Finite Group Databasebeta

← #34056526

Subgroups — #34056526

Order 19072.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750315C211yesmaximal, characteristic, complemented
2#23749979C211yesmaximal, characteristic, complemented
3#23749953C211yesmaximal, characteristic, complemented
4#23749946C211yesmaximal, characteristic, complemented
5#23749925C211yesmaximal, characteristic, complemented
6#23749864C211yesmaximal, characteristic, complemented
7#23749852C211yesmaximal, characteristic, complemented
8#23749844C211yesmaximal, characteristic, complemented
9#23749787C211yesmaximal, characteristic, complemented
10#23749776C211yesmaximal, characteristic, complemented
11C4×#14558724C211yesmaximal, characteristic, complemented
12D4×#11924746C211yesmaximal, characteristic, complemented
13#23749621C211yesmaximal, characteristic, complemented
14C2×#18011832C211yesmaximal, characteristic, complemented
15#546×C149C211yesmaximal, characteristic
16C2×#14558726C2211yescharacteristic, complemented
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C22×#11924746C2211yescharacteristic
20C22×#11924746C2211yescharacteristic, complemented
21#18011904—21no—
22#18011903C2211yescharacteristic, complemented
23#18011901—21no—
24#18011892—21no—
25#18011890C2211yescharacteristic
26#18011890C2211yescharacteristic, complemented
27C4×Dic298C2211yescharacteristic, complemented
28#18011870C2211yescharacteristic, complemented
29#18011867—21no—
30C2×C4⋊Dic149C2211yescharacteristic
31#18011844C2211yescharacteristic, complemented
32#18011842C2211yescharacteristic, complemented
33#18011842C2211yescharacteristic, complemented
34C4⋊#11924746C2211yescharacteristic, complemented
35#18011835C2211yescharacteristic, complemented
36#18011835C2211yescharacteristic, complemented
37#18011835C2211yescharacteristic, complemented
38#18011834C2211yescharacteristic, complemented
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic, complemented
47C4×#11924746C2211yescharacteristic, complemented
48C2×#41×C149C2211yescharacteristic
49C22×D4×C149C2211yescharacteristic
50#124×C149C2211yescharacteristic
51#123×C149—21no—
52C22⋊Q8×C149C2211yescharacteristic
53#121×C149—21no—
54#121×C149C2211yescharacteristic
55#120×C149—21no—
56C4×D4×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58C2×C22⋊C4×C149—21no—
59C2×Dic298C2311yescharacteristic
60C22×Dic149—21no—
61#14558726—41no—
62#14558724—22no—
63#14558724—41no—
64C2×#11924746—41no—
65C2×#11924746—41no—
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80C22⋊Dic149—21no—
81C22⋊Dic149—21no—
82C4×Dic149—21no—
83C4×Dic149—21no—
84C24×C149—21no—
85#41×C149—22no—
86#41×C149—41no—
87C2×Q8×C149C2311yescharacteristic
88C2×D4×C149—22no—
89C2×D4×C149—21no—
90C2×D4×C149—21no—
91C2×D4×C149—21no—
92C2×D4×C149—41no—
93C2×D4×C149D411yescharacteristic
94C2×D4×C149C2311yescharacteristic
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149—21no—
97C22×C4×C149—21no—
98C22×C4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149D411yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C22⋊C4×C149—21no—
108C22⋊C4×C149D411yescharacteristic
109C22⋊C4×C149D411yescharacteristic
110C42×C149C2311yescharacteristic
111Dic298—21no—
112Dic298—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—42no—
118#11924746—21no—
119#11924746—21no—
120#11924746—21no—
121#11924746—21no—
122C23×C149—21no—
123C23×C149—21no—
124C23×C149—42no—
125C23×C149—42no—
126C23×C149—81no—
127C23×C149C2×D411yescharacteristic
128C23×C149C2×D411yescharacteristic
129Q8×C149—21no—
130Q8×C149—21no—
131D4×C149—22no—
132D4×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135D4×C149—42no—
136D4×C149—42no—
137D4×C149—81no—
138D4×C149#4112yes—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—42no—
146C2×C4×C149—81no—
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2×D411yescharacteristic
150C2×C4×C149C2×D411yescharacteristic
151C2×C4×C149C2411yescharacteristic
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149—22no—
156C22×C149—21no—
157C22×C149—21no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—84no—
164C22×C149#13512yes—
165C22×C149C22×D411yescharacteristic
166C4×C149—21no—
167C4×C149—21no—
168C4×C149—21no—
169C4×C149—21no—
170C4×C149—41no—
171C4×C149—41no—
172C4×C149C2×#4111yescharacteristic
173C4×C149H(5,𝔽2)11yescharacteristic
174Dic149—41no—
175Dic149—41no—
176Dic149—41no—
177Dic149—41no—
178C2×C149—22no—
179C2×C149—41no—
180C2×C149—42no—
181C2×C149—81no—
