Finite Group Databasebeta

← #34056266

Subgroups — #34056266

Order 19072.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011944C211yesmaximal, characteristic, complemented
2C22×Dic596C211yesmaximal, characteristic, complemented
3D4×Dic298C211yesmaximal, characteristic, complemented
4#23750284C211yesmaximal, characteristic
5#23750019C211yesmaximal, characteristic, complemented
6#23749883C211yesmaximal, characteristic, complemented
7#23749854C211yesmaximal, characteristic, complemented
8#23749848C211yesmaximal, characteristic, complemented
9#23749836C211yesmaximal, characteristic, complemented
10#23749789C211yesmaximal, characteristic, complemented
11#23749783C211yesmaximal, characteristic, complemented
12#23749783C211yesmaximal, characteristic, complemented
13#23749766C211yesmaximal, characteristic, complemented
14#23749733C211yesmaximal, characteristic, complemented
15#435×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×Dic298C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C22×Dic298C2211yescharacteristic
20#18011944—24no—
21C2×Dic596—24no—
22C2×Dic596C2211yescharacteristic
23C2×Dic596C2211yescharacteristic
24C2×Dic596C2211yescharacteristic
25C2×Dic596C2211yescharacteristic
26C2×Dic596C2211yescharacteristic
27C2×Dic596C2211yescharacteristic
28C2×#14558725C2211yescharacteristic
29C2×#14558725C2211yescharacteristic
30C2×#14558725C2211yescharacteristic
31#18011911C2211yescharacteristic
32#18011910—21no—
33#18011899C2211yescharacteristic
34#18011897—21no—
35#18011890C2211yescharacteristic
36#18011890C2211yescharacteristic
37#18011890C2211yescharacteristic
38#18011889—21no—
39#18011888—21no—
40#18011888—21no—
41#18011885C2211yescharacteristic
42#18011883—21no—
43C4×Dic298C2211yescharacteristic
44C4×Dic298C2211yescharacteristic
45D4×Dic149—21no—
46#18011871—21no—
47#18011843C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011836C2211yescharacteristic
51#18011836C2211yescharacteristic
52#18011836C2211yescharacteristic
53#18011833C2211yescharacteristic
54C2×M16×C149C2211yescharacteristic
55C22×C8×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C4⋊C8×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C22⋊C8×C149C2211yescharacteristic
60#97×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—41no—
63C2×Dic298—22no—
64C2×Dic298—22no—
65C2×Dic298—22no—
66C2×Dic298—21no—
67C2×Dic298—21no—
68C2×Dic298—21no—
69C2×Dic298—41no—
70C2×Dic298—41no—
71C2×Dic298—41no—
72C2×Dic298C2311yescharacteristic
73C2×Dic298C2311yescharacteristic
74C2×Dic298C2311yescharacteristic
75C2×Dic298C2311yescharacteristic
76C2×Dic298C2311yescharacteristic
77C2×D596C2311yescharacteristic
78C2×C22⋊D149—21no—
79C2×C22⋊D149—21no—
80C22×Dic149—21no—
81C22×Dic149—21no—
82C22×Dic149—21no—
83C2×C4×D149—21no—
84Dic596—22no—
85Dic596—22no—
86Dic596—22no—
87Dic596—22no—
88Dic596—41no—
89Dic596D414yescomplemented
90#14558725—22no—
91#14558725—22no—
92#14558725—41no—
93C4⋊Dic149—21no—
94C4⋊Dic149—21no—
95C4⋊Dic149C2311yescharacteristic
96C4⋊Dic149C2311yescharacteristic
97#14558715—21no—
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—
108C4×Dic149—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—
124Dic298—21no—
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—42no—
133Dic298—42no—
134Dic298—42no—
135Dic298C2×D412yes—
136Dic298C2×D412yes—
137D596—21no—
138D596—21no—
139C22⋊D149—42no—
140C22⋊D149—42no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—21no—
146C2×Dic149—21no—
147C2×Dic149—21no—
148C2×Dic149—42no—
149C2×Dic149—42no—
150C2×Dic149—42no—
151C4×D149—42no—
152C23×C149C2×D411yescharacteristic
153C23×C149C2×D411yescharacteristic
154D4×C149—22no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2×D411yescharacteristic
161C2×C4×C149C2×D411yescharacteristic
162C2×C4×C149C2×D411yescharacteristic
163C2×C4×C149C2411yescharacteristic
164C8×C149—21no—
165C8×C149—21no—
166C8×C149—21no—
167C8×C149C2×D412yes—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—21no—
173C22×C149#13712yescomplemented
174C22×C149C22×D411yescharacteristic
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149C22×D411yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—22no—
185Dic149—22no—
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189Dic149—41no—
190Dic149—41no—
191C2×C149—22no—
192C2×C149—41no—
193C2×C149D4211yescharacteristic
194C2×C149C2×#13711yescharacteristic
195C2×C149#57811yescharacteristic
196D149—81no—
