Finite Group Databasebeta

← C151×#18636 #50323561

Subgroups — C151×#18636 #50323561

Order 38656.

960 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic
2#3226×C151C211yesmaximal, characteristic, complemented
3C2×#487×C151C211yesmaximal, characteristic, complemented
4#3039×C151C211yesmaximal, characteristic, complemented
5#1646×C151C214yesmaximal, complemented
6#1644×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1492×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic, complemented
10C2×#137×C151—21no—
11#556×C151—21no—
12#555×C151C2212yes—
13#554×C151C2212yes—
14#553×C151—22no—
15#548×C151—22no—
16#547×C151—21no—
17#542×C151—22no—
18#537×C151—21no—
19#533×C151—21no—
20#532×C151—21no—
21#532×C151C2211yescharacteristic
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#520×C151—21no—
25C4×#41×C151C2211yescharacteristic
26#500×C151—21no—
27#487×C151—22no—
28#487×C151C2214yes—
29#486×C151—21no—
30#480×C151—22no—
31#474×C151C2214yes—
32#462×C151—21no—
33#462×C151C2212yes—
34#461×C151—21no—
35#461×C151C2212yes—
36#431×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38#419×C151—21no—
39C2×#103×C151—22no—
40C2×C4×C8×C151C2211yescharacteristic
41#333×C151C2214yes—
42Q8⋊C8×C151C2212yes—
43D4⋊C8×C151C2214yes—
44D4⋊C8×C151C2212yes—
45C2×#41×C151—21no—
46C2×#41×C151—22no—
47C2×#41×C151D411yescharacteristic
48C22×Q8×C151—21no—
49C22×Q8×C151D412yes—
50#137×C151—44no—
51C2×Q16×C151—22no—
52C2×SD16×C151—22no—
53C2×M16×C151—21no—
54C22×C8×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D412yes—
62C4⋊Q8×C151C2312yes—
63C4⋊Q8×C151C2312yes—
64#127×C151D411yescharacteristic
65#126×C151—24no—
66#125×C151—22no—
67#124×C151—22no—
68#124×C151—21no—
69#124×C151—24no—
70#123×C151—24no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—24no—
75#121×C151—22no—
76#121×C151—24no—
77#121×C151—22no—
78#121×C151—22no—
79#121×C151—21no—
80#121×C151D412yes—
81C4×Q8×C151—22no—
82C4×Q8×C151—22no—
83C4×Q8×C151D411yescharacteristic
84C4×Q8×C151C2311yescharacteristic
85C4×D4×C151—22no—
86C4×D4×C151—24no—
87C4×D4×C151—22no—
88C4×D4×C151—21no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91C4×D4×C151D411yescharacteristic
92C4×D4×C151C2311yescharacteristic
93C4×D4×C151C2312yes—
94#117×C151—22no—
95#117×C151—22no—
96#117×C151—21no—
97#117×C151D411yescharacteristic
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C42×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#107×C151—24no—
106C4⋊C8×C151—21no—
107C4⋊C8×C151C2312yes—
108C4⋊C8×C151C2312yes—
109#103×C151—22no—
110#103×C151—22no—
111#103×C151—28no—
112#102×C151—24no—
113C22⋊C8×C151—21no—
114C4×C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151C2312yes—
117#41×C151—22no—
118#41×C151—22no—
119#41×C151—42no—
120#41×C151—42no—
121#41×C151—84no—
122C2×Q8×C151—21no—
123C2×Q8×C151—22no—
124C2×Q8×C151—22no—
125C2×Q8×C151—44no—
126C2×Q8×C151—41no—
127C2×Q8×C151—42no—
128C2×Q8×C151—42no—
129C2×Q8×C151C2×D411yescharacteristic
130C2×Q8×C151C2×D414yes—
131C2×D4×C151—21no—
132C2×D4×C151—22no—
133C2×D4×C151—24no—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151C2×D412yes—
137C2×D4×C151C2×D411yescharacteristic
138C22×C4×C151—24no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—22no—
144C22×C4×C151—41no—
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148Q16×C151—44no—
149SD16×C151—44no—
150M16×C151—42no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—22no—
154C2×C8×C151—42no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—41no—
167C4⋊C4×C151—41no—
168C4⋊C4×C151C2×D411yescharacteristic
169C4⋊C4×C151C2×D411yescharacteristic
