Finite Group Databasebeta

← C151×#11292 #50316217

Subgroups — C151×#11292 #50316217

Order 38656.

842 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C151C211yesmaximal, characteristic
2C2×#340×C151C211yesmaximal, characteristic
3C2×#340×C151C211yesmaximal, characteristic
4C2×#340×C151C211yesmaximal, characteristic
5C2×#340×C151C211yesmaximal, characteristic
6C2×#336×C151C211yesmaximal, characteristic
7C4⋊#95×C151C211yesmaximal, characteristic
8C23×C8×C151C2211yescharacteristic
9C23×C8×C151C2211yescharacteristic
10C22×C4⋊C4×C151—21no—
11C22×C4⋊C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C42×C151C2211yescharacteristic
16#389×C151—22no—
17#389×C151—22no—
18C2×#95×C151—21no—
19C2×#95×C151—21no—
20C2×#95×C151—21no—
21#340×C151—22no—
22#340×C151—22no—
23#340×C151—22no—
24#340×C151C414yescomplemented
25#336×C151—22no—
26C23×C4×C151—21no—
27C23×C4×C151—21no—
28C23×C4×C151—21no—
29C23×C4×C151—21no—
30C23×C4×C151D411yescharacteristic
31C23×C4×C151D411yescharacteristic
32C23×C4×C151C2311yescharacteristic
33C22×C8×C151—21no—
34C22×C8×C151—21no—
35C22×C8×C151—21no—
36C22×C8×C151—21no—
37C22×C8×C151—21no—
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C22×C8×C151—21no—
42C22×C8×C151—21no—
43C22×C8×C151—21no—
44C22×C8×C151—21no—
45C22×C8×C151C2×C412yes—
46C22×C8×C151D412yes—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—24no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—42no—
67C2×C4⋊C4×C151—42no—
68C2×C4⋊C4×C151C2×C412yes—
69C2×C4⋊C4×C151C2×C412yes—
70C2×C4⋊C4×C151D412yes—
71C2×C4⋊C4×C151D412yes—
72C2×C4⋊C4×C151Q812yes—
73C2×C4⋊C4×C151Q812yes—
74C2×C42×C151—21no—
75C2×C42×C151—21no—
76C2×C42×C151—21no—
77C2×C42×C151—21no—
78C2×C42×C151—21no—
79C2×C42×C151—21no—
80#95×C151—24no—
81#95×C151—42no—
82#95×C151—42no—
83C24×C151C2×D411yescharacteristic
84C22×C4×C151—22no—
85C22×C4×C151—21no—
86C22×C4×C151—22no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—22no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—41no—
107C22×C4×C151—41no—
108C22×C4×C151—41no—
109C22×C4×C151—41no—
110C22×C4×C151—41no—
111C22×C4×C151—41no—
112C22×C4×C151—41no—
113C22×C4×C151—41no—
114C22×C4×C151—41no—
115C22×C4×C151—41no—
116C22×C4×C151—41no—
117C22×C4×C151—41no—
118C22×C4×C151—41no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151—41no—
122C22×C4×C151—41no—
123C22×C4×C151—41no—
124C22×C4×C151D812yes—
125C22×C4×C151SD1612yes—
126C22×C4×C151C22×C411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×Q811yescharacteristic
131C22×C4×C151C2×Q811yescharacteristic
132C22×C4×C151#4111yescharacteristic
133C22×C4×C151#4111yescharacteristic
134C22×C4×C151#4111yescharacteristic
135C22×C4×C151#4111yescharacteristic
136C22×C4×C151#4111yescharacteristic
137C22×C4×C151#4111yescharacteristic
138C22×C4×C151#4111yescharacteristic
139C22×C4×C151#4111yescharacteristic
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—41no—
147C2×C8×C151—41no—
148C2×C8×C151—41no—
149C2×C8×C151—41no—
150C2×C8×C151—41no—
151C2×C8×C151—41no—
152C2×C8×C151—41no—
153C2×C8×C151—41no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—48no—
164C4⋊C4×C151—41no—
165C4⋊C4×C151—41no—
166C4⋊C4×C151—41no—
167C4⋊C4×C151—41no—
168C4⋊C4×C151—41no—
169C4⋊C4×C151—41no—
