Finite Group Databasebeta

← #34056534

Subgroups — #34056534

Order 19072.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750322C211yesmaximal, characteristic, complemented
2#23750263C211yesmaximal, characteristic, complemented
3#23749981C211yesmaximal, characteristic, complemented
4#23749959C211yesmaximal, characteristic, complemented
5#23749950C211yesmaximal, characteristic, complemented
6#23749927C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749851C211yesmaximal, characteristic, complemented
9#23749842C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic, complemented
11D8×Dic149C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13#23749621C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#449×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18C22×#11924746C2211yescharacteristic, complemented
19C2×C8×D149C2211yescharacteristic
20#18011904—21no—
21#18011902C2211yescharacteristic, complemented
22#18011900C2211yescharacteristic
23#18011894—21no—
24#18011892—21no—
25#18011887C2211yescharacteristic
26#18011885C2211yescharacteristic
27#18011883—21no—
28#18011882—21no—
29#18011882C2211yescharacteristic
30#18011879—21no—
31D4×Dic149C2211yescharacteristic
32D4×Dic149C2211yescharacteristic, complemented
33C4×C22⋊D149C2211yescharacteristic
34#18011871—21no—
35#18011870C2211yescharacteristic, complemented
36C4⋊C4×D149C2211yescharacteristic
37C2×#14558713—21no—
38#18011845C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011843C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011835C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic, complemented
52C2×#41×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic, complemented
54C2×D8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149D411yescharacteristic
65D4×D149—22no—
66D4×D149—41no—
67C22×Dic149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558721—41no—
72C2×#11924746—41no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C8×D149—41no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96#41×C149—22no—
97#41×C149—41no—
98C2×Q8×C149C2311yescharacteristic
99C2×D4×C149—21no—
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C2×D4×C149C2311yescharacteristic
103C22×C4×C149—21no—
104C22×C4×C149C2311yescharacteristic
105SD16×C149—41no—
106D8×C149—22no—
107C2×C8×C149C2311yescharacteristic
108C2×C8×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C22⋊C4×C149—21no—
111C22×D149—21no—
112C22×D149—42no—
113C22×D149—42no—
114C22×D149—81no—
115C22×D149C2×D411yescharacteristic
116D596—21no—
117D596—21no—
118C22⋊D149—22no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C22⋊D149—81no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—81no—
126C2×Dic149—81no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—81no—
133#11924746—21no—
134#11924746—21no—
135C23×C149—21no—
136C23×C149—21no—
137C23×C149C2×D411yescharacteristic
138Q8×C149—21no—
139Q8×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142D4×C149—21no—
143D4×C149—42no—
144D4×C149—81no—
145D4×C149#4112yes—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—42no—
151C2×C4×C149C2×D411yescharacteristic
152C2×C4×C149C2411yescharacteristic
153C8×C149—21no—
154C8×C149—21no—
155C22×C149—21no—
156C22×C149—22no—
157C22×C149—21no—
158C22×C149—21no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149—41no—
163C22×C149—41no—
164C22×C149C22×D411yescharacteristic
165C2×D149—21no—
166C2×D149—21no—
167C2×D149—41no—
168C2×D149—41no—
169C2×D149—41no—
170C2×D149—84no—
171C2×D149#13512yes—
172C4×C149—21no—
173C4×C149—41no—
174C4×C149—41no—
175C4×C149C2×#4111yescharacteristic
176C4×C149H(5,𝔽2)11yescharacteristic
177Dic149—21no—
178Dic149—21no—
179Dic149—21no—
180Dic149—41no—
181Dic149—41no—
182Dic149—41no—
183C2×C149—42no—
184C2×C149—41no—
185C2×C149—81no—
186C2×C149#54611yescharacteristic
187C2×C149C2×#13511yescharacteristic
188C2×C149#57611yescharacteristic
189D149—22no—
190D149—81no—
191C149#329711yescharacteristic, complemented, Sylow
192#3297—1491nomaximal, Sylow
193#553—1491no—
194#546—1491no—
195#488—1491no—
196#484—1491no—
197#482—1491no—
198#478—1491no—
199#466—1491no—
200#465—1491no—
201#463—1491no—
202#449D14911yescharacteristic, complemented
203#447—1491no—
204C4×D8—1491no—
205C8×D4—1491no—
206#416—1491no—
207C2×#102—1491no—
208C2×#41C2×D14911yescharacteristic
