Finite Group Databasebeta

← #34056543

Subgroups — #34056543

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750321C211yesmaximal, characteristic, complemented
2#23750271C211yesmaximal, characteristic, complemented
3#23749980C211yesmaximal, characteristic, complemented
4#23749961C211yesmaximal, characteristic, complemented
5#23749950C211yesmaximal, characteristic, complemented
6#23749926C211yesmaximal, characteristic, complemented
7#23749861C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749841C211yesmaximal, characteristic, complemented
10#23749772C211yesmaximal, characteristic, complemented
11#23749761C211yesmaximal, characteristic, complemented
12C4×D1192C211yesmaximal, characteristic, complemented
13#23749622C211yesmaximal, characteristic, complemented
14C2×#18011833C211yesmaximal, characteristic, complemented
15C8×D4×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C2×#14558725C2211yescharacteristic, complemented
19C2×D1192C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011906—21no—
22#18011903C2211yescharacteristic, complemented
23#18011899C2211yescharacteristic
24#18011896—21no—
25#18011893—21no—
26#18011890C2211yescharacteristic
27#18011885C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011885C2211yescharacteristic, complemented
30#18011884—21no—
31#18011883—21no—
32#18011879—21no—
33C4×D596C2211yescharacteristic
34C4×D596C2211yescharacteristic, complemented
35#18011871—21no—
36#18011870C2211yescharacteristic, complemented
37C2×C4⋊Dic149C2211yescharacteristic
38C22⋊C4×D149—21no—
39#18011845C2211yescharacteristic, complemented
40#18011845C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic, complemented
52C22×C8×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic, complemented
54C4×D4×C149C2211yescharacteristic
55C4⋊C8×C149C2211yescharacteristic, complemented
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558736—22no—
61#14558736—41no—
62C2×Dic298C2311yescharacteristic
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—41no—
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C22×Dic149—21no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77#14558725—41no—
78D1192—22no—
79D1192—41no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97C4×Dic149—21no—
98C2×D4×C149D411yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C2×C8×C149—41no—
102C2×C8×C149—41no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149D411yescharacteristic
108C22⋊C4×C149D411yescharacteristic
109C22⋊C4×C149D411yescharacteristic
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149—81no—
117Dic298—21no—
118Dic298—21no—
119D596—21no—
120D596—21no—
121D596—21no—
122D596—21no—
123D596—21no—
124D596—42no—
125D596#4112yes—
126C22⋊D149—42no—
127C22⋊D149—42no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—81no—
136C4×D149—42no—
137C4×D149—81no—
138C4×D149—81no—
139C23×C149C2×D411yescharacteristic
140C23×C149C2×D411yescharacteristic
141D4×C149—22no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2411yescharacteristic
151C8×C149—21no—
152C8×C149—21no—
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—21no—
159C22×C149—21no—
160C22×C149#13512yes—
161C22×C149C22×D411yescharacteristic
162C2×D149—22no—
163C2×D149—41no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—41no—
171C2×D149—84no—
172C4×C149—21no—
173C4×C149—21no—
174C4×C149—21no—
175C4×C149—21no—
176C4×C149C2×#4111yescharacteristic
177C4×C149H(5,𝔽2)11yescharacteristic
178Dic149—41no—
179Dic149—41no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—22no—
184C2×C149—41no—
185C2×C149#54611yescharacteristic
186C2×C149C2×#13511yescharacteristic
187C2×C149#57611yescharacteristic
188D149—42no—
189D149—81no—
190D149—81no—
191C149#329711yescharacteristic, complemented, Sylow
192#3297—1491nomaximal, Sylow
193#553—1491no—
194#546—1491no—
195#488—1491no—
196#484—1491no—
197#482—1491no—
198#478—1491no—
199#466—1491no—
200#465—1491no—
201#463—1491no—
202#449—1491no—
203#447—1491no—
204C4×D8—1491no—
205C8×D4D14911yescharacteristic, complemented
206#416—1491no—
207C2×#102—1491no—
208C2×#41—1491no—
209C22×D4—1491no—
210C2×SD16—1491no—
