Finite Group Databasebeta

← C151×#11890 #50316815

Subgroups — C151×#11890 #50316815

Order 38656.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3050×C151C211yesmaximal, characteristic
2#2112×C151C211yesmaximal, characteristic, complemented
3#1808×C151C211yesmaximal, characteristic, complemented
4#1348×C151C212yesmaximal, complemented
5#1347×C151C212yesmaximal, complemented
6C2×#135×C151C411yescharacteristic, complemented
7C23×C8×C151C2211yescharacteristic
8#525×C151—21no—
9C2×M32×C151—21no—
10#467×C151C411yescharacteristic, complemented
11#467×C151C2211yescharacteristic
12#466×C151C411yescharacteristic, complemented
13#466×C151C2211yescharacteristic
14#465×C151—21no—
15#465×C151—21no—
16#427×C151C411yescharacteristic, complemented
17C2×#107×C151—21no—
18#416×C151—21no—
19#380×C151—21no—
20C22⋊C16×C151—21no—
21C22⋊C16×C151C2212yes—
22#340×C151C2212yes—
23C2×#41×C151—21no—
24C23×C4×C151D411yescharacteristic
25#135×C151—42no—
26C2×Q16×C151C2×C411yescharacteristic
27C2×SD16×C151—21no—
28C2×D8×C151C2×C411yescharacteristic
29C22×C8×C151—42no—
30C22×C8×C151C2×C411yescharacteristic
31C22×C8×C151C2×C411yescharacteristic
32C22×C8×C151D411yescharacteristic
33C22×C8×C151D411yescharacteristic
34C22×C8×C151D411yescharacteristic
35C22×C8×C151C2311yescharacteristic
36#123×C151—41no—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39#121×C151—21no—
40#121×C151—21no—
41#120×C151—41no—
42C4×D4×C151—41no—
43C4×D4×C151—41no—
44#117×C151—21no—
45C2×C4⋊C4×C151—22no—
46C2×C22⋊C4×C151—41no—
47M32×C151—42no—
48C2×C16×C151—22no—
49#107×C151—42no—
50#107×C151C2×C411yescharacteristic
51#107×C151C2×C411yescharacteristic
52#106×C151—21no—
53#103×C151—21no—
54#103×C151—21no—
55#102×C151—21no—
56#102×C151—21no—
57#95×C151—41no—
58C24×C151D811yescharacteristic
59#41×C151—42no—
60#41×C151—42no—
61C2×Q8×C151—21no—
62C2×D4×C151—21no—
63C2×D4×C151—41no—
64C2×D4×C151—41no—
65C2×D4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—41no—
69C22×C4×C151—42no—
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22⋊C411yescharacteristic
72C22×C4×C151D811yescharacteristic
73C22×C4×C151SD1611yescharacteristic
74C22×C4×C151SD1611yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76Q16×C151—41no—
77SD16×C151—42no—
78D8×C151—41no—
79C2×C8×C151—22no—
80C2×C8×C151—22no—
81C2×C8×C151—22no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151—41no—
85C2×C8×C151C22⋊C411yescharacteristic
86C2×C8×C151C22⋊C411yescharacteristic
87C2×C8×C151C22×C411yescharacteristic
88C2×C8×C151C2×D411yescharacteristic
89C4⋊C4×C151—21no—
90C4⋊C4×C151—21no—
91C4⋊C4×C151—42no—
92C4⋊C4×C151—42no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—41no—
95C22⋊C4×C151—41no—
96C22⋊C4×C151—41no—
97C22⋊C4×C151—41no—
98C22⋊C4×C151—41no—
99C22⋊C4×C151—41no—
100C22⋊C4×C151—82no—
101C42×C151—41no—
102C16×C151—42no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—41no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151#10211yescharacteristic
109C23×C151#10211yescharacteristic
110C23×C151C2×D811yescharacteristic
111Q8×C151—41no—
112Q8×C151—41no—
113D4×C151—41no—
114D4×C151—41no—
115D4×C151—82no—
116D4×C151—82no—
117D4×C151—81no—
118D4×C151—81no—
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—41no—
126C2×C4×C151—41no—
127C2×C4×C151—41no—
128C2×C4×C151—41no—
129C2×C4×C151—41no—
130C2×C4×C151—41no—
131C2×C4×C151—82no—
132C2×C4×C151—82no—
133C2×C4×C151—82no—
134C2×C4×C151—82no—
135C2×C4×C151#10211yescharacteristic
136C2×C4×C151#10211yescharacteristic
137C2×C4×C151C2×C22⋊C411yescharacteristic
138C2×C4×C151C2×SD1611yescharacteristic
139C8×C151—21no—
140C8×C151—21no—
141C8×C151—21no—
142C8×C151#9912yes—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—42no—
152C22×C151—42no—
153C22×C151—81no—
154C22×C151—81no—
155C22×C151—81no—
156C22×C151C2×#10211yescharacteristic
157C22×C151#50911yescharacteristic
158C22×C151#51011yescharacteristic
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—81no—
163C4×C151—81no—
164C4×C151—81no—
