Finite Group Databasebeta

← C151×#12990 #50317915

Subgroups — C151×#12990 #50317915

Order 38656.

518 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3050×C151C211yesmaximal, characteristic
2C22×#108×C151C211yesmaximal, characteristic, complemented
3C2×#359×C151C212yesmaximal, complemented
4C2×C22⋊C16×C151C211yesmaximal, characteristic, complemented
5#1382×C151C212yesmaximal, complemented
6C2×#135×C151C2211yescharacteristic
7C22×M16×C151—21no—
8C23×C8×C151C2211yescharacteristic
9#525×C151—21no—
10C22×C16×C151C2212yes—
11#467×C151C411yescharacteristic
12#467×C151C411yescharacteristic
13#466×C151C411yescharacteristic
14#466×C151C411yescharacteristic
15#465×C151—21no—
16#465×C151—21no—
17C2×#108×C151—21no—
18C2×#108×C151—24no—
19C2×#108×C151C2212yes—
20#427×C151C2211yescharacteristic
21#416×C151—21no—
22#359×C151—24no—
23C22⋊C16×C151—21no—
24C22⋊C16×C151—21no—
25C2×#41×C151—21no—
26C23×C4×C151D411yescharacteristic
27#135×C151—22no—
28#135×C151—22no—
29C2×Q16×C151C2×C411yescharacteristic
30C2×SD16×C151—21no—
31C2×D8×C151C2×C411yescharacteristic
32C2×M16×C151—24no—
33C2×M16×C151—22no—
34C2×M16×C151—42no—
35C2×M16×C151—41no—
36C22×C8×C151—22no—
37C22×C8×C151—22no—
38C22×C8×C151—41no—
39C22×C8×C151C2×C411yescharacteristic
40C22×C8×C151C2×C411yescharacteristic
41C22×C8×C151D411yescharacteristic
42C22×C8×C151D411yescharacteristic
43C22×C8×C151D411yescharacteristic
44C22×C8×C151C2311yescharacteristic
45#123×C151—41no—
46C22⋊Q8×C151—21no—
47C22⋊Q8×C151—21no—
48#121×C151—21no—
49#121×C151—21no—
50#120×C151—41no—
51C4×D4×C151—41no—
52C4×D4×C151—41no—
53#117×C151—21no—
54C2×C16×C151—22no—
55C2×C16×C151—22no—
56C2×C16×C151—22no—
57#108×C151—24no—
58#108×C151—22no—
59#108×C151D414yescomplemented
60#107×C151C2×C411yescharacteristic
61#107×C151C2×C411yescharacteristic
62#106×C151—21no—
63#103×C151—21no—
64#103×C151—21no—
65#102×C151—21no—
66#102×C151—21no—
67C24×C151SD1611yescharacteristic
68#41×C151—41no—
69#41×C151—41no—
70#41×C151—41no—
71#41×C151—41no—
72C2×Q8×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—41no—
75C2×D4×C151—41no—
76C2×D4×C151—41no—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151—21no—
81C22×C4×C151—41no—
82C22×C4×C151C22⋊C411yescharacteristic
83C22×C4×C151C22⋊C411yescharacteristic
84C22×C4×C151D811yescharacteristic
85C22×C4×C151D811yescharacteristic
86C22×C4×C151SD1611yescharacteristic
87C22×C4×C151C2×D411yescharacteristic
88Q16×C151—22no—
89SD16×C151—42no—
90D8×C151—22no—
91M16×C151—24no—
92M16×C151—44no—
93M16×C151—42no—
94C2×C8×C151—21no—
95C2×C8×C151—21no—
96C2×C8×C151—22no—
97C2×C8×C151—22no—
98C2×C8×C151—22no—
99C2×C8×C151—22no—
100C2×C8×C151—44no—
101C2×C8×C151—42no—
102C2×C8×C151C22⋊C411yescharacteristic
103C2×C8×C151C22⋊C411yescharacteristic
104C2×C8×C151C22×C411yescharacteristic
105C2×C8×C151C2×D412yes—
106C2×C8×C151C2×D411yescharacteristic
107C2×C8×C151#4112yes—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—41no—
111C4⋊C4×C151—41no—
112C22⋊C4×C151—41no—
113C22⋊C4×C151—41no—
114C22⋊C4×C151—41no—
115C22⋊C4×C151—41no—
116C22⋊C4×C151—41no—
117C42×C151—41no—
118C16×C151—42no—
119C23×C151—22no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151—41no—
123C23×C151—41no—
124C23×C151#10211yescharacteristic
125C23×C151#10211yescharacteristic
126C23×C151C2×SD1611yescharacteristic
127Q8×C151—41no—
128Q8×C151—41no—
129D4×C151—41no—
130D4×C151—41no—
131D4×C151—82no—
132D4×C151—82no—
133D4×C151—81no—
134D4×C151—81no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—81no—
149C2×C4×C151—81no—
150C2×C4×C151#10211yescharacteristic
151C2×C4×C151#10211yescharacteristic
152C2×C4×C151C2×C22⋊C411yescharacteristic
153C2×C4×C151#12011yescharacteristic
154C2×C4×C151#12311yescharacteristic
155C2×C4×C151C2×D811yescharacteristic
156C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C151#13711yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C8×C151—44no—
161C8×C151C4×D412yes—
162C8×C151#12112yes—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—42no—
171C22×C151—42no—
172C22×C151—81no—
173C22×C151—81no—
174C22×C151—81no—
175C22×C151#35912yescomplemented
176C22×C151C2×#10211yescharacteristic
177C22×C151#44811yescharacteristic
178C22×C151#48111yescharacteristic
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—81no—
182C4×C151—81no—
183C4×C151—81no—
184C4×C151#38611yescharacteristic
185C4×C151#41711yescharacteristic
186C4×C151#44711yescharacteristic
187C4×C151#48011yescharacteristic
188C2×C151—22no—
189C2×C151—21no—
190C2×C151—21no—
191C2×C151—41no—
192C2×C151—161no—
193C2×C151#187411yescharacteristic
194C2×C151C2×#35911yescharacteristic
