Finite Group Databasebeta

← #34079299

Subgroups — #34079299

Order 19328.

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#23752836C211yesmaximal, characteristic, complemented
2#23752684C211yesmaximal, characteristic, complemented
3#23752556C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752489C211yesmaximal, characteristic, complemented
6#23752428C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752364C211yesmaximal, characteristic, complemented
9#23752347C211yesmaximal, characteristic
10#23752323C211yesmaximal, characteristic, complemented
11#23752309C211yesmaximal, characteristic, complemented
12#23752299C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#476×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21#18012734—21no—
22#18012728—21no—
23#18012727C2211yescharacteristic, complemented
24#18012724—21no—
25#18012719C2211yescharacteristic
26#18012715—21no—
27#18012714C2211yescharacteristic
28#18012704C2211yescharacteristic, complemented
29C4×D604C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32#18012701C2211yescharacteristic, complemented
33C4×C22⋊D151—21no—
34(C22⋊D151)⋊C4—21no—
35#18012697C2211yescharacteristic
36#18012696C2211yescharacteristic
37C2×(C2×D151)⋊C4—21no—
38C22⋊C4×D151—21no—
39#18012672C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C4⋊Q8×C151C2211yescharacteristic, complemented
53C4×D4×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65D4×D151—22no—
66D4×D151—22no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558993—22no—
73#14558992—22no—
74D1208—22no—
75#14558989—22no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—24no—
110C22×D151—21no—
111C22×D151—81no—
112C22×D151—81no—
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—81no—
120D604#4112yes—
121C22⋊D151—24no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—81no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136Q8×C151—81no—
137D4×C151—21no—
138D4×C151#4112yes—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—81no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—22no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—22no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—84no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174C2×C151—42no—
175C2×C151#52511yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57711yescharacteristic
178D151—41no—
179D151—42no—
180D151—81no—
181C151#311811yescharacteristic, complemented, Sylow
182#3118—1511nomaximal, Sylow
183#542—1511no—
184#518—1511no—
185#485—1511no—
186#482—1511no—
187#476D15111yescharacteristic, complemented
188#474—1511no—
189#463—1511no—
190#463—1511no—
191#450—1511no—
192#447—1511no—
193#442—1511no—
194#440—1511no—
195C4×SD16—1511no—
196C4×D8—1511no—
197#433—1511no—
198C22×D4—1511no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C4⋊Q8C2×D15111yescharacteristic, complemented
204#126—3021no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210#121—1511no—
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4C2×D15111yescharacteristic
219#117—1511no—
220#117—1511no—
221C2×C22⋊C4—3021no—
222C2×C22⋊C4—3021no—
223#107—1511no—
224#107—1511no—
225#106C2×D15111yescharacteristic, complemented
226#106C2×D15111yescharacteristic, complemented
227C4⋊C8—1511no—
228C4⋊C8C2×D15111yescharacteristic, complemented
229#103—1511no—
230#103—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236#102C2×D15111yescharacteristic
237C22⋊C8—1511no—
238C22⋊C8—1511no—
239#97—1511no—
240C4×C8—1511no—
241C24—3021no—
242C2×Q8—21no—
243C2×Q8—1511no—
244C2×D4—3021no—
245C2×D4—3022no—
246C2×D4—3022no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—1511no—
257SD16—3022no—
258SD16—3022no—
259D8—3022no—
260D8—3022no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4C22×D15111yescharacteristic
272C4⋊C4C22×D15111yescharacteristic
273C4⋊C4C22×D15111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—1511no—
285C22⋊C4—1511no—
286C42—3021no—
287C42—3021no—
288C42—1511no—
289C42C22×D15111yescharacteristic
290C23—21no—
291C23—3024no—
292C23—3021no—
293C23—3021no—
294C23—1511no—
295C23—12081no—
296C23—12081no—
297Q8—81no—
298Q8—3021no—
299Q8—3021no—
300D4—21no—
301D4—3024no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—1512no—
306D4—12081no—
307D4#1455900512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4—12081no—
323C2×C4D4×D15111yescharacteristic
324C2×C4D4×D15111yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3021no—
329C8—3021no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—3021no—
334C22—3022no—
335C22—3021no—
336C22—3021no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—12084no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3021no—
350C4—3021no—
351C4—3021no—
352C4—6041no—
353C4—6041no—
354C4#41×D15111yescharacteristic
355C4C2×#1455900511yescharacteristic
356C2—42no—
357C2—6041no—
358C2—6042no—
359C2—12081no—
360C2#2375272511yescharacteristic
361C2#2375301611yescharacteristic
362C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#476×C151C2
socleC22×C151C22×D4
prime radical#23752347C2
hypercenter#476D151
hypocenterC151#3118
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #23752836C2semidirect
2. #23752684C2semidirect
3. #23752556C2semidirect
4. #23752538C2semidirect
5. #23752489C2semidirect
6. #23752428C2semidirect
7. #23752427C2semidirect
8. #23752364C2semidirect
10. #23752323C2semidirect
11. #23752309C2semidirect
12. #23752299C2semidirect
13. #23752292C2semidirect
14. #23752272C2semidirect
15. #476×C151C2semidirect
23. #18012727C22semidirect
28. #18012704C22semidirect
32. #18012701C22semidirect
39. #18012672C22semidirect
40. #18012672C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
44. #18012661C22semidirect
47. #18012659C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
52. C4⋊Q8×C151C22semidirect
54. #106×C151C22semidirect
55. #106×C151C22semidirect
56. C4⋊C8×C151C22semidirect
181. C151#3118semidirect
187. #476D151semidirect
203. C4⋊Q8C2×D151semidirect
225. #106C2×D151semidirect
226. #106C2×D151semidirect
228. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237526842
#237525562
#237525382
#237524892
#237524282
#237524272
#237523642
#237523472
#237523232
#237523092
#237522992
#237522922
#237522722
#476×C1512
#3118151