Finite Group Databasebeta

← #34056502

Subgroups — #34056502

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#23750276C211yesmaximal, characteristic, complemented
2#23750259C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749940C211yesmaximal, characteristic, complemented
5#23749904C211yesmaximal, characteristic, complemented
6#23749862C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749819C211yesmaximal, characteristic, complemented
9#23749761C211yesmaximal, characteristic, complemented
10#23749760C211yesmaximal, characteristic, complemented
11#23749707C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13C2×#18011831C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#480×C149C211yesmaximal, characteristic, complemented
16C2×#14558736—21no—
17C22×D596C2211yescharacteristic
18C2×D4×D149—21no—
19C2×D4×D149C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×D1192C2211yescharacteristic, complemented
22C2×#14558721C2211yescharacteristic, complemented
23C22×#11924746C2211yescharacteristic, complemented
24C2×C8×D149C2211yescharacteristic, complemented
25#18011910C2211yescharacteristic, complemented
26#18011907C2211yescharacteristic
27#18011896—21no—
28#18011894—21no—
29#18011889—21no—
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic, complemented
32#18011885C2211yescharacteristic, complemented
33#18011884—21no—
34#18011881—21no—
35#18011879—21no—
36#18011873C2211yescharacteristic
37#18011873C2211yescharacteristic, complemented
38C4×C22⋊D149C2211yescharacteristic
39C4⋊C4×D149C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic
43#18011833C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic, complemented
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#121×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic, complemented
54#107×C149C2211yescharacteristic, complemented
55#107×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149—21no—
61#14558736—44no—
62C2×Dic298—21no—
63C2×D596—22no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—41no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×D596C2311yescharacteristic
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149D411yescharacteristic
76D4×D149—22no—
77D4×D149—41no—
78D4×D149—44no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149C2311yescharacteristic
83D1192—22no—
84D1192—41no—
85#14558721—41no—
86C2×#11924746—41no—
87C2×#11924746C2311yescharacteristic
88C2×#11924746C2311yescharacteristic
89C8×D149—41no—
90C4⋊Dic149C2311yescharacteristic
91#14558715—21no—
92#14558715—21no—
93#14558715D411yescharacteristic
94C22⋊Dic149D411yescharacteristic
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713D411yescharacteristic
101C4×Dic149C2311yescharacteristic
102C2×D4×C149—21no—
103C2×D4×C149C2311yescharacteristic
104C22×C4×C149—21no—
105C22×C4×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149—21no—
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22⋊C4×C149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—42no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149—42no—
120C22×D149—81no—
121C22×D149—81no—
122C22×D149C2×D411yescharacteristic
123Dic298—42no—
124D596—21no—
125D596—21no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—42no—
130D596—42no—
131D596—42no—
132D596#4112yescomplemented
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—42no—
136C22⋊D149—81no—
137C22⋊D149D814yescomplemented
138C2×Dic149—21no—
139C2×Dic149C2×D411yescharacteristic
140C2×Dic149C2×D411yescharacteristic
141C2×Dic149C2×D411yescharacteristic
142C4×D149—21no—
143C4×D149—21no—
144C4×D149—42no—
145C4×D149—42no—
146C4×D149—42no—
147#11924746—21no—
148#11924746—21no—
149C23×C149—21no—
150C23×C149C2×D411yescharacteristic
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—42no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—42no—
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×C149C2×D812yes—
170C22×C149C22×D411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—22no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
