Finite Group Databasebeta

← #34055623

Subgroups — #34055623

Order 19072.

438 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750174C211yesmaximal, characteristic, complemented
2#23750172C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749974C211yesmaximal, characteristic, complemented
6#23749970C211yesmaximal, characteristic, complemented
7#23749841C211yesmaximal, characteristic, complemented
8#23749840C211yesmaximal, characteristic, complemented
9#23749837C211yesmaximal, characteristic, complemented
10#23749773C211yesmaximal, characteristic, complemented
11#23749771C211yesmaximal, characteristic, complemented
12#23749769C211yesmaximal, characteristic, complemented
13#23749767C211yesmaximal, characteristic, complemented
14#23749677C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736—21no—
18C2×#14558735C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×D1192C2211yescharacteristic
23C2×#14558721C2211yescharacteristic
24C2×#14558721C2211yescharacteristic
25#18011910C2211yescharacteristic
26#18011909C2211yescharacteristic
27#18011907C2211yescharacteristic
28#18011907C2211yescharacteristic
29#18011899C2211yescharacteristic
30#18011897—21no—
31#18011886C2211yescharacteristic
32#18011884—21no—
33#18011884—21no—
34#18011884—21no—
35#18011882C2211yescharacteristic
36C4×D596C2211yescharacteristic
37C4×C22⋊D149—21no—
38#18011871—21no—
39#18011871—21no—
40C42×D149C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558736—44no—
62#14558735—41no—
63#14558735—41no—
64C2×Dic298—21no—
65C2×Dic298C2311yescharacteristic
66C2×D596—21no—
67C2×D596—21no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C22×Dic149—21no—
77C2×C4×D149—21no—
78C2×C4×D149—21no—
79C2×C4×D149D411yescharacteristic
80C2×C4×D149D411yescharacteristic
81C2×C4×D149C2311yescharacteristic
82#14558725—41no—
83#14558724—41no—
84#14558723—41no—
85D1192—41no—
86#14558721—41no—
87#14558721—41no—
88C2×#11924746C2311yescharacteristic
89C2×#11924746C2311yescharacteristic
90C4⋊Dic149C2311yescharacteristic
91#14558715—21no—
92#14558715—21no—
93#14558715—21no—
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99C4×Dic149D411yescharacteristic
100C4×Dic149D411yescharacteristic
101C4×Dic149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149—21no—
106SD16×C149—41no—
107D8×C149—41no—
108C2×C8×C149C2311yescharacteristic
109C2×C8×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C42×C149C2311yescharacteristic
115C22×D149—21no—
116C22×D149—21no—
117C22×D149C2×D411yescharacteristic
118Dic298—21no—
119Dic298—21no—
120Dic298—42no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—42no—
126D596—42no—
127C22⋊D149—42no—
128C22⋊D149—42no—
129C22⋊D149—42no—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—42no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C2×Dic149C2×D411yescharacteristic
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—22no—
142C4×D149—22no—
143C4×D149—42no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149—21no—
148C23×C149—21no—
149Q8×C149—21no—
150Q8×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—42no—
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2411yescharacteristic
161C8×C149—21no—
162C8×C149—21no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149C22×D411yescharacteristic
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C2×D149—41no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188Dic149#13512yes—
189Dic149AGL(1,ℤ/8)12yes—
190C2×C149—81no—
191C2×C149—81no—
192C2×C149#53511yescharacteristic
193C2×C149C2×#13511yescharacteristic
194C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
195D149—41no—
196D149—81no—
197D149—81no—
198C149#320711yescharacteristic, complemented, Sylow
199#3207—1491nomaximal, Sylow
200#532—1491no—
201#532—1491no—
202#493—1491no—
203#492—1491no—
204#487—1491no—
205#486—1491no—
206#463—1491no—
207#463—1491no—
208#463—1491no—
209#463D14911yescharacteristic, complemented
