Finite Group Databasebeta

← #34054874

Subgroups — #34054874

Order 19072.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750244C211yesmaximal, characteristic, complemented
2#23750097C211yesmaximal, characteristic, complemented
3#23749964C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749916C211yesmaximal, characteristic, complemented
6#23749905C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749774C211yesmaximal, characteristic, complemented
9#23749757C211yesmaximal, characteristic
10#23749737C211yesmaximal, characteristic, complemented
11#23749728C211yesmaximal, characteristic, complemented
12SD16×Dic149C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19#18011911C2211yescharacteristic, complemented
20#18011904—21no—
21#18011897—21no—
22#18011895—21no—
23#18011888—21no—
24#18011887C2211yescharacteristic
25#18011882C2211yescharacteristic
26Q8×Dic149C2211yescharacteristic, complemented
27C4×D596C2211yescharacteristic
28D4×Dic149C2211yescharacteristic
29D4×Dic149C2211yescharacteristic, complemented
30#18011873C2211yescharacteristic
31C4×C22⋊D149—21no—
32#18011871—21no—
33#18011869C2211yescharacteristic
34#18011868C2211yescharacteristic
35C2×#14558713—21no—
36C22⋊C4×D149—21no—
37#18011844C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic, complemented
55C4×D4×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58#102×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×D596C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64D4×D149—22no—
65D4×D149—22no—
66C22×Dic149—21no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558723—22no—
72#14558721—22no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91#14558713D411yescharacteristic
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C2×Q8×C149C2311yescharacteristic
96C2×D4×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99SD16×C149—22no—
100D8×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—24no—
110C22×D149—81no—
111C22×D149—81no—
112C22×D149C2×D411yescharacteristic
113Dic298—81no—
114D596—21no—
115D596#4112yes—
116C22⋊D149—24no—
117C22⋊D149—81no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—81no—
122C2×Dic149—81no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—21no—
127C4×D149—21no—
128C4×D149—81no—
129C4×D149—81no—
130#11924746—21no—
131#11924746—21no—
132C23×C149—21no—
133C23×C149—21no—
134Q8×C149—21no—
135Q8×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149—21no—
139D4×C149#4112yes—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—81no—
143C2×C4×C149C2×D411yescharacteristic
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—22no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149—41no—
154C22×C149C22×D411yescharacteristic
155C2×D149—21no—
156C2×D149—22no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—84no—
162C4×C149—21no—
163C4×C149—21no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149C2×#4111yescharacteristic
167C4×C149C2×#4111yescharacteristic
168Dic149—21no—
169Dic149—21no—
170Dic149—21no—
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174C2×C149—42no—
175C2×C149—81no—
176C2×C149#52511yescharacteristic
177C2×C149#57611yescharacteristic
178C2×C149#57711yescharacteristic
179D149—41no—
180D149—42no—
181C149#311811yescharacteristic, complemented, Sylow
182#3118—1491nomaximal, Sylow
183#542—1491no—
184#518—1491no—
185#485—1491no—
186#482—1491no—
187#476—1491no—
188#474—1491no—
189#463—1491no—
190#463D14911yescharacteristic, complemented
191#450—1491no—
192#447—1491no—
193#442—1491no—
194#440—1491no—
195C4×SD16—1491no—
196C4×D8—1491no—
197#433—1491no—
198C22×D4—1491no—
199C2×SD16—1491no—
200C2×SD16C2×D14911yescharacteristic
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C4⋊Q8—1491no—
204#126—2981no—
205#124—2981no—
206#124C2×D14911yescharacteristic, complemented
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210#121—1491no—
211C4×Q8—1491no—
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218C4×D4C2×D14911yescharacteristic
219#117—1491no—
220#117—1491no—
221C2×C22⋊C4—2981no—
222C2×C22⋊C4—2981no—
223#107—1491no—
224#107—1491no—
225#106—1491no—
226#106—1491no—
227C4⋊C8—1491no—
228C4⋊C8C2×D14911yescharacteristic, complemented
229#103—1491no—
230#103C2×D14911yescharacteristic, complemented
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102C2×D14911yescharacteristic, complemented
237C22⋊C8—1491no—
238C22⋊C8—1491no—
239#97—1491no—
240C4×C8—1491no—
241C24—2981no—
242C2×Q8—2981no—
243C2×Q8C22×D14911yescharacteristic
244C2×D4—2982no—
245C2×D4—2982no—
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C22×C4—21no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—1491no—
257SD16—22no—
258SD16—2982no—
259D8—22no—
260D8—2982no—
261C2×C8—1491no—
262C2×C8—1491no—
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—1491no—
269C4⋊C4—1491no—
270C4⋊C4—1491no—
271C4⋊C4—1491no—
272C4⋊C4—1491no—
273C4⋊C4C22×D14911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—1491no—
285C22⋊C4—1491no—
286C42—2981no—
287C42—2981no—
288C42—1491no—
289C42C22×D14911yescharacteristic
290C23—21no—
291C23—21no—
292C23—2984no—
293C23—2981no—
294C23—1491no—
295C23—11921no—
296C23—11921no—
297Q8—21no—
298Q8—21no—
299Q8—11921no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2984no—
304D4—2981no—
305D4—1492no—
306D4—11921no—
307D4#1455873512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—11921no—
320C2×C4—11921no—
321C2×C4—11921no—
322C2×C4—11921no—
323C2×C4D4×D14911yescharacteristic
324C2×C4D4×D14911yescharacteristic
325C2×C4C23×D14911yescharacteristic
326C8—21no—
327C8—21no—
328C8—2981no—
329C8—2981no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—2981no—
337C22—2981no—
338C22—2981no—
339C22—2982no—
340C22—5961no—
341C22—5961no—
342C22—11924no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—2981no—
349C4—2981no—
350C4—2981no—
351C4—5961no—
352C4—5961no—
353C4—5961no—
354C4#41×D14911yescharacteristic
355C4C2×#1455873511yescharacteristic
356C2—42no—
357C2—81no—
358C2—5961no—
359C2—5962no—
360C2#2375013511yescharacteristic
361C2#2375042911yescharacteristic
362C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
prime radical#23749757C2
hypercenter#463D149
hypocenterC149#3118
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23750244C2semidirect
2. #23750097C2semidirect
3. #23749964C2semidirect
4. #23749948C2semidirect
5. #23749916C2semidirect
6. #23749905C2semidirect
7. #23749837C2semidirect
8. #23749774C2semidirect
10. #23749737C2semidirect
11. #23749728C2semidirect
12. SD16×Dic149C2semidirect
13. #23749705C2semidirect
14. #23749685C2semidirect
15. #463×C149C2semidirect
19. #18011911C22semidirect
26. Q8×Dic149C22semidirect
29. D4×Dic149C22semidirect
37. #18011844C22semidirect
38. #18011844C22semidirect
39. #18011843C22semidirect
40. #18011843C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011835C22semidirect
47. #18011832C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
54. #124×C149C22semidirect
56. C4⋊C8×C149C22semidirect
57. #103×C149C22semidirect
58. #102×C149C22semidirect
181. C149#3118semidirect
190. #463D149semidirect
206. #124C2×D149semidirect
228. C4⋊C8C2×D149semidirect
230. #103C2×D149semidirect
236. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502442
#237500972
#237499642
#237499482
#237499162
#237499052
#237498372
#237497742
#237497572
#237497372
#237497282
SD16×Dic1492
#237497052
#237496852
#463×C1492
#3118149