Finite Group Databasebeta

← #31817918

Subgroups — #31817918

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×#17984871C211yesmaximal, characteristic, complemented
2C22×#14555773C211yesmaximal, characteristic, complemented
3#22581616C211yesmaximal, characteristic, complemented
4#22581597C211yesmaximal, characteristic
5#22581344C211yesmaximal, characteristic, complemented
6#22581198C211yesmaximal, characteristic, complemented
7#22581192C211yesmaximal, characteristic, complemented
8#22581174C211yesmaximal, characteristic, complemented
9#22581156C211yesmaximal, characteristic, complemented
10#22581116C211yesmaximal, characteristic, complemented
11#22581111C211yesmaximal, characteristic, complemented
12#22581090C211yesmaximal, characteristic, complemented
13#22581050C211yesmaximal, characteristic, complemented
14#22581021C211yesmaximal, characteristic, complemented
15#450×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C22×Dic278C2211yescharacteristic
18C2×Q8×D139C2211yescharacteristic, complemented
19#17984871—24no—
20C2×Dic556C2211yescharacteristic, complemented
21C2×Dic556C2211yescharacteristic, complemented
22C2×#14555775C2211yescharacteristic, complemented
23C2×#14555773—24no—
24C2×#14555773C2211yescharacteristic
25C2×#14555773C2211yescharacteristic
26C2×#14555773C2211yescharacteristic
27C2×#14555773C2211yescharacteristic
28C2×#14555768C2211yescharacteristic, complemented
29C22×C139⋊C8C2211yescharacteristic
30#17984841—21no—
31#17984840C2211yescharacteristic, complemented
32#17984829C2211yescharacteristic
33#17984823—21no—
34#17984822C2211yescharacteristic, complemented
35#17984821C2211yescharacteristic
36#17984820—21no—
37#17984819—21no—
38#17984814—21no—
39#17984813C2211yescharacteristic
40#17984811—21no—
41#17984807C2211yescharacteristic, complemented
42D4×Dic139C2211yescharacteristic
43C4×C22⋊D139C2211yescharacteristic
44(C22⋊D139)⋊C4—21no—
45C2×C22⋊Dic139—21no—
46#17984775C2211yescharacteristic, complemented
47Dic139⋊C8C2211yescharacteristic, complemented
48#17984767C2211yescharacteristic, complemented
49#17984767C2211yescharacteristic, complemented
50#17984766C2211yescharacteristic, complemented
51#17984765C2211yescharacteristic, complemented
52(C2×D139)⋊C8C2211yescharacteristic, complemented
53#17984752C2211yescharacteristic, complemented
54C22×D4×C139C2211yescharacteristic
55C2×SD16×C139C2211yescharacteristic
56C2×SD16×C139C2211yescharacteristic
57C22⋊Q8×C139C2211yescharacteristic
58#102×C139C2211yescharacteristic
59#102×C139C2211yescharacteristic
60C22⋊C8×C139C2211yescharacteristic
61#14555784—22no—
62#14555784—41no—
63C2×Dic278—21no—
64C2×Dic278—22no—
65C2×Dic278—21no—
66C2×Dic278—41no—
67C2×Dic278C2311yescharacteristic
68C2×Dic278C2311yescharacteristic
69C2×Dic278C2311yescharacteristic
70Q8×D139—22no—
71Q8×D139—41no—
72C2×C22⋊D139—21no—
73C2×C22⋊D139—21no—
74C2×C22⋊D139D411yescharacteristic
75C22×Dic139—21no—
76C22×Dic139—21no—
77C22×Dic139—21no—
78C2×C4×D139—21no—
79C2×C4×D139C2311yescharacteristic
80Dic556—22no—
81Dic556—41no—
82#14555775—22no—
83#14555773—22no—
84#14555773—22no—
85#14555773—22no—
86#14555773D414yescomplemented
