Finite Group Databasebeta

← C151×#9230 #50314155

Subgroups — C151×#9230 #50314155

Order 38656.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C151C211yesmaximal, characteristic
2C2×#446×C151C211yesmaximal, characteristic, complemented
3#1957×C151C211yesmaximal, characteristic
4#1803×C151C211yesmaximal, characteristic, complemented
5C2×#331×C151C211yesmaximal, characteristic
6#1296×C151C211yesmaximal, characteristic, complemented
7#1277×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—21no—
9C2×#127×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#460×C151—22no—
12#460×C151C414yescomplemented
13#446×C151—22no—
14#446×C151—22no—
15C2×C4⋊C8×C151—21no—
16C2×C4⋊C8×C151C2211yescharacteristic
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#103×C151—21no—
20C2×#102×C151—21no—
21C2×#102×C151—21no—
22C2×#102×C151—21no—
23C2×#97×C151—21no—
24C2×C4×C8×C151C2211yescharacteristic
25#384×C151C2211yescharacteristic
26#340×C151—21no—
27#331×C151—22no—
28C22×Q8×C151D411yescharacteristic
29C22×D4×C151—21no—
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C2×SD16×C151—24no—
33C2×SD16×C151—42no—
34C2×SD16×C151—42no—
35C22×C8×C151—21no—
36C22×C8×C151—21no—
37C22×C8×C151—21no—
38C22×C8×C151D411yescharacteristic
39C22×C8×C151D411yescharacteristic
40#127×C151—21no—
41#127×C151—21no—
42#127×C151—21no—
43#127×C151C2×C412yes—
44C4×Q8×C151—21no—
45C4×Q8×C151—21no—
46C4×Q8×C151C2×C412yes—
47C4×Q8×C151D412yes—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151D411yescharacteristic
53C2×C42×C151—21no—
54C2×C42×C151C2311yescharacteristic
55C4⋊C8×C151—24no—
56C4⋊C8×C151—21no—
57C4⋊C8×C151—21no—
58C4⋊C8×C151—21no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151C2×C412yes—
61C4⋊C8×C151D412yes—
62#103×C151—42no—
63#102×C151—24no—
64#102×C151—42no—
65#102×C151—42no—
66#97×C151—24no—
67C4×C8×C151—21no—
68C4×C8×C151—21no—
69C24×C151—41no—
70C2×Q8×C151—21no—
71C2×Q8×C151—21no—
72C2×Q8×C151—21no—
73C2×Q8×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151C22⋊C412yes—
76C2×D4×C151—22no—
77C2×D4×C151—22no—
78C2×D4×C151—22no—
79C2×D4×C151—41no—
80C2×D4×C151—41no—
81C2×D4×C151—41no—
82C2×D4×C151—41no—
83C2×D4×C151—41no—
84C2×D4×C151—41no—
85C2×D4×C151—41no—
86C2×D4×C151—41no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—81no—
91C2×D4×C151—81no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—41no—
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151C2×D411yescharacteristic
97C22×C4×C151#4111yescharacteristic
98SD16×C151—48no—
99C2×C8×C151—21no—
100C2×C8×C151—21no—
101C2×C8×C151—22no—
102C2×C8×C151—21no—
103C2×C8×C151—22no—
104C2×C8×C151—21no—
105C2×C8×C151—21no—
106C2×C8×C151—41no—
107C2×C8×C151—41no—
108C2×C8×C151—41no—
109C2×C8×C151—41no—
110C2×C8×C151—41no—
111C2×C8×C151—41no—
112C2×C8×C151—41no—
113C2×C8×C151SD1612yescomplemented
114C4⋊C4×C151—22no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—81no—
122C4⋊C4×C151C22⋊C412yes—
123C42×C151—22no—
124C42×C151—22no—
125C42×C151C22×C411yescharacteristic
126C42×C151C2×D411yescharacteristic
127C42×C151C2×D411yescharacteristic
128C42×C151#4111yescharacteristic
129C23×C151—42no—
130C23×C151—81no—
131C23×C151—81no—
132C23×C151—81no—
133C23×C151—81no—
134C23×C151—81no—
135C23×C151—81no—
136C23×C151#12111yescharacteristic
137Q8×C151—22no—
138Q8×C151—22no—
