Finite Group Databasebeta

← #34056218

Subgroups — #34056218

Order 19072.

500 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×#18011935C211yesmaximal, characteristic, complemented
2C2×#18011930C211yesmaximal, characteristic, complemented
3#23750279C211yesmaximal, characteristic, complemented
4#23750270C211yesmaximal, characteristic, complemented
5#23750019C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic, complemented
7#23749855C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749830C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749788C211yesmaximal, characteristic, complemented
12#23749777C211yesmaximal, characteristic, complemented
13#23749771C211yesmaximal, characteristic, complemented
14#23749698C211yesmaximal, characteristic, complemented
15#442×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×#14558735C2211yescharacteristic, complemented
19C2×D4×D149C2211yescharacteristic
20#18011935—24no—
21#18011930—24no—
22C2×Dic596C2211yescharacteristic, complemented
23C2×Dic596C2211yescharacteristic, complemented
24C2×#14558725C2211yescharacteristic
25C2×#14558725C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558724C2211yescharacteristic
28C2×#14558724C2211yescharacteristic, complemented
29C2×#14558721C2211yescharacteristic
30C2×#14558719C2211yescharacteristic
31C2×C8×D149C2211yescharacteristic, complemented
32#18011911C2211yescharacteristic, complemented
33#18011899C2211yescharacteristic
34#18011895—21no—
35#18011895—21no—
36#18011895—21no—
37#18011891C2211yescharacteristic
38#18011891C2211yescharacteristic
39#18011891C2211yescharacteristic, complemented
40#18011886C2211yescharacteristic
41#18011885—21no—
42#18011885—21no—
43#18011881—21no—
44C4×D596C2211yescharacteristic
45C2×C4⋊Dic149—21no—
46C2×#14558713—21no—
47C4⋊#11924746C2211yescharacteristic, complemented
48#18011834C2211yescharacteristic, complemented
49#18011834C2211yescharacteristic, complemented
50#18011834C2211yescharacteristic, complemented
51#18011831C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011823C2211yescharacteristic, complemented
54C2×D8×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic, complemented
57#106×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic
59#102×C149C2211yescharacteristic, complemented
60#97×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558735—22no—
63#14558735—22no—
64#14558735—22no—
65#14558735—41no—
66#14558735—41no—
67#14558735—41no—
68C2×Dic298C2311yescharacteristic
69C2×Dic298C2311yescharacteristic
70C2×Dic298C2311yescharacteristic
71C2×D596—21no—
72C2×D596D411yescharacteristic
73C2×D596C2311yescharacteristic
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78D4×D149—22no—
79D4×D149—41no—
80C22×Dic149—21no—
81C22×Dic149—21no—
82C22×Dic149—21no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85Dic596—22no—
86Dic596—41no—
87#14558725—22no—
88#14558725—41no—
89#14558724—22no—
90#14558724—22no—
91#14558724—22no—
92#14558721—22no—
93#14558719—22no—
94C2×#11924746C2311yescharacteristic
95C2×#11924746C2311yescharacteristic
96C8×D149—22no—
97C4⋊Dic149—21no—
98C4⋊Dic149—21no—
99C4⋊Dic149—21no—
100C4⋊Dic149—21no—
101C4⋊Dic149—21no—
102C4⋊Dic149D411yescharacteristic
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713—21no—
109#14558713D411yescharacteristic
110#14558713D411yescharacteristic
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114C22×C4×C149—21no—
115D8×C149D414yescomplemented