210#449—1491no—
211#449—1491no—
212#449—1491no—
213#449—1491no—
214#431—1491no—
215C2×#41—2981no—
216C2×#41—1491no—
217C2×#41—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×SD16—1491no—
221C2×SD16C2×D14911yescharacteristic
222C2×D8—1491no—
223C2×D8—1491no—
224C2×D8—1491no—
225C2×D8C2×D14911yescharacteristic
226C4⋊Q8—1491no—
227C4⋊Q8—1491no—
228#127—1491no—
229#127—1491no—
230#124—2981no—
231#124—1491no—
232#124C2×D14911yescharacteristic
233#121—2981no—
234#121—2981no—
235#121—2981no—
236#121—1491no—
237#121—1491no—
238C4×D4—2981no—
239C4×D4—2981no—
240C4×D4—2981no—
241C4×D4—1491no—
242C4×D4C2×D14911yescharacteristic
243C2×C42—1491no—
244C4⋊C8—1491no—
245C4⋊C8C2×D14911yescharacteristic
246#103—1491no—
247#103—1491no—
248#103—1491no—
249#103C2×D14911yescharacteristic
250#102—1491no—
251#102—1491no—
252#102—1491no—
253#102C2×D14911yescharacteristic
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C4×C8—1491no—
257C4×C8—1491no—
258#41—5964no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262#41—5961no—
263C2×Q8—2981no—
264C2×Q8—1491no—
265C2×Q8C22×D14911yescharacteristic
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—2981no—
271C2×D4—2981no—
272C2×D4—2981no—
273C2×D4—2981no—
274C2×D4—1491no—
275C2×D4—1491no—
276C2×D4C22×D14911yescharacteristic
277C2×D4C22×D14911yescharacteristic
278C22×C4—21no—
279C22×C4—2981no—
280C22×C4—2981no—
281C22×C4—2981no—
282C22×C4—1491no—
283C22×C4—1491no—
284C22×C4—1491no—
285SD16—41no—
286SD16—5961no—
287SD16—5961no—
288SD16—5961no—
289D8—41no—
290D8—5961no—
291D8—5961no—
292D8—5961no—
293C2×C8—1491no—
294C2×C8—1491no—
295C2×C8C22×D14911yescharacteristic
296C2×C8C22×D14911yescharacteristic
297C4⋊C4—2981no—
298C4⋊C4—2981no—
299C4⋊C4—2981no—
300C4⋊C4—1491no—
301C4⋊C4C22×D14911yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C42—1491no—
311C42—1491no—
312C42—1491no—
313C42C22×D14911yescharacteristic
314C23—21no—
315C23—21no—
316C23—2981no—
317C23—2981no—
318C23—1491no—
319Q8—21no—
320Q8—21no—
321Q8—2981no—
322Q8—2981no—
323Q8—5962no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—2981no—
329D4—2981no—
330D4—2981no—
331D4—2981no—
332D4—5962no—
333D4—5962no—
334D4—5962no—
335D4—5962no—
336D4—5962no—
337D4—5962no—
338D4—5962no—
339D4—5962no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2982no—
344C2×C4—2982no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—5962no—
350C2×C4—5962no—
351C2×C4—5962no—
352C2×C4—1491no—
353C2×C4—1491no—
354C2×C4—1491no—
355C2×C4D4×D14911yescharacteristic
356C2×C4D4×D14911yescharacteristic
357C2×C4C23×D14911yescharacteristic
358C8—21no—
359C8—21no—
360C8—2981no—
361C8—2981no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22—5961no—
375C22—5961no—
376C22—5961no—
377C22C2×D4×D14911yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—2981no—
383C4—5961no—
384C4—5961no—
385C4—1492no—
386C4—1492no—
387C4#1801195611yescharacteristic
388C4#1801195711yescharacteristic
389C2—81no—
390C2—81no—
391C2—5961no—
392C2—11921no—
393C2—11921no—
394C2#2375019111yescharacteristic
395C2#135×D14911yescharacteristic
396C2AGL(1,ℤ/8)×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3207
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750174C2semidirect
2. #23750172C2semidirect
3. #23750000C2semidirect
4. #23749996C2semidirect
5. #23749974C2semidirect
6. #23749970C2semidirect
7. #23749841C2semidirect
8. #23749840C2semidirect
9. #23749837C2semidirect
10. #23749773C2semidirect
11. #23749771C2semidirect
12. #23749769C2semidirect
13. #23749767C2semidirect
14. #23749677C2semidirect
15. #463×C149C2semidirect
198. C149#3207semidirect
209. #463D149semidirect

Maximal subgroups

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

subgroupindex
#237501742
#237501722
#237500002
#237499962
#237499742
#237499702
#237498412
#237498402
#237498372
#237497732
#237497712
#237497692
#237497672
#237496772
#463×C1492
#3207149