Finite Group Databasebeta

← #34056206

Subgroups — #34056206

Order 19072.

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×#18011944C211yesmaximal, characteristic, complemented
2C22×#14558725C211yesmaximal, characteristic, complemented
3D4×Dic298C211yesmaximal, characteristic, complemented
4#23750271C211yesmaximal, characteristic
5#23750019C211yesmaximal, characteristic, complemented
6#23749871C211yesmaximal, characteristic, complemented
7#23749866C211yesmaximal, characteristic, complemented
8#23749848C211yesmaximal, characteristic, complemented
9#23749831C211yesmaximal, characteristic, complemented
10#23749789C211yesmaximal, characteristic, complemented
11#23749783C211yesmaximal, characteristic, complemented
12#23749778C211yesmaximal, characteristic, complemented
13#23749766C211yesmaximal, characteristic, complemented
14#23749727C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C22×Dic298C2211yescharacteristic, complemented
19C22×D596C2211yescharacteristic
20#18011944—24no—
21C2×Dic596C2211yescharacteristic, complemented
22C2×Dic596C2211yescharacteristic, complemented
23C2×Dic596C2211yescharacteristic, complemented
24C2×#14558725—24no—
25C2×#14558725C2211yescharacteristic
26C2×#14558725C2211yescharacteristic
27C2×#14558725C2211yescharacteristic
28C2×#14558725C2211yescharacteristic
29C2×#14558725C2211yescharacteristic
30C2×#14558725C2211yescharacteristic
31#18011911C2211yescharacteristic, complemented
32#18011910—21no—
33#18011899C2211yescharacteristic
34#18011896—21no—
35#18011890C2211yescharacteristic
36#18011890C2211yescharacteristic
37#18011890C2211yescharacteristic, complemented
38#18011888—21no—
39#18011888—21no—
40#18011885C2211yescharacteristic
41#18011884—21no—
42#18011879—21no—
43C4×Dic298C2211yescharacteristic, complemented
44C4×D596C2211yescharacteristic
45D4×Dic149—21no—
46C22⋊C4×D149—21no—
47#18011845C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011836C2211yescharacteristic, complemented
50#18011836C2211yescharacteristic, complemented
51#18011836C2211yescharacteristic, complemented
52#18011833C2211yescharacteristic
53#18011833C2211yescharacteristic
54C2×M16×C149C2211yescharacteristic, complemented
55C22×C8×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C4⋊C8×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C22⋊C8×C149C2211yescharacteristic, complemented
60#97×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558736—22no—
63#14558736—41no—
64C2×Dic298—22no—
65C2×Dic298—22no—
66C2×Dic298—21no—
67C2×Dic298—21no—
68C2×Dic298—41no—
69C2×Dic298—41no—
70C2×Dic298C2311yescharacteristic
71C2×Dic298C2311yescharacteristic
72C2×Dic298C2311yescharacteristic
73C2×Dic298C2311yescharacteristic
74C2×D596—22no—
75C2×D596—21no—
76C2×D596—41no—
77C2×D596C2311yescharacteristic
78C2×D596C2311yescharacteristic
79C2×C22⋊D149—21no—
80C2×C22⋊D149—21no—
81C22×Dic149—21no—
82C22×Dic149—21no—
83C2×C4×D149—21no—
84C2×C4×D149—21no—
85Dic596—22no—
86Dic596—22no—
87Dic596—41no—
88#14558725—22no—
89#14558725—22no—
90#14558725—22no—
91#14558725—22no—
92#14558725—41no—
93#14558725D414yescomplemented
94C4⋊Dic149—21no—
95C4⋊Dic149—21no—
96C4⋊Dic149C2311yescharacteristic
97C4⋊Dic149C2311yescharacteristic
98#14558715—21no—
99#14558715—21no—
100#14558715—21no—
101#14558715—21no—
102C22⋊Dic149—21no—
103C22⋊Dic149—21no—
104C22⋊Dic149—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713—21no—
109C4×Dic149—21no—
110C2×D4×C149D411yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113M16×C149—22no—
