Finite Group Databasebeta

← #34080958

Subgroups — #34080958

Order 19328.

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#23752910C211yesmaximal, characteristic, complemented
2#23752853C211yesmaximal, characteristic, complemented
3#23752568C211yesmaximal, characteristic, complemented
4#23752539C211yesmaximal, characteristic, complemented
5#23752515C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752430C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752348C211yesmaximal, characteristic, complemented
11#23752294C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14C2×#18012659C211yesmaximal, characteristic, complemented
15#484×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×#14558991C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic, complemented
23#18012734—21no—
24#18012730C2211yescharacteristic, complemented
25#18012728C2211yescharacteristic
26#18012724—21no—
27#18012724—21no—
28#18012714—21no—
29#18012714C2211yescharacteristic
30#18012714C2211yescharacteristic, complemented
31#18012713—21no—
32#18012713C2211yescharacteristic
33#18012709—21no—
34#18012701C2211yescharacteristic
35#18012701C2211yescharacteristic, complemented
36C4×C22⋊D151—21no—
37C4×C22⋊D151C2211yescharacteristic
38#18012697C2211yescharacteristic, complemented
39C22⋊C4×D151—21no—
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22⋊Q8×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151—21no—
60#14559005—22no—
61#14559005—41no—
62C2×D604—22no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—41no—
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151D411yescharacteristic
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77#14558991—41no—
78D1208—22no—
79D1208—41no—
80C2×C151⋊C8—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C8×D151—41no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4D411yescharacteristic
88C22⋊Dic151D411yescharacteristic
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151—21no—
99C4×Dic151C2311yescharacteristic
100C2×Q8×C151C2311yescharacteristic
101C22×C4×C151—21no—
102C22×C4×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118D604—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—21no—
123D604—42no—
124D604—42no—
125D604—81no—
126D604—81no—
127D604#4112yes—
128C22⋊D151—22no—
129C22⋊D151—42no—
130C2×Dic151—21no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—42no—
137C4×D151—81no—
138C4×D151—81no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151C2×D411yescharacteristic
142Q8×C151—21no—
143Q8×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—81no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151#13512yes—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—22no—
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—84no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151C2×#4111yescharacteristic
178C4×C151H(5,𝔽2)11yescharacteristic
179Dic151—21no—
180Dic151—21no—
181Dic151—21no—
182Dic151—41no—
183C2×C151—22no—
184C2×C151#54611yescharacteristic
185C2×C151C2×#13511yescharacteristic
186C2×C151#57611yescharacteristic
187D151—41no—
188D151—42no—
189D151—81no—
190D151—81no—
191C151#329711yescharacteristic, complemented, Sylow
192#3297—1511nomaximal, Sylow
193#553—1511no—
194#546—1511no—
195#488—1511no—
196#484D15111yescharacteristic, complemented
197#482—1511no—
198#478—1511no—
199#466—1511no—
200#465—1511no—
201#463—1511no—
202#449—1511no—
203#447—1511no—
204C4×D8—1511no—
205C8×D4—1511no—
206#416—1511no—
207C2×#102—1511no—
208C2×#41—1511no—
209C22×D4—1511no—
210C2×SD16—1511no—
211C2×D8—1511no—
212C2×D8—1511no—
213C22×C8—1511no—
214C22×C8—1511no—
215#126—3021no—
216#125—1511no—
217#124—1511no—
218#123—3021no—
219#123—3021no—
220C22⋊Q8C2×D15111yescharacteristic
221#121—3021no—
222#121—3021no—
223#121—1511no—
224#121—1511no—
225#121—1511no—
226#120—3021no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230C4×D4—1511no—
231#117—1511no—
232C2×C4⋊C4C2×D15111yescharacteristic
233C2×C22⋊C4—3021no—
234#107C2×D15111yescharacteristic, complemented
235#107C2×D15111yescharacteristic, complemented
236#106—1511no—
237C4⋊C8—1511no—
238#103—1511no—
239#103C2×D15111yescharacteristic, complemented
240#103C2×D15111yescharacteristic, complemented
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248C22⋊C8—1511no—
249C22⋊C8C2×D15111yescharacteristic
250C4×C8—1511no—
251C24—3021no—
252#41—3022no—
253#41—6041no—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—3022no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—6041no—
262C2×D4—1511no—
263C2×D4—1511no—
264C2×D4—1511no—
265C2×D4—1511no—
266C22×C4—21no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—1511no—
271C22×C4C22×D15111yescharacteristic
272SD16—6041no—
273D8—3022no—
274D8—6041no—
275C2×C8—6041no—
276C2×C8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—1511no—
300C22⋊C4—1511no—
301C42—3021no—
302C42—1511no—
303C23—3021no—
304C23—3021no—
305C23—3021no—
306C23—6042no—
307C23—6042no—
308C23—1511no—
309C23—12081no—
310C23D4×D15111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—3022no—
314D4—3021no—
315D4—3021no—
316D4—3021no—
317D4—3021no—
318D4—3021no—
319D4—6042no—
320D4—6042no—
321D4—6042no—
322D4—1512no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—6042no—
336C2×C4—1511no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—12081no—
340C2×C4—12081no—
341C2×C4D4×D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3021no—
346C8—3021no—
347C22—21no—
348C22—21no—
349C22—3021no—
350C22—3021no—
351C22—3021no—
352C22—3022no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22—12084no—
362C22#1801276212yes—
363C22C2×D4×D15111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3021no—
370C4—3021no—
371C4—3021no—
372C4—6041no—
373C4#41×D15111yescharacteristic
374C4#1801278511yescharacteristic
375C2—22no—
376C2—6041no—
377C2—6042no—
378C2—12081no—
379C2—12081no—
380C2#2375285411yescharacteristic
381C2C2×#1801276211yescharacteristic
382C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#484×C151C2
socleC22×C151C22×D4
hypercenter#484D151
hypocenterC151#3297
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #23752910C2semidirect
2. #23752853C2semidirect
3. #23752568C2semidirect
4. #23752539C2semidirect
5. #23752515C2semidirect
6. #23752449C2semidirect
7. #23752443C2semidirect
8. #23752430C2semidirect
9. #23752360C2semidirect
10. #23752348C2semidirect
11. #23752294C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752207C2semidirect
14. C2×#18012659C2semidirect
15. #484×C151C2semidirect
18. C2×#14558991C22semidirect
22. C2×C8×D151C22semidirect
24. #18012730C22semidirect
30. #18012714C22semidirect
35. #18012701C22semidirect
38. #18012697C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012663C22semidirect
49. #18012659C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. C8×Dic151C22semidirect
54. #107×C151C22semidirect
55. #107×C151C22semidirect
56. #103×C151C22semidirect
57. #103×C151C22semidirect
191. C151#3297semidirect
196. #484D151semidirect
234. #107C2×D151semidirect
235. #107C2×D151semidirect
239. #103C2×D151semidirect
240. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529102
#237528532
#237525682
#237525392
#237525152
#237524492
#237524432
#237524302
#237523602
#237523482
#237522942
(C22⋊D151)⋊C82
#237522072
C2×#180126592
#484×C1512
#3297151