209C22×D4—1491no—
210C2×SD16C2×D14911yescharacteristic, complemented
211C2×D8—1491no—
212C2×D8C2×D14911yescharacteristic
213C22×C8—1491no—
214C22×C8—1491no—
215#126—2981no—
216#125—1491no—
217#124—1491no—
218#123—2981no—
219#123—2981no—
220C22⋊Q8—1491no—
221#121—2981no—
222#121—2981no—
223#121—1491no—
224#121—1491no—
225#121C2×D14911yescharacteristic, complemented
226#120—2981no—
227C4×D4—2981no—
228C4×D4—1491no—
229C4×D4—1491no—
230C4×D4—1491no—
231#117—1491no—
232C2×C4⋊C4—1491no—
233C2×C22⋊C4—2981no—
234#107—1491no—
235#107—1491no—
236#106—1491no—
237C4⋊C8—1491no—
238#103—1491no—
239#103—1491no—
240#103C2×D14911yescharacteristic, complemented
241#102—1491no—
242#102—1491no—
243#102—1491no—
244#102—1491no—
245#102—1491no—
246#102—1491no—
247#102C2×D14911yescharacteristic
248C22⋊C8—1491no—
249C22⋊C8C2×D14911yescharacteristic, complemented
250C4×C8—1491no—
251C24—2981no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D14911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2982no—
258C2×D4—2981no—
259C2×D4—2981no—
260C2×D4—2981no—
261C2×D4—5961no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4C22×D14911yescharacteristic
265C2×D4C22×D14911yescharacteristic
266C22×C4—21no—
267C22×C4—2981no—
268C22×C4—2981no—
269C22×C4—2981no—
270C22×C4—1491no—
271C22×C4C22×D14911yescharacteristic
272SD16—41no—
273D8—22no—
274D8—5961no—
275C2×C8—5961no—
276C2×C8—5961no—
277C2×C8—1491no—
278C2×C8—1491no—
279C2×C8C22×D14911yescharacteristic
280C2×C8C22×D14911yescharacteristic
281C4⋊C4—2981no—
282C4⋊C4—2981no—
283C4⋊C4—2981no—
284C4⋊C4—2981no—
285C4⋊C4—1491no—
286C4⋊C4—1491no—
287C4⋊C4—1491no—
288C4⋊C4—1491no—
289C4⋊C4C22×D14911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2981no—
292C22⋊C4—2981no—
293C22⋊C4—2981no—
294C22⋊C4—2981no—
295C22⋊C4—2981no—
296C22⋊C4—2981no—
297C22⋊C4—2981no—
298C22⋊C4—2981no—
299C22⋊C4—1491no—
300C22⋊C4—1491no—
301C42—2981no—
302C42—1491no—
303C23—21no—
304C23—21no—
305C23—2981no—
306C23—5962no—
307C23—5962no—
308C23—1491no—
309C23—11921no—
310C23D4×D14911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—2982no—
319D4—2981no—
320D4—2981no—
321D4—5962no—
322D4—5962no—
323D4—11921no—
324D4#1455873512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—1491no—
336C2×C4—1491no—
337C2×C4—1491no—
338C2×C4—11921no—
339C2×C4—11921no—
340C2×C4—11921no—
341C2×C4D4×D14911yescharacteristic
342C2×C4C23×D14911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2981no—
346C8—2981no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—2981no—
357C22—2981no—
358C22—5961no—
359C22—5961no—
360C22—5961no—
361C22—1492no—
362C22—11924no—
363C22C2×D4×D14911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—2981no—
368C4—2981no—
369C4—2981no—
370C4—5961no—
371C4—5961no—
372C4—5961no—
373C4C2×#1455873511yescharacteristic
374C4#1801195611yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—2982no—
379C2—11921no—
380C2#2375026211yescharacteristic
381C2#135×D14911yescharacteristic
382C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#449×C149C2
socleC22×C149C22×D4
hypercenter#449D149
hypocenterC149#3297
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23750322C2semidirect
2. #23750263C2semidirect
3. #23749981C2semidirect
4. #23749959C2semidirect
5. #23749950C2semidirect
6. #23749927C2semidirect
7. #23749859C2semidirect
8. #23749851C2semidirect
9. #23749842C2semidirect
10. #23749757C2semidirect
11. D8×Dic149C2semidirect
12. #23749688C2semidirect
13. #23749621C2semidirect
14. #102×D149C2semidirect
15. #449×C149C2semidirect
18. C22×#11924746C22semidirect
21. #18011902C22semidirect
32. D4×Dic149C22semidirect
35. #18011870C22semidirect
38. #18011845C22semidirect
39. #18011844C22semidirect
40. #18011843C22semidirect
41. #18011840C22semidirect
42. #18011835C22semidirect
43. #18011835C22semidirect
48. #18011832C22semidirect
51. C8×Dic149C22semidirect
53. C2×SD16×C149C22semidirect
55. #121×C149C22semidirect
56. #103×C149C22semidirect
58. C22⋊C8×C149C22semidirect
191. C149#3297semidirect
202. #449D149semidirect
210. C2×SD16C2×D149semidirect
225. #121C2×D149semidirect
240. #103C2×D149semidirect
249. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503222
#237502632
#237499812
#237499592
#237499502
#237499272
#237498592
#237498512
#237498422
#237497572
D8×Dic1492
#237496882
#237496212
#102×D1492
#449×C1492
#3297149