Finite Group Databasebeta

← C151×#23547 #50328472

Subgroups — C151×#23547 #50328472

Order 38656.

1458 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2C2×#423×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic
4C2×#419×C151C211yesmaximal, characteristic, complemented
5#2297×C151C211yesmaximal, characteristic
6C2×#391×C151C211yesmaximal, characteristic, complemented
7#2056×C151C214yesmaximal, complemented
8#2055×C151C214yesmaximal, complemented
9#1736×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C23×Q8×C151C2211yescharacteristic
12C2×#137×C151—24no—
13C2×#137×C151—24no—
14C2×#137×C151—24no—
15C22×Q16×C151C2212yes—
16C22×SD16×C151C2212yes—
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19C2×#117×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#423×C151—24no—
23C2×C4⋊C8×C151C2214yes—
24#419×C151—24no—
25#417×C151—24no—
26C2×#103×C151C2214yes—
27C2×#103×C151C2212yes—
28C2×#102×C151C2212yes—
29#391×C151—21no—
30#391×C151—21no—
31#391×C151C2214yes—
32#391×C151C2212yes—
33#390×C151C2212yes—
34#386×C151—22no—
35C4×C22⋊C4×C151—21no—
36C4×C22⋊C4×C151—21no—
37C2×#95×C151—22no—
38#340×C151C2214yes—
39C2×#41×C151—22no—
40C2×#41×C151—22no—
41C2×#41×C151—22no—
42C2×#41×C151—22no—
43C2×#41×C151—22no—
44C2×#41×C151D414yes—
45C22×Q8×C151—22no—
46C22×Q8×C151—22no—
47C22×Q8×C151—22no—
48C22×Q8×C151—22no—
49C22×Q8×C151—21no—
50C22×Q8×C151—22no—
51C22×Q8×C151D414yes—
52C22×Q8×C151C2312yes—
53C22×Q8×C151C2311yescharacteristic
54C22×D4×C151—21no—
55C22×D4×C151C2311yescharacteristic
56C23×C4×C151—21no—
57C23×C4×C151—21no—
58C23×C4×C151—21no—
59C23×C4×C151D412yes—
60C23×C4×C151C2311yescharacteristic
61#137×C151—232no—
62C2×Q16×C151—24no—
63C2×Q16×C151—24no—
64C2×Q16×C151—24no—
65C2×SD16×C151—24no—
66C2×SD16×C151—24no—
67C2×SD16×C151—24no—
68C2×M16×C151—22no—
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151D414yes—
74C22×C8×C151C2312yes—
75C22×C8×C151C2312yes—
76#117×C151—22no—
77#117×C151—22no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C42×C151—22no—
87C2×C42×C151—22no—
88C2×C42×C151—21no—
89C2×C42×C151D411yescharacteristic
90C2×C42×C151D411yescharacteristic
91C2×C42×C151C2312yes—
92C4⋊C8×C151—28no—
93#103×C151—24no—
94#103×C151—28no—
95#102×C151—24no—
96#95×C151—24no—
97#95×C151—24no—
98#95×C151—22no—
99#95×C151—22no—
100C24×C151—21no—
101C24×C151C2×D411yescharacteristic
102#41×C151—28no—
103#41×C151—28no—
104#41×C151—44no—
105#41×C151—44no—
106C2×Q8×C151—24no—
107C2×Q8×C151—22no—
108C2×Q8×C151—21no—
109C2×Q8×C151—28no—
110C2×Q8×C151—28no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151—42no—
120C2×Q8×C151—42no—
121C2×Q8×C151—44no—
122C2×Q8×C151—44no—
123C2×Q8×C151C2×D414yes—
124C2×Q8×C151C2×D412yes—
125C2×D4×C151—24no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151—21no—
131C2×D4×C151—42no—
132C2×D4×C151—42no—
133C2×D4×C151C2×D412yes—
134C22×C4×C151—24no—
135C22×C4×C151—24no—
136C22×C4×C151—21no—
137C22×C4×C151—22no—
138C22×C4×C151—24no—
139C22×C4×C151—24no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—42no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151—42no—
147C22×C4×C151—44no—
148C22×C4×C151—42no—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×D412yes—
152C22×C4×C151C2×D412yes—
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151#4112yes—
156C22×C4×C151#4112yes—
157C22×C4×C151#4112yes—
158C22×C4×C151C2411yescharacteristic
159Q16×C151—216no—
160SD16×C151—216no—
161M16×C151—28no—
162M16×C151—44no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151C2×D414yes—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—42no—
174C22⋊C4×C151—44no—
175C22⋊C4×C151—42no—
