Finite Group Databasebeta

← #34079027

Subgroups — #34079027

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752724C211yesmaximal, characteristic
2#117×D151C211yesmaximal, characteristic, complemented
3#23752556C211yesmaximal, characteristic, complemented
4#23752555C211yesmaximal, characteristic, complemented
5#23752549C211yesmaximal, characteristic, complemented
6#23752544C211yesmaximal, characteristic, complemented
7#23752539C211yesmaximal, characteristic, complemented
8#23752538C211yesmaximal, characteristic, complemented
9#23752532C211yesmaximal, characteristic, complemented
10#23752527C211yesmaximal, characteristic, complemented
11#23752248C211yesmaximal, characteristic, complemented
12#23752209C211yesmaximal, characteristic, complemented
13#23752206C211yesmaximal, characteristic, complemented
14C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
15#427×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic
19#18012723—21no—
20#18012719C2211yescharacteristic
21#18012719C2211yescharacteristic
22#18012714C2211yescharacteristic
23#18012714C2211yescharacteristic
24#18012709—21no—
25C4×D604—21no—
26C4×D604—21no—
27#18012698C2211yescharacteristic
28#18012697C2211yescharacteristic
29#18012697C2211yescharacteristic
30#18012696—21no—
31#18012695—21no—
32C4⋊C4×D151C2211yescharacteristic
33C4⋊C4×D151C2211yescharacteristic
34C22⋊C4×D151—21no—
35C42×D151—21no—
36#18012672C2211yescharacteristic, complemented
37#18012672C2211yescharacteristic, complemented
38#18012670C2211yescharacteristic, complemented
39#18012670C2211yescharacteristic, complemented
40#18012664C2211yescharacteristic, complemented
41#18012664C2211yescharacteristic, complemented
42#18012662C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22×C8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#117×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic, complemented
56#107×C151C2211yescharacteristic, complemented
57#106×C151C2211yescharacteristic, complemented
58#106×C151C2211yescharacteristic, complemented
59C23×D151D411yescharacteristic
60#14559004—22no—
61#14559004—22no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C22×Dic151D411yescharacteristic
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—22no—
72C2×C4×D151—22no—
73C2×C4×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76C2×C4×D151C2311yescharacteristic
77C2×C151⋊C8—22no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151—21no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—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)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C22×C4×C151C2311yescharacteristic
97C2×C8×C151—22no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151—21no—
108C22×D151—22no—
109C22×D151—22no—
110C22×D151—21no—
111C22×D151—41no—
112C22×D151C2×D411yescharacteristic
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116D604—21no—
117D604—21no—
118D604—42no—
119D604—42no—
120C22⋊D151—42no—
121C2×Dic151—22no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—22no—
128C4×D151—22no—
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—42no—
134C4×D151—42no—
135C4×D151—42no—
136C151⋊C8—21no—
137C151⋊C8—21no—
138C23×C151C2×D411yescharacteristic
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151#4112yes—
145C2×C4×C151#4112yes—
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151#12312yes—
152C22×C151C22×D411yescharacteristic
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—44no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151#13512yes—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151#12312yes—
168C4×C151C2×#4111yescharacteristic
169C4×C151C2×#4111yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175C2×C151—22no—
176C2×C151C2×#12311yescharacteristic
177C2×C151C2×#13511yescharacteristic
178C2×C151#57511yescharacteristic
179D151—22no—
180D151—41no—
181D151—81no—
182C151#309111yescharacteristic, complemented, Sylow
183#3091—1511nomaximal, Sylow
184#525—1511no—
185C2×#117—1511no—
186#485—1511no—
187#485—1511no—
188#484—1511no—
189#483—1511no—
190#482—1511no—
191#482—1511no—
192#481—1511no—
193#480—1511no—
194#427—1511no—
195#427D15111yescharacteristic, complemented
