Finite Group Databasebeta

← C151×#9233 #50314158

Subgroups — C151×#9233 #50314158

Order 38656.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3100×C151C211yesmaximal, characteristic
2C42×D4×C151C211yesmaximal, characteristic, complemented
3#1962×C151C211yesmaximal, characteristic, complemented
4#1502×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic, complemented
6#1303×C151C211yesmaximal, characteristic, complemented
7#1276×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×C4×D4×C151—21no—
10C2×C4×D4×C151C2211yescharacteristic
11C22×C42×C151—21no—
12#480×C151—21no—
13#474×C151C412yescomplemented
14#459×C151C412yescomplemented
15#447×C151—21no—
16C4×D8×C151—22no—
17#431×C151C2211yescharacteristic
18#431×C151C2211yescharacteristic
19#423×C151C2211yescharacteristic
20C2×#104×C151—21no—
21C2×#104×C151—21no—
22C4×C4⋊C4×C151—21no—
23C4×C4⋊C4×C151C2211yescharacteristic
24C4×C22⋊C4×C151—21no—
25C4×C22⋊C4×C151—22no—
26C43×C151C2211yescharacteristic
27#327×C151—22no—
28D4⋊C8×C151—22no—
29C2×#41×C151—21no—
30C22×D4×C151D411yescharacteristic
31C23×C4×C151—22no—
32C23×C4×C151—21no—
33C2×D8×C151—22no—
34C2×M16×C151—21no—
35C4⋊Q8×C151C2×C411yescharacteristic, complemented
36#127×C151C2×C411yescharacteristic, complemented
37#124×C151—21no—
38#121×C151—21no—
39#121×C151—21no—
40C4×D4×C151—28no—
41C4×D4×C151—21no—
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151—21no—
45C4×D4×C151C2×C412yes—
46C4×D4×C151D412yes—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151D411yescharacteristic
49C2×C22⋊C4×C151—22no—
50C2×C22⋊C4×C151—21no—
51C2×C42×C151—21no—
52C2×C42×C151—22no—
53C2×C42×C151—21no—
54C2×C42×C151—21no—
55C2×C42×C151—42no—
56C2×C42×C151—42no—
57C2×C42×C151D411yescharacteristic
58C2×C42×C151D411yescharacteristic
59C2×C42×C151C2311yescharacteristic
60#107×C151—22no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151C2×C412yescomplemented
65#104×C151—42no—
66#104×C151—42no—
67#102×C151—22no—
68#102×C151—22no—
69C22⋊C8×C151—21no—
70C22⋊C8×C151—21no—
71C4×C8×C151—21no—
72C4×C8×C151—21no—
73#95×C151—22no—
74#95×C151D412yes—
75C24×C151—21no—
76#41×C151—41no—
77#41×C151—41no—
78#41×C151—41no—
79#41×C151—41no—
80C2×Q8×C151—21no—
81C2×D4×C151—24no—
82C2×D4×C151—21no—
83C2×D4×C151—21no—
84C2×D4×C151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—41no—
87C2×D4×C151C22⋊C412yes—
88C22×C4×C151—21no—
89C22×C4×C151—28no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—44no—
96C22×C4×C151—44no—
97C22×C4×C151—41no—
98C22×C4×C151—41no—
99C22×C4×C151—41no—
100C22×C4×C151—41no—
101C22×C4×C151—41no—
102C22×C4×C151C2×D411yescharacteristic
103C22×C4×C151C2×D411yescharacteristic
104C22×C4×C151C2×D411yescharacteristic
105D8×C151—44no—
106M16×C151—41no—
107M16×C151—41no—
108C2×C8×C151—22no—
109C2×C8×C151—41no—
110C2×C8×C151—41no—
111C4⋊C4×C151—24no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151C22⋊C412yes—
116C22⋊C4×C151—28no—
117C22⋊C4×C151—22no—
118C22⋊C4×C151—22no—
119C22⋊C4×C151—41no—
120C22⋊C4×C151—41no—
121C42×C151—24no—
122C42×C151—21no—
123C42×C151—21no—
124C42×C151—21no—
125C42×C151—42no—
126C42×C151—44no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151D812yescomplemented
130C42×C151C22×C411yescharacteristic
131C42×C151C2×D411yescharacteristic
132C42×C151#4111yescharacteristic
133C42×C151#4111yescharacteristic
134C23×C151—24no—
135C23×C151—22no—
