Finite Group Databasebeta

← C151×#14813 #50319738

Subgroups — C151×#14813 #50319738

Order 38656.

1786 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C151C211yesmaximal, characteristic
2C2×#390×C151C211yesmaximal, characteristic
3C2×#388×C151C212yesmaximal, complemented
4C2×#387×C151C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
6#1442×C151C211yesmaximal, characteristic, complemented
7#1441×C151C211yesmaximal, characteristic, complemented
8#1439×C151C212yesmaximal, complemented
9#1439×C151C212yesmaximal, complemented
10#1438×C151C211yesmaximal, characteristic
11#1437×C151C212yesmaximal, complemented
12C23×D4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C42×C151C2212yes—
24C22×C42×C151C2211yescharacteristic
25#394×C151—24no—
26#390×C151—24no—
27#388×C151—28no—
28#387×C151—24no—
29C4×C4⋊C4×C151—24no—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2212yes—
39C2×#95×C151C2211yescharacteristic
40C25×C151C2312yes—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151—22no—
44C22×D4×C151—24no—
45C22×D4×C151—42no—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2312yes—
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2312yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—42no—
66C2×C4⋊C4×C151D414yescomplemented
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—24no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—42no—
82C2×C22⋊C4×C151—42no—
83C2×C22⋊C4×C151—42no—
84C2×C22⋊C4×C151—42no—
85C2×C42×C151—22no—
86C2×C42×C151—22no—
87C2×C42×C151—24no—
88C2×C42×C151—24no—
89C2×C42×C151—42no—
90C2×C42×C151D414yes—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151—22no—
96#95×C151—24no—
97#95×C151—24no—
98#95×C151—42no—
99#95×C151—42no—
100#95×C151D414yes—
101C24×C151—22no—
102C24×C151—22no—
103C24×C151—22no—
104C24×C151—22no—
105C24×C151—22no—
106C24×C151—22no—
107C24×C151—22no—
108C24×C151—22no—
109C24×C151—22no—
110C24×C151—22no—
111C24×C151—22no—
112C24×C151—22no—
113C24×C151—22no—
114C24×C151—22no—
115C24×C151#4114yes—
116C24×C151C2411yescharacteristic
117C2×D4×C151—28no—
118C2×D4×C151—48no—
119C2×D4×C151—48no—
120C2×D4×C151—44no—
121C2×D4×C151—44no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—21no—
156C22×C4×C151—22no—
157C22×C4×C151—21no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—22no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—21no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151C2×D412yes—
171C22×C4×C151C2×D412yes—
172C22×C4×C151C2×D414yes—
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2×D412yes—
175C22×C4×C151C2×D412yes—
176C22×C4×C151C2×D412yes—
177C22×C4×C151C2×D412yes—
178C22×C4×C151#4114yes—
179C22×C4×C151#4112yes—
180C22×C4×C151#4112yes—
181C22×C4×C151#4114yes—
182C4⋊C4×C151—216no—
183C4⋊C4×C151—28no—
184C4⋊C4×C151—44no—
185C4⋊C4×C151—44no—
186C22⋊C4×C151—216no—
187C22⋊C4×C151—48no—
188C22⋊C4×C151—48no—
189C22⋊C4×C151—48no—
190C22⋊C4×C151—48no—
191C22⋊C4×C151—48no—
192C42×C151—28no—
193C42×C151—48no—
194C23×C151—24no—
195C23×C151—24no—
196C23×C151—24no—
197C23×C151—24no—
198C23×C151—24no—
199C23×C151—24no—
200C23×C151—24no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—42no—
210C23×C151—42no—
211C23×C151—42no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—42no—
218C23×C151—42no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—42no—
224C23×C151—42no—
225C23×C151—42no—
226C23×C151—42no—
227C23×C151—42no—
228C23×C151—42no—
229C23×C151C22×D411yescharacteristic
230C23×C151C22×D411yescharacteristic
231C23×C151C22×D411yescharacteristic
232C23×C151C2×#4111yescharacteristic
233C23×C151C2×#4111yescharacteristic
234C23×C151C2×#4112yes—
235C23×C151C2×#4112yes—
236C23×C151C2×#4112yes—
237C23×C151H(5,𝔽2)12yes—
238C23×C151H(5,𝔽2)11yescharacteristic
239C23×C1512−1+411yescharacteristic
240D4×C151—416no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—24no—
244C2×C4×C151—22no—
