Finite Group Databasebeta

← #34056510

Subgroups — #34056510

Order 19072.

462 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#23750333C211yesmaximal, characteristic, complemented
2#23750259C211yesmaximal, characteristic
3#23749970C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic, complemented
5#23749941C211yesmaximal, characteristic, complemented
6#23749914C211yesmaximal, characteristic, complemented
7#23749857C211yesmaximal, characteristic, complemented
8#23749823C211yesmaximal, characteristic, complemented
9#23749775C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11#23749710C211yesmaximal, characteristic, complemented
12C8×C22⋊D149C211yesmaximal, characteristic, complemented
13C2×#18011833C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×D4×D149—21no—
18C2×D4×D149C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic, complemented
22#18011910C2211yescharacteristic, complemented
23#18011907C2211yescharacteristic
24#18011901—21no—
25#18011891—21no—
26#18011888—21no—
27#18011887C2211yescharacteristic, complemented
28#18011886C2211yescharacteristic
29#18011884—21no—
30#18011881—21no—
31#18011879—21no—
32Q8×Dic149C2211yescharacteristic, complemented
33#18011873C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35#18011871—21no—
36C2×C4⋊Dic149C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic, complemented
38#18011842C2211yescharacteristic, complemented
39#18011842C2211yescharacteristic, complemented
40#18011840C2211yescharacteristic, complemented
41#18011833C2211yescharacteristic
42#18011833C2211yescharacteristic
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011832C2211yescharacteristic, complemented
46#18011832C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic, complemented
53C22×C8×C149C2211yescharacteristic, complemented
54C22⋊Q8×C149C2211yescharacteristic, complemented
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149—21no—
61C2×Dic298—21no—
62C2×D596—22no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596—41no—
66C2×D596C2311yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149D411yescharacteristic
72D4×D149—22no—
73D4×D149—41no—
74D4×D149—44no—
75C22×Dic149—21no—
76C2×C4×D149—21no—
77C2×C4×D149—21no—
78C2×C4×D149C2311yescharacteristic
79#14558723—22no—
80#14558723—41no—
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C8×D149—41no—
84C4⋊Dic149—21no—
85C4⋊Dic149—21no—
86C4⋊Dic149C2311yescharacteristic
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558715—21no—
90#14558715—21no—
91#14558715D411yescharacteristic
92C22⋊Dic149D411yescharacteristic
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713D411yescharacteristic
97C4×Dic149—21no—
98C4×Dic149C2311yescharacteristic
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149C2311yescharacteristic
103SD16×C149—41no—
104C2×C8×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22⋊C4×C149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—81no—
119C22×D149—81no—
120C22×D149C2×D411yescharacteristic
121Dic298—81no—
122D596—21no—
123D596—21no—
124D596—21no—
125D596—42no—
126D596—42no—
127D596#4112yes—
128C22⋊D149—42no—
129C22⋊D149—42no—
130C22⋊D149—81no—
131C22⋊D149SD1614yescomplemented
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—81no—
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C2×Dic149C2×D411yescharacteristic
138C4×D149—21no—
139C4×D149—21no—
140C4×D149—42no—
141C4×D149—81no—
142#11924746—21no—
143#11924746—21no—
144C23×C149—21no—
145C23×C149C2×D411yescharacteristic
146Q8×C149—21no—
147Q8×C149—21no—
148D4×C149—21no—
149D4×C149—21no—
150D4×C149—42no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149C2×D411yescharacteristic
157C2×C4×C149C2411yescharacteristic
158C8×C149—21no—
159C8×C149—21no—
160C22×C149—21no—
161C22×C149—21no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149—41no—
165C22×C149C2×SD1612yes—
166C22×C149C22×D411yescharacteristic
167C2×D149—21no—
168C2×D149—21no—
169C2×D149—22no—
170C2×D149—41no—
171C2×D149—41no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—84no—
176C2×D149—84no—
177C2×D149C2×SD1612yes—
178C4×C149—21no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182C4×C149C2×#4111yescharacteristic
183C4×C149H(5,𝔽2)11yescharacteristic
184Dic149—21no—
185Dic149—21no—
186Dic149—41no—
187Dic149—41no—
188Dic149C2×SD1612yes—
189C2×C149—22no—
190C2×C149—81no—
191C2×C149#54611yescharacteristic
192C2×C149C22×SD1611yescharacteristic
193C2×C149#57611yescharacteristic
194D149—22no—
195D149—42no—
196D149—81no—
197C149#329511yescharacteristic, complemented, Sylow
198#3295—1491nomaximal, Sylow
199#554—1491no—
200D42—1491no—
201#486—1491no—
202#481—1491no—
203#481—1491no—
204#476—1491no—
205#465—1491no—
206#465D14911yescharacteristic, complemented
207#460—1491no—
208#450—1491no—
209#450—1491no—