136C23×C151—42no—
137C23×C151—41no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151#12011yescharacteristic
141Q8×C151—41no—
142Q8×C151—41no—
143D4×C151—24no—
144D4×C151—22no—
145D4×C151—42no—
146D4×C151—41no—
147D4×C151—41no—
148D4×C151—81no—
149D4×C151—81no—
150D4×C151—81no—
151D4×C151#10414yescomplemented
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—22no—
157C2×C4×C151—24no—
158C2×C4×C151—22no—
159C2×C4×C151—41no—
160C2×C4×C151—416no—
161C2×C4×C151—41no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—41no—
172C2×C4×C151—81no—
173C2×C4×C151—81no—
174C2×C4×C151C2×C22⋊C411yescharacteristic
175C2×C4×C151C4×D411yescharacteristic
176C2×C4×C151C4×D411yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151#12111yescharacteristic
179C2×C4×C151#12311yescharacteristic
180C2×C4×C151C2×D811yescharacteristic
181C2×C4×C151#13511yescharacteristic
182C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
184C8×C151—42no—
185C8×C151—81no—
186C8×C151—81no—
187C22×C151—21no—
188C22×C151—21no—
189C22×C151—24no—
190C22×C151—44no—
191C22×C151—44no—
192C22×C151—42no—
193C22×C151—42no—
194C22×C151—81no—
195C22×C151—81no—
196C22×C151—81no—
197C22×C151#38611yescharacteristic
198C22×C151#44711yescharacteristic
199C22×C151#44911yescharacteristic
200C4×C151—24no—
201C4×C151—21no—
202C4×C151—21no—
203C4×C151—21no—
204C4×C151—42no—
205C4×C151—44no—
206C4×C151—42no—
207C4×C151—81no—
208C4×C151C2×#10412yes—
209C4×C151C4×D811yescharacteristic
210C4×C151#44211yescharacteristic
211C4×C151#45911yescharacteristic
212C4×C151#46311yescharacteristic
213C2×C151—21no—
214C2×C151—21no—
215C2×C151—44no—
216C2×C151—161no—
217C2×C151#187911yescharacteristic
218C2×C151#189611yescharacteristic
219C2×C151#190611yescharacteristic
220#9233C15111yesmaximal, characteristic, direct product factor, Sylow
221C151#923311yescharacteristic, direct product factor, Sylow
222#3100C2×C15111yescharacteristic
223C42×D4C2×C15111yescharacteristic, complemented
224#1962C2×C15111yescharacteristic, complemented
225#1502C2×C15111yescharacteristic, complemented
226#1486C2×C15111yescharacteristic, complemented
227#1303C2×C15111yescharacteristic, complemented
228#1276C2×C15111yescharacteristic, complemented
229#532C22×C15111yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4C22×C15111yescharacteristic
232C22×C42—21no—
233#480—21no—
234#474C4×C15112yescomplemented
235#459C4×C15112yescomplemented
236#447—21no—
237C4×D8—22no—
238#431C22×C15111yescharacteristic
239#431C22×C15111yescharacteristic
240#423C22×C15111yescharacteristic
241C2×#104—21no—
242C2×#104—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C22×C15111yescharacteristic
245C4×C22⋊C4—21no—
246C4×C22⋊C4—22no—
247C43C22×C15111yescharacteristic
248#327—22no—
249D4⋊C8—22no—
250C2×#41—21no—
251C22×D4D4×C15111yescharacteristic
252C23×C4—22no—
253C23×C4—21no—
254C2×D8—22no—
255C2×M16—21no—
256C4⋊Q8C2×C4×C15111yescharacteristic, complemented
257#127C2×C4×C15111yescharacteristic, complemented
258#124—21no—
259#121—21no—
260#121—21no—
261C4×D4—28no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4C2×C4×C15112yes—
267C4×D4D4×C15112yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C15111yescharacteristic
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—42no—
277C2×C42—42no—
278C2×C42D4×C15111yescharacteristic
279C2×C42D4×C15111yescharacteristic
