Finite Group Databasebeta

← C151×#8876 #50313801

Subgroups — C151×#8876 #50313801

Order 38656.

380 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
1#2992×C151C211yesmaximal, characteristic
2#1843×C151C211yesmaximal, characteristic, complemented
3#1573×C151C211yesmaximal, characteristic, complemented
4#1500×C151C211yesmaximal, characteristic
5#1483×C151C211yesmaximal, characteristic
6#1300×C151C211yesmaximal, characteristic, complemented
7#1283×C151C211yesmaximal, characteristic, complemented
8#529×C151C2211yescharacteristic
9#446×C151—21no—
10#435×C151—21no—
11#435×C151—21no—
12C8×D4×C151—21no—
13#433×C151—21no—
14#432×C151C2211yescharacteristic
15#431×C151C2211yescharacteristic
16#424×C151—21no—
17C2×C4⋊C8×C151—21no—
18C2×C4⋊C8×C151—21no—
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C4×M16×C151C2211yescharacteristic
22#376×C151C2211yescharacteristic
23#335×C151—21no—
24#334×C151—21no—
25#328×C151C411yescharacteristic
26#328×C151C411yescharacteristic
27#327×C151C411yescharacteristic
28#327×C151C411yescharacteristic
29Q8⋊C8×C151—21no—
30D4⋊C8×C151—21no—
31C2×M16×C151—21no—
32C2×M16×C151—21no—
33C22×C8×C151—21no—
34C22×C8×C151—21no—
35C22×C8×C151D411yescharacteristic
36C22×C8×C151D411yescharacteristic
37#126×C151—21no—
38#125×C151Q811yescharacteristic
39#124×C151Q811yescharacteristic
40#123×C151—21no—
41C22⋊Q8×C151C2×C411yescharacteristic
42#121×C151C2×C411yescharacteristic
43C4×Q8×C151D411yescharacteristic
44C4×D4×C151—21no—
45C4×D4×C151D411yescharacteristic
46#117×C151—21no—
47C2×C42×C151—21no—
48C2×C42×C151C2311yescharacteristic
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55C4⋊C8×C151—21no—
56C4⋊C8×C151—42no—
57C4⋊C8×C151—42no—
58C4⋊C8×C151D411yescharacteristic
59C4⋊C8×C151D411yescharacteristic
60C22⋊C8×C151—21no—
61C22⋊C8×C151—21no—
62C22⋊C8×C151—21no—
63C22⋊C8×C151C2×C411yescharacteristic
64C22⋊C8×C151C2×C411yescharacteristic
65#97×C151—21no—
66#97×C151—21no—
67#97×C151—21no—
68C4×C8×C151—21no—
69C4×C8×C151—21no—
70C4×C8×C151—21no—
71#95×C151—21no—
72#95×C151C2×C411yescharacteristic
73#95×C151C2×C411yescharacteristic
74C2×Q8×C151C4⋊C411yescharacteristic
75C2×D4×C151—21no—
76C2×D4×C151C4⋊C411yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151C22×C411yescharacteristic
81C22×C4×C151C2×D411yescharacteristic
82C22×C4×C151#4111yescharacteristic
83M16×C151—22no—
84M16×C151—41no—
85M16×C151—81no—
86C2×C8×C151—21no—
87C2×C8×C151—21no—
88C2×C8×C151—21no—
89C2×C8×C151—21no—
90C2×C8×C151—21no—
91C2×C8×C151—21no—
92C2×C8×C151—41no—
93C2×C8×C151—41no—
94C2×C8×C151—41no—
95C2×C8×C151—41no—
96C2×C8×C151—41no—
97C2×C8×C151—41no—
98C2×C8×C151—81no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C4⋊C411yescharacteristic
104C4⋊C4×C151C4⋊C411yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C42×C151—22no—
111C42×C151—22no—
112C42×C151—21no—
113C42×C151C2×D411yescharacteristic
114C42×C151C2×D411yescharacteristic
115C42×C151C2×Q811yescharacteristic
116C42×C151#4111yescharacteristic
117C23×C151—21no—
118C23×C151C4×D411yescharacteristic
119Q8×C151—41no—
120D4×C151—41no—
121D4×C151—41no—
122D4×C151—41no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151C2×C4⋊C411yescharacteristic
140C2×C4×C151C4×D411yescharacteristic
141C2×C4×C151#12011yescharacteristic
142C2×C4×C151C22⋊Q811yescharacteristic
143C2×C4×C151C22⋊Q811yescharacteristic
144C2×C4×C151#12311yescharacteristic
145C8×C151—41no—
146C8×C151—41no—
147C8×C151—42no—
148C8×C151—41no—
149C8×C151—41no—
150C8×C151—41no—
151C8×C151—41no—
152C8×C151—81no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151#38511yescharacteristic
159C22×C151#44311yescharacteristic
160C22×C151#44411yescharacteristic
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—42no—
167C4×C151—42no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151#45311yescharacteristic
172C4×C151#45611yescharacteristic
173C2×C151—21no—
174C2×C151—21no—
175C2×C151—81no—
176C2×C151#185911yescharacteristic
