Finite Group Databasebeta

← #34080918

Subgroups — #34080918

Order 19328.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752862C211yesmaximal, characteristic, complemented
2#23752846C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752527C211yesmaximal, characteristic, complemented
5#23752523C211yesmaximal, characteristic, complemented
6#23752491C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752345C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic, complemented
11#23752292C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13C2×#18012661C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#466×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C22×D604C2211yescharacteristic
18C2×D4×D151—21no—
19C2×D4×D151C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558989C2211yescharacteristic, complemented
22C2×C8×D151C2211yescharacteristic, complemented
23#18012738C2211yescharacteristic, complemented
24#18012735C2211yescharacteristic
25#18012721—21no—
26#18012720—21no—
27#18012716—21no—
28#18012714C2211yescharacteristic
29#18012712—21no—
30#18012710C2211yescharacteristic, complemented
31#18012709—21no—
32#18012707—21no—
33D4×Dic151C2211yescharacteristic, complemented
34#18012701C2211yescharacteristic
35C4×C22⋊D151C2211yescharacteristic
36C2×C4⋊Dic151C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40Dic151⋊C8C2211yescharacteristic, complemented
41#18012661C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic, complemented
54#121×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic, complemented
56#107×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151—21no—
61#14559003—44no—
62C2×Dic302—21no—
63C2×D604—22no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—41no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74D4×D151—22no—
75D4×D151—41no—
76D4×D151—44no—
77C22×Dic151—21no—
78C22×Dic151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151C2311yescharacteristic
82#14558989—22no—
83#14558989—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C8×D151—41no—
87C4⋊Dic151—21no—
88C4⋊Dic151C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4D411yescharacteristic
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151D411yescharacteristic
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4D411yescharacteristic
99C4×Dic151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105D8×C151—41no—
106C2×C8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151—42no—
119C22×D151—81no—
120C22×D151—81no—
121C22×D151C2×D411yescharacteristic
122Dic302—42no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—42no—
127D604—42no—
128D604#4112yescomplemented
129C22⋊D151—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C22⋊D151—81no—
133C22⋊D151D814yescomplemented
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—42no—
137C2×Dic151—42no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—42no—
144C4×D151—42no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—42no—
155D4×C151—42no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151C2×D812yes—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—22no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—84no—
183C2×D151—84no—
184C2×D151C2×D812yes—
185C4×C151—21no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151C2×#4111yescharacteristic
189C4×C151H(5,𝔽2)11yescharacteristic
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193Dic151—41no—
194Dic151C2×D812yes—
195C2×C151—22no—
196C2×C151—81no—
197C2×C151—81no—
198C2×C151#54611yescharacteristic
199C2×C151C22×D811yescharacteristic
200C2×C151#57711yescharacteristic
201D151—22no—
202D151—42no—
203D151—81no—
204C151#329411yescharacteristic, complemented, Sylow
205#3294—1511nomaximal, Sylow
206#547—1511no—
207D42—1511no—
208#486—1511no—
209#480—1511no—
210#480—1511no—
211#474—1511no—
212#466—1511no—
213#466D15111yescharacteristic, complemented
214#459—1511no—
215#447—1511no—
216#447—1511no—
217C4×D8—1511no—
218C8×D4—1511no—
219C2×#102—1511no—
220C2×#102—1511no—
221C2×#41—3021no—
222C22×D4—3021no—
223C22×D4—1511no—
224C22×D4—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×D8C2×D15111yescharacteristic, complemented
228C22×C8—1511no—
229C22×C8C2×D15111yescharacteristic, complemented
230C4⋊Q8—1511no—
231#127—1511no—