170C4⋊C4×C151C4⋊C414yes—
171C42×C151—41no—
172C42×C151—41no—
173C42×C151—41no—
174C42×C151—41no—
175C23×C151C4×D411yescharacteristic
176C23×C151#12011yescharacteristic
177C23×C151#12111yescharacteristic
178C23×C151C22⋊Q811yescharacteristic
179C23×C151C22⋊Q811yescharacteristic
180C23×C151#12311yescharacteristic
181C23×C151#12411yescharacteristic
182C23×C151C2×D811yescharacteristic
183C23×C151C2×SD1611yescharacteristic
184C23×C151#13511yescharacteristic
185C23×C151#13511yescharacteristic
186C23×C151AGL(1,ℤ/8)11yescharacteristic
187C23×C151#13711yescharacteristic
188C23×C151#13711yescharacteristic
189C23×C151#13711yescharacteristic
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—81no—
221C2×C4×C151—81no—
222C2×C4×C151—81no—
223C2×C4×C151—81no—
224C2×C4×C151—81no—
225C2×C4×C151—81no—
226C2×C4×C151—81no—
227C2×C4×C151—81no—
228C2×C4×C151—81no—
229C2×C4×C151—81no—
230C2×C4×C151—81no—
231C2×C4×C151—81no—
232C2×C4×C151C2×C4⋊C411yescharacteristic
233C2×C4×C151#11711yescharacteristic
234C2×C4×C151#11711yescharacteristic
235C2×C4×C151C4×D411yescharacteristic
236C2×C4×C151C4×D411yescharacteristic
237C2×C4×C151C4×Q811yescharacteristic
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12111yescharacteristic
240C2×C4×C151C22⋊Q811yescharacteristic
241C2×C4×C151C22⋊Q811yescharacteristic
242C2×C4×C151C22⋊Q811yescharacteristic
243C2×C4×C151#12311yescharacteristic
244C2×C4×C151#12311yescharacteristic
245C2×C4×C151#12311yescharacteristic
246C2×C4×C151#12311yescharacteristic
247C2×C4×C151#12411yescharacteristic
248C2×C4×C151#12411yescharacteristic
249C2×C4×C151#12411yescharacteristic
250C2×C4×C151#12511yescharacteristic
251C2×C4×C151#12511yescharacteristic
252C2×C4×C151#12511yescharacteristic
253C2×C4×C151#12511yescharacteristic
254C2×C4×C151#12511yescharacteristic
255C2×C4×C151#12611yescharacteristic
256C2×C4×C151#12611yescharacteristic
257C2×C4×C151#12611yescharacteristic
258C2×C4×C151#12611yescharacteristic
259C2×C4×C151C4⋊Q811yescharacteristic
260C8×C151—42no—
261C8×C151—42no—
262C22×C151#38511yescharacteristic
263C22×C151#38711yescharacteristic
264C22×C151#38811yescharacteristic
265C22×C151#39311yescharacteristic
266C22×C151#39411yescharacteristic
267C22×C151#39811yescharacteristic
268C22×C151#40011yescharacteristic
269C22×C151C4×D811yescharacteristic
270C22×C151C4×SD1611yescharacteristic
271C22×C151#44011yescharacteristic
272C22×C151#44111yescharacteristic
273C22×C151#44711yescharacteristic
274C22×C151#44811yescharacteristic
275C22×C151#45211yescharacteristic
276C22×C151#45211yescharacteristic
277C22×C151#46511yescharacteristic
278C22×C151#46611yescharacteristic
279C22×C151#46811yescharacteristic
280C22×C151#47011yescharacteristic
281C22×C151#47411yescharacteristic
282C22×C151#47411yescharacteristic
283C22×C151#47511yescharacteristic
284C22×C151#47611yescharacteristic
285C22×C151#47811yescharacteristic
286C22×C151#47911yescharacteristic
287C22×C151#47911yescharacteristic
288C22×C151#47911yescharacteristic
289C22×C151#48011yescharacteristic
290C22×C151#48211yescharacteristic
291C22×C151#48311yescharacteristic
292C22×C151#48511yescharacteristic
293C22×C151#48611yescharacteristic
294C22×C151#48811yescharacteristic
295C22×C151#48911yescharacteristic