165C4×C151—162no—
166C4×C151C2×#9911yescharacteristic
167C4×C151#42111yescharacteristic
168C2×C151—21no—
169C2×C151—21no—
170C2×C151—41no—
171C2×C151—41no—
172C2×C151—161no—
173C2×C151#151911yescharacteristic
174C2×C151#213911yescharacteristic
175C2×C151#214511yescharacteristic
176#11890C15111yesmaximal, characteristic, direct product factor, Sylow
177C151#1189011yescharacteristic, direct product factor, Sylow
178#3050C2×C15111yescharacteristic
179#2112C2×C15111yescharacteristic, complemented
180#1808C2×C15111yescharacteristic, complemented
181#1348C2×C15112yescomplemented
182#1347C2×C15112yescomplemented
183C2×#135C4×C15111yescharacteristic, complemented
184C23×C8C22×C15111yescharacteristic
185#525—21no—
186C2×M32—21no—
187#467C4×C15111yescharacteristic, complemented
188#467C22×C15111yescharacteristic
189#466C4×C15111yescharacteristic, complemented
190#466C22×C15111yescharacteristic
191#465—21no—
192#465—21no—
193#427C4×C15111yescharacteristic, complemented
194C2×#107—21no—
195#416—21no—
196#380—21no—
197C22⋊C16—21no—
198C22⋊C16C22×C15112yes—
199#340C22×C15112yes—
200C2×#41—21no—
201C23×C4D4×C15111yescharacteristic
202#135—42no—
203C2×Q16C2×C4×C15111yescharacteristic
204C2×SD16—21no—
205C2×D8C2×C4×C15111yescharacteristic
206C22×C8—42no—
207C22×C8C2×C4×C15111yescharacteristic
208C22×C8C2×C4×C15111yescharacteristic
209C22×C8D4×C15111yescharacteristic
210C22×C8D4×C15111yescharacteristic
211C22×C8D4×C15111yescharacteristic
212C22×C8C23×C15111yescharacteristic
213#123—41no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216#121—21no—
217#121—21no—
218#120—41no—
219C4×D4—41no—
220C4×D4—41no—
221#117—21no—
222C2×C4⋊C4—22no—
223C2×C22⋊C4—41no—
224M32—42no—
225C2×C16—22no—
226#107—42no—
227#107C2×C4×C15111yescharacteristic
228#107C2×C4×C15111yescharacteristic
229#106—21no—
230#103—21no—
231#103—21no—
232#102—21no—
233#102—21no—
234#95—41no—
235C24D8×C15111yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4C22⋊C4×C15111yescharacteristic
248C22×C4C22⋊C4×C15111yescharacteristic
249C22×C4D8×C15111yescharacteristic
250C22×C4SD16×C15111yescharacteristic
251C22×C4SD16×C15111yescharacteristic
252C22×C4C2×D4×C15111yescharacteristic
253Q16—41no—
254SD16—42no—
255D8—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C22⋊C4×C15111yescharacteristic
263C2×C8C22⋊C4×C15111yescharacteristic
264C2×C8C22×C4×C15111yescharacteristic
265C2×C8C2×D4×C15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—82no—
278C42—41no—
279C16—42no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#102×C15111yescharacteristic
286C23#102×C15111yescharacteristic
287C23C2×D8×C15111yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4#102×C15111yescharacteristic
313C2×C4#102×C15111yescharacteristic
314C2×C4C2×C22⋊C4×C15111yescharacteristic
315C2×C4C2×SD16×C15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8#99×C15112yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#102×C15111yescharacteristic
334C22#509×C15111yescharacteristic
335C22#510×C15111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—162no—
343C4C2×#99×C15111yescharacteristic
344C4#421×C15111yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2#1519×C15111yescharacteristic
351C2#2139×C15111yescharacteristic
352C2#2145×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radical#3050×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2112×C151C2semidirect
3. #1808×C151C2semidirect
4. #1348×C151C2semidirect
5. #1347×C151C2semidirect
6. C2×#135×C151C4semidirect
10. #467×C151C4semidirect
12. #466×C151C4semidirect
16. #427×C151C4semidirect
176. #11890C151direct (N × H)
177. C151#11890direct (N × H)
179. #2112C2×C151semidirect
180. #1808C2×C151semidirect
181. #1348C2×C151semidirect
182. #1347C2×C151semidirect
183. C2×#135C4×C151semidirect
187. #467C4×C151semidirect
189. #466C4×C151semidirect
193. #427C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3050×C1512
#2112×C1512
#1808×C1512
#1348×C1512
#1347×C1512
#11890151