Finite Group Databasebeta

← #34055509

Subgroups — #34055509

Order 19072.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750137C211yesmaximal, characteristic, complemented
2#121×D149C211yesmaximal, characteristic, complemented
3#23749957C211yesmaximal, characteristic, complemented
4#23749949C211yesmaximal, characteristic, complemented
5#23749940C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749872C211yesmaximal, characteristic, complemented
9#23749870C211yesmaximal, characteristic, complemented
10#23749777C211yesmaximal, characteristic, complemented
11#23749772C211yesmaximal, characteristic, complemented
12#23749768C211yesmaximal, characteristic, complemented
13#23749760C211yesmaximal, characteristic, complemented
14#23749587C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic, complemented
17C2×D4×D149—21no—
18C2×D4×D149C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558724C2211yescharacteristic, complemented
22C2×D1192C2211yescharacteristic, complemented
23C2×#14558721C2211yescharacteristic, complemented
24C2×#14558719C2211yescharacteristic, complemented
25C2×#14558719C2211yescharacteristic, complemented
26#18011895—21no—
27#18011891C2211yescharacteristic
28#18011891C2211yescharacteristic, complemented
29#18011886C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic, complemented
32#18011885C2211yescharacteristic
33#18011884—21no—
34#18011883—21no—
35#18011882C2211yescharacteristic
36#18011881—21no—
37C4×D596—21no—
38C4×D596—21no—
39C4⋊C4×D149C2211yescharacteristic
40C22⋊C4×D149—21no—
41#18011844C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic, complemented
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149D411yescharacteristic
61#14558736—41no—
62#14558736—41no—
63C2×Dic298C2311yescharacteristic
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73D4×D149—41no—
74D4×D149—41no—
75D4×D149—44no—
76C22×Dic149D411yescharacteristic
77C2×C4×D149—21no—
78C2×C4×D149—21no—
79C2×C4×D149—41no—
80C2×C4×D149—41no—
81C2×C4×D149D411yescharacteristic
82C2×C4×D149D411yescharacteristic
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85#14558725—41no—
86#14558724—41no—
87D1192—41no—
88#14558721—41no—
89#14558719—41no—
90#14558719—41no—
91C2×#11924746C2311yescharacteristic
92C2×#11924746C2311yescharacteristic
93C4⋊Dic149—21no—
94C4⋊Dic149—21no—
95C4⋊Dic149C2311yescharacteristic
96#14558715—21no—
97C22⋊Dic149—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713—21no—
103#14558713—21no—
104C2×D4×C149—21no—
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22⋊C4×C149—21no—
113C22⋊C4×C149—21no—
114C42×C149—21no—
115C22×D149—22no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—41no—
119C22×D149—41no—
120C22×D149—42no—
121C22×D149—42no—
122C22×D149—42no—
123C22×D149C2×D411yescharacteristic
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127D596—21no—
128D596—21no—
129D596—21no—
130D596—21no—
131D596—42no—
132D596—42no—
133D596—42no—
134C22⋊D149—42no—
135C22⋊D149—42no—
136C22⋊D149—42no—
137C22⋊D149—42no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—41no—
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C4×D149—21no—
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—21no—
147C4×D149—41no—
148C4×D149—41no—
149C4×D149—42no—
150C4×D149—42no—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154C23×C149C2×D411yescharacteristic
155D4×C149—21no—
156D4×C149—21no—
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×C149C2×D411yescharacteristic
164C2×C4×C149C2411yescharacteristic
165C8×C149—21no—
166C8×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149C22×D411yescharacteristic
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—44no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—84no—
187C2×D149AGL(1,ℤ/8)12yes—
188C4×C149—21no—
189C4×C149—41no—
190C4×C149—41no—
191C4×C149—41no—
192C4×C149H(5,𝔽2)11yescharacteristic
193C4×C149H(5,𝔽2)11yescharacteristic
194Dic149—21no—
195Dic149—21no—
196Dic149—41no—
197Dic149—41no—
198C2×C149—41no—
199C2×C149—81no—
200C2×C149#53411yescharacteristic
201C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
202C2×C149#57511yescharacteristic
203D149—22no—
204D149—41no—
205D149—81no—
206D149—81no—
207C149#319411yescharacteristic, complemented, Sylow
208#3194—1491nomaximal, Sylow
209#525—1491no—
210C2×#121—1491no—
211#483—1491no—
212#482—1491no—
213#482D14911yescharacteristic, complemented
214#480—1491no—
215#469—1491no—
216#469—1491no—
217#468—1491no—
218#468—1491no—
219#450—1491no—
220#449—1491no—
221#449—1491no—
222#447—1491no—
223#407—1491no—
224C2×#41—1491no—
