Finite Group Databasebeta

← C151×#18953 #50323878

Subgroups — C151×#18953 #50323878

Order 38656.

846 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C151C211yesmaximal, characteristic
2#3249×C151C211yesmaximal, characteristic, complemented
3#3235×C151C211yesmaximal, characteristic
4#3231×C151C211yesmaximal, characteristic, complemented
5#1652×C151C212yesmaximal, complemented
6#1649×C151C212yesmaximal, complemented
7#1638×C151C212yesmaximal, complemented
8#1637×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1480×C151C211yesmaximal, characteristic
12#563×C151—22no—
13#559×C151—21no—
14Q82×C151—21no—
15#556×C151—21no—
16#556×C151C2212yes—
17D4×Q8×C151—21no—
18D4×Q8×C151C2212yes—
19#542×C151—22no—
20#542×C151—22no—
21#536×C151—22no—
22#533×C151C2211yescharacteristic
23#533×C151C2211yescharacteristic
24#533×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#501×C151—21no—
27#500×C151C2211yescharacteristic
28#498×C151C2211yescharacteristic
29#490×C151—21no—
30#487×C151C2211yescharacteristic
31#487×C151C2211yescharacteristic
32#485×C151—22no—
33#482×C151—22no—
34#479×C151—22no—
35#477×C151—21no—
36#477×C151C2212yes—
37#476×C151C2212yes—
38#474×C151C2212yes—
39#467×C151—22no—
40#462×C151—21no—
41#462×C151C2212yes—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#332×C151C2212yes—
46#332×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C22×Q8×C151—22no—
53C2×Q16×C151—22no—
54C22×C8×C151—21no—
55C4⋊Q8×C151—24no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151D411yescharacteristic
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151C2311yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65#127×C151D411yescharacteristic
66#126×C151—24no—
67#126×C151—24no—
68#125×C151—21no—
69#125×C151—21no—
70#125×C151D412yes—
71#124×C151—24no—
72#124×C151—22no—
73#124×C151—22no—
74#124×C151—21no—
75#123×C151—24no—
76#123×C151—24no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151D412yes—
87#121×C151—21no—
88#121×C151D412yes—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2312yes—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—21no—
100C4×D4×C151C2312yes—
101#117×C151—21no—
102#117×C151—22no—
103#117×C151—21no—
104#117×C151D412yes—
105C2×C42×C151C2311yescharacteristic
106#107×C151—22no—
107#107×C151—22no—
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#103×C151—22no—
118#103×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—81no—
127#41×C151—81no—
128C2×Q8×C151—24no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—82no—
136C2×Q8×C151—82no—
137C2×Q8×C151C2×D412yes—
138C2×D4×C151—22no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151C2×D412yes—
142C22×C4×C151—24no—
143C22×C4×C151—22no—
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147Q16×C151—82no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—81no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—41no—
170C4⋊C4×C151—41no—
171C4⋊C4×C151C2×D412yes—
172C4⋊C4×C151C2×D412yes—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D412yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—41no—
183C42×C151—24no—
184C42×C151—22no—
185C42×C151—22no—
186C42×C151—41no—
187C42×C151C2×D411yescharacteristic
188C42×C151C2×D411yescharacteristic
189C42×C151C2×D411yescharacteristic
190C42×C151C2411yescharacteristic
191C23×C151—22no—
192C23×C151#12011yescharacteristic
193Q8×C151—22no—
194Q8×C151—22no—
195Q8×C151—42no—
196Q8×C151—42no—
197Q8×C151—41no—
198Q8×C151—41no—
199Q8×C151—42no—
200Q8×C151—41no—
201Q8×C151—41no—
202Q8×C151—81no—
203Q8×C151—84no—
204D4×C151—24no—
205D4×C151—42no—
206D4×C151—81no—
207D4×C151—82no—
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—42no—
218C2×C4×C151—42no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—84no—
222C2×C4×C151#12011yescharacteristic
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151#12011yescharacteristic
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C22×D411yescharacteristic
227C2×C4×C151C22×D411yescharacteristic
228C8×C151—41no—
229C8×C151—41no—
230C8×C151—42no—
231C8×C151—42no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151C2×#12011yescharacteristic
239C4×C151—21no—
240C4×C151—21no—
241C4×C151—21no—
242C4×C151—21no—
243C4×C151—42no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—81no—
249C4×C151—81no—
250C4×C151#57611yescharacteristic
251C4×C151#57711yescharacteristic
252C4×C151#57812yes—
253C2×C151—41no—
254C2×C151—82no—
255C2×C151#301111yescharacteristic
256C2×C151#301211yescharacteristic
257C2×C151#302011yescharacteristic
258#18953C15111yesmaximal, characteristic, direct product factor, Sylow
259C151#1895311yescharacteristic, direct product factor, Sylow
260#3550C2×C15111yescharacteristic
261#3249C2×C15111yescharacteristic, complemented
262#3235C2×C15111yescharacteristic
