Finite Group Databasebeta

← #2721×C151 #34066053

Subgroups — #2721×C151 #34066053

Order 19328.

434 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×C151C211yesmaximal, characteristic
2C2×#125×C151C211yesmaximal, characteristic, complemented
3#399×C151C211yesmaximal, characteristic
4#399×C151C211yesmaximal, characteristic
5#398×C151C211yesmaximal, characteristic, complemented
6#398×C151C211yesmaximal, characteristic, complemented
7#397×C151C211yesmaximal, characteristic
8#396×C151C211yesmaximal, characteristic
9#389×C151C211yesmaximal, characteristic, complemented
10#388×C151C211yesmaximal, characteristic
11#388×C151C211yesmaximal, characteristic
12#387×C151C211yesmaximal, characteristic, complemented
13#387×C151C211yesmaximal, characteristic, complemented
14#387×C151C211yesmaximal, characteristic, complemented
15#384×C151C211yesmaximal, characteristic, complemented
16#126×C151—24no—
17#125×C151—24no—
18C2×C4⋊C4×C151C2211yescharacteristic
19C2×C4⋊C4×C151C2211yescharacteristic
20C2×C4⋊C4×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24C2×C4⋊C4×C151C2211yescharacteristic
25C2×C4⋊C4×C151C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30C2×C4⋊C4×C151C2211yescharacteristic
31C2×C4⋊C4×C151C2211yescharacteristic
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2211yescharacteristic
36C2×C22⋊C4×C151C2211yescharacteristic
37C2×C22⋊C4×C151C2211yescharacteristic
38C2×C22⋊C4×C151C2211yescharacteristic
39C2×C22⋊C4×C151C2211yescharacteristic
40C2×C42×C151C2211yescharacteristic
41C2×C42×C151C2211yescharacteristic
42C2×C42×C151C2211yescharacteristic
43#95×C151C2211yescharacteristic
44#95×C151C2211yescharacteristic
45#95×C151C2211yescharacteristic
46#95×C151C2211yescharacteristic
47#95×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C24×C151C2311yescharacteristic
54C22×C4×C151C2311yescharacteristic
55C22×C4×C151C2311yescharacteristic
56C22×C4×C151C2311yescharacteristic
57C22×C4×C151C2311yescharacteristic
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63C22×C4×C151C2311yescharacteristic
64C22×C4×C151C2311yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C22×C4×C151C2311yescharacteristic
67C22×C4×C151C2311yescharacteristic
68C4⋊C4×C151—22no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—22no—
71C4⋊C4×C151—22no—
72C4⋊C4×C151—22no—
73C4⋊C4×C151—22no—
74C4⋊C4×C151—22no—
75C4⋊C4×C151—22no—
76C4⋊C4×C151—22no—
77C4⋊C4×C151—22no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151D414yes—
83C22⋊C4×C151—22no—
84C22⋊C4×C151—22no—
85C22⋊C4×C151—22no—
86C22⋊C4×C151—22no—
87C22⋊C4×C151—22no—
88C22⋊C4×C151—41no—
89C22⋊C4×C151—41no—
90C42×C151—22no—
91C42×C151—22no—
92C42×C151—22no—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151—21no—
97C23×C151—21no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151C2411yescharacteristic
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D412yes—
139C2×C4×C151C2×D412yes—
140C2×C4×C151C2×D412yes—
141C2×C4×C151#4112yes—
142C2×C4×C151#4112yes—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151C22×D411yescharacteristic
151C22×C151C2×#4111yescharacteristic
152C22×C151C2×#4111yescharacteristic
153C22×C151H(5,𝔽2)11yescharacteristic
154C22×C1512−1+411yescharacteristic
155C22×C1512−1+411yescharacteristic
156C22×C1512−1+411yescharacteristic
157C4×C151—22no—
158C4×C151—22no—
159C4×C151—22no—
160C4×C151—22no—
161C4×C151—22no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C2×C151—81no—
172C2×C151#53611yescharacteristic
173C2×C151#53911yescharacteristic
174C2×C151#54111yescharacteristic
175C2×C151#54711yescharacteristic
176C2×C151#55011yescharacteristic
177C2×C151#55211yescharacteristic
178C2×C151#56311yescharacteristic
179C151#272111yescharacteristic, direct product factor, Sylow
180#2721C15111yesmaximal, characteristic, direct product factor, Sylow
181C2×#126C2×C15111yescharacteristic
182C2×#125C2×C15111yescharacteristic, complemented
183#399C2×C15111yescharacteristic
184#399C2×C15111yescharacteristic
185#398C2×C15111yescharacteristic, complemented
