Finite Group Databasebeta

← #34056499

Subgroups — #34056499

Order 19072.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750275C211yesmaximal, characteristic, complemented
2#23750259C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749940C211yesmaximal, characteristic, complemented
5#23749936C211yesmaximal, characteristic, complemented
6#23749904C211yesmaximal, characteristic, complemented
7#23749860C211yesmaximal, characteristic, complemented
8#23749818C211yesmaximal, characteristic, complemented
9#23749758C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic, complemented
11#23749705C211yesmaximal, characteristic, complemented
12C8×C22⋊D149C211yesmaximal, characteristic, complemented
13C2×#18011833C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#466×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C22×D596C2211yescharacteristic
18C2×D4×D149—21no—
19C2×D4×D149C2211yescharacteristic
20C2×#14558721C2211yescharacteristic
21C2×#14558721C2211yescharacteristic, complemented
22C2×C8×D149C2211yescharacteristic, complemented
23#18011910C2211yescharacteristic, complemented
24#18011907C2211yescharacteristic
25#18011893—21no—
26#18011892—21no—
27#18011888—21no—
28#18011886C2211yescharacteristic
29#18011884—21no—
30#18011882C2211yescharacteristic, complemented
31#18011881—21no—
32#18011879—21no—
33D4×Dic149C2211yescharacteristic, complemented
34#18011873C2211yescharacteristic
35C4×C22⋊D149C2211yescharacteristic
36C2×C4⋊Dic149C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, 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×D8×C149C2211yescharacteristic, complemented
53C22×C8×C149C2211yescharacteristic, complemented
54#121×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic, complemented
56#107×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149—21no—
61#14558735—44no—
62C2×Dic298—21no—
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—41no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149D411yescharacteristic
74D4×D149—22no—
75D4×D149—41no—
76D4×D149—44no—
77C22×Dic149—21no—
78C22×Dic149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82#14558721—22no—
83#14558721—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C8×D149—41no—
87C4⋊Dic149—21no—
88C4⋊Dic149C2311yescharacteristic
89C4⋊Dic149C2311yescharacteristic
90#14558715—21no—
91#14558715—21no—
92#14558715D411yescharacteristic
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95C22⋊Dic149D411yescharacteristic
96#14558713—21no—
97#14558713—21no—
98#14558713D411yescharacteristic
99C4×Dic149C2311yescharacteristic
100C2×D4×C149—21no—
101C2×D4×C149—21no—
102C2×D4×C149C2311yescharacteristic
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105D8×C149—41no—
106C2×C8×C149—41no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—42no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149—81no—
120C22×D149—81no—
121C22×D149C2×D411yescharacteristic
122Dic298—42no—
123D596—21no—
124D596—21no—
125D596—21no—
126D596—42no—
127D596—42no—
128D596#4112yescomplemented
129C22⋊D149—42no—
130C22⋊D149—42no—
131C22⋊D149—42no—
132C22⋊D149—81no—
133C22⋊D149D814yescomplemented
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—42no—
137C2×Dic149—42no—
138C2×Dic149C2×D411yescharacteristic
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C4×D149—21no—
142C4×D149—21no—
143C4×D149—42no—
144C4×D149—42no—
145#11924746—21no—
146#11924746—21no—
147C23×C149—21no—
148C23×C149—21no—
149C23×C149C2×D411yescharacteristic
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—42no—
155D4×C149—42no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149C2×D411yescharacteristic
161C2×C4×C149C2411yescharacteristic
162C8×C149—21no—
163C8×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149C2×D812yes—
173C22×C149C22×D411yescharacteristic
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—22no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—84no—
183C2×D149—84no—
184C2×D149C2×D812yes—
185C4×C149—21no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149C2×#4111yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—21no—
192Dic149—41no—
193Dic149—41no—
194Dic149C2×D812yes—
195C2×C149—22no—
196C2×C149—81no—
197C2×C149—81no—
198C2×C149#54611yescharacteristic
199C2×C149C22×D811yescharacteristic
200C2×C149#57711yescharacteristic
201D149—22no—
202D149—42no—
203D149—81no—
204C149#329411yescharacteristic, complemented, Sylow
205#3294—1491nomaximal, Sylow
206#547—1491no—
207D42—1491no—
208#486—1491no—
209#480—1491no—
210#480—1491no—
211#474—1491no—
212#466—1491no—
213#466D14911yescharacteristic, complemented
214#459—1491no—