263#3231C2×C15111yescharacteristic, complemented
264#1652C2×C15112yescomplemented
265#1649C2×C15112yescomplemented
266#1638C2×C15112yescomplemented
267#1637C2×C15112yescomplemented
268#1552C2×C15111yescharacteristic, complemented
269#1497C2×C15111yescharacteristic, complemented
270#1480C2×C15111yescharacteristic
271#563—22no—
272#559—21no—
273Q82—21no—
274#556—21no—
275#556C22×C15112yes—
276D4×Q8—21no—
277D4×Q8C22×C15112yes—
278#542—22no—
279#542—22no—
280#536—22no—
281#533C22×C15111yescharacteristic
282#533C22×C15111yescharacteristic
283#533C22×C15111yescharacteristic
284#532C22×C15111yescharacteristic
285#501—21no—
286#500C22×C15111yescharacteristic
287#498C22×C15111yescharacteristic
288#490—21no—
289#487C22×C15111yescharacteristic
290#487C22×C15111yescharacteristic
291#485—22no—
292#482—22no—
293#479—22no—
294#477—21no—
295#477C22×C15112yes—
296#476C22×C15112yes—
297#474C22×C15112yes—
298#467—22no—
299#462—21no—
300#462C22×C15112yes—
301#432C22×C15111yescharacteristic
302#431C22×C15111yescharacteristic
303C2×C4⋊C8C22×C15111yescharacteristic
304#332C22×C15112yes—
305#332C22×C15112yes—
306Q8⋊C8C22×C15112yes—
307Q8⋊C8C22×C15112yes—
308D4⋊C8C22×C15112yes—
309D4⋊C8C22×C15112yes—
310C2×#41—21no—
311C22×Q8—22no—
312C2×Q16—22no—
313C22×C8—21no—
314C4⋊Q8—24no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8D4×C15111yescharacteristic
318C4⋊Q8D4×C15111yescharacteristic
319C4⋊Q8D4×C15111yescharacteristic
320C4⋊Q8C23×C15111yescharacteristic
321C4⋊Q8C23×C15111yescharacteristic
322C4⋊Q8C23×C15111yescharacteristic
323C4⋊Q8C23×C15111yescharacteristic
324#127D4×C15111yescharacteristic
325#126—24no—
326#126—24no—
327#125—21no—
328#125—21no—
329#125D4×C15112yes—
330#124—24no—
331#124—22no—
332#124—22no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—24no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8D4×C15112yes—
346#121—21no—
347#121D4×C15112yes—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C23×C15112yes—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4C23×C15112yes—
360#117—21no—
361#117—22no—
362#117—21no—
363#117D4×C15112yes—
364C2×C42C23×C15111yescharacteristic
365#107—22no—
366#107—22no—
367#107—22no—
368#106—22no—
369#106—22no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8C23×C15112yes—
373C4⋊C8C23×C15112yes—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379#102—22no—
380C22⋊C8—21no—
381C22⋊C8—21no—
382#97—21no—
383C4×C8C23×C15111yescharacteristic
384C4×C8C23×C15111yescharacteristic
385#41—81no—
386#41—81no—
387C2×Q8—24no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—82no—
395C2×Q8—82no—
396C2×Q8C2×D4×C15112yes—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4C2×D4×C15112yes—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406Q16—82no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—81no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4C2×D4×C15112yes—
431C4⋊C4C2×D4×C15112yes—
432C4⋊C4C2×D4×C15112yes—
433C4⋊C4C2×D4×C15112yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C42—24no—
443C42—22no—
444C42—22no—
445C42—41no—
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C2×D4×C15111yescharacteristic
449C42C24×C15111yescharacteristic
450C23—22no—
451C23#120×C15111yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—42no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—42no—
459Q8—41no—
460Q8—41no—
461Q8—81no—
462Q8—84no—
463D4—24no—
464D4—42no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—84no—
481C2×C4#120×C15111yescharacteristic
482C2×C4#120×C15111yescharacteristic
483C2×C4#120×C15111yescharacteristic
484C2×C4C22×D4×C15111yescharacteristic
485C2×C4C22×D4×C15111yescharacteristic
486C2×C4C22×D4×C15111yescharacteristic
487C8—41no—
488C8—41no—
489C8—42no—
490C8—42no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22C2×#120×C15111yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4#576×C15111yescharacteristic
510C4#577×C15111yescharacteristic
511C4#578×C15112yes—
512C2—41no—
513C2—82no—
514C2#3011×C15111yescharacteristic
515C2#3012×C15111yescharacteristic
516C2#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
2. #3249×C151C2semidirect
4. #3231×C151C2semidirect
5. #1652×C151C2semidirect
6. #1649×C151C2semidirect
7. #1638×C151C2semidirect
8. #1637×C151C2semidirect
9. #1552×C151C2semidirect
10. #1497×C151C2semidirect
258. #18953C151direct (N × H)
259. C151#18953direct (N × H)
261. #3249C2×C151semidirect
263. #3231C2×C151semidirect
264. #1652C2×C151semidirect
265. #1649C2×C151semidirect
266. #1638C2×C151semidirect
267. #1637C2×C151semidirect
268. #1552C2×C151semidirect
269. #1497C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3550×C1512
#3249×C1512
#3235×C1512
#3231×C1512
#1652×C1512
#1649×C1512
#1638×C1512
#1637×C1512
#1552×C1512
#1497×C1512
#1480×C1512
#18953151