186#398C2×C15111yescharacteristic, complemented
187#397C2×C15111yescharacteristic
188#396C2×C15111yescharacteristic
189#389C2×C15111yescharacteristic, complemented
190#388C2×C15111yescharacteristic
191#388C2×C15111yescharacteristic
192#387C2×C15111yescharacteristic, complemented
193#387C2×C15111yescharacteristic, complemented
194#387C2×C15111yescharacteristic, complemented
195#384C2×C15111yescharacteristic, complemented
196#126—24no—
197#125—24no—
198C2×C4⋊C4C22×C15111yescharacteristic
199C2×C4⋊C4C22×C15111yescharacteristic
200C2×C4⋊C4C22×C15111yescharacteristic
201C2×C4⋊C4C22×C15111yescharacteristic
202C2×C4⋊C4C22×C15111yescharacteristic
203C2×C4⋊C4C22×C15111yescharacteristic
204C2×C4⋊C4C22×C15111yescharacteristic
205C2×C4⋊C4C22×C15111yescharacteristic
206C2×C4⋊C4C22×C15111yescharacteristic
207C2×C4⋊C4C22×C15111yescharacteristic
208C2×C4⋊C4C22×C15111yescharacteristic
209C2×C4⋊C4C22×C15111yescharacteristic
210C2×C4⋊C4C22×C15111yescharacteristic
211C2×C4⋊C4C22×C15111yescharacteristic
212C2×C4⋊C4C22×C15111yescharacteristic
213C2×C22⋊C4C22×C15111yescharacteristic
214C2×C22⋊C4C22×C15111yescharacteristic
215C2×C22⋊C4C22×C15111yescharacteristic
216C2×C22⋊C4C22×C15111yescharacteristic
217C2×C22⋊C4C22×C15111yescharacteristic
218C2×C22⋊C4C22×C15111yescharacteristic
219C2×C22⋊C4C22×C15111yescharacteristic
220C2×C42C22×C15111yescharacteristic
221C2×C42C22×C15111yescharacteristic
222C2×C42C22×C15111yescharacteristic
223#95C22×C15111yescharacteristic
224#95C22×C15111yescharacteristic
225#95C22×C15111yescharacteristic
226#95C22×C15111yescharacteristic
227#95C22×C15111yescharacteristic
228#95C22×C15111yescharacteristic
229#95C22×C15111yescharacteristic
230#95C22×C15111yescharacteristic
231#95C22×C15111yescharacteristic
232#95C22×C15111yescharacteristic
233C24C23×C15111yescharacteristic
234C22×C4C23×C15111yescharacteristic
235C22×C4C23×C15111yescharacteristic
236C22×C4C23×C15111yescharacteristic
237C22×C4C23×C15111yescharacteristic
238C22×C4C23×C15111yescharacteristic
239C22×C4C23×C15111yescharacteristic
240C22×C4C23×C15111yescharacteristic
241C22×C4C23×C15111yescharacteristic
242C22×C4C23×C15111yescharacteristic
243C22×C4C23×C15111yescharacteristic
244C22×C4C23×C15111yescharacteristic
245C22×C4C23×C15111yescharacteristic
246C22×C4C23×C15111yescharacteristic
247C22×C4C23×C15111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4D4×C15114yes—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—22no—
271C42—22no—
272C42—22no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23C24×C15111yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4C2×D4×C15112yes—
319C2×C4C2×D4×C15112yes—
320C2×C4C2×D4×C15112yes—
321C2×C4#41×C15112yes—
322C2×C4#41×C15112yes—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×D4×C15111yescharacteristic
331C22C2×#41×C15111yescharacteristic
332C22C2×#41×C15111yescharacteristic
333C22H(5,𝔽2)×C15111yescharacteristic
334C222−1+4×C15111yescharacteristic
335C222−1+4×C15111yescharacteristic
336C222−1+4×C15111yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C2—81no—
352C2#536×C15111yescharacteristic
353C2#539×C15111yescharacteristic
354C2#541×C15111yescharacteristic
355C2#547×C15111yescharacteristic
356C2#550×C15111yescharacteristic
357C2#552×C15111yescharacteristic
358C2#563×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC24×C151C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#125×C151C2semidirect
5. #398×C151C2semidirect
6. #398×C151C2semidirect
9. #389×C151C2semidirect
12. #387×C151C2semidirect
13. #387×C151C2semidirect
14. #387×C151C2semidirect
15. #384×C151C2semidirect
179. C151#2721direct (N × H)
180. #2721C151direct (N × H)
182. C2×#125C2×C151semidirect
185. #398C2×C151semidirect
186. #398C2×C151semidirect
189. #389C2×C151semidirect
192. #387C2×C151semidirect
193. #387C2×C151semidirect
194. #387C2×C151semidirect
195. #384C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#126×C1512
C2×#125×C1512
#399×C1512
#398×C1512
#397×C1512
#396×C1512
#389×C1512
#388×C1512
#387×C1512
#384×C1512
#2721151