182C2×C149#54611yescharacteristic
183C2×C149C2×#13511yescharacteristic
184C2×C149#57711yescharacteristic
185C149#329611yescharacteristic, complemented, Sylow
186#3296—1491nomaximal, Sylow
187#552—1491no—
188#546D14911yescharacteristic
189#488—1491no—
190#483—1491no—
191#482—1491no—
192#478—1491no—
193#467—1491no—
194#465—1491no—
195#464—1491no—
196#452—1491no—
197#450—1491no—
198C4×SD16—1491no—
199C8×D4—1491no—
200#416—1491no—
201C2×#102—1491no—
202C2×#41C2×D14911yescharacteristic
203C22×D4C2×D14911yescharacteristic
204C2×Q16—1491no—
205C2×SD16—1491no—
206C2×SD16—1491no—
207C22×C8—1491no—
208C22×C8—1491no—
209#126—2981no—
210#125—2981no—
211#125—1491no—
212#124C2×D14911yescharacteristic
213#123—21no—
214#123—2981no—
215C22⋊Q8—1491no—
216C22⋊Q8—1491no—
217C22⋊Q8C2×D14911yescharacteristic
218#121—21no—
219#121C2×D14911yescharacteristic
220#120—21no—
221C4×Q8—1491no—
222C4×D4C2×D14911yescharacteristic
223C4×D4C2×D14911yescharacteristic
224#117—2981no—
225#117—1491no—
226C2×C4⋊C4—1491no—
227C2×C22⋊C4—21no—
228#107—1491no—
229#106—1491no—
230#106—1491no—
231C4⋊C8—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103—1491no—
236#102—1491no—
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241#102—1491no—
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C4×C8—1491no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—1491no—
249C2×Q8C22×D14911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D14911yescharacteristic
256C2×D4C22×D14911yescharacteristic
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2981no—
261C22×C4C22×D14911yescharacteristic
262C22×C4C22×D14911yescharacteristic
263Q16—5961no—
264SD16—2982no—
265SD16—5961no—
266C2×C8—5961no—
267C2×C8—5961no—
268C2×C8—1491no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8—1491no—
272C4⋊C4—21no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—2981no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4—1491no—
282C4⋊C4C22⋊D14911yescharacteristic
283C4⋊C4C22×D14911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—2981no—
292C22⋊C4C22⋊D14911yescharacteristic
293C22⋊C4C22⋊D14911yescharacteristic
294C42—2981no—
295C42—2981no—
296C42C22×D14911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D14911yescharacteristic
303C23C2×C22⋊D14911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2981no—
307Q8—2981no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1455873512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—2981no—
325C2×C4—2981no—
326C2×C4—2981no—
327C2×C4—2981no—
328C2×C4—5962no—
329C2×C4C2×C22⋊D14911yescharacteristic
330C2×C4C2×C22⋊D14911yescharacteristic
331C2×C4C2×C22⋊D14911yescharacteristic
332C2×C4C2×C22⋊D14911yescharacteristic
333C2×C4C23×D14911yescharacteristic
334C8—2981no—
335C8—2981no—
336C8—2981no—
337C8—2981no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1801193112yes—
351C22C22×C22⋊D14911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—5961no—
359C4—5961no—
360C4—5961no—
361C4—5961no—
362C4C2×#1455873511yescharacteristic
363C4#1801195611yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#2375026911yescharacteristic
369C2C2×#1801193111yescharacteristic
370C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#546×C149C2
socleC22×C149C22×D4
hypercenter#546D149
hypocenterC149#3296
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #23750315C2semidirect
2. #23749979C2semidirect
3. #23749953C2semidirect
4. #23749946C2semidirect
5. #23749925C2semidirect
6. #23749864C2semidirect
7. #23749852C2semidirect
8. #23749844C2semidirect
9. #23749787C2semidirect
10. #23749776C2semidirect
11. C4×#14558724C2semidirect
12. D4×#11924746C2semidirect
13. #23749621C2semidirect
14. C2×#18011832C2semidirect
16. C2×#14558726C22semidirect
20. C22×#11924746C22semidirect
22. #18011903C22semidirect
26. #18011890C22semidirect
27. C4×Dic298C22semidirect
28. #18011870C22semidirect
31. #18011844C22semidirect
32. #18011842C22semidirect
33. #18011842C22semidirect
34. C4⋊#11924746C22semidirect
35. #18011835C22semidirect
36. #18011835C22semidirect
37. #18011835C22semidirect
38. #18011834C22semidirect
46. C22⋊#11924746C22semidirect
47. C4×#11924746C22semidirect
185. C149#3296semidirect

Maximal subgroups

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

subgroupindex
#237503152
#237499792
#237499532
#237499462
#237499252
#237498642
#237498522
#237498442
#237497872
#237497762
C4×#145587242
D4×#119247462
#237496212
C2×#180118322
#546×C1492
#3296149