177C2×C151#186611yescharacteristic
178C2×C151#186811yescharacteristic
179#8876C15111yesmaximal, characteristic, direct product factor, Sylow
180C151#887611yescharacteristic, direct product factor, Sylow
181#2992C2×C15111yescharacteristic
182#1843C2×C15111yescharacteristic, complemented
183#1573C2×C15111yescharacteristic, complemented
184#1500C2×C15111yescharacteristic
185#1483C2×C15111yescharacteristic
186#1300C2×C15111yescharacteristic, complemented
187#1283C2×C15111yescharacteristic, complemented
188#529C22×C15111yescharacteristic
189#446—21no—
190#435—21no—
191#435—21no—
192C8×D4—21no—
193#433—21no—
194#432C22×C15111yescharacteristic
195#431C22×C15111yescharacteristic
196#424—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8—21no—
199C2×C4⋊C8C22×C15111yescharacteristic
200C2×C4⋊C8C22×C15111yescharacteristic
201C4×M16C22×C15111yescharacteristic
202#376C22×C15111yescharacteristic
203#335—21no—
204#334—21no—
205#328C4×C15111yescharacteristic
206#328C4×C15111yescharacteristic
207#327C4×C15111yescharacteristic
208#327C4×C15111yescharacteristic
209Q8⋊C8—21no—
210D4⋊C8—21no—
211C2×M16—21no—
212C2×M16—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8D4×C15111yescharacteristic
216C22×C8D4×C15111yescharacteristic
217#126—21no—
218#125Q8×C15111yescharacteristic
219#124Q8×C15111yescharacteristic
220#123—21no—
221C22⋊Q8C2×C4×C15111yescharacteristic
222#121C2×C4×C15111yescharacteristic
223C4×Q8D4×C15111yescharacteristic
224C4×D4—21no—
225C4×D4D4×C15111yescharacteristic
226#117—21no—
227C2×C42—21no—
228C2×C42C23×C15111yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—42no—
237C4⋊C8—42no—
238C4⋊C8D4×C15111yescharacteristic
239C4⋊C8D4×C15111yescharacteristic
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8C2×C4×C15111yescharacteristic
244C22⋊C8C2×C4×C15111yescharacteristic
245#97—21no—
246#97—21no—
247#97—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—21no—
251#95—21no—
252#95C2×C4×C15111yescharacteristic
253#95C2×C4×C15111yescharacteristic
254C2×Q8C4⋊C4×C15111yescharacteristic
255C2×D4—21no—
256C2×D4C4⋊C4×C15111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C22×C4×C15111yescharacteristic
261C22×C4C2×D4×C15111yescharacteristic
262C22×C4#41×C15111yescharacteristic
263M16—22no—
264M16—41no—
265M16—81no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—81no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4C4⋊C4×C15111yescharacteristic
284C4⋊C4C4⋊C4×C15111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C42—22no—
291C42—22no—
292C42—21no—
293C42C2×D4×C15111yescharacteristic
294C42C2×D4×C15111yescharacteristic
295C42C2×Q8×C15111yescharacteristic
296C42#41×C15111yescharacteristic
297C23—21no—
298C23C4×D4×C15111yescharacteristic
299Q8—41no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4C2×C4⋊C4×C15111yescharacteristic
320C2×C4C4×D4×C15111yescharacteristic
321C2×C4#120×C15111yescharacteristic
322C2×C4C22⋊Q8×C15111yescharacteristic
323C2×C4C22⋊Q8×C15111yescharacteristic
324C2×C4#123×C15111yescharacteristic
325C8—41no—
326C8—41no—
327C8—42no—
328C8—41no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22#385×C15111yescharacteristic
339C22#443×C15111yescharacteristic
340C22#444×C15111yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4#453×C15111yescharacteristic
352C4#456×C15111yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2#1859×C15111yescharacteristic
357C2#1866×C15111yescharacteristic
358C2#1868×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#385
prime radical#121×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1843×C151C2semidirect
3. #1573×C151C2semidirect
6. #1300×C151C2semidirect
7. #1283×C151C2semidirect
179. #8876C151direct (N × H)
180. C151#8876direct (N × H)
182. #1843C2×C151semidirect
183. #1573C2×C151semidirect
186. #1300C2×C151semidirect
187. #1283C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2992×C1512
#1843×C1512
#1573×C1512
#1500×C1512
#1483×C1512
#1300×C1512
#1283×C1512
#8876151