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149C2311yescharacteristic
119C4⋊C4×C149C2311yescharacteristic
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—42no—
125C22×D149—42no—
126C22×D149—81no—
127C22×D149C2×D411yescharacteristic
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—21no—
133Dic298—21no—
134Dic298—21no—
135D596—21no—
136D596—21no—
137D596—41no—
138D596—81no—
139C22⋊D149—42no—
140C22⋊D149—42no—
141C22⋊D149—42no—
142C22⋊D149—42no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—21no—
146C2×Dic149—42no—
147C2×Dic149—42no—
148C2×Dic149—42no—
149C2×Dic149C2×D411yescharacteristic
150C2×Dic149C2×D411yescharacteristic
151C4×D149—21no—
152C4×D149—21no—
153C4×D149—21no—
154C4×D149—21no—
155#11924746—21no—
156#11924746—21no—
157C23×C149—21no—
158C23×C149—21no—
159D4×C149—21no—
160D4×C149—21no—
161D4×C149C2×D412yes—
162D4×C149C2×D412yes—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—42no—
166C2×C4×C149—81no—
167C2×C4×C149C2×D411yescharacteristic
168C2×C4×C149C2×D411yescharacteristic
169C2×C4×C149C2411yescharacteristic
170C8×C149—21no—
171C8×C149C2×D412yes—
172C22×C149—22no—
173C22×C149—22no—
174C22×C149—41no—
175C22×C149—41no—
176C22×C149—41no—
177C22×C149—41no—
178C22×C149C22×D411yescharacteristic
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C2×D149—21no—
183C2×D149—21no—
184C2×D149—21no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—84no—
189C4×C149—21no—
190C4×C149—21no—
191C4×C149—41no—
192C4×C149—41no—
193C4×C149C22×D411yescharacteristic
194C4×C149H(5,𝔽2)11yescharacteristic
195Dic149—21no—
196Dic149—21no—
197Dic149—41no—
198Dic149—41no—
199Dic149—41no—
200C2×C149—42no—
201C2×C149—42no—
202C2×C149D4211yescharacteristic
203C2×C149#57511yescharacteristic
204C2×C149#57711yescharacteristic
205D149—41no—
206D149—41no—
207D149—81no—
208C149#326711yescharacteristic, complemented, Sylow
209#3267—1491nomaximal, Sylow
210C2×AGL(1,ℤ/8)—1491no—
211C2×#135—1491no—
212#547—1491no—
213#546—1491no—
214#497—1491no—
215#470—1491no—
216#465—1491no—
217#463—1491no—
218#461—1491no—
219#452—1491no—
220#452—1491no—
221#450—1491no—
222#449—1491no—
223#442D14911yescharacteristic, complemented
224#435—1491no—
225C2×#41—1491no—
226C2×#41—1491no—
227C2×#41—1491no—
228C22×D4—1491no—
229AGL(1,ℤ/8)—2984no—
230#135—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×D8C2×D14911yescharacteristic
240C2×M16—1491no—
241C22×C8—1491no—
242C4⋊Q8—1491no—
243#124—1491no—
244#123—2981no—
245#123—2981no—
246#123—2981no—
247C22⋊Q8—1491no—
248C22⋊Q8—1491no—
249C22⋊Q8—1491no—
250#121—2981no—
251#121—2981no—
252#121—1491no—
253#120—2981no—
254C4×D4—1491no—
255C4×D4C2×D14911yescharacteristic
256C4×D4C2×D14911yescharacteristic, complemented
257C2×C4⋊C4—2981no—
258C2×C22⋊C4—2981no—
259#106C2×D14911yescharacteristic, complemented
260C4⋊C8—1491no—
261#103—1491no—
262#103—1491no—
263#103—1491no—
264#102—1491no—
265#102C2×D14911yescharacteristic
266#102C2×D14911yescharacteristic, complemented
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269#97C2×D14911yescharacteristic, complemented
270C24—2981no—
271#41—2982no—
272#41—2982no—
273#41—2982no—
274#41—5961no—
275#41—5961no—
276#41—5961no—
277C2×Q8—1491no—
278C2×Q8—1491no—
279C2×Q8—1491no—
280C2×D4—2981no—
281C2×D4—2982no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—2981no—
286C2×D4—5961no—
287C2×D4—1491no—
288C2×D4—1491no—
289C2×D4C22×D14911yescharacteristic
290C2×D4C22×D14911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—2981no—