296C22×C151#49111yescharacteristic
297C4×C151—44no—
298C4×C151—42no—
299C4×C151—42no—
300C4×C151—82no—
301C4×C151—82no—
302C4×C151—82no—
303C4×C151#38211yescharacteristic
304C4×C151#38711yescharacteristic
305C4×C151#38811yescharacteristic
306C4×C151#38911yescharacteristic
307C4×C151#39711yescharacteristic
308C4×C151#39811yescharacteristic
309C4×C151#40011yescharacteristic
310C4×C151#40011yescharacteristic
311C2×C151#144211yescharacteristic
312C2×C151#186211yescharacteristic
313C2×C151#186511yescharacteristic
314C2×C151#191811yescharacteristic
315C2×C151#192011yescharacteristic
316C2×C151#193411yescharacteristic
317C2×C151#193511yescharacteristic
318C2×C151#202311yescharacteristic
319C2×C151#202611yescharacteristic
320C2×C151#203311yescharacteristic
321C2×C151#203511yescharacteristic
322C2×C151#208611yescharacteristic
323C2×C151#208811yescharacteristic
324C2×C151#209911yescharacteristic
325C2×C151#210111yescharacteristic
326#11292C15111yesmaximal, characteristic, direct product factor, Sylow
327C151#1129211yescharacteristic, direct product factor, Sylow
328C2×#389C2×C15111yescharacteristic
329C2×#340C2×C15111yescharacteristic
330C2×#340C2×C15111yescharacteristic
331C2×#340C2×C15111yescharacteristic
332C2×#340C2×C15111yescharacteristic
333C2×#336C2×C15111yescharacteristic
334C4⋊#95C2×C15111yescharacteristic
335C23×C8C22×C15111yescharacteristic
336C23×C8C22×C15111yescharacteristic
337C22×C4⋊C4—21no—
338C22×C4⋊C4C22×C15111yescharacteristic
339C22×C4⋊C4C22×C15111yescharacteristic
340C22×C4⋊C4C22×C15111yescharacteristic
341C22×C4⋊C4C22×C15111yescharacteristic
342C22×C42C22×C15111yescharacteristic
343#389—22no—
344#389—22no—
345C2×#95—21no—
346C2×#95—21no—
347C2×#95—21no—
348#340—22no—
349#340—22no—
350#340—22no—
351#340C4×C15114yescomplemented
352#336—22no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C15111yescharacteristic
358C23×C4D4×C15111yescharacteristic
359C23×C4C23×C15111yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8C2×C4×C15112yes—
373C22×C8D4×C15112yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4C2×C4×C15112yes—
396C2×C4⋊C4C2×C4×C15112yes—
397C2×C4⋊C4D4×C15112yes—
398C2×C4⋊C4D4×C15112yes—
399C2×C4⋊C4Q8×C15112yes—
400C2×C4⋊C4Q8×C15112yes—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407#95—24no—
408#95—42no—
409#95—42no—
410C24C2×D4×C15111yescharacteristic
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4D8×C15112yes—
452C22×C4SD16×C15112yes—
453C22×C4C22×C4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15111yescharacteristic
456C22×C4C2×D4×C15111yescharacteristic
457C22×C4C2×Q8×C15111yescharacteristic
458C22×C4C2×Q8×C15111yescharacteristic
459C22×C4#41×C15111yescharacteristic
460C22×C4#41×C15111yescharacteristic
461C22×C4#41×C15111yescharacteristic
462C22×C4#41×C15111yescharacteristic
463C22×C4#41×C15111yescharacteristic
464C22×C4#41×C15111yescharacteristic
465C22×C4#41×C15111yescharacteristic
466C22×C4#41×C15111yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—48no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C4⋊C4×C15114yes—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C23C4×D4×C15111yescharacteristic
503C23#120×C15111yescharacteristic
504C23#121×C15111yescharacteristic