170C4⋊C4×C151C2×D412yes—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—21no—
175C22⋊C4×C151—21no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—21no—
178C22⋊C4×C151—22no—
179C42×C151—24no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151C2×D411yescharacteristic
184C42×C151C2×D411yescharacteristic
185C42×C151C2×D411yescharacteristic
186C42×C151C2411yescharacteristic
187C23×C151—21no—
188C23×C151—22no—
189C23×C151#12011yescharacteristic
190Q8×C151—21no—
191Q8×C151—21no—
192Q8×C151—44no—
193Q8×C151—42no—
194Q8×C151—44no—
195Q8×C151—42no—
196Q8×C151—42no—
197Q8×C151—82no—
198D4×C151—21no—
199D4×C151—21no—
200D4×C151—24no—
201D4×C151—42no—
202D4×C151—44no—
203D4×C151—42no—
204D4×C151—42no—
205D4×C151—84no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—82no—
220C2×C4×C151—84no—
221C2×C4×C151—82no—
222C2×C4×C151#12011yescharacteristic
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151#12011yescharacteristic
225C2×C4×C151#13512yes—
226C2×C4×C151AGL(1,ℤ/8)12yes—
227C2×C4×C151C22×D411yescharacteristic
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C22×D411yescharacteristic
230C8×C151—42no—
231C8×C151—42no—
232C8×C151—42no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—41no—
236C22×C151—42no—
237C22×C151—41no—
238C22×C151—42no—
239C22×C151—41no—
240C22×C151—42no—
241C22×C151#44912yes—
242C22×C151C2×#12011yescharacteristic
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—41no—
246C4×C151—42no—
247C4×C151—41no—
248C4×C151—41no—
249C4×C151—44no—
250C4×C151—82no—
251C4×C151#44912yes—
252C4×C151#45512yes—
253C4×C151C2×#13511yescharacteristic
254C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C151#57812yes—
256C2×C151—22no—
257C2×C151—81no—
258C2×C151—82no—
259C2×C151C2×#44911yescharacteristic
260C2×C151#301111yescharacteristic
261C2×C151C2×#45511yescharacteristic
262#18636C15111yesmaximal, characteristic, direct product factor, Sylow
263C151#1863611yescharacteristic, direct product factor, Sylow
264#3511C2×C15111yescharacteristic
265#3226C2×C15111yescharacteristic, complemented
266C2×#487C2×C15111yescharacteristic, complemented
267#3039C2×C15111yescharacteristic, complemented
268#1646C2×C15114yescomplemented
269#1644C2×C15114yescomplemented
270#1548C2×C15111yescharacteristic, complemented
271#1492C2×C15111yescharacteristic, complemented
272#1476C2×C15111yescharacteristic, complemented
273C2×#137—21no—
274#556—21no—
275#555C22×C15112yes—
276#554C22×C15112yes—
277#553—22no—
278#548—22no—
279#547—21no—
280#542—22no—
281#537—21no—
282#533—21no—
283#532—21no—
284#532C22×C15111yescharacteristic
285C2×C4⋊Q8C22×C15111yescharacteristic
286C2×C4⋊Q8C22×C15111yescharacteristic
287#520—21no—
288C4×#41C22×C15111yescharacteristic
289#500—21no—
290#487—22no—
291#487C22×C15114yes—
292#486—21no—
293#480—22no—
294#474C22×C15114yes—
295#462—21no—
296#462C22×C15112yes—
297#461—21no—
298#461C22×C15112yes—
299#431C22×C15111yescharacteristic
300#423C22×C15111yescharacteristic
301#419—21no—
302C2×#103—22no—
303C2×C4×C8C22×C15111yescharacteristic
304#333C22×C15114yes—
305Q8⋊C8C22×C15112yes—
306D4⋊C8C22×C15114yes—
307D4⋊C8C22×C15112yes—
308C2×#41—22no—
309C2×#41—21no—
310C2×#41D4×C15111yescharacteristic
311C22×Q8—21no—
312C22×Q8D4×C15112yes—
313#137—44no—
314C2×Q16—22no—
315C2×SD16—22no—
316C2×M16—21no—
317C22×C8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8D4×C15112yes—
324C4⋊Q8D4×C15111yescharacteristic
325C4⋊Q8C23×C15112yes—
326C4⋊Q8C23×C15112yes—
327#127D4×C15111yescharacteristic
328#126—24no—
329#125—22no—
330#124—22no—
331#124—24no—
332#124—21no—
