Finite Group Databasebeta

← #34078934

Subgroups — #34078934

Order 19328.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752839C211yesmaximal, characteristic, complemented
2#23752684C211yesmaximal, characteristic
3#23752515C211yesmaximal, characteristic, complemented
4#23752513C211yesmaximal, characteristic, complemented
5#23752512C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752500C211yesmaximal, characteristic, complemented
8#23752499C211yesmaximal, characteristic, complemented
9#23752491C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#23752249C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic
14#102×D151C211yesmaximal, characteristic
15#474×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×#14558987C2211yescharacteristic
18C2×C8×D151C2211yescharacteristic
19#18012738C2211yescharacteristic, complemented
20#18012737—21no—
21#18012731C2211yescharacteristic, complemented
22#18012730C2211yescharacteristic, complemented
23#18012729—21no—
24#18012717—21no—
25#18012715—21no—
26C4×D604C2211yescharacteristic
27D4×Dic151C2211yescharacteristic
28#18012701C2211yescharacteristic
29C4×C22⋊D151—21no—
30(C22⋊D151)⋊C4—21no—
31#18012697C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35C2×(C2×D151)⋊C4—21no—
36C22⋊C4×D151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43C4⋊(C151⋊C8)C2211yescharacteristic, complemented
44Dic151⋊C8C2211yescharacteristic, complemented
45Dic151⋊C8C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic, complemented
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63D4×D151—22no—
64D4×D151Q814yescomplemented
65C22×Dic151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151C2311yescharacteristic
70#14558987—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C8×D151—22no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4D411yescharacteristic
91(C2×D151)⋊C4D411yescharacteristic
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151—21no—
96C2×D4×C151C2311yescharacteristic
97C22×C4×C151—21no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C42×C151C2311yescharacteristic
106C22×D151—21no—
107C22×D151—24no—
108C22×D151—81no—
109C22×D151—81no—
110C22×D151C2×D411yescharacteristic
111Dic302—81no—
112D604—21no—
113D604C2×Q812yes—
114C22⋊D151—24no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—81no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—81no—
123C4×D151—81no—
124C4×D151—81no—
125C4×D151C2×Q812yes—
126C4×D151#4112yes—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130Q8×C151—81no—
131D4×C151—21no—
132D4×C151C2×Q812yes—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—81no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—21no—
141C8×C151—21no—
142C22×C151—22no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151C22×D411yescharacteristic
146C2×D151—21no—
147C2×D151—21no—
148C2×D151—22no—
149C2×D151—41no—
150C2×D151—41no—
151C2×D151—84no—
152C2×D151C22⋊Q812yes—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151C22×Q811yescharacteristic
159C4×C151C2×#4111yescharacteristic
160Dic151—21no—
161Dic151—21no—
162Dic151—41no—
163Dic151—41no—
164Dic151—41no—
165Dic151C22⋊Q812yes—
166C2×C151—42no—
167C2×C151C2×C22⋊Q811yescharacteristic
168C2×C151#57611yescharacteristic
169C2×C151#57711yescharacteristic
170D151—22no—
171D151—42no—
172C151#308111yescharacteristic, complemented, Sylow
173#3081—1511nomaximal, Sylow
174#544—1511no—
175#518—1511no—
176#478—1511no—
177#478—1511no—
178#478—1511no—
179#478—1511no—
180#476—1511no—
181#476—1511no—
182#474—1511no—
183#474D15111yescharacteristic, complemented
184#428—1511no—
185#427—1511no—
186#424—1511no—
187#418—1511no—
188C2×#102—1511no—
189C22×D4—1511no—
190C2×M16—1511no—
191C22×C8—1511no—