280C2×C42C23×C15111yescharacteristic
281#107—22no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8C2×C4×C15112yescomplemented
286#104—42no—
287#104—42no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294#95—22no—
295#95D4×C15112yes—
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4C22⋊C4×C15112yes—
309C22×C4—21no—
310C22×C4—28no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C2×D4×C15111yescharacteristic
324C22×C4C2×D4×C15111yescharacteristic
325C22×C4C2×D4×C15111yescharacteristic
326D8—44no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊C4×C15112yes—
337C22⋊C4—28no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—24no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—44no—
347C42—42no—
348C42—41no—
349C42—41no—
350C42D8×C15112yescomplemented
351C42C22×C4×C15111yescharacteristic
352C42C2×D4×C15111yescharacteristic
353C42#41×C15111yescharacteristic
354C42#41×C15111yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#120×C15111yescharacteristic
362Q8—41no—
363Q8—41no—
364D4—24no—
365D4—22no—
366D4—42no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4#104×C15114yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—416no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C2×C22⋊C4×C15111yescharacteristic
396C2×C4C4×D4×C15111yescharacteristic
397C2×C4C4×D4×C15111yescharacteristic
398C2×C4#121×C15111yescharacteristic
399C2×C4#121×C15111yescharacteristic
400C2×C4#123×C15111yescharacteristic
401C2×C4C2×D8×C15111yescharacteristic
402C2×C4#135×C15111yescharacteristic
403C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
404C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
405C8—42no—
406C8—81no—
407C8—81no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22#386×C15111yescharacteristic
419C22#447×C15111yescharacteristic
420C22#449×C15111yescharacteristic
421C4—24no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—44no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4C2×#104×C15112yes—
430C4C4×D8×C15111yescharacteristic
431C4#442×C15111yescharacteristic
432C4#459×C15111yescharacteristic
433C4#463×C15111yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—161no—
438C2#1879×C15111yescharacteristic
439C2#1896×C15111yescharacteristic
440C2#1906×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radical#3100×C151C2
LCSG ▷ C42 ▷ 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. C42×D4×C151C2semidirect
3. #1962×C151C2semidirect
4. #1502×C151C2semidirect
5. #1486×C151C2semidirect
6. #1303×C151C2semidirect
7. #1276×C151C2semidirect
13. #474×C151C4semidirect
14. #459×C151C4semidirect
35. C4⋊Q8×C151C2×C4semidirect
36. #127×C151C2×C4semidirect
64. C4⋊C8×C151C2×C4semidirect
129. C42×C151D8semidirect
151. D4×C151#104semidirect
220. #9233C151direct (N × H)
221. C151#9233direct (N × H)
223. C42×D4C2×C151semidirect
224. #1962C2×C151semidirect
225. #1502C2×C151semidirect
226. #1486C2×C151semidirect
227. #1303C2×C151semidirect
228. #1276C2×C151semidirect
234. #474C4×C151semidirect
235. #459C4×C151semidirect
256. C4⋊Q8C2×C4×C151semidirect
257. #127C2×C4×C151semidirect
285. C4⋊C8C2×C4×C151semidirect
350. C42D8×C151semidirect
372. D4#104×C151semidirect

Maximal subgroups

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

subgroupindex
#3100×C1512
C42×D4×C1512
#1962×C1512
#1502×C1512
#1486×C1512
#1303×C1512
#1276×C1512
#9233151