114C2×C8×C149—22no—
115C2×C8×C149C2311yescharacteristic
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C2×C8×C149C2311yescharacteristic
119C4⋊C4×C149D411yescharacteristic
120C22⋊C4×C149D411yescharacteristic
121C22⋊C4×C149D411yescharacteristic
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128Dic298—21no—
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—21no—
133Dic298—21no—
134Dic298—21no—
135Dic298—42no—
136Dic298—42no—
137Dic298C2×D412yes—
138D596—21no—
139D596—21no—
140D596—21no—
141D596—42no—
142D596C2×D412yes—
143C22⋊D149—42no—
144C22⋊D149—81no—
145C2×Dic149—21no—
146C2×Dic149—21no—
147C2×Dic149—21no—
148C2×Dic149—21no—
149C2×Dic149—21no—
150C2×Dic149—21no—
151C2×Dic149—42no—
152C2×Dic149—42no—
153C4×D149—42no—
154C4×D149—81no—
155C23×C149C2×D411yescharacteristic
156C23×C149C2×D411yescharacteristic
157D4×C149—22no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149C2×D411yescharacteristic
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2411yescharacteristic
167C8×C149—21no—
168C8×C149—21no—
169C8×C149—21no—
170C8×C149C2×D412yes—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149—21no—
174C22×C149—21no—
175C22×C149—21no—
176C22×C149#13712yescomplemented
177C22×C149C22×D411yescharacteristic
178C2×D149—22no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—84no—
185C4×C149—21no—
186C4×C149—21no—
187C4×C149—21no—
188C4×C149—21no—
189C4×C149C22×D411yescharacteristic
190C4×C149H(5,𝔽2)11yescharacteristic
191Dic149—22no—
192Dic149—41no—
193Dic149—41no—
194Dic149—41no—
195Dic149—41no—
196Dic149—41no—
197C2×C149—22no—
198C2×C149—41no—
199C2×C149D4211yescharacteristic
200C2×C149C2×#13711yescharacteristic
201C2×C149#57711yescharacteristic
202D149—42no—
203D149—81no—
204C149#326611yescharacteristic, complemented, Sylow
205#3266—1491nomaximal, Sylow
206C2×#137—1491no—
207C22×SD16—1491no—
208D4×Q8—1491no—
209#546—1491no—
210#497—1491no—
211#468—1491no—
212#467—1491no—
213#464—1491no—
214#461—1491no—
215#452—1491no—
216#451—1491no—
217#450—1491no—
218#448—1491no—
219#440—1491no—
220#435D14911yescharacteristic, complemented
221C2×#41—1491no—
222C22×Q8—1491no—
223C22×Q8—1491no—
224C22×D4—1491no—
225#137—2984no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×Q16—1491no—
229C2×SD16—2984no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×SD16—1491no—
233C2×SD16—1491no—
234C2×SD16—1491no—
235C2×SD16—1491no—
236C2×M16C2×D14911yescharacteristic, complemented
237C22×C8C2×D14911yescharacteristic
238C4⋊Q8—2981no—
239C4⋊Q8—1491no—
240#124—1491no—
241#123—2981no—
242C22⋊Q8—2981no—
243C22⋊Q8—2981no—
244C22⋊Q8—1491no—
245C22⋊Q8—1491no—
246C22⋊Q8—1491no—
247#121—2981no—
248#121—1491no—
249#120—2981no—
250C4×Q8—1491no—
251C4×D4—2981no—
252C4×D4—1491no—
253C4×D4C2×D14911yescharacteristic
254C2×C22⋊C4—2981no—
255#107—1491no—
256C4⋊C8C2×D14911yescharacteristic, complemented
257#103—1491no—
258#103—1491no—
259#103—1491no—
260#103—1491no—
261#102—1491no—
262#102—1491no—
263C22⋊C8C2×D14911yescharacteristic
264C22⋊C8C2×D14911yescharacteristic, complemented
265#97C2×D14911yescharacteristic, complemented
266C24—2981no—
267#41—2982no—
268#41—5961no—
269C2×Q8—2982no—
270C2×Q8—2982no—
271C2×Q8—2981no—
272C2×Q8—2981no—
273C2×Q8—5961no—
274C2×Q8—5961no—
275C2×Q8—1491no—
276C2×Q8—1491no—
277C2×Q8—1491no—
278C2×Q8—1491no—
279C2×D4—2982no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—5961no—
284C2×D4—1491no—
285C2×D4—1491no—
286C2×D4D59611yescharacteristic