232#123—3021no—
233#123—3021no—
234C22⋊Q8—3021no—
235#121—3021no—
236#121—1511no—
237#121—1511no—
238#121C2×D15111yescharacteristic
239#121C2×D15111yescharacteristic, complemented
240#120—3021no—
241#120—3021no—
242C4×D4—1511no—
243C4×D4—1511no—
244C4×D4—1511no—
245C2×C4⋊C4—1511no—
246C2×C4⋊C4—1511no—
247#107—1511no—
248#107—1511no—
249#107C2×D15111yescharacteristic, complemented
250C4⋊C8—1511no—
251#102—1511no—
252#102—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102—1511no—
259#102C2×D15111yescharacteristic, complemented
260#102C2×D15111yescharacteristic, complemented
261C22⋊C8—1511no—
262C22⋊C8—1511no—
263C4×C8—1511no—
264C24—3021no—
265C24—3021no—
266#41—6044no—
267C2×Q8—3021no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—3022no—
271C2×D4—3021no—
272C2×D4—3022no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—6041no—
279C2×D4—6041no—
280C2×D4—6044no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4—1511no—
284C2×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—1511no—
291C22×C4C22×D15111yescharacteristic
292D8—41no—
293D8—3022no—
294D8—6041no—
295C2×C8—41no—
296C2×C8—6041no—
297C2×C8—1511no—
298C2×C8—1511no—
299C2×C8C22×D15111yescharacteristic
300C2×C8C22×D15111yescharacteristic
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—1511no—
305C4⋊C4—1511no—
306C4⋊C4—1511no—
307C4⋊C4C22×D15111yescharacteristic
308C4⋊C4C22×D15111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—1511no—
316C22⋊C4—1511no—
317C42—1511no—
318C23—21no—
319C23—21no—
320C23—3021no—
321C23—3021no—
322C23—6042no—
323C23—6042no—
324C23—6042no—
325C23—6042no—
326C23—1511no—
327C23—12081no—
328C23—12081no—
329C23D4×D15111yescharacteristic
330Q8—6042no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—3021no—
338D4—3021no—
339D4—3021no—
340D4—6042no—
341D4—6042no—
342D4—6042no—
343D4—6042no—
344D4—6042no—
345D4—1514no—
346D4—1512no—
347D4—12081no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—6042no—
357C2×C4—6042no—
358C2×C4—6042no—
359C2×C4—6042no—
360C2×C4—1511no—
361C2×C4—1511no—
362C2×C4—1511no—
363C2×C4D4×D15111yescharacteristic
364C2×C4C23×D15111yescharacteristic
365C8—21no—
366C8—21no—
367C8—3021no—
368C8—3021no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3021no—
378C22—3021no—
379C22—3022no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—1512no—
386C22—12084no—
387C22—12084no—
388C22D8×D15112yes—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—3021no—
394C4—3021no—
395C4—6041no—
396C4—6041no—
397C4—1512no—
398C4#41×D15111yescharacteristic
399C4#1801278411yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—3022no—
404C2—6042no—
405C2—12081no—
406C2#2375285111yescharacteristic
407C2C2×D8×D15111yescharacteristic
408C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23752862C2semidirect
2. #23752846C2semidirect
3. #23752557C2semidirect
4. #23752527C2semidirect
5. #23752523C2semidirect
6. #23752491C2semidirect
7. #23752447C2semidirect
8. #23752405C2semidirect
9. #23752345C2semidirect
10. #23752344C2semidirect
11. #23752292C2semidirect
12. C8×C22⋊D151C2semidirect
13. C2×#18012661C2semidirect
14. #102×D151C2semidirect
15. #466×C151C2semidirect
21. C2×#14558989C22semidirect
22. C2×C8×D151C22semidirect
23. #18012738C22semidirect
30. #18012710C22semidirect
33. D4×Dic151C22semidirect
36. C2×C4⋊Dic151C22semidirect
37. C4⋊C4×D151C22semidirect
38. #18012672C22semidirect
39. #18012672C22semidirect
40. Dic151⋊C8C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
45. #18012660C22semidirect
46. #18012660C22semidirect
48. #18012659C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. C8×Dic151C22semidirect
52. C2×D8×C151C22semidirect
53. C22×C8×C151C22semidirect
55. #121×C151C22semidirect
56. #107×C151C22semidirect
57. #102×C151C22semidirect
58. #102×C151C22semidirect
128. D604#41semidirect
133. C22⋊D151D8semidirect
204. C151#3294semidirect
213. #466D151semidirect
227. C2×D8C2×D151semidirect
229. C22×C8C2×D151semidirect
239. #121C2×D151semidirect
249. #107C2×D151semidirect
259. #102C2×D151semidirect
260. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528622
#237528462
#237525572
#237525272
#237525232
#237524912
#237524472
#237524052
#237523452
#237523442
#237522922
C8×C22⋊D1512
C2×#180126612
#102×D1512
#466×C1512
#3294151