Sylow
205#3266—1391nomaximal, Sylow
206C2×#137—1391no—
207C22×SD16—1391no—
208D4×Q8—1391no—
209#546—1391no—
210#497—1391no—
211#468—1391no—
212#467—1391no—
213#464—1391no—
214#461—1391no—
215#452—1391no—
216#451D13911yescharacteristic, complemented
217#450—1391no—
218#448—1391no—
219#440—1391no—
220#435—1391no—
221C2×#41—1391no—
222C22×Q8—1391no—
223C22×Q8C2×D13911yescharacteristic
224C22×D4—1391no—
225#137—2784no—
226C2×Q16—1391no—
227C2×Q16C2×D13911yescharacteristic, complemented
228C2×Q16C2×D13911yescharacteristic, complemented
229C2×SD16—2784no—
230C2×SD16—1391no—
231C2×SD16—1391no—
232C2×SD16—1391no—
233C2×SD16—1391no—
234C2×SD16—1391no—
235C2×SD16—1391no—
236C2×M16—1391no—
237C22×C8—1391no—
238C4⋊Q8—2781no—
239C4⋊Q8—1391no—
240#124—1391no—
241#123—2781no—
242C22⋊Q8—2781no—
243C22⋊Q8—2781no—
244C22⋊Q8—1391no—
245C22⋊Q8—1391no—
246C22⋊Q8C2×D13911yescharacteristic
247#121—2781no—
248#121—1391no—
249#120—2781no—
250C4×Q8—1391no—
251C4×D4—2781no—
252C4×D4—1391no—
253C4×D4—1391no—
254C2×C22⋊C4—2781no—
255#107—1391no—
256C4⋊C8—1391no—
257#103—1391no—
258#103—1391no—
259#103C2×D13911yescharacteristic, complemented
260#103C2×D13911yescharacteristic, complemented
261#102—1391no—
262#102—1391no—
263C22⋊C8—1391no—
264C22⋊C8C2×D13911yescharacteristic
265#97—1391no—
266C24—2781no—
267#41—2782no—
268#41—5561no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2781no—
273C2×Q8—2782no—
274C2×Q8—5561no—
275C2×Q8—1391no—
276C2×Q8C22×D13911yescharacteristic
277C2×Q8C22×D13911yescharacteristic
278C2×Q8C22×D13911yescharacteristic
279C2×D4—2782no—
280C2×D4—2781no—
281C2×D4—2781no—
282C2×D4—2781no—
283C2×D4—5561no—
284C2×D4—1391no—
285C2×D4—1391no—
286C2×D4—1391no—
287C22×C4—21no—
288C22×C4—2781no—
289C22×C4—2781no—
290C22×C4—2781no—
291C22×C4—1391no—
292C22×C4C22×D13911yescharacteristic
293Q16—22no—
294Q16—41no—
295Q16—2782no—
296SD16—2782no—
297SD16—2782no—
298SD16—2782no—
299SD16—2782no—
300SD16—5561no—
301SD16—1394no—
302M16—2782no—
303C2×C8—2782no—
304C2×C8—1391no—
305C2×C8—1391no—
306C2×C8C22×D13911yescharacteristic
307C2×C8C22×D13911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—2781no—
310C4⋊C4—2781no—
311C4⋊C4—2781no—
312C4⋊C4—2781no—
313C4⋊C4—2781no—
314C4⋊C4—1391no—
315C4⋊C4—1391no—
316C4⋊C4C22×D13911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—2781no—
319C22⋊C4—2781no—
320C22⋊C4—2781no—
321C22⋊C4—2781no—
322C22⋊C4—2781no—
323C22⋊C4—2781no—
324C22⋊C4—1391no—
325C22⋊C4—1391no—
326C42—2781no—
327C42—1391no—
328C23—2781no—
329C23—2781no—
330C23—5562no—
331C23—5562no—
332C23—11121no—
333C23—1391no—
334C23D4×D13911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—2781no—
342Q8—2781no—
343Q8—5562no—
344Q8D4×D13912yes—
345D4—2782no—
346D4—2781no—
347D4—2781no—
348D4—2781no—
349D4—5562no—
350D4—5562no—
351D4—11121no—
352D4—1392no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—2781no—
361C2×C4—2781no—
362C2×C4—2781no—
363C2×C4—2781no—
364C2×C4—5562no—
365C2×C4—5562no—
366C2×C4—11121no—
367C2×C4—1391no—
368C2×C4—1391no—
369C2×C4—1391no—
370C2×C4D4×D13911yescharacteristic
371C2×C4C23×D13911yescharacteristic
372C8—21no—
373C8—21no—
374C8—2781no—
375C8—1392no—
376C22—21no—
377C22—21no—
378C22—2781no—
379C22—2781no—
380C22—2782no—
381C22—2781no—
382C22—5561no—
383C22—5561no—
384C22—5561no—
385C22—5561no—
386C22—5561no—
387C22—11124no—
388C22#1798487412yescomplemented
389C22C2×D4×D13911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—2781no—
396C4—2781no—
397C4—2781no—
398C4—5561no—
399C4—5561no—
400C4C2×D4×D13911yescharacteristic
401C4#1798488711yescharacteristic
402C2—22no—
403C2—5561no—
404C2—5562no—
405C2—11121no—
406C2#2258158511yescharacteristic
407C2C2×#1798487411yescharacteristic
408C2#2258176211yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#451×C139C2
socleC22×C139C22×D4
prime radical#22581594C2
hypercenter#451D139
hypocenterC139#3266
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#17984874C2semidirect
2. C22×#14555772C2semidirect
3. Q8×C22⋊D139C2semidirect
5. #22581346C2semidirect
6. #22581202C2semidirect
7. #22581192C2semidirect
8. #22581177C2semidirect
9. #22581157C2semidirect
10. #22581114C2semidirect
11. #22581106C2semidirect
12. #22581093C2semidirect
13. #22581056C2semidirect
14. #22581021C2semidirect
15. #451×C139C2semidirect
17. C2×Q8×D139C22semidirect
20. C2×#14555775C22semidirect
28. C2×#14555768C22semidirect
31. #17984840C22semidirect
37. #17984818C22semidirect
41. Q8×Dic139C22semidirect
46. #17984775C22semidirect
47. Dic139⋊C8C22semidirect
48. #17984766C22semidirect
49. #17984765C22semidirect
52. (C2×D139)⋊C8C22semidirect
53. #17984752C22semidirect
55. C2×Q16×C139C22semidirect
56. C2×Q16×C139C22semidirect
58. #103×C139C22semidirect
59. #103×C139C22semidirect
86. #14555772D4semidirect
173. C22×C139#137semidirect
204. C139#3266semidirect
216. #451D139semidirect
227. C2×Q16C2×D139semidirect
228. C2×Q16C2×D139semidirect
259. #103C2×D139semidirect
260. #103C2×D139semidirect
388. C22#17984874semidirect

Maximal subgroups

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

subgroupindex
C2×#179848742
C22×#145557722
Q8×C22⋊D1392
#225815942
#225813462
#225812022
#225811922
#225811772
#225811572
#225811142
#225811062
#225810932
#225810562
#225810212
#451×C1392
#3266139