Finite Group Databasebeta

← #34079306

Subgroups — #34079306

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#23752691C211yesmaximal, characteristic, complemented
3#23752529C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752520C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752409C211yesmaximal, characteristic, complemented
8#23752354C211yesmaximal, characteristic, complemented
9#23752354C211yesmaximal, characteristic, complemented
10#23752324C211yesmaximal, characteristic, complemented
11#23752309C211yesmaximal, characteristic, complemented
12#23752303C211yesmaximal, characteristic, complemented
13D8×Dic151C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19#18012731C2211yescharacteristic
20#18012720—21no—
21#18012720—21no—
22#18012711—21no—
23#18012711—21no—
24#18012710C2211yescharacteristic
25#18012710C2211yescharacteristic
26C4×Dic302C2211yescharacteristic
27#18012704C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33#18012696C2211yescharacteristic
34#18012695—21no—
35C2×Dic151⋊C4—21no—
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—22no—
61C2×Dic302C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C22×Dic151—21no—
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71#14558992—22no—
72#14558992—22no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
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—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4D411yescharacteristic
91(C2×D151)⋊C4D411yescharacteristic
92C4×Dic151—21no—
93C4×Dic151—21no—
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—22no—
102D8×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—21no—
110Dic302#4112yes—
111C22⋊D151—24no—
112C22⋊D151—81no—
113C22⋊D151—81no—
114C2×Dic151—24no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C2×Dic151—81no—
121C2×Dic151—81no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—21no—
126C4×D151—21no—
127C4×D151—81no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133D4×C151—21no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—81no—
139D4×C151—81no—
140D4×C151#4112yes—
141C2×C4×C151—21no—
142C2×C4×C151—81no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—22no—
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×C151C22×D411yescharacteristic
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151C2×#4111yescharacteristic
165C4×C151C2×#4111yescharacteristic
166Dic151—21no—
167Dic151—22no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—42no—
174C2×C151—81no—
175C2×C151—81no—
176C2×C151#52511yescharacteristic
177C2×C151#57611yescharacteristic
178C2×C151#57711yescharacteristic
179D151—41no—
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#460—1511no—
189#459D15111yescharacteristic, complemented
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×SD16—1511no—
199C2×SD16—1511no—
200C2×D8C2×D15111yescharacteristic
201C2×D8C2×D15111yescharacteristic
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×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4C2×D15111yescharacteristic
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×Q8—1511no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4C22×D15111yescharacteristic
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—1511no—
258SD16—3022no—
259SD16—3022no—
260D8—22no—
261D8—22no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—3021no—
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—21no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—1511no—
284C22⋊C4—1511no—
285C42—3021no—
286C42—3021no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—1511no—
293Q8—3021no—
294Q8—1512no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—3024no—
303D4—12081no—
304D4—12081no—
305D4#1455900312yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—3024no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
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—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3021no—
339C22—3021no—
340C22—3021no—
341C22C2×D4×D15111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—3021no—
346C4—3022no—
347C4—3021no—
348C4—3021no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4C2×#1455900311yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—6041no—
358C2#2375272211yescharacteristic
359C2#2375301311yescharacteristic
360C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3119
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. #23752691C2semidirect
3. #23752529C2semidirect
4. #23752524C2semidirect
5. #23752520C2semidirect
6. #23752512C2semidirect
7. #23752409C2semidirect
8. #23752354C2semidirect
9. #23752354C2semidirect
10. #23752324C2semidirect
11. #23752309C2semidirect
12. #23752303C2semidirect
13. D8×Dic151C2semidirect
14. #23752272C2semidirect
15. #459×C151C2semidirect
180. C151#3119semidirect
189. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237526912
#237525292
#237525242
#237525202
#237525122
#237524092
#237523542
#237523242
#237523092
#237523032
D8×Dic1512
#237522722
#459×C1512
#3119151