294C22×C4—2981no—
295C22×C4—2981no—
296C22×C4—1491no—
297C22×C4—1491no—
298Q16—2982no—
299Q16—5961no—
300SD16—2982no—
301SD16—2982no—
302SD16—2982no—
303SD16—2982no—
304SD16—5961no—
305D8—2982no—
306D8D59614yescomplemented
307M16—2982no—
308C2×C8—2982no—
309C2×C8—1491no—
310C2×C8—1491no—
311C2×C8C22×D14911yescharacteristic
312C2×C8C22×D14911yescharacteristic
313C4⋊C4—2981no—
314C4⋊C4—2981no—
315C4⋊C4—2981no—
316C4⋊C4—2981no—
317C4⋊C4—2981no—
318C4⋊C4—1491no—
319C4⋊C4C22×D14911yescharacteristic
320C4⋊C4C22×D14911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—2981no—
324C22⋊C4—2981no—
325C22⋊C4—2981no—
326C22⋊C4—2981no—
327C22⋊C4—2981no—
328C22⋊C4—2981no—
329C22⋊C4—1491no—
330C22⋊C4—1491no—
331C42C22×D14911yescharacteristic
332C23—21no—
333C23—21no—
334C23—2981no—
335C23—5962no—
336C23—5962no—
337C23—1491no—
338C23—1491no—
339C23—11921no—
340Q8—2981no—
341Q8—2981no—
342Q8—2981no—
343Q8—2981no—
344Q8—2981no—
345Q8—2981no—
346D4—21no—
347D4—21no—
348D4—2981no—
349D4—2981no—
350D4—5961no—
351D4—5962no—
352D4—5962no—
353D4—5962no—
354D4—5962no—
355D4—11921no—
356D4C2×D59612yes—
357D4C2×D59612yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—2981no—
363C2×C4—2981no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—5962no—
370C2×C4—5962no—
371C2×C4—5962no—
372C2×C4—1491no—
373C2×C4—1491no—
374C2×C4D4×D14911yescharacteristic
375C2×C4D4×D14911yescharacteristic
376C2×C4C23×D14911yescharacteristic
377C8—21no—
378C8—2981no—
379C8—2981no—
380C8C2×D59612yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—2981no—
388C22—2981no—
389C22—2981no—
390C22—2981no—
391C22—2981no—
392C22—2981no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—11924no—
397C22C2×D4×D14911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2981no—
403C4—2981no—
404C4—5961no—
405C4—5961no—
406C4—5961no—
407C4C22×D59611yescharacteristic
408C4#1801195711yescharacteristic
409C2—42no—
410C2—42no—
411C2—5961no—
412C2—5961no—
413C2—11921no—
414C2D4×D59611yescharacteristic
415C2#2375042111yescharacteristic
416C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
hypercenter#442D149
hypocenterC149#3267
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#18011935C2semidirect
2. C2×#18011930C2semidirect
3. #23750279C2semidirect
4. #23750270C2semidirect
5. #23750019C2semidirect
6. #23749884C2semidirect
7. #23749855C2semidirect
8. #23749840C2semidirect
9. #23749830C2semidirect
10. #23749788C2semidirect
11. #23749788C2semidirect
12. #23749777C2semidirect
13. #23749771C2semidirect
14. #23749698C2semidirect
15. #442×C149C2semidirect
18. C2×#14558735C22semidirect
22. C2×Dic596C22semidirect
23. C2×Dic596C22semidirect
28. C2×#14558724C22semidirect
31. C2×C8×D149C22semidirect
32. #18011911C22semidirect
39. #18011891C22semidirect
47. C4⋊#11924746C22semidirect
48. #18011834C22semidirect
49. #18011834C22semidirect
50. #18011834C22semidirect
53. #18011823C22semidirect
56. C4×D4×C149C22semidirect
57. #106×C149C22semidirect
59. #102×C149C22semidirect
60. #97×C149C22semidirect
115. D8×C149D4semidirect
208. C149#3267semidirect
223. #442D149semidirect
256. C4×D4C2×D149semidirect
259. #106C2×D149semidirect
266. #102C2×D149semidirect
269. #97C2×D149semidirect
306. D8D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119352
C2×#180119302
#237502792
#237502702
#237500192
#237498842
#237498552
#237498402
#237498302
#237497882
#237497772
#237497712
#237496982
#442×C1492
#3267149