192C4⋊Q8—3021no—
193C4⋊Q8—1511no—
194C4⋊Q8C2×D15111yescharacteristic, complemented
195#125—3021no—
196#125—1511no—
197#125—1511no—
198C22⋊Q8—3021no—
199C22⋊Q8—3021no—
200C4×D4—3021no—
201C4×D4—3021no—
202C4×D4—1511no—
203C4×D4—1511no—
204C4×D4—1511no—
205C4×D4C2×D15111yescharacteristic
206#117—1511no—
207#117—1511no—
208#117—1511no—
209C2×C4⋊C4—1511no—
210C2×C22⋊C4—3021no—
211C2×C22⋊C4—3021no—
212#107—1511no—
213#107—1511no—
214#107C2×D15111yescharacteristic, complemented
215#107C2×D15111yescharacteristic, complemented
216#106—1511no—
217#106—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222C4⋊C8—1511no—
223C4⋊C8C2×D15111yescharacteristic, complemented
224#102—1511no—
225#102—1511no—
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230#102C2×D15111yescharacteristic
231#102C2×D15111yescharacteristic
232C24—3021no—
233C2×Q8—21no—
234C2×Q8—3021no—
235C2×D4—3022no—
236C2×D4—3021no—
237C2×D4—1514no—
238C2×D4—1511no—
239C2×D4C22×D15111yescharacteristic
240C22×C4—21no—
241C22×C4—3021no—
242C22×C4—3021no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—1511no—
246M16—3022no—
247C2×C8—3022no—
248C2×C8—1511no—
249C2×C8—1511no—
250C2×C8C22×D15111yescharacteristic
251C2×C8C22×D15111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4—1511no—
264C4⋊C4C22×D15111yescharacteristic
265C4⋊C4C22×D15111yescharacteristic
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—1511no—
274C22⋊C4—1511no—
275C42—3021no—
276C42—3021no—
277C42—1511no—
278C42C22×D15111yescharacteristic
279C23—21no—
280C23—3024no—
281C23—3021no—
282C23—1511no—
283C23—12081no—
284C23—12081no—
285Q8—81no—
286Q8—12081no—
287D4—21no—
288D4—3024no—
289D4—3021no—
290D4—1512no—
291D4Q8×D15112yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—1511no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—1512no—
303C2×C4—1512no—
304C2×C4—12081no—
305C2×C4—12081no—
306C2×C4—12081no—
307C2×C4—12081no—
308C2×C4D4×D15111yescharacteristic
309C2×C4D4×D15111yescharacteristic
310C2×C4C23×D15111yescharacteristic
311C8—21no—
312C8—21no—
313C8—3021no—
314C8—3021no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—3021no—
319C22—3021no—
320C22—3022no—
321C22—6041no—
322C22—6041no—
323C22—1512no—
324C22—12084no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3021no—
332C4—3021no—
333C4—6041no—
334C4—6041no—
335C4—6041no—
336C4—1512no—
337C4C2×Q8×D15111yescharacteristic
338C4#41×D15111yescharacteristic
339C2—42no—
340C2—3022no—
341C2—6042no—
342C2C22⋊Q8×D15111yescharacteristic
343C2#2375301311yescharacteristic
344C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#474D151
hypocenterC151#3081
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752839C2semidirect
3. #23752515C2semidirect
4. #23752513C2semidirect
5. #23752512C2semidirect
6. #23752510C2semidirect
7. #23752500C2semidirect
8. #23752499C2semidirect
9. #23752491C2semidirect
10. #23752253C2semidirect
11. #23752249C2semidirect
12. #23752237C2semidirect
15. #474×C151C2semidirect
19. #18012738C22semidirect
21. #18012731C22semidirect
22. #18012730C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. #18012670C22semidirect
42. #18012670C22semidirect
43. C4⋊(C151⋊C8)C22semidirect
44. Dic151⋊C8C22semidirect
45. Dic151⋊C8C22semidirect
52. C4⋊Q8×C151C22semidirect
54. #107×C151C22semidirect
55. #107×C151C22semidirect
56. C4⋊C8×C151C22semidirect
64. D4×D151Q8semidirect
172. C151#3081semidirect
183. #474D151semidirect
194. C4⋊Q8C2×D151semidirect
214. #107C2×D151semidirect
215. #107C2×D151semidirect
223. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528392
#237526842
#237525152
#237525132
#237525122
#237525102
#237525002
#237524992
#237524912
#237522532
#237522492
#237522372
#237522152
#102×D1512
#474×C1512
#3081151