Finite Group Databasebeta

← C151×#19062 #50323987

Subgroups — C151×#19062 #50323987

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C151C211yesmaximal, characteristic, complemented
2#3235×C151C211yesmaximal, characteristic, complemented
3#3214×C151C211yesmaximal, characteristic
4#3135×C151C211yesmaximal, characteristic, complemented
5#1664×C151C214yesmaximal, complemented
6#1657×C151C214yesmaximal, complemented
7#1537×C151C211yesmaximal, characteristic, complemented
8#1531×C151C211yesmaximal, characteristic, complemented
9#1530×C151C211yesmaximal, characteristic, complemented
10#563×C151C2214yes—
11#559×C151—21no—
12Q82×C151—21no—
13#556×C151—21no—
14#556×C151—21no—
15D4×Q8×C151—21no—
16D4×Q8×C151—21no—
17#542×C151—22no—
18#542×C151—22no—
19#536×C151—22no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24#501×C151C2212yes—
25#496×C151C2212yes—
26#491×C151C2212yes—
27#490×C151C2212yes—
28#490×C151C2212yes—
29#489×C151—21no—
30#489×C151—21no—
31#489×C151C2212yes—
32#482×C151—22no—
33#476×C151—21no—
34#474×C151—21no—
35#461×C151—21no—
36#459×C151—21no—
37#449×C151—22no—
38#432×C151C2211yescharacteristic
39#432×C151C2211yescharacteristic
40#416×C151—22no—
41C2×#97×C151C2211yescharacteristic
42#330×C151C2214yes—
43#330×C151C2214yes—
44#329×C151C2214yes—
45C2×#41×C151—21no—
46C2×#41×C151D412yes—
47C22×Q8×C151—22no—
48C2×SD16×C151—22no—
49C2×D8×C151—22no—
50C22×C8×C151—21no—
51C4⋊Q8×C151—22no—
52C4⋊Q8×C151—22no—
53C4⋊Q8×C151—24no—
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151D411yescharacteristic
57C4⋊Q8×C151D411yescharacteristic
58C4⋊Q8×C151D411yescharacteristic
59C4⋊Q8×C151C2311yescharacteristic
60#127×C151D411yescharacteristic
61#127×C151C2311yescharacteristic
62#126×C151—24no—
63#126×C151—24no—
64#125×C151C2312yes—
65#125×C151C2312yes—
66#124×C151—24no—
67#124×C151—22no—
68#124×C151—22no—
69#124×C151—21no—
70#124×C151C2312yes—
71#123×C151—24no—
72#123×C151—24no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—22no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—24no—
81#121×C151—21no—
82#121×C151—21no—
83#121×C151—21no—
84#121×C151—21no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97#117×C151—22no—
98#117×C151D412yes—
99#117×C151D412yes—
100C2×C42×C151C2311yescharacteristic
101#107×C151—22no—
102#106×C151—22no—
103C4⋊C8×C151—21no—
104C4⋊C8×C151—21no—
105#103×C151—22no—
106#103×C151—22no—
107#103×C151—22no—
108#102×C151—22no—
109#102×C151—22no—
110#102×C151—22no—
111#102×C151—22no—
112#102×C151—22no—
113C22⋊C8×C151—21no—
114C22⋊C8×C151—21no—
115#97×C151—21no—
116#97×C151C2312yes—
117#97×C151C2312yes—
118#97×C151C2312yes—
119#41×C151—44no—
120#41×C151—82no—
121C2×Q8×C151—24no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×Q8×C151—84no—
128C2×Q8×C151C2×D412yes—
129C2×D4×C151—22no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151—41no—
136C2×D4×C151C2×D412yes—
137C22×C4×C151—24no—
138C22×C4×C151—22no—
139C22×C4×C151—41no—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143SD16×C151—82no—
144D8×C151—82no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—42no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151C2×D412yes—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151C2×D412yes—
166C4⋊C4×C151C2×D412yes—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—24no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—41no—
175C22⋊C4×C151—41no—
176C42×C151—24no—
177C42×C151—22no—
178C42×C151—22no—
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2411yescharacteristic
183C23×C151—22no—
184C23×C151—41no—
185C23×C151#12011yescharacteristic
186Q8×C151—42no—
187Q8×C151—42no—
188Q8×C151—42no—
189Q8×C151—42no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151—84no—
193D4×C151—42no—
194D4×C151—42no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—41no—
198D4×C151—42no—
199D4×C151—42no—
200D4×C151—82no—
201D4×C151—82no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—44no—
211C2×C4×C151—41no—
212C2×C4×C151—84no—
213C2×C4×C151—82no—
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C22×D411yescharacteristic
220C8×C151—42no—
221C8×C151—42no—
222C8×C151—42no—
223C22×C151—21no—
224C22×C151—21no—
225C22×C151—21no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—81no—
230C22×C151—81no—
231C22×C151—81no—
232C22×C151C2×#12011yescharacteristic
233C4×C151—21no—
234C4×C151—21no—
235C4×C151—21no—
236C4×C151—21no—
237C4×C151—21no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—81no—
244C4×C151#45412yes—
245C2×C151—41no—
246C2×C151—82no—
247C2×C151—161no—
248C2×C151C2×#45411yescharacteristic
249C2×C151#301911yescharacteristic
250C2×C151#302011yescharacteristic
251#19062C15111yesmaximal, characteristic, direct product factor, Sylow
