Finite Group Databasebeta

← #34054871

Subgroups — #34054871

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#23750240C211yesmaximal, characteristic, complemented
2#23750097C211yesmaximal, characteristic, complemented
3#23749968C211yesmaximal, characteristic, complemented
4#23749948C211yesmaximal, characteristic, complemented
5#23749913C211yesmaximal, characteristic, complemented
6#23749904C211yesmaximal, characteristic, complemented
7#23749839C211yesmaximal, characteristic, complemented
8#23749838C211yesmaximal, characteristic, complemented
9#23749777C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic
11#23749735C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic, complemented
13C4×#14558725C211yesmaximal, characteristic, complemented
14#23749684C211yesmaximal, characteristic, complemented
15C4×D8×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20#18011910C2211yescharacteristic, complemented
21#18011904—21no—
22#18011898C2211yescharacteristic, complemented
23#18011897—21no—
24#18011894—21no—
25#18011891C2211yescharacteristic
26#18011890—21no—
27#18011882C2211yescharacteristic
28C4×Dic298C2211yescharacteristic, complemented
29C4×D596C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011869C2211yescharacteristic
35#18011868C2211yescharacteristic
36C2×#14558713—21no—
37C22⋊C4×D149—21no—
38#18011844C2211yescharacteristic, complemented
39#18011843C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic, complemented
52C2×D8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic, complemented
55#107×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65D4×D149—22no—
66D4×D149—22no—
67C22×Dic149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71#14558725—22no—
72#14558724—22no—
73#14558721—22no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713D411yescharacteristic
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96C2×D4×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C22×C4×C149—21no—
100D8×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
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—21no—
114Dic298—21no—
115Dic298—81no—
116D596—21no—
117D596#4112yes—
118C22⋊D149—24no—
119C22⋊D149—81no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—81no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—81no—
130C4×D149—81no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134C23×C149—21no—
135D4×C149—21no—
136D4×C149—21no—
137D4×C149—21no—
138D4×C149#4112yes—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—81no—
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#463—1491no—
191#450—1491no—
192#447—1491no—
193#442—1491no—
194#440—1491no—
195C4×SD16—1491no—
196C4×D8D14911yescharacteristic, complemented
197#433—1491no—
198C22×D4—1491no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×D8—1491no—
202C2×D8C2×D14911yescharacteristic
203C4⋊Q8—1491no—
204#126—2981no—
205#124—2981no—
206#124—1491no—
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×D4C2×D14911yescharacteristic
218C4×D4C2×D14911yescharacteristic, complemented
219#117—1491no—
220#117—1491no—
221C2×C22⋊C4—2981no—
222C2×C22⋊C4—2981no—
223#107—1491no—
224#107C2×D14911yescharacteristic, complemented
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, complemented
237C22⋊C8—1491no—
238C22⋊C8—1491no—
239#97—1491no—
240C4×C8C2×D14911yescharacteristic, complemented
241C24—2981no—
242C2×Q8—2981no—
243C2×Q8—1491no—
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—21no—
253C22×C4—2981no—
254C22×C4—2981no—
255C22×C4—2981no—
256C22×C4—1491no—
257SD16—2982no—
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⋊C4C22×D14911yescharacteristic
273C4⋊C4C22×D14911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
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—
289C42C22×D14911yescharacteristic
290C23—21no—
291C23—21no—
292C23—2984no—
293C23—2981no—
294C23—1491no—
295C23—11921no—
296C23—11921no—
297Q8—2981no—
298Q8—2981no—
299Q8—11921no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2984no—
304D4—2981no—
305D4—1492no—
306D4—11921no—
307D4#1455873612yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—1491no—
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×#1455873611yescharacteristic
356C2—42no—
357C2—81no—
358C2—5961no—
359C2—5962no—
360C2#2375013411yescharacteristic
361C2#2375042611yescharacteristic
362C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
prime radical#23749757C2
hypercenterC4×D8D149
hypocenterC149#3118
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750240C2semidirect
2. #23750097C2semidirect
3. #23749968C2semidirect
4. #23749948C2semidirect
5. #23749913C2semidirect
6. #23749904C2semidirect
7. #23749839C2semidirect
8. #23749838C2semidirect
9. #23749777C2semidirect
11. #23749735C2semidirect
12. #23749725C2semidirect
13. C4×#14558725C2semidirect
14. #23749684C2semidirect
15. C4×D8×C149C2semidirect
20. #18011910C22semidirect
22. #18011898C22semidirect
28. C4×Dic298C22semidirect
38. #18011844C22semidirect
39. #18011843C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
47. #18011832C22semidirect
51. #18011822C22semidirect
54. C4×D4×C149C22semidirect
55. #107×C149C22semidirect
57. #102×C149C22semidirect
58. C4×C8×C149C22semidirect
181. C149#3118semidirect
196. C4×D8D149semidirect
218. C4×D4C2×D149semidirect
224. #107C2×D149semidirect
236. #102C2×D149semidirect
240. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502402
#237500972
#237499682
#237499482
#237499132
#237499042
#237498392
#237498382
#237497772
#237497572
#237497352
#237497252
C4×#145587252
#237496842
C4×D8×C1492
#3118149