Finite Group Databasebeta

← #34080929

Subgroups — #34080929

Order 19328.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752920C211yesmaximal, characteristic, complemented
2#23752846C211yesmaximal, characteristic
3#23752557C211yesmaximal, characteristic, complemented
4#23752532C211yesmaximal, characteristic, complemented
5#23752528C211yesmaximal, characteristic, complemented
6#23752501C211yesmaximal, characteristic, complemented
7#23752444C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752362C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11#23752297C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13C2×#18012661C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558991C2211yescharacteristic, complemented
21C2×C8×D151C2211yescharacteristic, complemented
22#18012738C2211yescharacteristic, complemented
23#18012735C2211yescharacteristic
24#18012729—21no—
25#18012719—21no—
26#18012716—21no—
27#18012715C2211yescharacteristic, complemented
28#18012714C2211yescharacteristic
29#18012712—21no—
30#18012709—21no—
31#18012707—21no—
32Q8×Dic151C2211yescharacteristic, complemented
33#18012701C2211yescharacteristic
34C4×C22⋊D151C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36C2×C4⋊Dic151C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic, complemented
38#18012670C2211yescharacteristic, complemented
39#18012670C2211yescharacteristic, 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×SD16×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic, complemented
54C22⋊Q8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151—21no—
61C2×Dic302—21no—
62C2×D604—22no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—41no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151D411yescharacteristic
72D4×D151—22no—
73D4×D151—41no—
74D4×D151—44no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558991—22no—
80#14558991—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C8×D151—41no—
84C4⋊Dic151—21no—
85C4⋊Dic151—21no—
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4D411yescharacteristic
92C22⋊Dic151D411yescharacteristic
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151—21no—
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103SD16×C151—41no—
104C2×C8×C151—41no—
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120C22×D151C2×D411yescharacteristic
121Dic302—81no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—42no—
126D604—42no—
127D604#4112yes—
128C22⋊D151—42no—
129C22⋊D151—42no—
130C22⋊D151—81no—
131C22⋊D151SD1614yescomplemented
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—81no—
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—42no—
141C4×D151—81no—
142C151⋊C8—21no—
143C151⋊C8—21no—
144C23×C151—21no—
145C23×C151C2×D411yescharacteristic
146Q8×C151—21no—
147Q8×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—42no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151C2×SD1612yes—
166C22×C151C22×D411yescharacteristic
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—22no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—84no—
176C2×D151—84no—
177C2×D151C2×SD1612yes—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151C2×#4111yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151C2×SD1612yes—
189C2×C151—22no—
190C2×C151—81no—
191C2×C151#54611yescharacteristic
192C2×C151C22×SD1611yescharacteristic
193C2×C151#57611yescharacteristic
194D151—22no—
195D151—42no—
196D151—81no—
197C151#329511yescharacteristic, complemented, Sylow
198#3295—1511nomaximal, Sylow
199#554—1511no—
200D42—1511no—
201#486—1511no—
202#481—1511no—
203#481—1511no—
204#476—1511no—
205#465—1511no—
206#465D15111yescharacteristic, complemented
207#460—1511no—
208#450—1511no—
209#450—1511no—
210C4×SD16—1511no—
211C8×D4—1511no—
212C2×#102—1511no—
213C2×#102—1511no—
214C22×D4—3021no—
215C22×D4—1511no—
216C22×D4—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic, complemented
220C22×C8—1511no—
221C22×C8C2×D15111yescharacteristic, complemented
222C4⋊Q8—1511no—
223#127—1511no—
224#125—3021no—