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⋊Dic139—21no—
100C22⋊Dic139—21no—
101C22⋊Dic139—21no—
102C22⋊Dic139—21no—
103C22⋊Dic139D411yescharacteristic
104(C2×D139)⋊C4—21no—
105(C2×D139)⋊C4D411yescharacteristic
106C4×Dic139—21no—
107C4×Dic139C2311yescharacteristic
108C24×C139—21no—
109C2×Q8×C139C2311yescharacteristic
110C2×D4×C139—22no—
111C2×D4×C139—21no—
112C2×D4×C139—41no—
113C2×D4×C139C2311yescharacteristic
114C2×D4×C139C2311yescharacteristic
115C22×C4×C139C2311yescharacteristic
116SD16×C139—22no—
117SD16×C139—41no—
118C2×C8×C139C2311yescharacteristic
119C2×C8×C139C2311yescharacteristic
120C4⋊C4×C139—21no—
121C4⋊C4×C139C2311yescharacteristic
122C22⋊C4×C139—21no—
123C22×D139C2×D411yescharacteristic
124Dic278—21no—
125Dic278—21no—
126Dic278—21no—
127Dic278—21no—
128Dic278—21no—
129Dic278—42no—
130Dic278—42no—
131Dic278C2×D412yes—
132C22⋊D139—22no—
133C22⋊D139—42no—
134C22⋊D139—81no—
135C2×Dic139—21no—
136C2×Dic139—21no—
137C2×Dic139—21no—
138C2×Dic139—21no—
139C2×Dic139—42no—
140C2×Dic139—42no—
141C2×Dic139—81no—
142C2×Dic139C2×D411yescharacteristic
143C2×Dic139C2×D411yescharacteristic
144C2×Dic139C2×D411yescharacteristic
145C4×D139—21no—
146C4×D139—21no—
147C4×D139—42no—
148C139⋊C8—21no—
149C139⋊C8C2×D412yes—
150C23×C139—21no—
151C23×C139—21no—
152C23×C139—42no—
153C23×C139—42no—
154C23×C139—81no—
155C23×C139C2×D411yescharacteristic
156Q8×C139—21no—
157Q8×C139—21no—
158D4×C139—21no—
159D4×C139—21no—
160D4×C139—21no—
161D4×C139—42no—
162D4×C139C2×D412yes—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—21no—
166C2×C4×C139—21no—
167C2×C4×C139C2×D411yescharacteristic
168C2×C4×C139C2411yescharacteristic
169C8×C139—21no—
170C8×C139—21no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—22no—
174C22×C139—41no—
175C22×C139—41no—
176C22×C139—41no—
177C22×C139—41no—
178C22×C139—41no—
179C22×C139—84no—
180C22×C139#13712yescomplemented
181C22×C139C22×D411yescharacteristic
182C2×D139—21no—
183C2×D139—21no—
184C2×D139—21no—
185C4×C139—21no—
186C4×C139—41no—
187C4×C139—41no—
188C4×C139C22×D411yescharacteristic
189C4×C139H(5,𝔽2)11yescharacteristic
190Dic139—21no—
191Dic139—22no—
192Dic139—21no—
193Dic139—21no—
194Dic139—41no—
195Dic139—41no—
196Dic139—41no—
197C2×C139—22no—
198C2×C139—42no—
199C2×C139—81no—
200C2×C139D4211yescharacteristic
201C2×C139C2×#13711yescharacteristic
202C2×C139#57711yescharacteristic
203D139—41no—
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#451—1391no—
217#450D13911yescharacteristic, complemented
218#448—1391no—
219#440—1391no—
220#435—1391no—
221C2×#41—1391no—
222C22×Q8—1391no—
223C22×Q8—1391no—
224C22×D4C2×D13911yescharacteristic
225#137—2784no—
226C2×Q16—1391no—
227C2×Q16—1391no—
228C2×Q16—1391no—
229C2×SD16—2784no—
230C2×SD16—1391no—
231C2×SD16—1391no—
232C2×SD16—1391no—
233C2×SD16—1391no—
234C2×SD16C2×D13911yescharacteristic
235C2×SD16C2×D13911yescharacteristic
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#103—1391no—
260#103—1391no—
261#102C2×D13911yescharacteristic
262#102C2×D13911yescharacteristic
263C22⋊C8—1391no—
264C22⋊C8C2×D13911yescharacteristic
265#97—1391no—
266C24—21no—
267#41—2782no—