333#123—24no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338#121—22no—
339#121—24no—
340#121—22no—
341#121—22no—
342#121—21no—
343#121D4×C15112yes—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8D4×C15111yescharacteristic
347C4×Q8C23×C15111yescharacteristic
348C4×D4—22no—
349C4×D4—24no—
350C4×D4—22no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4D4×C15111yescharacteristic
355C4×D4C23×C15111yescharacteristic
356C4×D4C23×C15112yes—
357#117—22no—
358#117—22no—
359#117—21no—
360#117D4×C15111yescharacteristic
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C42—21no—
367C2×C42C23×C15111yescharacteristic
368#107—24no—
369C4⋊C8—21no—
370C4⋊C8C23×C15112yes—
371C4⋊C8C23×C15112yes—
372#103—28no—
373#103—22no—
374#103—22no—
375#102—24no—
376C22⋊C8—21no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8C23×C15112yes—
380#41—22no—
381#41—22no—
382#41—42no—
383#41—42no—
384#41—84no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—44no—
389C2×Q8—41no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8C2×D4×C15111yescharacteristic
393C2×Q8C2×D4×C15114yes—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4C2×D4×C15112yes—
400C2×D4C2×D4×C15111yescharacteristic
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411Q16—44no—
412SD16—44no—
413M16—42no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—42no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C2×D4×C15111yescharacteristic
432C4⋊C4C2×D4×C15111yescharacteristic
433C4⋊C4C2×D4×C15112yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—22no—
442C42—24no—
443C42—21no—
444C42—21no—
445C42—21no—
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C2×D4×C15111yescharacteristic
449C42C24×C15111yescharacteristic
450C23—21no—
451C23—22no—
452C23#120×C15111yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—44no—
456Q8—42no—
457Q8—44no—
458Q8—42no—
459Q8—42no—
460Q8—82no—
461D4—21no—
462D4—21no—
463D4—24no—
464D4—42no—
465D4—44no—
466D4—42no—
467D4—42no—
468D4—84no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4—82no—
485C2×C4#120×C15111yescharacteristic
486C2×C4#120×C15111yescharacteristic
487C2×C4#120×C15111yescharacteristic
488C2×C4#135×C15112yes—
489C2×C4AGL(1,ℤ/8)×C15112yes—
490C2×C4C22×D4×C15111yescharacteristic
491C2×C4C22×D4×C15111yescharacteristic
492C2×C4C22×D4×C15111yescharacteristic
493C8—42no—
494C8—42no—
495C8—42no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22#449×C15112yes—
505C22C2×#120×C15111yescharacteristic
506C4—21no—
507C4—21no—
508C4—41no—
509C4—42no—
510C4—41no—
511C4—41no—
512C4—44no—
513C4—82no—
514C4#449×C15112yes—
515C4#455×C15112yes—
516C4C2×#135×C15111yescharacteristic
517C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
518C4#578×C15112yes—
519C2—22no—
520C2—81no—
521C2—82no—
522C2C2×#449×C15111yescharacteristic
523C2#3011×C15111yescharacteristic
524C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3511×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3226×C151C2semidirect
3. C2×#487×C151C2semidirect
4. #3039×C151C2semidirect
5. #1646×C151C2semidirect
6. #1644×C151C2semidirect
7. #1548×C151C2semidirect
8. #1492×C151C2semidirect
9. #1476×C151C2semidirect
262. #18636C151direct (N × H)
263. C151#18636direct (N × H)
265. #3226C2×C151semidirect
266. C2×#487C2×C151semidirect
267. #3039C2×C151semidirect
268. #1646C2×C151semidirect
269. #1644C2×C151semidirect
270. #1548C2×C151semidirect
271. #1492C2×C151semidirect
272. #1476C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#3226×C1512
C2×#487×C1512
#3039×C1512
#1646×C1512
#1644×C1512
#1548×C1512
#1492×C1512
#1476×C1512
#18636151