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4C22×D14911yescharacteristic
292C22×C4C22×D14911yescharacteristic
293Q16—2982no—
294Q16—2982no—
295Q16—5961no—
296SD16—2982no—
297SD16—2982no—
298SD16—2982no—
299SD16—2982no—
300SD16—5961no—
301SD16—1494no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D14911yescharacteristic
305C2×C8C22×D14911yescharacteristic
306C2×C8C22×D14911yescharacteristic
307C2×C8C22×D14911yescharacteristic
308C4⋊C4—2981no—
309C4⋊C4—2981no—
310C4⋊C4—2981no—
311C4⋊C4—2981no—
312C4⋊C4—2981no—
313C4⋊C4—2981no—
314C4⋊C4—1491no—
315C4⋊C4—1491no—
316C4⋊C4D59611yescharacteristic
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C22⋊C4—2981no—
324C22⋊C4D59611yescharacteristic
325C22⋊C4D59611yescharacteristic
326C42—2981no—
327C42C22×D14911yescharacteristic
328C23—2981no—
329C23—2981no—
330C23—5962no—
331C23—5962no—
332C23—11921no—
333C23C2×D59611yescharacteristic
334C23C2×D59611yescharacteristic
335Q8—2981no—
336Q8—2981no—
337Q8—2981no—
338Q8—2981no—
339Q8—2981no—
340Q8—2981no—
341Q8—2981no—
342Q8—5962no—
343Q8—5962no—
344Q8—1492no—
345D4—22no—
346D4—2981no—
347D4—2981no—
348D4—2981no—
349D4—5962no—
350D4—5962no—
351D4—1492no—
352D4—11921no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—2981no—
363C2×C4—5962no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—11921no—
367C2×C4C2×D59611yescharacteristic
368C2×C4C2×D59611yescharacteristic
369C2×C4C2×D59611yescharacteristic
370C2×C4C2×D59611yescharacteristic
371C2×C4C23×D14911yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D14912yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—2982no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22—11924no—
388C22#1801194412yescomplemented
389C22C22×D59611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—2982no—
395C4—5961no—
396C4—5961no—
397C4—5961no—
398C4—5961no—
399C4—5961no—
400C4C2×D4×D14911yescharacteristic
401C4#1801195711yescharacteristic
402C2—22no—
403C2—41no—
404C2—5962no—
405C2—11921no—
406C2D4×D59611yescharacteristic
407C2C2×#1801194411yescharacteristic
408C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
prime radical#23750271C2
hypercenter#435D149
hypocenterC149#3266
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C22×#14558725C2semidirect
3. D4×Dic298C2semidirect
5. #23750019C2semidirect
6. #23749871C2semidirect
7. #23749866C2semidirect
8. #23749848C2semidirect
9. #23749831C2semidirect
10. #23749789C2semidirect
11. #23749783C2semidirect
12. #23749778C2semidirect
13. #23749766C2semidirect
14. #23749727C2semidirect
15. #435×C149C2semidirect
18. C22×Dic298C22semidirect
21. C2×Dic596C22semidirect
22. C2×Dic596C22semidirect
23. C2×Dic596C22semidirect
31. #18011911C22semidirect
37. #18011890C22semidirect
43. C4×Dic298C22semidirect
47. #18011845C22semidirect
48. #18011836C22semidirect
49. #18011836C22semidirect
50. #18011836C22semidirect
51. #18011836C22semidirect
54. C2×M16×C149C22semidirect
57. C4⋊C8×C149C22semidirect
59. C22⋊C8×C149C22semidirect
60. #97×C149C22semidirect
93. #14558725D4semidirect
176. C22×C149#137semidirect
204. C149#3266semidirect
220. #435D149semidirect
236. C2×M16C2×D149semidirect
256. C4⋊C8C2×D149semidirect
264. C22⋊C8C2×D149semidirect
265. #97C2×D149semidirect
388. C22#18011944semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C22×#145587252
D4×Dic2982
#237502712
#237500192
#237498712
#237498662
#237498482
#237498312
#237497892
#237497832
#237497782
#237497662
#237497272
#435×C1492
#3266149