245C2×C4×C151—24no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—24no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—24no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—24no—
258C2×C4×C151—24no—
259C2×C4×C151—24no—
260C2×C4×C151—24no—
261C2×C4×C151—24no—
262C2×C4×C151—24no—
263C2×C4×C151—22no—
264C2×C4×C151—24no—
265C2×C4×C151—22no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—42no—
269C2×C4×C151—42no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151—41no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151—41no—
279C2×C4×C151—42no—
280C2×C4×C151—42no—
281C2×C4×C151—42no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—42no—
285C2×C4×C151—41no—
286C2×C4×C151—42no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—42no—
293C2×C4×C151—42no—
294C2×C4×C151—42no—
295C2×C4×C151—42no—
296C2×C4×C151—42no—
297C2×C4×C151—42no—
298C2×C4×C151#12114yes—
299C2×C4×C151#12114yes—
300C2×C4×C151#12414yes—
301C22×C151—44no—
302C22×C151—44no—
303C22×C151—44no—
304C22×C151—44no—
305C22×C151—44no—
306C22×C151—44no—
307C22×C151—44no—
308C22×C151—82no—
309C22×C151—82no—
310C22×C151—82no—
311C22×C151—82no—
312C22×C151—82no—
313C22×C151—82no—
314C22×C151—82no—
315C22×C151—82no—
316C22×C151C2×#12111yescharacteristic
317C22×C151C2×#12111yescharacteristic
318C22×C151#52511yescharacteristic
319C22×C151#52512yes—
320C22×C151#52512yes—
321C22×C151C2×#12411yescharacteristic
322C22×C151#52912yes—
323C22×C151#52912yes—
324C22×C151#53211yescharacteristic
325C22×C151#53511yescharacteristic
326C22×C151#53711yescharacteristic
327C22×C151#53812yes—
328C22×C151#54212yes—
329C22×C151D4211yescharacteristic
330C22×C151#54612yes—
331C22×C151#54711yescharacteristic
332C22×C151#54811yescharacteristic
333C22×C151#55012yes—
334C22×C151#55112yes—
335C22×C151#55212yes—
336C22×C151#55312yes—
337C22×C151#55311yescharacteristic
338C22×C151#55912yes—
339C4×C151—24no—
340C4×C151—24no—
341C4×C151—24no—
342C4×C151—42no—
343C4×C151—42no—
344C4×C151—44no—
345C4×C151—44no—
346C4×C151—81no—
347C4×C151—81no—
348C4×C151—82no—
349C2×C151—84no—
350C2×C151#239211yescharacteristic
351C2×C151#241111yescharacteristic
352C2×C151#241611yescharacteristic
353C2×C151#245612yes—
354C2×C151#245812yes—
355C2×C151#247912yes—
356C2×C151#254811yescharacteristic
357C2×C151#256211yescharacteristic
358C2×C151#259712yes—
359C2×C151#266211yescharacteristic
360C2×C151#285011yescharacteristic
361#14813C15111yesmaximal, characteristic, direct product factor, Sylow
362C151#1481311yescharacteristic, direct product factor, Sylow
363C2×#394C2×C15111yescharacteristic
364C2×#390C2×C15111yescharacteristic
365C2×#388C2×C15112yescomplemented
366C2×#387C2×C15111yescharacteristic, complemented
367C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
368#1442C2×C15111yescharacteristic, complemented
369#1441C2×C15111yescharacteristic, complemented
370#1439C2×C15112yescomplemented
371#1439C2×C15112yescomplemented
372#1438C2×C15111yescharacteristic
373#1437C2×C15112yescomplemented
374C23×D4C22×C15111yescharacteristic
375C22×C4⋊C4C22×C15111yescharacteristic
376C22×C4⋊C4C22×C15112yes—
377C22×C4⋊C4C22×C15111yescharacteristic
378C22×C4⋊C4C22×C15111yescharacteristic
379C22×C22⋊C4C22×C15112yes—
380C22×C22⋊C4C22×C15112yes—
381C22×C22⋊C4C22×C15112yes—
382C22×C22⋊C4C22×C15112yes—
383C22×C22⋊C4C22×C15112yes—
384C22×C22⋊C4C22×C15112yes—
385C22×C42C22×C15112yes—
386C22×C42C22×C15111yescharacteristic
387#394—24no—
388#390—24no—
389#388—28no—
390#387—24no—
391C4×C4⋊C4—24no—
392C2×#95C22×C15111yescharacteristic
393C2×#95C22×C15111yescharacteristic
394C2×#95C22×C15111yescharacteristic
395C2×#95C22×C15111yescharacteristic
396C2×#95C22×C15111yescharacteristic
397C2×#95C22×C15112yes—
398C2×#95C22×C15112yes—
399C2×#95C22×C15112yes—
400C2×#95C22×C15112yes—
401C2×#95C22×C15111yescharacteristic
402C25C23×C15112yes—
403C22×D4—24no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—42no—