225C22⋊Q8—3021no—
226C22⋊Q8—3021no—
227C22⋊Q8—1511no—
228C22⋊Q8C2×D15111yescharacteristic, complemented
229#121—3021no—
230#121—1511no—
231#121C2×D15111yescharacteristic
232#120—3021no—
233#120—3021no—
234C4×Q8—1511no—
235C4×D4—3021no—
236C4×D4—1511no—
237C4×D4—1511no—
238C2×C4⋊C4—1511no—
239C2×C4⋊C4—1511no—
240#106—1511no—
241#106—1511no—
242#106C2×D15111yescharacteristic, complemented
243C4⋊C8—1511no—
244#103C2×D15111yescharacteristic, complemented
245#102—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102—1511no—
253#102C2×D15111yescharacteristic, complemented
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C4×C8—1511no—
257C24—3021no—
258C24—3021no—
259C2×Q8—3021no—
260C2×Q8C22×D15111yescharacteristic
261C2×D4—21no—
262C2×D4—3022no—
263C2×D4—3021no—
264C2×D4—3022no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—6041no—
270C2×D4—6041no—
271C2×D4—6044no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4C22×D15111yescharacteristic
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4C22×D15111yescharacteristic
281SD16—41no—
282SD16—3022no—
283SD16—6041no—
284C2×C8—41no—
285C2×C8—6041no—
286C2×C8—1511no—
287C2×C8—1511no—
288C2×C8C22×D15111yescharacteristic
289C2×C8C22×D15111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4—1511no—
299C4⋊C4C22×D15111yescharacteristic
300C4⋊C4C22×D15111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—1511no—
307C22⋊C4—1511no—
308C42—3021no—
309C42—1511no—
310C23—21no—
311C23—3021no—
312C23—3021no—
313C23—6042no—
314C23—6042no—
315C23—6042no—
316C23—6042no—
317C23—1511no—
318C23—12081no—
319C23—12081no—
320C23D4×D15111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3021no—
328D4—3021no—
329D4—3021no—
330D4—6042no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334D4—1514no—
335D4—1512no—
336D4—12081no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6042no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1511no—
350C2×C4—12081no—
351C2×C4—12081no—
352C2×C4D4×D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3021no—
357C8—3021no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3021no—
364C22—3021no—
365C22—3022no—
366C22—6041no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—1512no—
372C22—12084no—
373C22—12084no—
374C22SD16×D15112yes—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3021no—
381C4—3021no—
382C4—6041no—
383C4—6041no—
384C4—1512no—
385C4#41×D15111yescharacteristic
386C4#1801278411yescharacteristic
387C2—22no—
388C2—81no—
389C2—3022no—
390C2—6042no—
391C2—12081no—
392C2#2375285111yescharacteristic
393C2C2×SD16×D15111yescharacteristic
394C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752846C2
hypercenter#465D151
hypocenterC151#3295
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752920C2semidirect
3. #23752557C2semidirect
4. #23752532C2semidirect
5. #23752528C2semidirect
6. #23752501C2semidirect
7. #23752444C2semidirect
8. #23752410C2semidirect
9. #23752362C2semidirect
10. #23752361C2semidirect
11. #23752297C2semidirect
12. C8×C22⋊D151C2semidirect
13. C2×#18012661C2semidirect
14. #102×D151C2semidirect
15. #465×C151C2semidirect
20. C2×#14558991C22semidirect
21. C2×C8×D151C22semidirect
22. #18012738C22semidirect
27. #18012715C22semidirect
32. Q8×Dic151C22semidirect
36. C2×C4⋊Dic151C22semidirect
37. C4⋊C4×D151C22semidirect
38. #18012670C22semidirect
39. #18012670C22semidirect
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×SD16×C151C22semidirect
53. C22×C8×C151C22semidirect
54. C22⋊Q8×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
58. #102×C151C22semidirect
131. C22⋊D151SD16semidirect
197. C151#3295semidirect
206. #465D151semidirect
219. C2×SD16C2×D151semidirect
221. C22×C8C2×D151semidirect
228. C22⋊Q8C2×D151semidirect
242. #106C2×D151semidirect
244. #103C2×D151semidirect
253. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529202
#237528462
#237525572
#237525322
#237525282
#237525012
#237524442
#237524102
#237523622
#237523612
#237522972
C8×C22⋊D1512
C2×#180126612
#102×D1512
#465×C1512
#3295151