268#41—5561no—
269C2×Q8—2781no—
270C2×Q8—2782no—
271C2×Q8—2781no—
272C2×Q8—2782no—
273C2×Q8—5561no—
274C2×Q8—5561no—
275C2×Q8—1391no—
276C2×Q8—1391no—
277C2×Q8—1391no—
278C2×Q8C22×D13911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—2781no—
283C2×D4—2781no—
284C2×D4—1391no—
285C2×D4C22×D13911yescharacteristic
286C2×D4C22×D13911yescharacteristic
287C22×C4—2781no—
288C22×C4—2781no—
289C22×C4—2781no—
290C22×C4—2781no—
291C22×C4—1391no—
292C22×C4C22×D13911yescharacteristic
293Q16—2782no—
294Q16—2782no—
295Q16—5561no—
296SD16—22no—
297SD16—41no—
298SD16—2782no—
299SD16—2782no—
300SD16—2782no—
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—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—1391no—
334C23D4×D13911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—2781no—
338Q8—2781no—
339Q8—2781no—
340Q8—2781no—
341Q8—2781no—
342Q8—5562no—
343Q8—5562no—
344Q8—1392no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—2782no—
350D4—5562no—
351D4—11121no—
352D4D4×D13912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2781no—
358C2×C4—2781no—
359C2×C4—2781no—
360C2×C4—2781no—
361C2×C4—2781no—
362C2×C4—2781no—
363C2×C4—5562no—
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—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—2781no—
386C22—2781no—
387C22—2781no—
388C22#1798487112yescomplemented
389C22C2×D4×D13911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2781no—
394C4—2781no—
395C4—2782no—
396C4—2781no—
397C4—5561no—
398C4—5561no—
399C4—5561no—
400C4C2×D4×D13911yescharacteristic
401C4#1798488711yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—5561no—
406C2#2258158511yescharacteristic
407C2C2×#1798487111yescharacteristic
408C2#2258176311yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#450×C139C2
socleC22×C139C22×D4
prime radical#22581597C2
hypercenter#450D139
hypocenterC139#3266
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#17984871C2semidirect
2. C22×#14555773C2semidirect
3. #22581616C2semidirect
5. #22581344C2semidirect
6. #22581198C2semidirect
7. #22581192C2semidirect
8. #22581174C2semidirect
9. #22581156C2semidirect
10. #22581116C2semidirect
11. #22581111C2semidirect
12. #22581090C2semidirect
13. #22581050C2semidirect
14. #22581021C2semidirect
15. #450×C139C2semidirect
18. C2×Q8×D139C22semidirect
20. C2×Dic556C22semidirect
21. C2×Dic556C22semidirect
22. C2×#14555775C22semidirect
28. C2×#14555768C22semidirect
31. #17984840C22semidirect
34. #17984822C22semidirect
41. #17984807C22semidirect
46. #17984775C22semidirect
47. Dic139⋊C8C22semidirect
48. #17984767C22semidirect
49. #17984767C22semidirect
50. #17984766C22semidirect
51. #17984765C22semidirect
52. (C2×D139)⋊C8C22semidirect
53. #17984752C22semidirect
86. #14555773D4semidirect
180. C22×C139#137semidirect
204. C139#3266semidirect
217. #450D139semidirect
388. C22#17984871semidirect

Maximal subgroups

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

subgroupindex
C2×#179848712
C22×#145557732
#225816162
#225815972
#225813442
#225811982
#225811922
#225811742
#225811562
#225811162
#225811112
#225810902
#225810502
#225810212
#450×C1392
#3266139