176C22⋊C4×C151—44no—
177C42×C151—22no—
178C42×C151—22no—
179C42×C151—22no—
180C42×C151—22no—
181C42×C151—42no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151#12112yes—
190C23×C151#12112yes—
191C23×C151#12112yes—
192C23×C151C22×D411yescharacteristic
193Q8×C151—24no—
194Q8×C151—22no—
195Q8×C151—24no—
196Q8×C151—22no—
197Q8×C151—42no—
198Q8×C151—41no—
199Q8×C151—42no—
200Q8×C151—41no—
201Q8×C151—48no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—48no—
205D4×C151—41no—
206D4×C151—41no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—24no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—48no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—48no—
220C2×C4×C151—48no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—44no—
226C2×C4×C151—84no—
227C2×C4×C151#12014yes—
228C2×C4×C151#12112yes—
229C2×C4×C151#12112yes—
230C2×C4×C151#12112yes—
231C2×C4×C151#12314yes—
232C2×C4×C151#12314yes—
233C2×C4×C151#12414yes—
234C2×C4×C151#13714yescomplemented
235C2×C4×C151C22×D411yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C2×#4111yescharacteristic
239C2×C4×C151C2×#4111yescharacteristic
240C2×C4×C151C2×#4111yescharacteristic
241C8×C151—24no—
242C8×C151—42no—
243C22×C151—24no—
244C22×C151—22no—
245C22×C151—22no—
246C22×C151—24no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—82no—
251C22×C151—82no—
252C22×C151#39414yes—
253C22×C151C2×#12111yescharacteristic
254C22×C151C2×#12111yescharacteristic
255C22×C151C2×#12111yescharacteristic
256C22×C151C2×#13712yes—
257C22×C151#57512yes—
258C4×C151—24no—
259C4×C151—42no—
260C4×C151—44no—
261C4×C151—42no—
262C4×C151—82no—
263C4×C151—82no—
264C4×C151#39414yes—
265C4×C151C2×#12011yescharacteristic
266C4×C151C2×#12311yescharacteristic
267C4×C151C2×#12311yescharacteristic
268C4×C151C2×#12411yescharacteristic
269C2×C151—24no—
270C2×C151—82no—
271C2×C151C2×#39411yescharacteristic
272C2×C151#303712yes—
273C2×C151#303911yescharacteristic
274C2×C151#304011yescharacteristic
275C2×C151#305612yes—
276#23547C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#2354711yescharacteristic, direct product factor, Sylow
278C22×#137C2×C15111yescharacteristic
279C2×#423C2×C15111yescharacteristic, complemented
280C2×#417C2×C15111yescharacteristic
281C2×#419C2×C15111yescharacteristic, complemented
282#2297C2×C15111yescharacteristic
283C2×#391C2×C15111yescharacteristic, complemented
284#2056C2×C15114yescomplemented
285#2055C2×C15114yescomplemented
286#1736C2×C15111yescharacteristic, complemented
287C22×#41C22×C15111yescharacteristic
288C23×Q8C22×C15111yescharacteristic
289C2×#137—24no—
290C2×#137—24no—
291C2×#137—24no—
292C22×Q16C22×C15112yes—
293C22×SD16C22×C15112yes—
294C22×M16C22×C15111yescharacteristic
295C22×M16C22×C15111yescharacteristic
296C2×#117C22×C15111yescharacteristic
297C22×C4⋊C4C22×C15111yescharacteristic
298C22×C42C22×C15111yescharacteristic
299#423—24no—
300C2×C4⋊C8C22×C15114yes—
301#419—24no—
302#417—24no—
303C2×#103C22×C15114yes—
304C2×#103C22×C15112yes—
305C2×#102C22×C15112yes—
306#391—21no—
307#391—21no—
308#391C22×C15114yes—
309#391C22×C15112yes—
310#390C22×C15112yes—
311#386—22no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C2×#95—22no—
315#340C22×C15114yes—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41D4×C15114yes—
322C22×Q8—22no—
323C22×Q8—21no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8D4×C15114yes—
329C22×Q8C23×C15112yes—
330C22×Q8C23×C15111yescharacteristic
331C22×D4—21no—
332C22×D4C23×C15111yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4D4×C15112yes—
337C23×C4C23×C15111yescharacteristic
338#137—232no—
339C2×Q16—24no—
340C2×Q16—24no—
341C2×Q16—24no—