195C2×C151#214311yescharacteristic
196#12990C15111yesmaximal, characteristic, direct product factor, Sylow
197C151#1299011yescharacteristic, direct product factor, Sylow
198#3050C2×C15111yescharacteristic
199C22×#108C2×C15111yescharacteristic, complemented
200C2×#359C2×C15112yescomplemented
201C2×C22⋊C16C2×C15111yescharacteristic, complemented
202#1382C2×C15112yescomplemented
203C2×#135C22×C15111yescharacteristic
204C22×M16—21no—
205C23×C8C22×C15111yescharacteristic
206#525—21no—
207C22×C16C22×C15112yes—
208#467C4×C15111yescharacteristic
209#467C4×C15111yescharacteristic
210#466C4×C15111yescharacteristic
211#466C4×C15111yescharacteristic
212#465—21no—
213#465—21no—
214C2×#108—21no—
215C2×#108—24no—
216C2×#108C22×C15112yes—
217#427C22×C15111yescharacteristic
218#416—21no—
219#359—24no—
220C22⋊C16—21no—
221C22⋊C16—21no—
222C2×#41—21no—
223C23×C4D4×C15111yescharacteristic
224#135—22no—
225#135—22no—
226C2×Q16C2×C4×C15111yescharacteristic
227C2×SD16—21no—
228C2×D8C2×C4×C15111yescharacteristic
229C2×M16—24no—
230C2×M16—22no—
231C2×M16—42no—
232C2×M16—41no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—41no—
236C22×C8C2×C4×C15111yescharacteristic
237C22×C8C2×C4×C15111yescharacteristic
238C22×C8D4×C15111yescharacteristic
239C22×C8D4×C15111yescharacteristic
240C22×C8D4×C15111yescharacteristic
241C22×C8C23×C15111yescharacteristic
242#123—41no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247#120—41no—
248C4×D4—41no—
249C4×D4—41no—
250#117—21no—
251C2×C16—22no—
252C2×C16—22no—
253C2×C16—22no—
254#108—24no—
255#108—22no—
256#108D4×C15114yescomplemented
257#107C2×C4×C15111yescharacteristic
258#107C2×C4×C15111yescharacteristic
259#106—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263#102—21no—
264C24SD16×C15111yescharacteristic
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4C22⋊C4×C15111yescharacteristic
280C22×C4C22⋊C4×C15111yescharacteristic
281C22×C4D8×C15111yescharacteristic
282C22×C4D8×C15111yescharacteristic
283C22×C4SD16×C15111yescharacteristic
284C22×C4C2×D4×C15111yescharacteristic
285Q16—22no—
286SD16—42no—
287D8—22no—
288M16—24no—
289M16—44no—
290M16—42no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—44no—
298C2×C8—42no—
299C2×C8C22⋊C4×C15111yescharacteristic
300C2×C8C22⋊C4×C15111yescharacteristic
301C2×C8C22×C4×C15111yescharacteristic
302C2×C8C2×D4×C15112yes—
303C2×C8C2×D4×C15111yescharacteristic
304C2×C8#41×C15112yes—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C42—41no—
315C16—42no—
316C23—22no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23#102×C15111yescharacteristic
322C23#102×C15111yescharacteristic
323C23C2×SD16×C15111yescharacteristic
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—82no—
329D4—82no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4#102×C15111yescharacteristic
348C2×C4#102×C15111yescharacteristic
349C2×C4C2×C22⋊C4×C15111yescharacteristic
350C2×C4#120×C15111yescharacteristic
351C2×C4#123×C15111yescharacteristic
352C2×C4C2×D8×C15111yescharacteristic
353C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
354C2×C4#137×C15111yescharacteristic
355C8—21no—
356C8—21no—
357C8—44no—
358C8C4×D4×C15112yes—
359C8#121×C15112yes—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22#359×C15112yescomplemented
373C22C2×#102×C15111yescharacteristic
374C22#448×C15111yescharacteristic
375C22#481×C15111yescharacteristic
376C4—21no—
377C4—21no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4#386×C15111yescharacteristic
382C4#417×C15111yescharacteristic
383C4#447×C15111yescharacteristic
384C4#480×C15111yescharacteristic
385C2—22no—
386C2—21no—
387C2—21no—
388C2—41no—
389C2—161no—
390C2#1874×C15111yescharacteristic
391C2C2×#359×C15111yescharacteristic
392C2#2143×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×D8
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
socleC22×C151C2×#102
prime radical#3050×C151C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C23×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#108×C151C2semidirect
3. C2×#359×C151C2semidirect
4. C2×C22⋊C16×C151C2semidirect
5. #1382×C151C2semidirect
59. #108×C151D4semidirect
175. C22×C151#359semidirect
196. #12990C151direct (N × H)
197. C151#12990direct (N × H)
199. C22×#108C2×C151semidirect
200. C2×#359C2×C151semidirect
201. C2×C22⋊C16C2×C151semidirect
202. #1382C2×C151semidirect
256. #108D4×C151semidirect
372. C22#359×C151semidirect

Maximal subgroups

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

subgroupindex
#3050×C1512
C22×#108×C1512
C2×#359×C1512
C2×C22⋊C16×C1512
#1382×C1512
#12990151