Finite Group Databasebeta

← #34079308

Subgroups — #34079308

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752816C211yesmaximal, characteristic, complemented
2#23752694C211yesmaximal, characteristic, complemented
3#23752529C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752519C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752404C211yesmaximal, characteristic, complemented
8#23752356C211yesmaximal, characteristic, complemented
9#23752356C211yesmaximal, characteristic, complemented
10#23752321C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12SD16×Dic151C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#460×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19#18012731C2211yescharacteristic
20#18012720—21no—
21#18012720—21no—
22#18012711—21no—
23#18012711—21no—
24#18012710C2211yescharacteristic
25#18012710C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27C4×D604—21no—
28C4×D604C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31#18012701—21no—
32#18012701C2211yescharacteristic
33#18012696—21no—
34#18012696C2211yescharacteristic
35C4⋊C4×D151—21no—
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558989—22no—
73#14558989—22no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100SD16×C151—22no—
101SD16×C151—22no—
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110D604—24no—
111D604—21no—
112D604#4112yes—
113C22⋊D151—81no—
114C22⋊D151—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—81no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—24no—
124C4×D151—21no—
125C4×D151—21no—
126C4×D151—81no—
127C4×D151—81no—
128C4×D151—81no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132C23×C151—21no—
133Q8×C151—21no—
134Q8×C151#4112yes—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—81no—
140D4×C151—81no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151C22×D411yescharacteristic
155C2×D151—21no—
156C2×D151—22no—
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—41no—
160C2×D151—41no—
161C4×C151—22no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151C2×#4111yescharacteristic
166C4×C151C2×#4111yescharacteristic
167Dic151—21no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—81no—
174C2×C151—81no—
175C2×C151#52511yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57711yescharacteristic
178D151—41no—
179D151—42no—
180C151#311911yescharacteristic, complemented, Sylow
181#3119—1511nomaximal, Sylow
182#540—1511no—
183#520—1511no—
184#481—1511no—
185#480—1511no—
186#479—1511no—
187#478—1511no—
188#460D15111yescharacteristic, complemented
189#459—1511no—
190#449—1511no—
191#449—1511no—
192#442—1511no—
193#440—1511no—
194C4×SD16—1511no—
195C4×D8—1511no—
196#433—1511no—
197C2×#41—1511no—
198C2×SD16C2×D15111yescharacteristic
199C2×SD16C2×D15111yescharacteristic
200C2×D8—1511no—
201C2×D8—1511no—
202#127C2×D15111yescharacteristic
203#125—1511no—
204#123—3021no—
205#123—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8—1511no—
211C4×Q8C2×D15111yescharacteristic
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—3021no—
221C2×C4⋊C4—1511no—
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8C2×D15111yescharacteristic
228#103—1511no—
229#103—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102C2×D15111yescharacteristic
235#102C2×D15111yescharacteristic
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97—1511no—
239C4×C8—1511no—
240#41—3022no—
241#41—3022no—
242C2×Q8C22×D15111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—1511no—
258SD16—22no—
259SD16—22no—
260D8—3022no—
261D8—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—1511no—
284C22⋊C4—1511no—
285C42—21no—
286C42—3021no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—21no—
291C23—3021no—
292C23—1511no—
293Q8—21no—
294Q8#1455900312yes—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—3024no—
302D4—3021no—
303D4—1512no—
304D4—12081no—
305D4—12081no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3024no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—1511no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4D4×D15111yescharacteristic
323C2×C4D4×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3021no—
328C8—3021no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—3021no—
336C22—3022no—
337C22—3021no—
338C22—3021no—
339C22—6041no—
340C22—6041no—
341C22C2×D4×D15111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—3021no—
347C4—3021no—
348C4—3021no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4C2×#1455900311yescharacteristic
354C2—81no—
355C2—81no—
356C2—6041no—
357C2—6042no—
358C2#2375272211yescharacteristic
359C2#2375301611yescharacteristic
360C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#460×C151C2
socleC22×C151C22×D4
hypercenter#460D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23752816C2semidirect
2. #23752694C2semidirect
3. #23752529C2semidirect
4. #23752524C2semidirect
5. #23752519C2semidirect
6. #23752513C2semidirect
7. #23752404C2semidirect
8. #23752356C2semidirect
9. #23752356C2semidirect
10. #23752321C2semidirect
11. #23752313C2semidirect
12. SD16×Dic151C2semidirect
13. #23752292C2semidirect
14. #23752272C2semidirect
15. #460×C151C2semidirect
180. C151#3119semidirect
188. #460D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237526942
#237525292
#237525242
#237525192
#237525132
#237524042
#237523562
#237523212
#237523132
SD16×Dic1512
#237522922
#237522722
#460×C1512
#3119151