342C2×SD16—24no—
343C2×SD16—24no—
344C2×SD16—24no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16D4×C15114yes—
351C22×C8C23×C15112yes—
352C22×C8C23×C15112yes—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C23×C15112yes—
359C2×C4⋊C4C23×C15112yes—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42D4×C15111yescharacteristic
367C2×C42D4×C15111yescharacteristic
368C2×C42C23×C15112yes—
369C4⋊C8—28no—
370#103—24no—
371#103—28no—
372#102—24no—
373#95—24no—
374#95—24no—
375#95—22no—
376#95—22no—
377C24—21no—
378C24C2×D4×C15111yescharacteristic
379#41—28no—
380#41—28no—
381#41—44no—
382#41—44no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—44no—
399C2×Q8—44no—
400C2×Q8C2×D4×C15114yes—
401C2×Q8C2×D4×C15112yes—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4C2×D4×C15112yes—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4C2×D4×C15112yes—
427C22×C4C2×D4×C15112yes—
428C22×C4C2×D4×C15112yes—
429C22×C4C2×D4×C15112yes—
430C22×C4C2×D4×C15112yes—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4#41×C15112yes—
433C22×C4#41×C15112yes—
434C22×C4#41×C15112yes—
435C22×C4C24×C15111yescharacteristic
436Q16—216no—
437SD16—216no—
438M16—28no—
439M16—44no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8C2×D4×C15114yes—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C22⋊C4—44no—
452C22⋊C4—42no—
453C22⋊C4—44no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—42no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23#121×C15112yes—
467C23#121×C15112yes—
468C23#121×C15112yes—
469C23C22×D4×C15111yescharacteristic
470Q8—24no—
471Q8—22no—
472Q8—24no—
473Q8—22no—
474Q8—48no—
475Q8—42no—
476Q8—41no—
477Q8—42no—
478Q8—41no—
479D4—22no—
480D4—22no—
481D4—48no—
482D4—41no—
483D4—41no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—48no—
492C2×C4—48no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—84no—
504C2×C4#120×C15114yes—
505C2×C4#121×C15112yes—
506C2×C4#121×C15112yes—
507C2×C4#121×C15112yes—
508C2×C4#123×C15114yes—
509C2×C4#123×C15114yes—
510C2×C4#124×C15114yes—
511C2×C4#137×C15114yescomplemented
512C2×C4C22×D4×C15111yescharacteristic
513C2×C4C22×D4×C15111yescharacteristic
514C2×C4C22×D4×C15111yescharacteristic
515C2×C4C2×#41×C15111yescharacteristic
516C2×C4C2×#41×C15111yescharacteristic
517C2×C4C2×#41×C15111yescharacteristic
518C8—24no—
519C8—42no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22#394×C15114yes—
530C22C2×#121×C15111yescharacteristic
531C22C2×#121×C15111yescharacteristic
532C22C2×#121×C15111yescharacteristic
533C22C2×#137×C15112yes—
534C22#575×C15112yes—
535C4—24no—
536C4—42no—
537C4—44no—
538C4—42no—
539C4—82no—
540C4—82no—
541C4#394×C15114yes—
542C4C2×#120×C15111yescharacteristic
543C4C2×#123×C15111yescharacteristic
544C4C2×#123×C15111yescharacteristic
545C4C2×#124×C15111yescharacteristic
546C2—24no—
547C2—82no—
548C2C2×#394×C15111yescharacteristic
549C2#3037×C15112yes—
550C2#3039×C15111yescharacteristic
551C2#3040×C15111yescharacteristic
552C2#3056×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#423×C151C2semidirect
4. C2×#419×C151C2semidirect
6. C2×#391×C151C2semidirect
7. #2056×C151C2semidirect
8. #2055×C151C2semidirect
9. #1736×C151C2semidirect
234. C2×C4×C151#137semidirect
276. #23547C151direct (N × H)
277. C151#23547direct (N × H)
279. C2×#423C2×C151semidirect
281. C2×#419C2×C151semidirect
283. C2×#391C2×C151semidirect
284. #2056C2×C151semidirect
285. #2055C2×C151semidirect
286. #1736C2×C151semidirect
511. C2×C4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#423×C1512
C2×#417×C1512
C2×#419×C1512
#2297×C1512
C2×#391×C1512
#2056×C1512
#2055×C1512
#1736×C1512
#23547151