Finite Group Databasebeta

← #34055486

Subgroups — #34055486

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#23750138C211yesmaximal, characteristic, complemented
2#23750137C211yesmaximal, characteristic, complemented
3#23749968C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749949C211yesmaximal, characteristic, complemented
6#23749865C211yesmaximal, characteristic, complemented
7#23749862C211yesmaximal, characteristic, complemented
8#23749857C211yesmaximal, characteristic, complemented
9#23749855C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749785C211yesmaximal, characteristic, complemented
12#23749773C211yesmaximal, characteristic, complemented
13#23749772C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558736C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C2×#14558726C2211yescharacteristic, complemented
20C2×#14558725C2211yescharacteristic, complemented
21C2×#14558723C2211yescharacteristic, complemented
22C2×D1192C2211yescharacteristic, complemented
23C2×C8×D149C2211yescharacteristic
24C2×C8×D149C2211yescharacteristic
25#18011896—21no—
26#18011895—21no—
27#18011891C2211yescharacteristic
28#18011891C2211yescharacteristic
29#18011887C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic
32#18011886C2211yescharacteristic
33#18011885C2211yescharacteristic
34#18011881—21no—
35#18011881—21no—
36C4×D596—21no—
37C4×D596—21no—
38#18011873—21no—
39#18011871—21no—
40#18011869C2211yescharacteristic
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
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149D411yescharacteristic
60#14558737—41no—
61#14558737—41no—
62#14558736—41no—
63#14558736—41no—
64C2×Dic298C2311yescharacteristic
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596C2311yescharacteristic
70C2×D596C2311yescharacteristic
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C22×Dic149D411yescharacteristic
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149—41no—
77C2×C4×D149—41no—
78C2×C4×D149D411yescharacteristic
79C2×C4×D149D411yescharacteristic
80C2×C4×D149C2311yescharacteristic
81C2×C4×D149C2311yescharacteristic
82#14558726—41no—
83#14558725—41no—
84#14558723—41no—
85D1192—41no—
86C2×#11924746C2311yescharacteristic
87C2×#11924746C2311yescharacteristic
88C8×D149—41no—
89C8×D149—41no—
90C4⋊Dic149—21no—
91C4⋊Dic149—21no—
92C4⋊Dic149C2311yescharacteristic
93#14558715—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102C4×Dic149—21no—
103C2×Q8×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149—21no—
114C22×D149—22no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—41no—
118C22×D149—41no—
119C22×D149C2×D411yescharacteristic
120C22×D149C2×D411yescharacteristic
121Dic298—21no—
122Dic298—21no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—42no—
128D596—42no—
129D596—42no—
130D596—42no—
131C22⋊D149—42no—
132C22⋊D149—42no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—41no—
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—21no—
141C4×D149—21no—
142C4×D149—41no—
143C4×D149—41no—
144C4×D149—42no—
145C4×D149—42no—
146#11924746—21no—
147#11924746—21no—
148C23×C149C2×D411yescharacteristic
149Q8×C149—21no—
150Q8×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149C2×D411yescharacteristic
158C2×C4×C149C2411yescharacteristic
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—44no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149#13512yes—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149—41no—
183C4×C149H(5,𝔽2)11yescharacteristic
184C4×C149H(5,𝔽2)11yescharacteristic
185Dic149—21no—
186Dic149—21no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—41no—
190C2×C149#53411yescharacteristic
191C2×C149C2×#13511yescharacteristic
192C2×C149#57511yescharacteristic
193D149—22no—
194D149—41no—
195D149—81no—
196D149—81no—
197C149#319111yescharacteristic, complemented, Sylow
198#3191—1491nomaximal, Sylow
199#525—1491no—
200#525—1491no—
201#485—1491no—
202#485D14911yescharacteristic, complemented
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×#41—1491no—
