Finite Group Databasebeta

← C151×#18950 #50323875

Subgroups — C151×#18950 #50323875

Order 38656.

824 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3556×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic
3#3228×C151C211yesmaximal, characteristic
4#3216×C151C211yesmaximal, characteristic
5#1653×C151C212yesmaximal, complemented
6#1648×C151C212yesmaximal, complemented
7#1626×C151C212yesmaximal, complemented
8#1626×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1481×C151C211yesmaximal, characteristic, complemented
12#564×C151—22no—
13#557×C151—21no—
14#557×C151—21no—
15#557×C151—21no—
16#557×C151—21no—
17#557×C151C2212yes—
18#557×C151C2212yes—
19#541×C151—22no—
20#541×C151—22no—
21#541×C151—22no—
22#533×C151C2211yescharacteristic
23#533×C151C2211yescharacteristic
24#533×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#500×C151C2211yescharacteristic
27#498×C151C2211yescharacteristic
28#497×C151—21no—
29#489×C151—21no—
30#486×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#482×C151—22no—
33#478×C151—22no—
34#476×C151—21no—
35#475×C151C2212yes—
36#465×C151—22no—
37#462×C151C2212yes—
38#461×C151—21no—
39#460×C151C2212yes—
40#460×C151C2212yes—
41#452×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#332×C151C2212yes—
46#332×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C2×Q16×C151—22no—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C22×C8×C151—21no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151D411yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65C4⋊Q8×C151C2311yescharacteristic
66#127×C151C2311yescharacteristic
67#126×C151—24no—
68#126×C151—24no—
69#125×C151—22no—
70#125×C151—24no—
71#125×C151—24no—
72#125×C151—24no—
73#125×C151—24no—
74#125×C151—22no—
75#125×C151—22no—
76#125×C151—24no—
77#125×C151—24no—
78#125×C151—21no—
79#125×C151—21no—
80#125×C151D412yes—
81#124×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151D412yes—
87C22⋊Q8×C151D412yes—
88#121×C151—21no—
89#121×C151—21no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—22no—
99C4×Q8×C151—22no—
100C4×Q8×C151C2312yes—
101C4×Q8×C151C2312yes—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104#117×C151—21no—
105#117×C151—21no—
106#117×C151D412yes—
107C2×C42×C151C2311yescharacteristic
108#107×C151—22no—
109#106×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—82no—
127C2×Q8×C151—21no—
128C2×Q8×C151—21no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151C2×D412yes—
133C2×Q8×C151C2×D412yes—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—41no—
138C22×C4×C151—41no—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142Q16×C151—82no—
143SD16×C151—82no—
144SD16×C151—82no—
145C2×C8×C151—21no—
146C2×C8×C151—21no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—81no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151C2×D412yes—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D412yes—
175C4⋊C4×C151C2×D412yes—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—41no—
180C22⋊C4×C151—41no—
181C42×C151—24no—
182C42×C151—24no—
183C42×C151—22no—
184C42×C151—22no—
185C42×C151—22no—
186C42×C151C2×D411yescharacteristic
187C42×C151C2×D411yescharacteristic
188C42×C151C2×D411yescharacteristic
189C42×C151C2411yescharacteristic
190C23×C151—41no—
191C23×C151#12011yescharacteristic
192Q8×C151—22no—
193Q8×C151—22no—
194Q8×C151—22no—
195Q8×C151—22no—
196Q8×C151—42no—
197Q8×C151—42no—
198Q8×C151—42no—
199Q8×C151—41no—
200Q8×C151—41no—
201Q8×C151—42no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—41no—
205D4×C151—41no—
206D4×C151—82no—
207C2×C4×C151—22no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—82no—
219C2×C4×C151#12011yescharacteristic
220C2×C4×C151#12011yescharacteristic
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C2×C4×C151C22×D411yescharacteristic
224C2×C4×C151C22×D411yescharacteristic
225C8×C151—41no—
226C8×C151—41no—
227C8×C151—42no—
228C8×C151—42no—
229C22×C151—21no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—81no—
233C22×C151—81no—
234C22×C151—81no—
235C22×C151C2×#12011yescharacteristic
236C4×C151—21no—
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—21no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—81no—
247C4×C151#57712yes—
248C4×C151#57711yescharacteristic
249C4×C151#57811yescharacteristic
250C2×C151—41no—
251C2×C151—161no—
252C2×C151#301011yescharacteristic
253C2×C151#301311yescharacteristic
254C2×C151#302011yescharacteristic
255#18950C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#1895011yescharacteristic, direct product factor, Sylow
257#3556C2×C15111yescharacteristic, complemented
258#3246C2×C15111yescharacteristic
259#3228C2×C15111yescharacteristic
260#3216C2×C15111yescharacteristic
261#1653C2×C15112yescomplemented
