Finite Group Databasebeta

← #34079218

Subgroups — #34079218

Order 19328.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752741C211yesmaximal, characteristic, complemented
2C4×#14559005C211yesmaximal, characteristic, complemented
3#23752552C211yesmaximal, characteristic, complemented
4#23752535C211yesmaximal, characteristic, complemented
5#23752519C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752373C211yesmaximal, characteristic, complemented
9#23752356C211yesmaximal, characteristic
10#23752321C211yesmaximal, characteristic, complemented
11#23752319C211yesmaximal, characteristic, complemented
12#23752315C211yesmaximal, characteristic, complemented
13#23752313C211yesmaximal, characteristic, complemented
14#23752268C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19#18012732—21no—
20#18012731C2211yescharacteristic
21#18012721—21no—
22#18012715C2211yescharacteristic
23#18012710C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic
26C4×D604—21no—
27C4×D604C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29#18012701—21no—
30#18012701C2211yescharacteristic
31(C22⋊D151)⋊C4—21no—
32#18012697—21no—
33#18012697C2211yescharacteristic
34#18012695—21no—
35C42×D151—21no—
36C42×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151D411yescharacteristic
69C2×C4×D151D411yescharacteristic
70C2×C4×D151C2311yescharacteristic
71#14558991—22no—
72#14558989—22no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151D411yescharacteristic
93C4×Dic151D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98Q16×C151—22no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110D604—24no—
111D604—21no—
112D604#4112yes—
113C22⋊D151—42no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—42no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—24no—
122C4×D151—21no—
123C4×D151—21no—
124C4×D151—41no—
125C4×D151—41no—
126C4×D151—42no—
127C4×D151—42no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134Q8×C151#4112yes—
135D4×C151—21no—
136D4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—22no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—22no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151C2×#4111yescharacteristic
161C4×C151C2×#4111yescharacteristic
162Dic151—21no—
163Dic151—21no—
164Dic151—21no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—81no—
169C2×C151#52511yescharacteristic
170C2×C151#57511yescharacteristic
171C2×C151#57511yescharacteristic
172D151—41no—
173D151—42no—
174C151#311111yescharacteristic, complemented, Sylow
175#3111—1511nomaximal, Sylow
176#529—1511no—
177C4×#41—1511no—
178#485—1511no—
179#482—1511no—
180#479—1511no—
181#478—1511no—
182#464D15111yescharacteristic, complemented
183#463—1511no—
184#452—1511no—
185#449—1511no—
186#442—1511no—
187#441—1511no—
188#440—1511no—
189#440—1511no—
190#432—1511no—
191C2×#41—1511no—
192C2×Q16C2×D15111yescharacteristic
193C2×SD16—1511no—
194C2×SD16C2×D15111yescharacteristic
195C2×D8—1511no—
196#126—3021no—
197#125—1511no—
198#124C2×D15111yescharacteristic
199#123—3021no—
200C22⋊Q8—1511no—
201#121—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8C2×D15111yescharacteristic
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—3021no—
208C4×D4—1511no—
209C4×D4—1511no—
210C4×D4—1511no—
211#117—3021no—
212#117—3021no—
213#117—1511no—
214C2×C42—3021no—
215C2×C42—1511no—
216#107—1511no—
217#107—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8C2×D15111yescharacteristic
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233#97—1511no—
234#41—3022no—
235#41—3022no—
236C2×Q8C22×D15111yescharacteristic
237C2×Q8C22×D15111yescharacteristic
238C2×D4—3021no—
239C2×D4—3021no—
240C2×D4—1511no—
241C2×D4C22×D15111yescharacteristic
242C22×C4—3021no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—1511no—
247C22×C4—1511no—
248C22×C4—1511no—
249Q16—22no—
250SD16—22no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—3021no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3021no—
285C23—1511no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#1455900312yes—
290D4—21no—
291D4—21no—
292D4—3024no—
293D4—3021no—
294D4—6042no—
295D4—1512no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3024no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—6041no—
306C2×C4—6041no—
307C2×C4—6042no—
308C2×C4—6042no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1511no—
313C2×C4D4×D15111yescharacteristic
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—3021no—
324C22—3022no—
325C22—3021no—
326C22—3021no—
327C22—6041no—
328C22—6041no—
329C22C2×D4×D15111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—3021no—
336C4—3021no—
337C4—3021no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4C2×#1455900311yescharacteristic
343C2—81no—
344C2—6041no—
345C2—6042no—
346C2#2375272211yescharacteristic
347C2#2375300911yescharacteristic
348C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752356C2
hypercenter#464D151
hypocenterC151#3111
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23752741C2semidirect
2. C4×#14559005C2semidirect
3. #23752552C2semidirect
4. #23752535C2semidirect
5. #23752519C2semidirect
6. #23752513C2semidirect
7. #23752424C2semidirect
8. #23752373C2semidirect
10. #23752321C2semidirect
11. #23752319C2semidirect
12. #23752315C2semidirect
13. #23752313C2semidirect
14. #23752268C2semidirect
15. #464×C151C2semidirect
174. C151#3111semidirect
182. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237527412
C4×#145590052
#237525522
#237525352
#237525192
#237525132
#237524242
#237523732
#237523562
#237523212
#237523192
#237523152
#237523132
#237522682
#464×C1512
#3111151