Finite Group Databasebeta

← #34056323

Subgroups — #34056323

Order 19072.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011942C211yesmaximal, characteristic, complemented
2C2×#18011936C211yesmaximal, characteristic, complemented
3#23750271C211yesmaximal, characteristic, complemented
4#23750007C211yesmaximal, characteristic, complemented
5#23749881C211yesmaximal, characteristic, complemented
6#23749876C211yesmaximal, characteristic, complemented
7#23749847C211yesmaximal, characteristic, complemented
8#23749837C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749775C211yesmaximal, characteristic, complemented
11#23749768C211yesmaximal, characteristic, complemented
12#23749764C211yesmaximal, characteristic, complemented
13C4×#14558723C211yesmaximal, characteristic, complemented
14#23749703C211yesmaximal, characteristic, complemented
15#548×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic
18#18011942—24no—
19#18011936—24no—
20C2×#14558726C2211yescharacteristic, complemented
21C2×#14558726C2211yescharacteristic, complemented
22C2×#14558724C2211yescharacteristic, complemented
23C2×#14558723C2211yescharacteristic
24C2×#14558723C2211yescharacteristic
25C2×#14558723C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27C2×#14558721C2211yescharacteristic
28C2×#14558721C2211yescharacteristic
29C2×#14558720C2211yescharacteristic
30C2×#14558720C2211yescharacteristic, complemented
31#18011899C2211yescharacteristic
32#18011896—21no—
33#18011890C2211yescharacteristic
34#18011885C2211yescharacteristic
35#18011884—21no—
36#18011879—21no—
37C4×D596C2211yescharacteristic
38C22⋊C4×D149—21no—
39#18011842C2211yescharacteristic, complemented
40C4⋊#11924746C2211yescharacteristic, complemented
41#18011835C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic, complemented
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47C22⋊#11924746C2211yescharacteristic
48C22⋊#11924746C2211yescharacteristic, complemented
49C4×#11924746C2211yescharacteristic, complemented
50C2×#41×C149C2211yescharacteristic
51C22×Q8×C149C2211yescharacteristic, complemented
52#124×C149—21no—
53#124×C149C2211yescharacteristic, complemented
54C22⋊Q8×C149—21no—
55C22⋊Q8×C149C2211yescharacteristic
56#121×C149—21no—
57#121×C149C2211yescharacteristic, complemented
58C4×Q8×C149C2211yescharacteristic, complemented
59C4×D4×C149—21no—
60C4×D4×C149C2211yescharacteristic
61C23×D149—21no—
62#14558736—22no—
63#14558736—41no—
64C2×Dic298C2311yescharacteristic
65C2×D596—22no—
66C2×D596—21no—
67C2×D596—41no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149—21no—
74#14558726—22no—
75#14558726—22no—
76#14558724—41no—
77#14558723—22no—
78#14558723—22no—
79#14558723—41no—
80#14558723D414yescomplemented
81#14558721—22no—
82#14558721—22no—
83#14558720—22no—
84#14558720—22no—
85C2×#11924746C2311yescharacteristic
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C2×#11924746C2311yescharacteristic
89C4⋊Dic149C2311yescharacteristic
90#14558715—21no—
91C22⋊Dic149—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#41×C149—22no—
97#41×C149—41no—
98C2×Q8×C149—21no—
99C2×Q8×C149—22no—
100C2×Q8×C149—41no—
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149—21no—
104C2×D4×C149—21no—
105C2×D4×C149D411yescharacteristic
106C2×D4×C149C2311yescharacteristic
107C22×C4×C149—21no—
108C22×C4×C149—21no—
109C22×C4×C149C2311yescharacteristic
110C22×C4×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149—21no—
113C4⋊C4×C149D411yescharacteristic
114C4⋊C4×C149C2311yescharacteristic
115C22⋊C4×C149—21no—
116C22⋊C4×C149—21no—
117C22⋊C4×C149—21no—
118C22⋊C4×C149—21no—
119C22⋊C4×C149D411yescharacteristic
120C22⋊C4×C149D411yescharacteristic
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128Dic298—21no—
129Dic298—21no—
130D596—21no—
131D596—21no—
132D596—21no—
133D596—42no—
134D596C2×D412yes—
135C22⋊D149—42no—
136C22⋊D149—81no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C4×D149—42no—
140C4×D149—81no—
141#11924746—21no—
142#11924746—21no—
143#11924746—21no—
144#11924746C2×D412yes—
145C23×C149—21no—
146C23×C149C2×D411yescharacteristic
147C23×C149C2×D411yescharacteristic
148Q8×C149—21no—
149Q8×C149—21no—
150Q8×C149—21no—
151Q8×C149—42no—
152Q8×C149C2×D412yes—
153D4×C149—21no—
154D4×C149—21no—
155D4×C149—41no—
156D4×C149—42no—
157D4×C149—42no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—42no—
166C2×C4×C149—42no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2×D411yescharacteristic
170C2×C4×C149C2×D411yescharacteristic
171C2×C4×C149C2411yescharacteristic
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149—21no—
177C22×C149—21no—
178C22×C149—41no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149C22×D411yescharacteristic
182C2×D149—22no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—21no—
190C4×C149—21no—
191C4×C149—22no—
192C4×C149—21no—
193C4×C149—21no—
194C4×C149—41no—
195C4×C149—41no—
196C4×C149C22×D411yescharacteristic
197C4×C149H(5,𝔽2)11yescharacteristic
198Dic149—41no—
199Dic149—41no—
200C2×C149—41no—
201C2×C149—41no—
202C2×C149—81no—