196#416—1511no—
197#416—1511no—
198C2×C22⋊C8—1511no—
199C2×#41—1511no—
200C23×C4—1511no—
201C22×C8—1511no—
202C22×C8C2×D15111yescharacteristic
203#123—3021no—
204C22⋊Q8—1511no—
205C22⋊Q8—1511no—
206#121—1511no—
207#121—1511no—
208#120—3021no—
209C4×D4—3021no—
210C4×D4—3021no—
211#117—3021no—
212#117—3021no—
213#117—1511no—
214#117—1511no—
215#117—1511no—
216#117C2×D15111yescharacteristic
217#117C2×D15111yescharacteristic
218C2×C4⋊C4—1511no—
219C2×C4⋊C4—1511no—
220C2×C22⋊C4—3021no—
221C2×C42—3021no—
222#107—1511no—
223#107—1511no—
224#107C2×D15111yescharacteristic, complemented
225#107C2×D15111yescharacteristic, complemented
226#106—1511no—
227#106—1511no—
228#106C2×D15111yescharacteristic, complemented
229#106C2×D15111yescharacteristic, complemented
230#103—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238C22⋊C8—1511no—
239C22⋊C8—1511no—
240C22⋊C8—1511no—
241C22⋊C8—1511no—
242C24—1511no—
243#41—3022no—
244#41—3022no—
245C2×Q8—1511no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—1511no—
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3022no—
253C22×C4—3022no—
254C22×C4—3021no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4—1511no—
258C22×C4—1511no—
259C22×C4—1511no—
260C22×C4C22×D15111yescharacteristic
261C2×C8—22no—
262C2×C8—3022no—
263C2×C8—1511no—
264C2×C8—1511no—
265C2×C8C22×D15111yescharacteristic
266C2×C8C22×D15111yescharacteristic
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22×D15111yescharacteristic
274C4⋊C4C22×D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C42—21no—
287C42—21no—
288C42—3021no—
289C42—3021no—
290C42—3021no—
291C23—3022no—
292C23—3022no—
293C23—3021no—
294C23—6041no—
295C23—1511no—
296C23—1511no—
297C23D4×D15111yescharacteristic
298Q8—3021no—
299Q8—3021no—
300D4—3021no—
301D4—3021no—
302D4—6042no—
303D4—6042no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3022no—
310C2×C4—3022no—
311C2×C4—3022no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—6042no—
320C2×C4—6042no—
321C2×C4—6042no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4D4×D15111yescharacteristic
325C2×C4#1455900412yes—
326C2×C4#1455900512yes—
327C2×C4C23×D15111yescharacteristic
328C8—21no—
329C8—21no—
330C8—3021no—
331C8—3021no—
332C22—21no—
333C22—21no—
334C22—3021no—
335C22—3021no—
336C22—3021no—
337C22—3021no—
338C22—3021no—
339C22—6044no—
340C22—6041no—
341C22—6041no—
342C22—6041no—
343C22—1512no—
344C22#1801272412yes—
345C22C2×D4×D15111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3021no—
351C4—3021no—
352C4—6041no—
353C4—6041no—
354C4—6041no—
355C4#1801272412yes—
356C4C2×#1455900411yescharacteristic
357C4C2×#1455900511yescharacteristic
358C2—22no—
359C2—3022no—
360C2—6041no—
361C2—12081no—
362C2C2×#1801272411yescharacteristic
363C2#135×D15111yescharacteristic
364C2#2375300911yescharacteristic
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#427×C151C2
socleC22×C151C22×D4
prime radical#23752724C2
hypercenter#427D151
hypocenterC151#3091
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D151C2semidirect
3. #23752556C2semidirect
4. #23752555C2semidirect
5. #23752549C2semidirect
6. #23752544C2semidirect
7. #23752539C2semidirect
8. #23752538C2semidirect
9. #23752532C2semidirect
10. #23752527C2semidirect
11. #23752248C2semidirect
12. #23752209C2semidirect
13. #23752206C2semidirect
14. C2×(C2×D151)⋊C8C2semidirect
15. #427×C151C2semidirect
36. #18012672C22semidirect
37. #18012672C22semidirect
38. #18012670C22semidirect
39. #18012670C22semidirect
40. #18012664C22semidirect
41. #18012664C22semidirect
42. #18012662C22semidirect
43. #18012662C22semidirect
44. #18012661C22semidirect
45. #18012661C22semidirect
46. #18012659C22semidirect
47. #18012659C22semidirect
55. #107×C151C22semidirect
56. #107×C151C22semidirect
57. #106×C151C22semidirect
58. #106×C151C22semidirect
182. C151#3091semidirect
195. #427D151semidirect
224. #107C2×D151semidirect
225. #107C2×D151semidirect
228. #106C2×D151semidirect
229. #106C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527242
#117×D1512
#237525562
#237525552
#237525492
#237525442
#237525392
#237525382
#237525322
#237525272
#237522482
#237522092
#237522062
C2×(C2×D151)⋊C82
#427×C1512
#3091151