Finite Group Databasebeta

← #34080547

Subgroups — #34080547

Order 19328.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752816C211yesmaximal, characteristic, complemented
2#23752813C211yesmaximal, characteristic, complemented
3#23752514C211yesmaximal, characteristic, complemented
4#23752513C211yesmaximal, characteristic, complemented
5#23752512C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752462C211yesmaximal, characteristic, complemented
9#23752447C211yesmaximal, characteristic, complemented
10#23752445C211yesmaximal, characteristic, complemented
11#23752405C211yesmaximal, characteristic, complemented
12#23752405C211yesmaximal, characteristic, complemented
13#23752404C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14558989C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012735C2211yescharacteristic
21#18012731C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012722—21no—
24#18012721—21no—
25#18012720—21no—
26#18012720—21no—
27#18012714C2211yescharacteristic
28#18012713—21no—
29#18012712—21no—
30#18012711—21no—
31#18012711—21no—
32#18012710C2211yescharacteristic
33#18012710C2211yescharacteristic
34#18012710C2211yescharacteristic
35C4×D604C2211yescharacteristic
36D4×Dic151C2211yescharacteristic
37D4×Dic151C2211yescharacteristic
38#18012696C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50#18012660C2211yescharacteristic
51#18012660C2211yescharacteristic
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×D604—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69C2×C4×D151C2311yescharacteristic
70#14558989—41no—
71#14558989—41no—
72#14558987—41no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C8×D151—41no—
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—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101D8×C151—41no—
102D8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110D604—21no—
111D604—21no—
112D604—81no—
113C22⋊D151—81no—
114C22⋊D151—81no—
115C22⋊D151—81no—
116C22⋊D151—81no—
117C22⋊D151—81no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—81no—
122C2×Dic151—81no—
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C4×D151—21no—
127C4×D151—21no—
128C4×D151—81no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—81no—
141D4×C151—81no—
142C2×C4×C151—21no—
143C2×C4×C151—81no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151H(5,𝔽2)11yescharacteristic
169C4×C1512−1+411yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176C2×C151—81no—
177C2×C151—81no—
178C2×C151—81no—
179C2×C151#53711yescharacteristic
180C2×C151#57611yescharacteristic
181C2×C151#57611yescharacteristic
182D151—41no—
183D151—81no—
184C151#325911yescharacteristic, complemented, Sylow
185#3259—1511nomaximal, Sylow
186#540—1511no—
187#540—1511no—
188#478—1511no—
189#478—1511no—
190#478—1511no—
191#478—1511no—
192#469—1511no—
193#469—1511no—
194#466—1511no—
195#466—1511no—
196#459—1511no—
197#459—1511no—
198#459—1511no—
199#459D15111yescharacteristic, complemented
200#424—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C2×D8C2×D15111yescharacteristic
204C2×D8C2×D15111yescharacteristic
205C2×M16—1511no—
206C22×C8—1511no—
207#127—1511no—
208#127C2×D15111yescharacteristic
209#125—1511no—
210#125—1511no—
211#123—3021no—
212#123—3021no—
213#123—3021no—
214#123—3021no—
215#121—3021no—
216#121—3021no—
217#121—3021no—
218#121—3021no—
219#121—1511no—
220#121—1511no—
221#121—1511no—
222#121—1511no—
223C4×D4—1511no—
224C4×D4—1511no—
225C4×D4—1511no—
226C4×D4C2×D15111yescharacteristic
227#117—1511no—
228#107—1511no—
229#107—1511no—
230#106—1511no—
231#106—1511no—
232C4⋊C8—1511no—
233C4⋊C8—1511no—
234C4⋊C8—1511no—
235C4⋊C8C2×D15111yescharacteristic
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102—1511no—
242#102C2×D15111yescharacteristic
243#102C2×D15111yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—3021no—
251C2×D4—3021no—
252C2×D4—1511no—
253C2×D4C22×D15111yescharacteristic
254C2×D4C22×D15111yescharacteristic
255C2×D4C22×D15111yescharacteristic
256C22×C4—21no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—1511no—
261D8—41no—
262D8—41no—
263D8—6041no—
264D8—6041no—
265M16—6041no—
266C2×C8—6041no—
267C2×C8—1511no—
268C2×C8—1511no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4C22×D15111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—1511no—
290C22⋊C4—1511no—
291C42—1511no—
292C42C22×D15111yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23—3021no—
297C23—1511no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—3021no—
307D4—3021no—
308D4—12081no—
309D4—12081no—
310D4—12081no—
311D4—12081no—
312D4—12081no—
313D4—12081no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—12081no—
325C2×C4—12081no—
326C2×C4—12081no—
327C2×C4D4×D15111yescharacteristic
328C2×C4D4×D15111yescharacteristic
329C2×C4C23×D15111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3021no—
333C8—3021no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3021no—
344C22—3021no—
345C22—3021no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—3021no—
354C4—3021no—
355C4—3021no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4#1801278411yescharacteristic
360C4#1801278611yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—6041no—
365C2—12081no—
366C2#2375279111yescharacteristic
367C2#2375301311yescharacteristic
368C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3259
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752816C2semidirect
2. #23752813C2semidirect
3. #23752514C2semidirect
4. #23752513C2semidirect
5. #23752512C2semidirect
6. #23752510C2semidirect
7. #23752464C2semidirect
8. #23752462C2semidirect
9. #23752447C2semidirect
10. #23752445C2semidirect
11. #23752405C2semidirect
12. #23752405C2semidirect
13. #23752404C2semidirect
14. #23752237C2semidirect
15. #459×C151C2semidirect
184. C151#3259semidirect
199. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237528132
#237525142
#237525132
#237525122
#237525102
#237524642
#237524622
#237524472
#237524452
#237524052
#237524042
#237522372
#459×C1512
#3259151