225C22×D4—2981no—
226C22×D4—1491no—
227C23×C4—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×D8—1491no—
231C2×D8—1491no—
232C2×M16—1491no—
233C2×M16—1491no—
234#123—2981no—
235C22⋊Q8—1491no—
236C22⋊Q8—1491no—
237#121—2981no—
238#121—2981no—
239#121—1491no—
240#121—1491no—
241#121—1491no—
242#121—1491no—
243#121—1491no—
244#121C2×D14911yescharacteristic
245#120—2981no—
246C4×D4—2981no—
247C4×D4—2981no—
248#117C2×D14911yescharacteristic, complemented
249C2×C4⋊C4—1491no—
250C2×C22⋊C4—2981no—
251#107—1491no—
252#107C2×D14911yescharacteristic, complemented
253#106—1491no—
254#106C2×D14911yescharacteristic, complemented
255#103—1491no—
256#103—1491no—
257#102—1491no—
258#102—1491no—
259#102—1491no—
260#102—1491no—
261#102C2×D14911yescharacteristic, complemented
262#102C2×D14911yescharacteristic, complemented
263C22⋊C8—1491no—
264C22⋊C8—1491no—
265C22⋊C8—1491no—
266C22⋊C8C2×D14911yescharacteristic, complemented
267C24—2981no—
268C24—1491no—
269#41—5961no—
270#41—5961no—
271C2×Q8—1491no—
272C2×D4—21no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—5961no—
281C2×D4—5961no—
282C2×D4—5964no—
283C2×D4—1491no—
284C2×D4—1491no—
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—5961no—
289C22×C4—5961no—
290C22×C4—1491no—
291C22×C4—1491no—
292C22×C4—1491no—
293C22×C4—1491no—
294C22×C4—1491no—
295C22×C4C22×D14911yescharacteristic
296SD16—5961no—
297SD16—5961no—
298D8—5961no—
299D8—5961no—
300M16—5961no—
301M16—5961no—
302C2×C8—1491no—
303C2×C8—1491no—
304C2×C8C22×D14911yescharacteristic
305C2×C8C22×D14911yescharacteristic
306C4⋊C4—2981no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4C22×D14911yescharacteristic
311C4⋊C4C22×D14911yescharacteristic
312C4⋊C4C22×D14911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C42—21no—
323C23—21no—
324C23—2982no—
325C23—2981no—
326C23—2981no—
327C23—5961no—
328C23—5961no—
329C23—5962no—
330C23—5962no—
331C23—5962no—
332C23—1491no—
333C23—1491no—
334C23D4×D14911yescharacteristic
335Q8—2981no—
336Q8—2981no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—2981no—
341D4—2981no—
342D4—2981no—
343D4—2981no—
344D4—5962no—
345D4—5962no—
346D4—5962no—
347D4—5962no—
348D4—5962no—
349D4—5962no—
350D4—5962no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—2981no—
359C2×C4—2981no—
360C2×C4—2981no—
361C2×C4—2981no—
362C2×C4—5961no—
363C2×C4—5961no—
364C2×C4—5962no—
365C2×C4—5962no—
366C2×C4—5961no—
367C2×C4—1491no—
368C2×C4—1491no—
369C2×C4D4×D14911yescharacteristic
370C2×C4C23×D14911yescharacteristic
371C8—21no—
372C8—21no—
373C8—2981no—
374C8—2981no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—2981no—
382C22—2981no—
383C22—2981no—
384C22—2981no—
385C22—2981no—
386C22—5964no—
387C22—5961no—
388C22—5961no—
389C22—5961no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—1492no—
394C22—11924no—
395C22C2×D4×D14911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—2981no—
401C4—2981no—
402C4—5961no—
403C4—5961no—
404C4#1801195711yescharacteristic
405C4#1801195711yescharacteristic
406C2—41no—
407C2—81no—
408C2—2982no—
409C2—5961no—
410C2—11921no—
411C2—11921no—
412C2#2375018611yescharacteristic
413C2AGL(1,ℤ/8)×D14911yescharacteristic
414C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
hypercenter#482D149
hypocenterC149#3194
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23750137C2semidirect
2. #121×D149C2semidirect
3. #23749957C2semidirect
4. #23749949C2semidirect
5. #23749940C2semidirect
6. #23749879C2semidirect
7. #23749877C2semidirect
8. #23749872C2semidirect
9. #23749870C2semidirect
10. #23749777C2semidirect
11. #23749772C2semidirect
12. #23749768C2semidirect
13. #23749760C2semidirect
14. #23749587C2semidirect
15. #482×C149C2semidirect
16. C2×#14558736C22semidirect
20. C2×#14558725C22semidirect
21. C2×#14558724C22semidirect
22. C2×D1192C22semidirect
23. C2×#14558721C22semidirect
24. C2×#14558719C22semidirect
25. C2×#14558719C22semidirect
28. #18011891C22semidirect
31. #18011886C22semidirect
41. #18011844C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
45. #18011833C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
53. #117×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
207. C149#3194semidirect
213. #482D149semidirect
248. #117C2×D149semidirect
252. #107C2×D149semidirect
254. #106C2×D149semidirect
261. #102C2×D149semidirect
262. #102C2×D149semidirect
266. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501372
#121×D1492
#237499572
#237499492
#237499402
#237498792
#237498772
#237498722
#237498702
#237497772
#237497722
#237497682
#237497602
#237495872
#482×C1492
#3194149