Finite Group Databasebeta

← #34054876

Subgroups — #34054876

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#23750248C211yesmaximal, characteristic, complemented
2#23750100C211yesmaximal, characteristic, complemented
3#23749963C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749913C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749842C211yesmaximal, characteristic, complemented
8#23749842C211yesmaximal, characteristic, complemented
9#23749759C211yesmaximal, characteristic
10#23749734C211yesmaximal, characteristic, complemented
11#23749726C211yesmaximal, characteristic, complemented
12SD16×Dic149C211yesmaximal, characteristic, complemented
13#23749705C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18#18011910C2211yescharacteristic, complemented
19#18011906—21no—
20#18011900C2211yescharacteristic, complemented
21#18011897—21no—
22#18011893—21no—
23#18011891—21no—
24#18011885C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic, complemented
26D4×Dic149—21no—
27D4×Dic149—21no—
28D4×Dic149C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic, complemented
33#18011870C2211yescharacteristic
34#18011870C2211yescharacteristic
35C2×C22⋊Dic149—21no—
36C2×C22⋊Dic149—21no—
37#18011845C2211yescharacteristic, complemented
38#18011844C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011835C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C22×Dic149—21no—
63C22×Dic149—21no—
64C22×Dic149—21no—
65C22×Dic149—21no—
66C2×C4×D149—21no—
67#14558721—22no—
68#14558721—22no—
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C4⋊Dic149—21no—
72C4⋊Dic149D411yescharacteristic
73C4⋊Dic149D411yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78C22⋊Dic149—21no—
79C22⋊Dic149—21no—
80C22⋊Dic149—21no—
81C22⋊Dic149—21no—
82C22⋊Dic149—21no—
83C22⋊Dic149D411yescharacteristic
84C22⋊Dic149D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93C24×C149—21no—
94C2×Q8×C149C2311yescharacteristic
95C2×D4×C149—22no—
96C2×D4×C149—22no—
97C2×D4×C149—21no—
98C2×D4×C149C2311yescharacteristic
99C2×D4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101SD16×C149—22no—
102SD16×C149—22no—
103C2×C8×C149C2311yescharacteristic
104C2×C8×C149C2311yescharacteristic
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22×D149—21no—
109Dic298—81no—
110D596—21no—
111D596—21no—
112C22⋊D149—81no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—81no—
117C2×Dic149—81no—
118C2×Dic149—81no—
119C2×Dic149—81no—
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127C23×C149—24no—
128C23×C149—21no—
129C23×C149—21no—
130C23×C149—81no—
131C23×C149—81no—
132C23×C149C2×D411yescharacteristic
133Q8×C149—21no—
134Q8×C149—21no—
135D4×C149—24no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149#4112yes—
139D4×C149#4112yes—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—21no—
147C8×C149—21no—
148C22×C149—21no—
149C22×C149—22no—
150C22×C149—22no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149—41no—
156C22×C149—41no—
157C22×C149—84no—
158C22×C149C22×D411yescharacteristic
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149C2×#4111yescharacteristic
166C4×C149C2×#4111yescharacteristic
167Dic149—21no—
168Dic149—21no—
169Dic149—21no—
170Dic149—21no—
171Dic149—41no—
172Dic149—41no—
173Dic149—41no—
174C2×C149—41no—
175C2×C149—42no—
176C2×C149—42no—
177C2×C149#52511yescharacteristic
178C2×C149#57611yescharacteristic
179C2×C149#57711yescharacteristic
180D149—81no—
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#463—1491no—
191#450D14911yescharacteristic, complemented
192#447—1491no—
193#442—1491no—
194#440—1491no—
195C4×SD16—1491no—
196C4×D8—1491no—
197#433—1491no—
198C22×D4C2×D14911yescharacteristic
199C2×SD16C2×D14911yescharacteristic
200C2×SD16C2×D14911yescharacteristic
201C2×D8—1491no—
202C2×D8—1491no—
203C4⋊Q8—1491no—
204#126—2981no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8C2×D14911yescharacteristic
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×D4—1491no—
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⋊C8—1491no—
229#103—1491no—
230#103—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102C2×D14911yescharacteristic
236#102C2×D14911yescharacteristic
237C22⋊C8—1491no—
238C22⋊C8C2×D14911yescharacteristic
239#97—1491no—
240C4×C8—1491no—
241C24—21no—
242C2×Q8—2981no—
243C2×Q8C22×D14911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C2×D4C22×D14911yescharacteristic
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4C22×D14911yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—2982no—
260D8—2982no—
261C2×C8—1491no—
262C2×C8—1491no—
263C2×C8C22×D14911yescharacteristic
264C2×C8C22×D14911yescharacteristic
265C4⋊C4—21no—
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—2981no—
276C22⋊C4—2981no—
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—
289C42—1491no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—2981no—
296C23D4×D14911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—11921no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—2981no—
304D4—2981no—
305D4—11921no—
306D4#1455873512yes—
307D4#1455873512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—1491no—
316C2×C4—1491no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—11921no—
320C2×C4—11921no—
321C2×C4—11921no—
322C2×C4—11921no—
323C2×C4—11921no—
324C2×C4D4×D14911yescharacteristic
325C2×C4C23×D14911yescharacteristic
326C8—21no—
327C8—21no—
328C8—2981no—
329C8—2981no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22C2×D4×D14911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—2981no—
350C4—2981no—
351C4—5961no—
352C4—5961no—
353C4—5961no—
354C4C2×#1455873511yescharacteristic
355C4C2×#1455873511yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—11921no—
360C2#2375013111yescharacteristic
361C2#2375042911yescharacteristic
362C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
prime radical#23749759C2
hypercenter#450D149
hypocenterC149#3118
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23750248C2semidirect
2. #23750100C2semidirect
3. #23749963C2semidirect
4. #23749950C2semidirect
5. #23749913C2semidirect
6. #23749903C2semidirect
7. #23749842C2semidirect
8. #23749842C2semidirect
10. #23749734C2semidirect
11. #23749726C2semidirect
12. SD16×Dic149C2semidirect
13. #23749705C2semidirect
14. #23749683C2semidirect
15. #450×C149C2semidirect
18. #18011910C22semidirect
20. #18011900C22semidirect
25. Q8×Dic149C22semidirect
32. #18011873C22semidirect
37. #18011845C22semidirect
38. #18011844C22semidirect
39. #18011843C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011835C22semidirect
44. #18011835C22semidirect
45. #18011833C22semidirect
46. #18011833C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
181. C149#3118semidirect
191. #450D149semidirect

Maximal subgroups

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

subgroupindex
#237502482
#237501002
#237499632
#237499502
#237499132
#237499032
#237498422
#237497592
#237497342
#237497262
SD16×Dic1492
#237497052
#237496832
#450×C1492
#3118149