215#447—1491no—
216#447—1491no—
217C4×D8—1491no—
218C8×D4—1491no—
219C2×#102—1491no—
220C2×#102—1491no—
221C2×#41—2981no—
222C22×D4—2981no—
223C22×D4—1491no—
224C22×D4—1491no—
225C2×D8—1491no—
226C2×D8—1491no—
227C2×D8C2×D14911yescharacteristic, complemented
228C22×C8—1491no—
229C22×C8C2×D14911yescharacteristic, complemented
230C4⋊Q8—1491no—
231#127—1491no—
232#123—2981no—
233#123—2981no—
234C22⋊Q8—2981no—
235#121—2981no—
236#121—1491no—
237#121—1491no—
238#121C2×D14911yescharacteristic
239#121C2×D14911yescharacteristic, complemented
240#120—2981no—
241#120—2981no—
242C4×D4—1491no—
243C4×D4—1491no—
244C4×D4—1491no—
245C2×C4⋊C4—1491no—
246C2×C4⋊C4—1491no—
247#107—1491no—
248#107—1491no—
249#107C2×D14911yescharacteristic, complemented
250C4⋊C8—1491no—
251#102—1491no—
252#102—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102—1491no—
257#102—1491no—
258#102—1491no—
259#102C2×D14911yescharacteristic, complemented
260#102C2×D14911yescharacteristic, complemented
261C22⋊C8—1491no—
262C22⋊C8—1491no—
263C4×C8—1491no—
264C24—2981no—
265C24—2981no—
266#41—5964no—
267C2×Q8—2981no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—2982no—
271C2×D4—2981no—
272C2×D4—2982no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—5961no—
279C2×D4—5961no—
280C2×D4—5964no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4—1491no—
284C2×D4C22×D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—1491no—
291C22×C4C22×D14911yescharacteristic
292D8—41no—
293D8—2982no—
294D8—5961no—
295C2×C8—41no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C4⋊C4—2981no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4—1491no—
307C4⋊C4C22×D14911yescharacteristic
308C4⋊C4C22×D14911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—1491no—
316C22⋊C4—1491no—
317C42—1491no—
318C23—21no—
319C23—21no—
320C23—2981no—
321C23—2981no—
322C23—5962no—
323C23—5962no—
324C23—5962no—
325C23—5962no—
326C23—1491no—
327C23—11921no—
328C23—11921no—
329C23D4×D14911yescharacteristic
330Q8—5962no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—2981no—
338D4—2981no—
339D4—2981no—
340D4—5962no—
341D4—5962no—
342D4—5962no—
343D4—5962no—
344D4—5962no—
345D4—1494no—
346D4—1492no—
347D4—11921no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—2981no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—5962no—
357C2×C4—5962no—
358C2×C4—5962no—
359C2×C4—5962no—
360C2×C4—1491no—
361C2×C4—1491no—
362C2×C4—1491no—
363C2×C4D4×D14911yescharacteristic
364C2×C4C23×D14911yescharacteristic
365C8—21no—
366C8—21no—
367C8—2981no—
368C8—2981no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2981no—
378C22—2981no—
379C22—2982no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—1492no—
386C22—11924no—
387C22—11924no—
388C22D8×D14912yes—
389C22C2×D4×D14911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2981no—
394C4—2981no—
395C4—5961no—
396C4—5961no—
397C4—1492no—
398C4#41×D14911yescharacteristic
399C4#1801195611yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—2982no—
404C2—5962no—
405C2—11921no—
406C2#2375026411yescharacteristic
407C2C2×D8×D14911yescharacteristic
408C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23750275C2semidirect
2. #23750259C2semidirect
3. #23749970C2semidirect
4. #23749940C2semidirect
5. #23749936C2semidirect
6. #23749904C2semidirect
7. #23749860C2semidirect
8. #23749818C2semidirect
9. #23749758C2semidirect
10. #23749757C2semidirect
11. #23749705C2semidirect
12. C8×C22⋊D149C2semidirect
13. C2×#18011833C2semidirect
14. #102×D149C2semidirect
15. #466×C149C2semidirect
21. C2×#14558721C22semidirect
22. C2×C8×D149C22semidirect
23. #18011910C22semidirect
30. #18011882C22semidirect
33. D4×Dic149C22semidirect
36. C2×C4⋊Dic149C22semidirect
37. C4⋊C4×D149C22semidirect
38. #18011844C22semidirect
39. #18011844C22semidirect
40. #18011840C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
45. #18011832C22semidirect
46. #18011832C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
52. C2×D8×C149C22semidirect
53. C22×C8×C149C22semidirect
55. #121×C149C22semidirect
56. #107×C149C22semidirect
57. #102×C149C22semidirect
58. #102×C149C22semidirect
128. D596#41semidirect
133. C22⋊D149D8semidirect
204. C149#3294semidirect
213. #466D149semidirect
227. C2×D8C2×D149semidirect
229. C22×C8C2×D149semidirect
239. #121C2×D149semidirect
249. #107C2×D149semidirect
259. #102C2×D149semidirect
260. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502752
#237502592
#237499702
#237499402
#237499362
#237499042
#237498602
#237498182
#237497582
#237497572
#237497052
C8×C22⋊D1492
C2×#180118332
#102×D1492
#466×C1492
#3294149