210C4×SD16—1491no—
211C8×D4—1491no—
212C2×#102—1491no—
213C2×#102—1491no—
214C22×D4—2981no—
215C22×D4—1491no—
216C22×D4—1491no—
217C2×SD16—1491no—
218C2×SD16—1491no—
219C2×SD16C2×D14911yescharacteristic, complemented
220C22×C8—1491no—
221C22×C8C2×D14911yescharacteristic, complemented
222C4⋊Q8—1491no—
223#127—1491no—
224#125—2981no—
225C22⋊Q8—2981no—
226C22⋊Q8—2981no—
227C22⋊Q8—1491no—
228C22⋊Q8C2×D14911yescharacteristic, complemented
229#121—2981no—
230#121—1491no—
231#121C2×D14911yescharacteristic
232#120—2981no—
233#120—2981no—
234C4×Q8—1491no—
235C4×D4—2981no—
236C4×D4—1491no—
237C4×D4—1491no—
238C2×C4⋊C4—1491no—
239C2×C4⋊C4—1491no—
240#106—1491no—
241#106—1491no—
242#106C2×D14911yescharacteristic, complemented
243C4⋊C8—1491no—
244#103C2×D14911yescharacteristic, complemented
245#102—1491no—
246#102—1491no—
247#102—1491no—
248#102—1491no—
249#102—1491no—
250#102—1491no—
251#102—1491no—
252#102—1491no—
253#102C2×D14911yescharacteristic, complemented
254C22⋊C8—1491no—
255C22⋊C8—1491no—
256C4×C8—1491no—
257C24—2981no—
258C24—2981no—
259C2×Q8—2981no—
260C2×Q8C22×D14911yescharacteristic
261C2×D4—21no—
262C2×D4—2982no—
263C2×D4—2981no—
264C2×D4—2982no—
265C2×D4—2981no—
266C2×D4—2981no—
267C2×D4—2981no—
268C2×D4—2981no—
269C2×D4—5961no—
270C2×D4—5961no—
271C2×D4—5964no—
272C2×D4—1491no—
273C2×D4—1491no—
274C2×D4—1491no—
275C2×D4C22×D14911yescharacteristic
276C22×C4—2981no—
277C22×C4—2981no—
278C22×C4—2981no—
279C22×C4—1491no—
280C22×C4C22×D14911yescharacteristic
281SD16—41no—
282SD16—2982no—
283SD16—5961no—
284C2×C8—41no—
285C2×C8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8C22×D14911yescharacteristic
289C2×C8C22×D14911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2981no—
292C4⋊C4—2981no—
293C4⋊C4—2981no—
294C4⋊C4—2981no—
295C4⋊C4—2981no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4C22×D14911yescharacteristic
300C4⋊C4C22×D14911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2981no—
304C22⋊C4—2981no—
305C22⋊C4—2981no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C42—2981no—
309C42—1491no—
310C23—21no—
311C23—2981no—
312C23—2981no—
313C23—5962no—
314C23—5962no—
315C23—5962no—
316C23—5962no—
317C23—1491no—
318C23—11921no—
319C23—11921no—
320C23D4×D14911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—11921no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2981no—
328D4—2981no—
329D4—2981no—
330D4—5962no—
331D4—5962no—
332D4—5962no—
333D4—5962no—
334D4—1494no—
335D4—1492no—
336D4—11921no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5962no—
347C2×C4—1491no—
348C2×C4—1491no—
349C2×C4—1491no—
350C2×C4—11921no—
351C2×C4—11921no—
352C2×C4D4×D14911yescharacteristic
353C2×C4C23×D14911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2981no—
357C8—2981no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2981no—
364C22—2981no—
365C22—2982no—
366C22—5961no—
367C22—5961no—
368C22—5961no—
369C22—5961no—
370C22—5961no—
371C22—1492no—
372C22—11924no—
373C22—11924no—
374C22SD16×D14912yes—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2981no—
381C4—2981no—
382C4—5961no—
383C4—5961no—
384C4—1492no—
385C4#41×D14911yescharacteristic
386C4#1801195611yescharacteristic
387C2—22no—
388C2—81no—
389C2—2982no—
390C2—5962no—
391C2—11921no—
392C2#2375026411yescharacteristic
393C2C2×SD16×D14911yescharacteristic
394C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
prime radical#23750259C2
hypercenter#465D149
hypocenterC149#3295
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23750333C2semidirect
3. #23749970C2semidirect
4. #23749945C2semidirect
5. #23749941C2semidirect
6. #23749914C2semidirect
7. #23749857C2semidirect
8. #23749823C2semidirect
9. #23749775C2semidirect
10. #23749774C2semidirect
11. #23749710C2semidirect
12. C8×C22⋊D149C2semidirect
13. C2×#18011833C2semidirect
14. #102×D149C2semidirect
15. #465×C149C2semidirect
20. C2×#14558723C22semidirect
21. C2×C8×D149C22semidirect
22. #18011910C22semidirect
27. #18011887C22semidirect
32. Q8×Dic149C22semidirect
36. C2×C4⋊Dic149C22semidirect
37. C4⋊C4×D149C22semidirect
38. #18011842C22semidirect
39. #18011842C22semidirect
40. #18011840C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
52. C2×SD16×C149C22semidirect
53. C22×C8×C149C22semidirect
54. C22⋊Q8×C149C22semidirect
56. #106×C149C22semidirect
57. #103×C149C22semidirect
58. #102×C149C22semidirect
131. C22⋊D149SD16semidirect
197. C149#3295semidirect
206. #465D149semidirect
219. C2×SD16C2×D149semidirect
221. C22×C8C2×D149semidirect
228. C22⋊Q8C2×D149semidirect
242. #106C2×D149semidirect
244. #103C2×D149semidirect
253. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503332
#237502592
#237499702
#237499452
#237499412
#237499142
#237498572
#237498232
#237497752
#237497742
#237497102
C8×C22⋊D1492
C2×#180118332
#102×D1492
#465×C1492
#3295149