203C2×C149D4211yescharacteristic
204C2×C149#57511yescharacteristic
205C2×C149#57711yescharacteristic
206D149—42no—
207D149—81no—
208C149#327511yescharacteristic, complemented, Sylow
209#3275—1491nomaximal, Sylow
210C2×#137—1491no—
211C2×AGL(1,ℤ/8)—1491no—
212#548D14911yescharacteristic, complemented
213#546—1491no—
214#495—1491no—
215#470—1491no—
216#469—1491no—
217#464—1491no—
218#463—1491no—
219#452—1491no—
220#450—1491no—
221#449—1491no—
222#448—1491no—
223C4×SD16—1491no—
224#436—1491no—
225C2×#41—1491no—
226C2×#41C2×D14911yescharacteristic
227C22×Q8C2×D14911yescharacteristic, complemented
228C22×D4—1491no—
229#137—2984no—
230AGL(1,ℤ/8)—2984no—
231C2×Q16—1491no—
232C2×Q16—1491no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×SD16—1491no—
237C2×SD16—1491no—
238C2×D8—1491no—
239C2×D8—1491no—
240C2×M16—1491no—
241C2×M16—1491no—
242#124—21no—
243#124—1491no—
244#124C2×D14911yescharacteristic, complemented
245#123—2981no—
246C22⋊Q8—21no—
247C22⋊Q8—1491no—
248C22⋊Q8C2×D14911yescharacteristic
249#121—21no—
250#121—2981no—
251#121—1491no—
252#121C2×D14911yescharacteristic, complemented
253#120—2981no—
254C4×Q8C2×D14911yescharacteristic, complemented
255C4×D4—21no—
256C4×D4—1491no—
257C4×D4C2×D14911yescharacteristic
258C2×C22⋊C4—2981no—
259#106—1491no—
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103—1491no—
264#102—1491no—
265#102—1491no—
266#102—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C4×C8—1491no—
270C24—2981no—
271#41—22no—
272#41—41no—
273#41—2982no—
274#41—5961no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—1491no—
279C2×Q8C22×D14911yescharacteristic
280C2×Q8C22×D14911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—2982no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—2981no—
287C2×D4—5961no—
288C2×D4—1491no—
289C2×D4—1491no—
290C2×D4C22⋊D14911yescharacteristic
291C2×D4C22×D14911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4C22×D14911yescharacteristic
297C22×C4C22×D14911yescharacteristic
298Q16—2982no—
299Q16—2982no—
300SD16—2982no—
301SD16—2982no—
302SD16—5961no—
303SD16—5961no—
304SD16—1494no—
305D8—2982no—
306D8—2982no—
307M16—2982no—
308M16—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8—1491no—
312C2×C8—1491no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—2981no—
316C4⋊C4—1491no—
317C4⋊C4C22⋊D14911yescharacteristic
318C4⋊C4C22×D14911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4C22⋊D14911yescharacteristic
329C22⋊C4C22⋊D14911yescharacteristic
330C42—21no—
331C42C22×D14911yescharacteristic
332C23—21no—
333C23—2981no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—11921no—
338C23C2×C22⋊D14911yescharacteristic
339C23C2×C22⋊D14911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—2981no—
345Q8—2981no—
346Q8D4×D14912yes—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—2981no—
353D4—2981no—
354D4—2981no—
355D4—5962no—
356D4—5962no—
357D4—1492no—
358D4—11921no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—5962no—
371C2×C4—11921no—
372C2×C4C2×C22⋊D14911yescharacteristic
373C2×C4C2×C22⋊D14911yescharacteristic
374C2×C4C2×C22⋊D14911yescharacteristic
375C2×C4C2×C22⋊D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—2981no—
378C8—2981no—
379C8—2981no—
380C8—1492no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—2982no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C22×C22⋊D14911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—5961no—
406C4—5961no—
407C4C2×D4×D14911yescharacteristic
408C4#1801195611yescharacteristic
409C2—41no—
410C2—41no—
411C2—81no—
412C2—5962no—
413C2—11921no—
414C2D4×C22⋊D14911yescharacteristic
415C2#2375042311yescharacteristic
416C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#548×C149C2
socleC22×C149C22×D4
hypercenter#548D149
hypocenterC149#3275
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
2. C2×#18011936C2semidirect
3. #23750271C2semidirect
4. #23750007C2semidirect
5. #23749881C2semidirect
6. #23749876C2semidirect
7. #23749847C2semidirect
8. #23749837C2semidirect
9. #23749787C2semidirect
10. #23749775C2semidirect
11. #23749768C2semidirect
12. #23749764C2semidirect
13. C4×#14558723C2semidirect
14. #23749703C2semidirect
15. #548×C149C2semidirect
20. C2×#14558726C22semidirect
21. C2×#14558726C22semidirect
22. C2×#14558724C22semidirect
30. C2×#14558720C22semidirect
39. #18011842C22semidirect
40. C4⋊#11924746C22semidirect
41. #18011835C22semidirect
42. #18011835C22semidirect
43. #18011834C22semidirect
44. #18011832C22semidirect
48. C22⋊#11924746C22semidirect
49. C4×#11924746C22semidirect
51. C22×Q8×C149C22semidirect
53. #124×C149C22semidirect
57. #121×C149C22semidirect
58. C4×Q8×C149C22semidirect
80. #14558723D4semidirect
208. C149#3275semidirect
212. #548D149semidirect
227. C22×Q8C2×D149semidirect
244. #124C2×D149semidirect
252. #121C2×D149semidirect
254. C4×Q8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C2×#180119362
#237502712
#237500072
#237498812
#237498762
#237498472
#237498372
#237497872
#237497752
#237497682
#237497642
C4×#145587232
#237497032
#548×C1492
#3275149