211C2×D8—1491no—
212C2×D8—1491no—
213C22×C8C2×D14911yescharacteristic
214C22×C8C2×D14911yescharacteristic, complemented
215#126—2981no—
216#125—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8—1491no—
221#121—2981no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121—1491no—
226#120—2981no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4—1491no—
230C4×D4C2×D14911yescharacteristic
231#117—1491no—
232C2×C4⋊C4—1491no—
233C2×C22⋊C4—2981no—
234#107—1491no—
235#107—1491no—
236#106—1491no—
237C4⋊C8C2×D14911yescharacteristic, complemented
238#103—1491no—
239#103—1491no—
240#103—1491no—
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102—1491no—
248C22⋊C8C2×D14911yescharacteristic
249C22⋊C8C2×D14911yescharacteristic, complemented
250C4×C8C2×D14911yescharacteristic, complemented
251C24—2981no—
252#41—2982no—
253#41—5961no—
254C2×Q8—1491no—
255C2×D4—2982no—
256C2×D4—2981no—
257C2×D4—2981no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—5961no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4D59611yescharacteristic
266C22×C4—2981no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272SD16—5961no—
273D8—2982no—
274D8—5961no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D14911yescharacteristic
278C2×C8C22×D14911yescharacteristic
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4—1491no—
288C4⋊C4—1491no—
289C4⋊C4D59611yescharacteristic
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4D59611yescharacteristic
300C22⋊C4D59611yescharacteristic
301C42—2981no—
302C42C22×D14911yescharacteristic
303C23—2981no—
304C23—2981no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—11921no—
309C23C2×D59611yescharacteristic
310C23C2×D59611yescharacteristic
311Q8—2981no—
312Q8—2981no—
313D4—22no—
314D4—2981no—
315D4—2981no—
316D4—2981no—
317D4—2981no—
318D4—2981no—
319D4—5962no—
320D4—5962no—
321D4—5962no—
322D4—1492no—
323D4—11921no—
324D4—11921no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—5962no—
335C2×C4—11921no—
336C2×C4—11921no—
337C2×C4—11921no—
338C2×C4C2×D59611yescharacteristic
339C2×C4C2×D59611yescharacteristic
340C2×C4C2×D59611yescharacteristic
341C2×C4C2×D59611yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2982no—
353C22—5961no—
354C22—5961no—
355C22—5961no—
356C22—5961no—
357C22—5961no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—11924no—
362C22#1801193312yes—
363C22C22×D59611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—5961no—
369C4—5961no—
370C4—5961no—
371C4—5961no—
372C4—5961no—
373C4#41×D14911yescharacteristic
374C4#1801195611yescharacteristic
375C2—22no—
376C2—41no—
377C2—5962no—
378C2—11921no—
379C2—11921no—
380C2#2375027011yescharacteristic
381C2C2×#1801193311yescharacteristic
382C2#2375043011yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC8×D4×C149C2
socleC22×C149C22×D4
hypercenterC8×D4D149
hypocenterC149#3297
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23750321C2semidirect
2. #23750271C2semidirect
3. #23749980C2semidirect
4. #23749961C2semidirect
5. #23749950C2semidirect
6. #23749926C2semidirect
7. #23749861C2semidirect
8. #23749854C2semidirect
9. #23749841C2semidirect
10. #23749772C2semidirect
11. #23749761C2semidirect
12. C4×D1192C2semidirect
13. #23749622C2semidirect
14. C2×#18011833C2semidirect
15. C8×D4×C149C2semidirect
18. C2×#14558725C22semidirect
22. #18011903C22semidirect
29. #18011885C22semidirect
34. C4×D596C22semidirect
36. #18011870C22semidirect
39. #18011845C22semidirect
40. #18011845C22semidirect
41. #18011843C22semidirect
42. #18011836C22semidirect
43. #18011836C22semidirect
44. #18011836C22semidirect
51. #18011833C22semidirect
53. C22×C8×C149C22semidirect
55. C4⋊C8×C149C22semidirect
57. C22⋊C8×C149C22semidirect
58. C4×C8×C149C22semidirect
191. C149#3297semidirect
205. C8×D4D149semidirect
214. C22×C8C2×D149semidirect
237. C4⋊C8C2×D149semidirect
249. C22⋊C8C2×D149semidirect
250. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503212
#237502712
#237499802
#237499612
#237499502
#237499262
#237498612
#237498542
#237498412
#237497722
#237497612
C4×D11922
#237496222
C2×#180118332
C8×D4×C1492
#3297149