Finite Group Databasebeta

← #34055479

Subgroups — #34055479

Order 19072.

424 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
1#23750136C211yesmaximal, characteristic, complemented
2#23749966C211yesmaximal, characteristic, complemented
3#23749963C211yesmaximal, characteristic, complemented
4#23749949C211yesmaximal, characteristic, complemented
5#23749946C211yesmaximal, characteristic, complemented
6#23749864C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749856C211yesmaximal, characteristic, complemented
9#23749852C211yesmaximal, characteristic, complemented
10#23749787C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749770C211yesmaximal, characteristic, complemented
13#23749768C211yesmaximal, characteristic, complemented
14C2×C22⋊#11924746C211yesmaximal, characteristic, complemented
15#525×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558726C2211yescharacteristic, complemented
18C2×#14558724C2211yescharacteristic, complemented
19C2×#14558723C2211yescharacteristic, complemented
20C2×#14558721C2211yescharacteristic, complemented
21C22×#11924746C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23#18011894—21no—
24#18011890C2211yescharacteristic
25#18011890C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011885C2211yescharacteristic
28#18011880—21no—
29C4×C22⋊D149—21no—
30C4×C22⋊D149—21no—
31#18011870C2211yescharacteristic
32#18011844C2211yescharacteristic, complemented
33#18011844C2211yescharacteristic, complemented
34#18011842C2211yescharacteristic, complemented
35#18011842C2211yescharacteristic, complemented
36#18011835C2211yescharacteristic, complemented
37#18011835C2211yescharacteristic, complemented
38#18011834C2211yescharacteristic, complemented
39#18011834C2211yescharacteristic, complemented
40#18011832C2211yescharacteristic, complemented
41#18011832C2211yescharacteristic, complemented
42#18011831C2211yescharacteristic, complemented
43#18011831C2211yescharacteristic, complemented
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47C22⋊#11924746C2211yescharacteristic
48C2×#41×C149C2211yescharacteristic
49C23×C4×C149C2211yescharacteristic
50#123×C149—21no—
51C22⋊Q8×C149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#121×C149C2211yescharacteristic
54#121×C149C2211yescharacteristic
55#120×C149—21no—
56C4×D4×C149—21no—
57C4×D4×C149—21no—
58#117×C149C2211yescharacteristic
59#14558736—41no—
60#14558736—41no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C4×D149—21no—
67#14558726—41no—
68#14558724—41no—
69#14558723—41no—
70#14558721—41no—
71C2×#11924746—41no—
72C2×#11924746—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84#14558713—21no—
85#14558713—21no—
86C4×Dic149—21no—
87C24×C149D411yescharacteristic
88#41×C149—41no—
89#41×C149—41no—
90C2×Q8×C149C2311yescharacteristic
91C2×D4×C149—21no—
92C2×D4×C149—21no—
93C2×D4×C149—21no—
94C2×D4×C149C2311yescharacteristic
95C22×C4×C149—21no—
96C22×C4×C149—41no—
97C22×C4×C149—41no—
98C22×C4×C149D411yescharacteristic
99C22×C4×C149D411yescharacteristic
100C22×C4×C149D411yescharacteristic
101C22×C4×C149C2311yescharacteristic
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149—21no—
114C22×D149—21no—
115Dic298—21no—
116Dic298—21no—
117D596—21no—
118D596—21no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C22⋊D149—42no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C4×D149—42no—
126#11924746—21no—
127#11924746—21no—
128#11924746—21no—
129#11924746—21no—
130C23×C149—22no—
131C23×C149—21no—
132C23×C149—41no—
133C23×C149—41no—
134C23×C149C2×D411yescharacteristic
135C23×C149C2×D411yescharacteristic
136C23×C149C2×D411yescharacteristic
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141D4×C149—42no—
142D4×C149—42no—
143D4×C149—42no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—41no—
154C2×C4×C149—41no—
155C2×C4×C149—41no—
156C2×C4×C149—42no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2×D411yescharacteristic
159C2×C4×C149C2×D411yescharacteristic
160C2×C4×C149C2411yescharacteristic
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—44no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149#13512yes—
174C22×C149C22×D411yescharacteristic
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149—41no—
184C4×C149H(5,𝔽2)11yescharacteristic
185C4×C149H(5,𝔽2)11yescharacteristic