216C23×C4—1491no—
217C2×Q16—1491no—
218C2×SD16—1491no—
219C2×SD16—1491no—
220C2×D8—1491no—
221C22×C8—1491no—
222C22×C8—1491no—
223#123—2981no—
224#123—2981no—
225C22⋊Q8—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228C22⋊Q8C2×D14911yescharacteristic
229#121—1491no—
230#121—1491no—
231#121—1491no—
232#121—1491no—
233#120—2981no—
234#120—2981no—
235C4×D4—2981no—
236C4×D4—2981no—
237C4×D4—2981no—
238C4×D4—2981no—
239#117—1491no—
240#117C2×D14911yescharacteristic
241#107—1491no—
242#107C2×D14911yescharacteristic, complemented
243#106—1491no—
244#106C2×D14911yescharacteristic, complemented
245#103—1491no—
246#103—1491no—
247#103C2×D14911yescharacteristic, complemented
248#103C2×D14911yescharacteristic, complemented
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102—1491no—
253C22⋊C8—1491no—
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C22⋊C8C2×D14911yescharacteristic
257C24—1491no—
258#41—5961no—
259#41—5961no—
260#41—5961no—
261#41—5961no—
262C2×Q8—1491no—
263C2×Q8C22×D14911yescharacteristic
264C2×D4—2981no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—2981no—
270C2×D4—1491no—
271C2×D4—1491no—
272C22×C4—2981no—
273C22×C4—2981no—
274C22×C4—5961no—
275C22×C4—5961no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4C22×D14911yescharacteristic
282Q16—5961no—
283SD16—5961no—
284SD16—5961no—
285D8—5961no—
286C2×C8—5961no—
287C2×C8—5961no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4C22×D14911yescharacteristic
298C4⋊C4C22×D14911yescharacteristic
299C4⋊C4C22×D14911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2981no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—2981no—
307C22⋊C4—2981no—
308C22⋊C4—2981no—
309C22⋊C4—2981no—
310C42—21no—
311C42—2981no—
312C23—2982no—
313C23—2981no—
314C23—2981no—
315C23—5961no—
316C23—5961no—
317C23—1491no—
318C23—1491no—
319C23D4×D14911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2981no—
323Q8—2981no—
324D4—2981no—
325D4—2981no—
326D4—2981no—
327D4—2981no—
328D4—5962no—
329D4—5962no—
330D4—5962no—
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—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5961no—
347C2×C4—5961no—
348C2×C4—5962no—
349C2×C4—5962no—
350C2×C4—5961no—
351C2×C4—1491no—
352C2×C4—1491no—
353C2×C4D4×D14911yescharacteristic
354C2×C4C23×D14911yescharacteristic
355C8—21no—
356C8—21no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—2981no—
363C22—2981no—
364C22—2981no—
365C22—2981no—
366C22—2981no—
367C22—5964no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22—1492no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2981no—
382C4—2981no—
383C4—5961no—
384C4—5961no—
385C4#1801195711yescharacteristic
386C4#1801195711yescharacteristic
387C2—41no—
388C2—2982no—
389C2—5961no—
390C2—11921no—
391C2—11921no—
392C2#2375018611yescharacteristic
393C2#135×D14911yescharacteristic
394C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
hypercenter#485D149
hypocenterC149#3191
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23750138C2semidirect
2. #23750137C2semidirect
3. #23749968C2semidirect
4. #23749951C2semidirect
5. #23749949C2semidirect
6. #23749865C2semidirect
7. #23749862C2semidirect
8. #23749857C2semidirect
9. #23749855C2semidirect
10. #23749790C2semidirect
11. #23749785C2semidirect
12. #23749773C2semidirect
13. #23749772C2semidirect
14. C22⋊C8×D149C2semidirect
15. #485×C149C2semidirect
19. C2×#14558726C22semidirect
20. C2×#14558725C22semidirect
21. C2×#14558723C22semidirect
22. C2×D1192C22semidirect
41. #18011844C22semidirect
42. #18011842C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
45. #18011833C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
197. C149#3191semidirect
202. #485D149semidirect
242. #107C2×D149semidirect
244. #106C2×D149semidirect
247. #103C2×D149semidirect
248. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501382
#237501372
#237499682
#237499512
#237499492
#237498652
#237498622
#237498572
#237498552
#237497902
#237497852
#237497732
#237497722
C22⋊C8×D1492
#485×C1492
#3191149