Finite Group Databasebeta

← #34079356

Subgroups — #34079356

Order 19328.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752822C211yesmaximal, characteristic, complemented
2#23752687C211yesmaximal, characteristic
3#23752554C211yesmaximal, characteristic, complemented
4#23752550C211yesmaximal, characteristic, complemented
5#23752514C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752415C211yesmaximal, characteristic, complemented
8#23752415C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic
10#23752313C211yesmaximal, characteristic, complemented
11#23752309C211yesmaximal, characteristic, complemented
12#23752303C211yesmaximal, characteristic, complemented
13SD16×Dic151C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic
16C2×#14558992C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18#18012737C2211yescharacteristic, complemented
19#18012732—21no—
20#18012732—21no—
21#18012730—21no—
22#18012730C2211yescharacteristic, complemented
23#18012729—21no—
24#18012718C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic, complemented
26#18012704C2211yescharacteristic, complemented
27D4×Dic151—21no—
28D4×Dic151—21no—
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33#18012698C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C22⋊Dic151—21no—
36C2×C22⋊Dic151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012663C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C22×Dic151—21no—
61C22×Dic151—21no—
62C22×Dic151—21no—
63C22×Dic151—21no—
64#14558992—22no—
65#14558992—22no—
66C2×C151⋊C8C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C4⋊Dic151—21no—
69C4⋊Dic151—21no—
70C4⋊Dic151D411yescharacteristic
71C4⋊Dic151D411yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80C22⋊Dic151—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151D411yescharacteristic
87C22⋊Dic151D411yescharacteristic
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C4×Dic151C2311yescharacteristic
93C24×C151—21no—
94C2×Q8×C151C2311yescharacteristic
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101SD16×C151—22no—
102SD16×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108Dic302—21no—
109Dic302—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—81no—
115C2×Dic151—81no—
116C2×Dic151—81no—
117C2×Dic151—81no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C151⋊C8—21no—
123C151⋊C8—21no—
124C23×C151—24no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—81no—
128C23×C151—81no—
129C23×C151C2×D411yescharacteristic
130Q8×C151—21no—
131Q8×C151—21no—
132D4×C151—24no—
133D4×C151—21no—
134D4×C151—21no—
135D4×C151#4112yes—
136D4×C151#4112yes—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—21no—
146C22×C151—22no—
147C22×C151—22no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—84no—
155C22×C151C22×D411yescharacteristic
156C4×C151—21no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151C2×#4111yescharacteristic
160C4×C151C2×#4111yescharacteristic
161Dic151—21no—
162Dic151—21no—
163Dic151—21no—
164Dic151—21no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168Dic151—41no—
169C2×C151—41no—
170C2×C151—42no—
171C2×C151—42no—
172C2×C151#52511yescharacteristic
173C2×C151#57711yescharacteristic
174C2×C151#57711yescharacteristic
175C151#312311yescharacteristic, complemented, Sylow
176#3123—1511nomaximal, Sylow
177#541—1511no—
178#518—1511no—
179#485—1511no—
180#485—1511no—
181#478—1511no—
182#478—1511no—
183#461—1511no—
184#461—1511no—
185#450—1511no—
186#450D15111yescharacteristic
187#440—1511no—
188#440—1511no—
189C4×SD16—1511no—
190C4×SD16—1511no—
191#433—1511no—
192C22×D4C2×D15111yescharacteristic
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×SD16C2×D15111yescharacteristic
196C2×SD16C2×D15111yescharacteristic
197C4⋊Q8—1511no—
198#126—3021no—
199#126—3021no—
200#125—3021no—
201#125—3021no—
202#125—1511no—
203C22⋊Q8—1511no—
204C22⋊Q8C2×D15111yescharacteristic
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×D4—3021no—
208C4×D4—3021no—
209C4×D4—1511no—
210C4×D4—1511no—
211C4×D4—1511no—
212C4×D4—1511no—
213#117—1511no—
214#117—1511no—
215C2×C22⋊C4—3021no—
216C2×C22⋊C4—3021no—
217#107—1511no—
218#107—1511no—
219#106—1511no—
220#106—1511no—
221C4⋊C8—1511no—
222C4⋊C8—1511no—
223#103—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230#102C2×D15111yescharacteristic
231C22⋊C8—1511no—
232C22⋊C8C2×D15111yescharacteristic
233#97—1511no—
234C4×C8—1511no—
235C24—21no—
236C2×Q8—1511no—
237C2×Q8C22×D15111yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D15111yescharacteristic
242C2×D4C22×D15111yescharacteristic
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4C22×D15111yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—3022no—
251SD16—3022no—
252C2×C8—1511no—
253C2×C8—1511no—
254C2×C8C22×D15111yescharacteristic
255C2×C8C22×D15111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—3021no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
266C4⋊C4—1511no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4C22×D15111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—1511no—
278C22⋊C4—1511no—
279C42—3021no—
280C42—3021no—
281C42—3021no—
282C42—1511no—
283C42—1511no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D15111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—3021no—
293Q8—3021no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1455900312yes—
298D4#1455900312yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—1511no—
308C2×C4—1511no—
309C2×C4—1511no—
310C2×C4—1511no—
311C2×C4—12081no—
312C2×C4—12081no—
313C2×C4—12081no—
314C2×C4—12081no—
315C2×C4D4×D15111yescharacteristic
316C2×C4C23×D15111yescharacteristic
317C8—21no—
318C8—21no—
319C8—3021no—
320C8—3021no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D15111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—3021no—
336C4—3021no—
337C4—3021no—
338C4—3021no—
339C4—6041no—
340C4—6041no—
341C4—6041no—
342C4—6041no—
343C4C2×#1455900311yescharacteristic
344C4C2×#1455900311yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#2375271811yescharacteristic
349C2#2375301811yescharacteristic
350C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radicalC22×D4×C151C22
hypercenter#450D151
hypocenterC151#3123
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752822C2semidirect
3. #23752554C2semidirect
4. #23752550C2semidirect
5. #23752514C2semidirect
6. #23752510C2semidirect
7. #23752415C2semidirect
8. #23752415C2semidirect
10. #23752313C2semidirect
11. #23752309C2semidirect
12. #23752303C2semidirect
13. SD16×Dic151C2semidirect
14. #23752270C2semidirect
18. #18012737C22semidirect
22. #18012730C22semidirect
25. Q8×Dic151C22semidirect
26. #18012704C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012663C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
175. C151#3123semidirect

Maximal subgroups

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

subgroupindex
#237528222
#237526872
#237525542
#237525502
#237525142
#237525102
#237524152
#237523632
#237523132
#237523092
#237523032
SD16×Dic1512
#237522702
#450×C1512
#3123151