186Dic149—41no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—22no—
190C2×C149—41no—
191C2×C149—41no—
192C2×C149—81no—
193C2×C149#53411yescharacteristic
194C2×C149C2×#13511yescharacteristic
195C2×C149#57511yescharacteristic
196D149—81no—
197C149#319111yescharacteristic, complemented, Sylow
198#3191—1491nomaximal, Sylow
199#525—1491no—
200#525D14911yescharacteristic, complemented
201#485—1491no—
202#485—1491no—
203#482—1491no—
204#482—1491no—
205#467—1491no—
206#466—1491no—
207#465—1491no—
208#465—1491no—
209#452—1491no—
210#452—1491no—
211#449—1491no—
212#449—1491no—
213C2×C22⋊C8—1491no—
214C2×#41—1491no—
215C2×#41C2×D14911yescharacteristic
216C23×C4C2×D14911yescharacteristic
217C2×Q16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×D8—1491no—
221C22×C8—1491no—
222C22×C8—1491no—
223#123—21no—
224#123—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8C2×D14911yescharacteristic
228C22⋊Q8C2×D14911yescharacteristic
229#121—1491no—
230#121—1491no—
231#121C2×D14911yescharacteristic
232#121C2×D14911yescharacteristic
233#120—21no—
234#120—2981no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—2981no—
238C4×D4—2981no—
239#117—1491no—
240#117C2×D14911yescharacteristic
241#107—1491no—
242#107—1491no—
243#106—1491no—
244#106—1491no—
245#103—1491no—
246#103—1491no—
247#103—1491no—
248#103—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8—1491no—
257C24C22⋊D14911yescharacteristic
258#41—41no—
259#41—41no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8C22×D14911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—1491no—
271C2×D4C22×D14911yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—2981no—
276C22×C4C22⋊D14911yescharacteristic
277C22×C4C22⋊D14911yescharacteristic
278C22×C4C22⋊D14911yescharacteristic
279C22×C4C22×D14911yescharacteristic
280C22×C4C22×D14911yescharacteristic
281C22×C4C22×D14911yescharacteristic
282Q16—5961no—
283SD16—5961no—
284SD16—5961no—
285D8—5961no—
286C2×C8—5961no—
287C2×C8—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8—1491no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
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—21no—
311C42—2981no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—2981no—
317C23C2×C22⋊D14911yescharacteristic
318C23C2×C22⋊D14911yescharacteristic
319C23C2×C22⋊D14911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2981no—
323Q8—2981no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—2981no—
330D4—2981no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—5962no—
351C2×C4C2×C22⋊D14911yescharacteristic
352C2×C4C2×C22⋊D14911yescharacteristic
353C2×C4C2×C22⋊D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22#1801193112yes—
375C22C22×C22⋊D14911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—5961no—
383C4—5961no—
384C4—5961no—
385C4#1801195611yescharacteristic
386C4#1801195611yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—11921no—
392C2#2375018411yescharacteristic
393C2C2×#1801193111yescharacteristic
394C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#525×C149C2
socleC22×C149C22×D4
hypercenter#525D149
hypocenterC149#3191
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #23750136C2semidirect
2. #23749966C2semidirect
3. #23749963C2semidirect
4. #23749949C2semidirect
5. #23749946C2semidirect
6. #23749864C2semidirect
7. #23749859C2semidirect
8. #23749856C2semidirect
9. #23749852C2semidirect
10. #23749787C2semidirect
11. #23749785C2semidirect
12. #23749770C2semidirect
13. #23749768C2semidirect
14. C2×C22⋊#11924746C2semidirect
15. #525×C149C2semidirect
17. C2×#14558726C22semidirect
18. C2×#14558724C22semidirect
19. C2×#14558723C22semidirect
20. C2×#14558721C22semidirect
32. #18011844C22semidirect
33. #18011844C22semidirect
34. #18011842C22semidirect
35. #18011842C22semidirect
36. #18011835C22semidirect
37. #18011835C22semidirect
38. #18011834C22semidirect
39. #18011834C22semidirect
40. #18011832C22semidirect
41. #18011832C22semidirect
42. #18011831C22semidirect
43. #18011831C22semidirect
197. C149#3191semidirect
200. #525D149semidirect

Maximal subgroups

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

subgroupindex
#237501362
#237499662
#237499632
#237499492
#237499462
#237498642
#237498592
#237498562
#237498522
#237497872
#237497852
#237497702
#237497682
C2×C22⋊#119247462
#525×C1492
#3191149