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×C149—41no—
189C4×C149C2×#4111yescharacteristic
190C4×C149H(5,𝔽2)11yescharacteristic
191Dic149—21no—
192Dic149—21no—
193Dic149—41no—
194Dic149C2×D812yes—
195C2×C149—22no—
196C2×C149—81no—
197C2×C149#54611yescharacteristic
198C2×C149C22×D811yescharacteristic
199C2×C149#57711yescharacteristic
200D149—22no—
201D149—42no—
202D149—81no—
203D149—81no—
204C149#329411yescharacteristic, complemented, Sylow
205#3294—1491nomaximal, Sylow
206#547—1491no—
207D42—1491no—
208#486—1491no—
209#480—1491no—
210#480D14911yescharacteristic, complemented
211#474—1491no—
212#466—1491no—
213#466—1491no—
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×D8—1491no—
228C22×C8—1491no—
229C22×C8—1491no—
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#121—1491no—
239#121C2×D14911yescharacteristic
240#120—2981no—
241#120—2981no—
242C4×D4—1491no—
243C4×D4—1491no—
244C4×D4—1491no—
245C2×C4⋊C4—1491no—
246C2×C4⋊C4C2×D14911yescharacteristic, complemented
247#107—1491no—
248#107C2×D14911yescharacteristic, complemented
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⋊C8C2×D14911yescharacteristic, complemented
263C4×C8—1491no—
264C24—2981no—
265C24—2981no—
266#41—5964no—
267C2×Q8—2981no—
268C2×D4—21no—
269C2×D4—2982no—
270C2×D4—2981no—
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×D4—1491no—
285C2×D4C22×D14911yescharacteristic
286C22×C4—21no—
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—1491no—
291C22×C4C22×D14911yescharacteristic
292D8—2982no—
293D8—5961no—
294D8—5961no—
295C2×C8—5961no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4C22×D14911yescharacteristic
307C4⋊C4C22×D14911yescharacteristic
308C4⋊C4C22×D14911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—1491no—
316C22⋊C4—1491no—
317C42—1491no—
318C23—21no—
319C23—2981no—
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—42no—
334D4—2981no—
335D4—2981no—
336D4—2981no—
337D4—2981no—
338D4—2981no—
339D4—5962no—
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—21no—
353C2×C4—42no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
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—2981no—
375C22—2981no—
376C22—2982no—
377C22—5961no—
378C22—5961no—
379C22—5961no—
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—41no—
394C4—2981no—
395C4—2981no—
396C4—5961no—
397C4—1492no—
398C4#41×D14911yescharacteristic
399C4#1801195711yescharacteristic
400C2—22no—
401C2—81no—
402C2—2982no—
403C2—5962no—
404C2—11921no—
405C2—11921no—
406C2#2375026711yescharacteristic
407C2C2×D8×D14911yescharacteristic
408C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
hypercenter#480D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23750276C2semidirect
2. #23750259C2semidirect
3. #23749970C2semidirect
4. #23749940C2semidirect
5. #23749904C2semidirect
6. #23749862C2semidirect
7. #23749859C2semidirect
8. #23749819C2semidirect
9. #23749761C2semidirect
10. #23749760C2semidirect
11. #23749707C2semidirect
12. #23749688C2semidirect
13. C2×#18011831C2semidirect
14. #102×D149C2semidirect
15. #480×C149C2semidirect
21. C2×D1192C22semidirect
22. C2×#14558721C22semidirect
23. C22×#11924746C22semidirect
24. C2×C8×D149C22semidirect
25. #18011910C22semidirect
31. #18011886C22semidirect
32. #18011885C22semidirect
37. #18011873C22semidirect
39. C4⋊C4×D149C22semidirect
40. #18011844C22semidirect
41. #18011840C22semidirect
43. #18011833C22semidirect
44. #18011832C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
53. C2×C4⋊C4×C149C22semidirect
54. #107×C149C22semidirect
55. #107×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
132. D596#41semidirect
137. C22⋊D149D8semidirect
204. C149#3294semidirect
210. #480D149semidirect
246. C2×C4⋊C4C2×D149semidirect
248. #107C2×D149semidirect
249. #107C2×D149semidirect
259. #102C2×D149semidirect
260. #102C2×D149semidirect
262. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502762
#237502592
#237499702
#237499402
#237499042
#237498622
#237498592
#237498192
#237497612
#237497602
#237497072
#237496882
C2×#180118312
#102×D1492
#480×C1492
#3294149