139Q8×C151—41no—
140Q8×C151—41no—
141D4×C151—42no—
142D4×C151—42no—
143D4×C151—42no—
144D4×C151—42no—
145D4×C151—82no—
146D4×C151—82no—
147D4×C151—81no—
148D4×C151—81no—
149D4×C151—81no—
150D4×C151—81no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—81no—
160C2×C4×C151—81no—
161C2×C4×C151—81no—
162C2×C4×C151C2×C22⋊C411yescharacteristic
163C2×C4×C151C4×D411yescharacteristic
164C2×C4×C151C4×D411yescharacteristic
165C2×C4×C151#12011yescharacteristic
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12311yescharacteristic
168C2×C4×C151C2×SD1611yescharacteristic
169C2×C4×C151#13511yescharacteristic
170C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C151#13711yescharacteristic
175C2×C4×C151#13711yescharacteristic
176C8×C151—22no—
177C8×C151—42no—
178C8×C151—41no—
179C8×C151—42no—
180C8×C151—81no—
181C22×C151—82no—
182C22×C151—82no—
183C22×C151—82no—
184C22×C151—161no—
185C22×C151—161no—
186C22×C151—161no—
187C22×C151—161no—
188C22×C151#38611yescharacteristic
189C22×C151#46011yescharacteristic
190C22×C151#46411yescharacteristic
191C22×C151#46811yescharacteristic
192C22×C151#46911yescharacteristic
193C22×C151#47111yescharacteristic
194C22×C151#47211yescharacteristic
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—42no—
198C4×C151—42no—
199C4×C151—161no—
200C4×C151#41711yescharacteristic
201C4×C151#41811yescharacteristic
202C4×C151C4×SD1611yescharacteristic
203C4×C151#44011yescharacteristic
204C4×C151#44811yescharacteristic
205C4×C151#44911yescharacteristic
206C4×C151#46811yescharacteristic
207C4×C151#46911yescharacteristic
208C2×C151—162no—
209C2×C151#168611yescharacteristic
210C2×C151#168811yescharacteristic
211C2×C151#169811yescharacteristic
212C2×C151#170211yescharacteristic
213C2×C151#188011yescharacteristic
214C2×C151#189511yescharacteristic
215C2×C151#190711yescharacteristic
216#9230C15111yesmaximal, characteristic, direct product factor, Sylow
217C151#923011yescharacteristic, direct product factor, Sylow
218C2×#460C2×C15111yescharacteristic
219C2×#446C2×C15111yescharacteristic, complemented
220#1957C2×C15111yescharacteristic
221#1803C2×C15111yescharacteristic, complemented
222C2×#331C2×C15111yescharacteristic
223#1296C2×C15111yescharacteristic, complemented
224#1277C2×C15111yescharacteristic, complemented
225C22×SD16—21no—
226C2×#127C22×C15111yescharacteristic
227C2×C4×Q8C22×C15111yescharacteristic
228#460—22no—
229#460C4×C15114yescomplemented
230#446—22no—
231#446—22no—
232C2×C4⋊C8—21no—
233C2×C4⋊C8C22×C15111yescharacteristic
234C2×C4⋊C8C22×C15111yescharacteristic
235C2×C4⋊C8C22×C15111yescharacteristic
236C2×#103—21no—
237C2×#102—21no—
238C2×#102—21no—
239C2×#102—21no—
240C2×#97—21no—
241C2×C4×C8C22×C15111yescharacteristic
242#384C22×C15111yescharacteristic
243#340—21no—
244#331—22no—
245C22×Q8D4×C15111yescharacteristic
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—21no—
249C2×SD16—24no—
250C2×SD16—42no—
251C2×SD16—42no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8D4×C15111yescharacteristic
256C22×C8D4×C15111yescharacteristic
257#127—21no—
258#127—21no—
259#127—21no—
260#127C2×C4×C15112yes—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8C2×C4×C15112yes—
264C4×Q8D4×C15112yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C15111yescharacteristic
270C2×C42—21no—