408C23×C4C23×C15112yes—
409C23×C4C23×C15111yescharacteristic
410C23×C4C23×C15111yescharacteristic
411C23×C4C23×C15112yes—
412C23×C4C23×C15111yescharacteristic
413C23×C4C23×C15111yescharacteristic
414C23×C4C23×C15112yes—
415C23×C4C23×C15111yescharacteristic
416C23×C4C23×C15111yescharacteristic
417C23×C4C23×C15111yescharacteristic
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4D4×C15114yescomplemented
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—42no—
452C2×C42D4×C15114yes—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—24no—
459#95—24no—
460#95—42no—
461#95—42no—
462#95D4×C15114yes—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24#41×C15114yes—
478C24C24×C15111yescharacteristic
479C2×D4—28no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—44no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4C2×D4×C15112yes—
533C22×C4C2×D4×C15112yes—
534C22×C4C2×D4×C15114yes—
535C22×C4C2×D4×C15112yes—
536C22×C4C2×D4×C15112yes—
537C22×C4C2×D4×C15112yes—
538C22×C4C2×D4×C15112yes—
539C22×C4C2×D4×C15112yes—
540C22×C4#41×C15114yes—
541C22×C4#41×C15112yes—
542C22×C4#41×C15112yes—
543C22×C4#41×C15114yes—
544C4⋊C4—216no—
545C4⋊C4—28no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C22⋊C4—216no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C42—28no—
555C42—48no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23C22×D4×C15111yescharacteristic
592C23C22×D4×C15111yescharacteristic
593C23C22×D4×C15111yescharacteristic
594C23C2×#41×C15111yescharacteristic
595C23C2×#41×C15111yescharacteristic
596C23C2×#41×C15112yes—
597C23C2×#41×C15112yes—
598C23C2×#41×C15112yes—
599C23H(5,𝔽2)×C15112yes—
600C23H(5,𝔽2)×C15111yescharacteristic
601C232−1+4×C15111yescharacteristic
602D4—416no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4#121×C15114yes—
661C2×C4#121×C15114yes—
662C2×C4#124×C15114yes—
663C22—44no—
664C22—44no—
665C22—44no—
666C22—44no—
667C22—44no—
668C22—44no—
669C22—44no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22C2×#121×C15111yescharacteristic
679C22C2×#121×C15111yescharacteristic
680C22#525×C15112yes—
681C22#525×C15111yescharacteristic
682C22#525×C15112yes—
683C22C2×#124×C15111yescharacteristic
684C22#529×C15112yes—
685C22#529×C15112yes—
686C22#532×C15111yescharacteristic
687C22#535×C15111yescharacteristic
688C22#537×C15111yescharacteristic
689C22#538×C15112yes—
690C22#542×C15112yes—
691C22D42×C15111yescharacteristic
692C22#546×C15112yes—
693C22#547×C15111yescharacteristic
694C22#548×C15111yescharacteristic
695C22#550×C15112yes—
696C22#551×C15112yes—
697C22#552×C15112yes—
698C22#553×C15111yescharacteristic
699C22#553×C15112yes—
700C22#559×C15112yes—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—42no—
706C4—44no—
707C4—44no—
708C4—81no—
709C4—81no—
710C4—82no—
711C2—84no—
712C2#2392×C15111yescharacteristic
713C2#2411×C15111yescharacteristic
714C2#2416×C15111yescharacteristic
715C2#2456×C15112yes—
716C2#2458×C15112yes—
717C2#2479×C15112yes—
718C2#2548×C15111yescharacteristic
719C2#2562×C15111yescharacteristic
720C2#2597×C15112yes—
721C2#2662×C15111yescharacteristic
722C2#2850×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#388×C151C2semidirect
4. C2×#387×C151C2semidirect
5. C2×C4×C4⋊C4×C151C2semidirect
6. #1442×C151C2semidirect
7. #1441×C151C2semidirect
8. #1439×C151C2semidirect
9. #1439×C151C2semidirect
11. #1437×C151C2semidirect
66. C2×C4⋊C4×C151D4semidirect
361. #14813C151direct (N × H)
362. C151#14813direct (N × H)
365. C2×#388C2×C151semidirect
366. C2×#387C2×C151semidirect
367. C2×C4×C4⋊C4C2×C151semidirect
368. #1442C2×C151semidirect
369. #1441C2×C151semidirect
370. #1439C2×C151semidirect
371. #1439C2×C151semidirect
373. #1437C2×C151semidirect
428. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1512
C2×#390×C1512
C2×#388×C1512
C2×#387×C1512
C2×C4×C4⋊C4×C1512
#1442×C1512
#1441×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#14813151