252C151#1906211yescharacteristic, direct product factor, Sylow
253#3550C2×C15111yescharacteristic, complemented
254#3235C2×C15111yescharacteristic, complemented
255#3214C2×C15111yescharacteristic
256#3135C2×C15111yescharacteristic, complemented
257#1664C2×C15114yescomplemented
258#1657C2×C15114yescomplemented
259#1537C2×C15111yescharacteristic, complemented
260#1531C2×C15111yescharacteristic, complemented
261#1530C2×C15111yescharacteristic, complemented
262#563C22×C15114yes—
263#559—21no—
264Q82—21no—
265#556—21no—
266#556—21no—
267D4×Q8—21no—
268D4×Q8—21no—
269#542—22no—
270#542—22no—
271#536—22no—
272#533C22×C15111yescharacteristic
273#533C22×C15111yescharacteristic
274#532C22×C15111yescharacteristic
275#532C22×C15111yescharacteristic
276#501C22×C15112yes—
277#496C22×C15112yes—
278#491C22×C15112yes—
279#490C22×C15112yes—
280#490C22×C15112yes—
281#489—21no—
282#489—21no—
283#489C22×C15112yes—
284#482—22no—
285#476—21no—
286#474—21no—
287#461—21no—
288#459—21no—
289#449—22no—
290#432C22×C15111yescharacteristic
291#432C22×C15111yescharacteristic
292#416—22no—
293C2×#97C22×C15111yescharacteristic
294#330C22×C15114yes—
295#330C22×C15114yes—
296#329C22×C15114yes—
297C2×#41—21no—
298C2×#41D4×C15112yes—
299C22×Q8—22no—
300C2×SD16—22no—
301C2×D8—22no—
302C22×C8—21no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—24no—
306C4⋊Q8D4×C15111yescharacteristic
307C4⋊Q8D4×C15111yescharacteristic
308C4⋊Q8D4×C15111yescharacteristic
309C4⋊Q8D4×C15111yescharacteristic
310C4⋊Q8D4×C15111yescharacteristic
311C4⋊Q8C23×C15111yescharacteristic
312#127D4×C15111yescharacteristic
313#127C23×C15111yescharacteristic
314#126—24no—
315#126—24no—
316#125C23×C15112yes—
317#125C23×C15112yes—
318#124—24no—
319#124—22no—
320#124—22no—
321#124—21no—
322#124C23×C15112yes—
323#123—24no—
324#123—24no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349#117—22no—
350#117D4×C15112yes—
351#117D4×C15112yes—
352C2×C42C23×C15111yescharacteristic
353#107—22no—
354#106—22no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357#103—22no—
358#103—22no—
359#103—22no—
360#102—22no—
361#102—22no—
362#102—22no—
363#102—22no—
364#102—22no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367#97—21no—
368#97C23×C15112yes—
369#97C23×C15112yes—
370#97C23×C15112yes—
371#41—44no—
372#41—82no—
373C2×Q8—24no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—84no—
380C2×Q8C2×D4×C15112yes—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4C2×D4×C15112yes—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—41no—
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395SD16—82no—
396D8—82no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—42no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4C2×D4×C15112yes—
416C4⋊C4C2×D4×C15112yes—
417C4⋊C4C2×D4×C15112yes—
418C4⋊C4C2×D4×C15112yes—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C42—24no—
429C42—22no—
430C42—22no—
431C42C2×D4×C15111yescharacteristic
432C42C2×D4×C15111yescharacteristic
433C42C2×D4×C15111yescharacteristic
434C42C24×C15111yescharacteristic
435C23—22no—
436C23—41no—
437C23#120×C15111yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—84no—
445D4—42no—
446D4—42no—
447D4—41no—
448D4—41no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—82no—
453D4—82no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—44no—
463C2×C4—41no—
464C2×C4—84no—
465C2×C4—82no—
466C2×C4#120×C15111yescharacteristic
467C2×C4#120×C15111yescharacteristic
468C2×C4#120×C15111yescharacteristic
469C2×C4C22×D4×C15111yescharacteristic
470C2×C4C22×D4×C15111yescharacteristic
471C2×C4C22×D4×C15111yescharacteristic
472C8—42no—
473C8—42no—
474C8—42no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22C2×#120×C15111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—81no—
496C4#454×C15112yes—
497C2—41no—
498C2—82no—
499C2—161no—
500C2C2×#454×C15111yescharacteristic
501C2#3019×C15111yescharacteristic
502C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3214×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
1. #3550×C151C2semidirect
2. #3235×C151C2semidirect
4. #3135×C151C2semidirect
5. #1664×C151C2semidirect
6. #1657×C151C2semidirect
7. #1537×C151C2semidirect
8. #1531×C151C2semidirect
9. #1530×C151C2semidirect
251. #19062C151direct (N × H)
252. C151#19062direct (N × H)
253. #3550C2×C151semidirect
254. #3235C2×C151semidirect
256. #3135C2×C151semidirect
257. #1664C2×C151semidirect
258. #1657C2×C151semidirect
259. #1537C2×C151semidirect
260. #1531C2×C151semidirect
261. #1530C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3550×C1512
#3235×C1512
#3214×C1512
#3135×C1512
#1664×C1512
#1657×C1512
#1537×C1512
#1531×C1512
#1530×C1512
#19062151