Finite Group Databasebeta

← #34080515

Subgroups — #34080515

Order 19328.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752833C211yesmaximal, characteristic, complemented
2#23752516C211yesmaximal, characteristic, complemented
3#23752509C211yesmaximal, characteristic, complemented
4#23752502C211yesmaximal, characteristic, complemented
5#23752492C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752456C211yesmaximal, characteristic, complemented
8#23752446C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752427C211yesmaximal, characteristic, complemented
11#23752427C211yesmaximal, characteristic, complemented
12#23752409C211yesmaximal, characteristic, complemented
13#23752404C211yesmaximal, characteristic, complemented
14#23752239C211yesmaximal, characteristic, complemented
15#540×C151C211yesmaximal, characteristic, complemented
16C2×#14558992C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558988C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22#18012739C2211yescharacteristic
23#18012734—21no—
24#18012727C2211yescharacteristic
25#18012725—21no—
26#18012721—21no—
27#18012718C2211yescharacteristic
28#18012717—21no—
29#18012713C2211yescharacteristic
30C4×Dic302C2211yescharacteristic
31C4×D604C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34#18012670C2211yescharacteristic
35#18012670C2211yescharacteristic
36C4⋊(C151⋊C8)C2211yescharacteristic
37C4⋊(C151⋊C8)C2211yescharacteristic
38C4⋊(C151⋊C8)C2211yescharacteristic
39C4⋊(C151⋊C8)C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#127×C151C2211yescharacteristic
49#125×C151C2211yescharacteristic
50#123×C151—21no—
51#123×C151—21no—
52#121×C151—21no—
53#121×C151—21no—
54#121×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58#117×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64#14558992—41no—
65#14558992—41no—
66#14558989—41no—
67#14558989—41no—
68#14558988—41no—
69C2×C151⋊C8—41no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79C22⋊Dic151—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84C4×Dic151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—21no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151C2311yescharacteristic
90C2×D4×C151C2311yescharacteristic
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151C2311yescharacteristic
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151D411yescharacteristic
97C4⋊C4×C151D411yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C22⋊C4×C151D411yescharacteristic
105C22⋊C4×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111Dic302—81no—
112D604—21no—
113D604—21no—
114C22⋊D151—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C23×C151—21no—
124C23×C151—21no—
125C23×C151C2×D411yescharacteristic
126D4×C151—21no—
127D4×C151—21no—
128D4×C151—21no—
129D4×C151—21no—
130D4×C151—81no—
131D4×C151—81no—
132D4×C151—81no—
133D4×C151—81no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—81no—
139C2×C4×C151—81no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151H(5,𝔽2)11yescharacteristic
167C4×C1512−1+411yescharacteristic
168Dic151—41no—
169Dic151—41no—
170Dic151—41no—
171C2×C151—41no—
172C2×C151—81no—
173C2×C151—81no—
174C2×C151#53711yescharacteristic
175C2×C151#57611yescharacteristic
176C2×C151#57711yescharacteristic
177D151—81no—
178C151#325711yescharacteristic, complemented, Sylow
179#3257—1511nomaximal, Sylow
180#542—1511no—
181#540D15111yescharacteristic, complemented
182#479—1511no—
183#478—1511no—
184#476—1511no—
185#474—1511no—
186#469—1511no—
187#468—1511no—
188#466—1511no—
189#465—1511no—
190#463—1511no—
191#463—1511no—
192#460—1511no—
193#459—1511no—
194#424—1511no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×D8—1511no—
198C2×D8—1511no—
199C2×M16—1511no—
200C22×C8—1511no—
201C4⋊Q8—1511no—
202#127C2×D15111yescharacteristic
203#126—3021no—
204#125C2×D15111yescharacteristic
205#124—3021no—
206#124—1511no—
207#123—21no—
208#123—21no—
209#123—3021no—
210C22⋊Q8—3021no—
211C22⋊Q8—1511no—
212#121—21no—
213#121—21no—
214#121—1511no—
215#121C2×D15111yescharacteristic
216#121C2×D15111yescharacteristic
217C4×Q8—1511no—
218C4×D4—1511no—
219C4×D4C2×D15111yescharacteristic
220C4×D4C2×D15111yescharacteristic
221#117C2×D15111yescharacteristic
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229C4⋊C8—1511no—
230#103—1511no—
231#103—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238C2×Q8—3021no—
239C2×Q8—1511no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—3021no—
245C2×D4—1511no—
246C2×D4C22×D15111yescharacteristic
247C2×D4C22×D15111yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3021no—
251C22×C4C22×D15111yescharacteristic
252SD16—6041no—
253SD16—6041no—
254D8—6041no—
255D8—6041no—
256M16—6041no—
257C2×C8—6041no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8—1511no—
261C2×C8—1511no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4C22⋊D15111yescharacteristic
270C4⋊C4C22⋊D15111yescharacteristic
271C4⋊C4C22×D15111yescharacteristic
272C4⋊C4C22×D15111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4C22⋊D15111yescharacteristic
283C22⋊C4C22⋊D15111yescharacteristic
284C42—3021no—
285C42C22×D15111yescharacteristic
286C42C22×D15111yescharacteristic
287C23—21no—
288C23—21no—
289C23—3021no—
290C23C2×C22⋊D15111yescharacteristic
291Q8—3021no—
292Q8—3021no—
293Q8—12081no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—3021no—
303D4—3021no—
304D4—12081no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—12081no—
315C2×C4C2×C22⋊D15111yescharacteristic
316C2×C4C2×C22⋊D15111yescharacteristic
317C2×C4C2×C22⋊D15111yescharacteristic
318C2×C4C2×C22⋊D15111yescharacteristic
319C2×C4C2×C22⋊D15111yescharacteristic
320C2×C4C23×D15111yescharacteristic
321C8—3021no—
322C8—3021no—
323C8—3021no—
324C8—3021no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—6041no—
335C22—6041no—
336C22—6041no—
337C22C22×C22⋊D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—6041no—
346C4—6041no—
347C4—6041no—
348C4#1801278511yescharacteristic
349C4#1801278611yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—12081no—
354C2#2375279011yescharacteristic
355C2#2375301511yescharacteristic
356C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#540×C151C2
socleC22×C151C22×D4
hypercenter#540D151
hypocenterC151#3257
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752516C2semidirect
3. #23752509C2semidirect
4. #23752502C2semidirect
5. #23752492C2semidirect
6. #23752463C2semidirect
7. #23752456C2semidirect
8. #23752446C2semidirect
9. #23752439C2semidirect
10. #23752427C2semidirect
11. #23752427C2semidirect
12. #23752409C2semidirect
13. #23752404C2semidirect
14. #23752239C2semidirect
15. #540×C151C2semidirect
178. C151#3257semidirect
181. #540D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237525162
#237525092
#237525022
#237524922
#237524632
#237524562
#237524462
#237524392
#237524272
#237524092
#237524042
#237522392
#540×C1512
#3257151