271C2×C42C23×C15111yescharacteristic
272C4⋊C8—24no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8C2×C4×C15112yes—
278C4⋊C8D4×C15112yes—
279#103—42no—
280#102—24no—
281#102—42no—
282#102—42no—
283#97—24no—
284C4×C8—21no—
285C4×C8—21no—
286C24—41no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C22⋊C4×C15112yes—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—81no—
308C2×D4—81no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4C2×D4×C15111yescharacteristic
313C22×C4C2×D4×C15111yescharacteristic
314C22×C4#41×C15111yescharacteristic
315SD16—48no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8SD16×C15112yescomplemented
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—81no—
339C4⋊C4C22⋊C4×C15112yes—
340C42—22no—
341C42—22no—
342C42C22×C4×C15111yescharacteristic
343C42C2×D4×C15111yescharacteristic
344C42C2×D4×C15111yescharacteristic
345C42#41×C15111yescharacteristic
346C23—42no—
347C23—81no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23—81no—
352C23—81no—
353C23#121×C15111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—42no—
362D4—82no—
363D4—82no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4C2×C22⋊C4×C15111yescharacteristic
380C2×C4C4×D4×C15111yescharacteristic
381C2×C4C4×D4×C15111yescharacteristic
382C2×C4#120×C15111yescharacteristic
383C2×C4#121×C15111yescharacteristic
384C2×C4#123×C15111yescharacteristic
385C2×C4C2×SD16×C15111yescharacteristic
386C2×C4#135×C15111yescharacteristic
387C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
388C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
389C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
390C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
391C2×C4#137×C15111yescharacteristic
392C2×C4#137×C15111yescharacteristic
393C8—22no—
394C8—42no—
395C8—41no—
396C8—42no—
397C8—81no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—161no—
402C22—161no—
403C22—161no—
404C22—161no—
405C22#386×C15111yescharacteristic
406C22#460×C15111yescharacteristic
407C22#464×C15111yescharacteristic
408C22#468×C15111yescharacteristic
409C22#469×C15111yescharacteristic
410C22#471×C15111yescharacteristic
411C22#472×C15111yescharacteristic
412C4—21no—
413C4—21no—
414C4—42no—
415C4—42no—
416C4—161no—
417C4#417×C15111yescharacteristic
418C4#418×C15111yescharacteristic
419C4C4×SD16×C15111yescharacteristic
420C4#440×C15111yescharacteristic
421C4#448×C15111yescharacteristic
422C4#449×C15111yescharacteristic
423C4#468×C15111yescharacteristic
424C4#469×C15111yescharacteristic
425C2—162no—
426C2#1686×C15111yescharacteristic
427C2#1688×C15111yescharacteristic
428C2#1698×C15111yescharacteristic
429C2#1702×C15111yescharacteristic
430C2#1880×C15111yescharacteristic
431C2#1895×C15111yescharacteristic
432C2#1907×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C151C2semidirect
4. #1803×C151C2semidirect
6. #1296×C151C2semidirect
7. #1277×C151C2semidirect
12. #460×C151C4semidirect
113. C2×C8×C151SD16semidirect
216. #9230C151direct (N × H)
217. C151#9230direct (N × H)
219. C2×#446C2×C151semidirect
221. #1803C2×C151semidirect
223. #1296C2×C151semidirect
224. #1277C2×C151semidirect
229. #460C4×C151semidirect
330. C2×C8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1512
C2×#446×C1512
#1957×C1512
#1803×C1512
C2×#331×C1512
#1296×C1512
#1277×C1512
#9230151