197C149#327011yescharacteristic, complemented, Sylow
198#3270—1491nomaximal, Sylow
199C2×#137—1491no—
200C22×Q16—1491no—
201D4×Q8—1491no—
202#548—1491no—
203#497—1491no—
204#470—1491no—
205#465—1491no—
206#464—1491no—
207#462—1491no—
208#452—1491no—
209#451—1491no—
210#451—1491no—
211#448—1491no—
212#441—1491no—
213#435D14911yescharacteristic, complemented
214C2×#41—1491no—
215C22×Q8—1491no—
216C22×Q8—1491no—
217C22×Q8—1491no—
218#137—2984no—
219C2×Q16—2984no—
220C2×Q16—1491no—
221C2×Q16—1491no—
222C2×Q16—1491no—
223C2×Q16—1491no—
224C2×Q16—1491no—
225C2×Q16—1491no—
226C2×SD16—1491no—
227C2×SD16—1491no—
228C2×SD16—1491no—
229C2×M16C2×D14911yescharacteristic
230C22×C8C2×D14911yescharacteristic
231C4⋊Q8—2981no—
232C4⋊Q8—1491no—
233#124—2981no—
234#124—1491no—
235C22⋊Q8—2981no—
236C22⋊Q8—2981no—
237C22⋊Q8—2981no—
238C22⋊Q8—1491no—
239C22⋊Q8—1491no—
240C22⋊Q8—1491no—
241#121—2981no—
242#121—1491no—
243C4×Q8—1491no—
244C4×Q8—1491no—
245C4×D4—2981no—
246C4×D4—2981no—
247C4×D4C2×D14911yescharacteristic
248#106—1491no—
249C4⋊C8C2×D14911yescharacteristic
250#103—1491no—
251#103—1491no—
252#103—1491no—
253#103—1491no—
254#103—1491no—
255#102—1491no—
256C22⋊C8C2×D14911yescharacteristic
257C22⋊C8C2×D14911yescharacteristic
258#97C2×D14911yescharacteristic
259#41—2982no—
260#41—5961no—
261C2×Q8—2982no—
262C2×Q8—2982no—
263C2×Q8—2982no—
264C2×Q8—2981no—
265C2×Q8—2981no—
266C2×Q8—2981no—
267C2×Q8—5961no—
268C2×Q8—5961no—
269C2×Q8—5961no—
270C2×Q8—1491no—
271C2×Q8—1491no—
272C2×Q8—1491no—
273C2×Q8—1491no—
274C2×Q8—1491no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—1491no—
278C2×D4D59611yescharacteristic
279C22×C4—2981no—
280C22×C4—2981no—
281C22×C4—2981no—
282C22×C4—2981no—
283C22×C4C22×D14911yescharacteristic
284C22×C4C22×D14911yescharacteristic
285Q16—2982no—
286Q16—2982no—
287Q16—2982no—
288Q16—2982no—
289Q16—5961no—
290Q16—1494no—
291SD16—2982no—
292SD16—2982no—
293SD16—5961no—
294M16—22no—
295C2×C8—22no—
296C2×C8C22×D14911yescharacteristic
297C2×C8C22×D14911yescharacteristic
298C2×C8C22×D14911yescharacteristic
299C2×C8C22×D14911yescharacteristic
300C4⋊C4—2981no—
301C4⋊C4—2981no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—2981no—
305C4⋊C4—2981no—
306C4⋊C4—2981no—
307C4⋊C4—1491no—
308C4⋊C4—1491no—
309C4⋊C4D59611yescharacteristic
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4D59611yescharacteristic
317C22⋊C4D59611yescharacteristic
318C42—2981no—
319C42—2981no—
320C42C22×D14911yescharacteristic
321C23—2981no—
322C23C2×D59611yescharacteristic
323C23C2×D59611yescharacteristic
324Q8—2981no—
325Q8—2981no—
326Q8—2981no—
327Q8—2981no—
328Q8—2981no—
329Q8—2981no—
330Q8—2981no—
331Q8—2981no—
332Q8—5962no—
333Q8—5962no—
334Q8—5962no—
335Q8—1492no—
336Q8—1492no—
337D4—22no—
338D4—2981no—
339D4—2981no—
340D4—5962no—
341D4—5962no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—5962no—
354C2×C4—5962no—
355C2×C4—5962no—
356C2×C4—5962no—
357C2×C4C2×D59611yescharacteristic
358C2×C4C2×D59611yescharacteristic
359C2×C4C2×D59611yescharacteristic
360C2×C4C2×D59611yescharacteristic
361C2×C4C23×D14911yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8D4×D14912yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22#1801194412yescomplemented
375C22C22×D59611yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—2982no—
381C4—2982no—
382C4—5961no—
383C4—5961no—
384C4—5961no—
385C4—5961no—
386C4—5961no—
387C4C2×D4×D14911yescharacteristic
388C4#1801195711yescharacteristic
389C2—22no—
390C2—41no—
391C2—11921no—
392C2D4×D59611yescharacteristic
393C2C2×#1801194411yescharacteristic
394C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#435×C149C2
socleC22×C149C22×D4
prime radical#23750284C2
hypercenter#435D149
hypocenterC149#3270
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×Dic596C2semidirect
3. D4×Dic298C2semidirect
5. #23750019C2semidirect
6. #23749883C2semidirect
7. #23749854C2semidirect
8. #23749848C2semidirect
9. #23749836C2semidirect
10. #23749789C2semidirect
11. #23749783C2semidirect
12. #23749783C2semidirect
13. #23749766C2semidirect
14. #23749733C2semidirect
15. #435×C149C2semidirect
89. Dic596D4semidirect
173. C22×C149#137semidirect
197. C149#3270semidirect
213. #435D149semidirect
374. 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×Dic5962
D4×Dic2982
#237502842
#237500192
#237498832
#237498542
#237498482
#237498362
#237497892
#237497832
#237497662
#237497332
#435×C1492
#3270149