262#1648C2×C15112yescomplemented
263#1626C2×C15112yescomplemented
264#1626C2×C15112yescomplemented
265#1552C2×C15111yescharacteristic, complemented
266#1497C2×C15111yescharacteristic, complemented
267#1481C2×C15111yescharacteristic, complemented
268#564—22no—
269#557—21no—
270#557—21no—
271#557—21no—
272#557—21no—
273#557C22×C15112yes—
274#557C22×C15112yes—
275#541—22no—
276#541—22no—
277#541—22no—
278#533C22×C15111yescharacteristic
279#533C22×C15111yescharacteristic
280#533C22×C15111yescharacteristic
281#532C22×C15111yescharacteristic
282#500C22×C15111yescharacteristic
283#498C22×C15111yescharacteristic
284#497—21no—
285#489—21no—
286#486C22×C15111yescharacteristic
287#486C22×C15111yescharacteristic
288#482—22no—
289#478—22no—
290#476—21no—
291#475C22×C15112yes—
292#465—22no—
293#462C22×C15112yes—
294#461—21no—
295#460C22×C15112yes—
296#460C22×C15112yes—
297#452—22no—
298#432C22×C15111yescharacteristic
299#431C22×C15111yescharacteristic
300C2×C4⋊C8C22×C15111yescharacteristic
301#332C22×C15112yes—
302#332C22×C15112yes—
303Q8⋊C8C22×C15112yes—
304Q8⋊C8C22×C15112yes—
305Q8⋊C8C22×C15112yes—
306Q8⋊C8C22×C15112yes—
307C2×#41—21no—
308C2×Q16—22no—
309C2×SD16—22no—
310C2×SD16—22no—
311C22×C8—21no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8D4×C15111yescharacteristic
316C4⋊Q8D4×C15111yescharacteristic
317C4⋊Q8D4×C15111yescharacteristic
318C4⋊Q8D4×C15111yescharacteristic
319C4⋊Q8C23×C15111yescharacteristic
320C4⋊Q8C23×C15111yescharacteristic
321C4⋊Q8C23×C15111yescharacteristic
322#127C23×C15111yescharacteristic
323#126—24no—
324#126—24no—
325#125—22no—
326#125—24no—
327#125—24no—
328#125—24no—
329#125—24no—
330#125—22no—
331#125—22no—
332#125—24no—
333#125—24no—
334#125—21no—
335#125—21no—
336#125D4×C15112yes—
337#124—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8D4×C15112yes—
343C22⋊Q8D4×C15112yes—
344#121—21no—
345#121—21no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C23×C15112yes—
357C4×Q8C23×C15112yes—
358C4×D4—21no—
359C4×D4—21no—
360#117—21no—
361#117—21no—
362#117D4×C15112yes—
363C2×C42C23×C15111yescharacteristic
364#107—22no—
365#106—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C15112yes—
370C4⋊C8C23×C15112yes—
371#103—22no—
372#103—22no—
373#102—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377C22⋊C8—21no—
378C22⋊C8—21no—
379#97—21no—
380C4×C8C23×C15111yescharacteristic
381C4×C8C23×C15111yescharacteristic
382#41—82no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C2×D4×C15112yes—
389C2×Q8C2×D4×C15112yes—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C22×C4—41no—
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C2×D4×C15111yescharacteristic
398Q16—82no—
399SD16—82no—
400SD16—82no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—81no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4C2×D4×C15112yes—
429C4⋊C4C2×D4×C15112yes—
430C4⋊C4C2×D4×C15112yes—
431C4⋊C4C2×D4×C15112yes—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C42—24no—
438C42—24no—
439C42—22no—
440C42—22no—
441C42—22no—
442C42C2×D4×C15111yescharacteristic
443C42C2×D4×C15111yescharacteristic
444C42C2×D4×C15111yescharacteristic
445C42C24×C15111yescharacteristic
446C23—41no—
447C23#120×C15111yescharacteristic
448Q8—22no—
449Q8—22no—
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—41no—
456Q8—41no—
457Q8—42no—
458D4—42no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—82no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4#120×C15111yescharacteristic
476C2×C4#120×C15111yescharacteristic
477C2×C4#120×C15111yescharacteristic
478C2×C4C22×D4×C15111yescharacteristic
479C2×C4C22×D4×C15111yescharacteristic
480C2×C4C22×D4×C15111yescharacteristic
481C8—41no—
482C8—41no—
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#120×C15111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—81no—
503C4#577×C15112yes—
504C4#577×C15111yescharacteristic
505C4#578×C15111yescharacteristic
506C2—41no—
507C2—161no—
508C2#3010×C15111yescharacteristic
509C2#3013×C15111yescharacteristic
510C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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
1. #3556×C151C2semidirect
5. #1653×C151C2semidirect
6. #1648×C151C2semidirect
7. #1626×C151C2semidirect
8. #1626×C151C2semidirect
9. #1552×C151C2semidirect
10. #1497×C151C2semidirect
11. #1481×C151C2semidirect
255. #18950C151direct (N × H)
256. C151#18950direct (N × H)
257. #3556C2×C151semidirect
261. #1653C2×C151semidirect
262. #1648C2×C151semidirect
263. #1626C2×C151semidirect
264. #1626C2×C151semidirect
265. #1552C2×C151semidirect
266. #1497C2×C151semidirect
267. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3556×C1512
#3246×C1512
#3228×C1512
#3216×C1512
#1653×C1512
#1648×C1512
#1626×C1512
#1552×C1512
#1497×C1512
#1481×C1512
#18950151