505C23C22⋊Q8×C15111yescharacteristic
506C23C22⋊Q8×C15111yescharacteristic
507C23#123×C15111yescharacteristic
508C23#124×C15111yescharacteristic
509C23C2×D8×C15111yescharacteristic
510C23C2×SD16×C15111yescharacteristic
511C23#135×C15111yescharacteristic
512C23#135×C15111yescharacteristic
513C23AGL(1,ℤ/8)×C15111yescharacteristic
514C23#137×C15111yescharacteristic
515C23#137×C15111yescharacteristic
516C23#137×C15111yescharacteristic
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4C2×C4⋊C4×C15111yescharacteristic
560C2×C4#117×C15111yescharacteristic
561C2×C4#117×C15111yescharacteristic
562C2×C4C4×D4×C15111yescharacteristic
563C2×C4C4×D4×C15111yescharacteristic
564C2×C4C4×Q8×C15111yescharacteristic
565C2×C4#121×C15111yescharacteristic
566C2×C4#121×C15111yescharacteristic
567C2×C4C22⋊Q8×C15111yescharacteristic
568C2×C4C22⋊Q8×C15111yescharacteristic
569C2×C4C22⋊Q8×C15111yescharacteristic
570C2×C4#123×C15111yescharacteristic
571C2×C4#123×C15111yescharacteristic
572C2×C4#123×C15111yescharacteristic
573C2×C4#123×C15111yescharacteristic
574C2×C4#124×C15111yescharacteristic
575C2×C4#124×C15111yescharacteristic
576C2×C4#124×C15111yescharacteristic
577C2×C4#125×C15111yescharacteristic
578C2×C4#125×C15111yescharacteristic
579C2×C4#125×C15111yescharacteristic
580C2×C4#125×C15111yescharacteristic
581C2×C4#125×C15111yescharacteristic
582C2×C4#126×C15111yescharacteristic
583C2×C4#126×C15111yescharacteristic
584C2×C4#126×C15111yescharacteristic
585C2×C4#126×C15111yescharacteristic
586C2×C4C4⋊Q8×C15111yescharacteristic
587C8—42no—
588C8—42no—
589C22#385×C15111yescharacteristic
590C22#387×C15111yescharacteristic
591C22#388×C15111yescharacteristic
592C22#393×C15111yescharacteristic
593C22#394×C15111yescharacteristic
594C22#398×C15111yescharacteristic
595C22#400×C15111yescharacteristic
596C22C4×D8×C15111yescharacteristic
597C22C4×SD16×C15111yescharacteristic
598C22#440×C15111yescharacteristic
599C22#441×C15111yescharacteristic
600C22#447×C15111yescharacteristic
601C22#448×C15111yescharacteristic
602C22#452×C15111yescharacteristic
603C22#452×C15111yescharacteristic
604C22#465×C15111yescharacteristic
605C22#466×C15111yescharacteristic
606C22#468×C15111yescharacteristic
607C22#470×C15111yescharacteristic
608C22#474×C15111yescharacteristic
609C22#474×C15111yescharacteristic
610C22#475×C15111yescharacteristic
611C22#476×C15111yescharacteristic
612C22#478×C15111yescharacteristic
613C22#479×C15111yescharacteristic
614C22#479×C15111yescharacteristic
615C22#479×C15111yescharacteristic
616C22#480×C15111yescharacteristic
617C22#482×C15111yescharacteristic
618C22#483×C15111yescharacteristic
619C22#485×C15111yescharacteristic
620C22#486×C15111yescharacteristic
621C22#488×C15111yescharacteristic
622C22#489×C15111yescharacteristic
623C22#491×C15111yescharacteristic
624C4—44no—
625C4—42no—
626C4—42no—
627C4—82no—
628C4—82no—
629C4—82no—
630C4#382×C15111yescharacteristic
631C4#387×C15111yescharacteristic
632C4#388×C15111yescharacteristic
633C4#389×C15111yescharacteristic
634C4#397×C15111yescharacteristic
635C4#398×C15111yescharacteristic
636C4#400×C15111yescharacteristic
637C4#400×C15111yescharacteristic
638C2#1442×C15111yescharacteristic
639C2#1862×C15111yescharacteristic
640C2#1865×C15111yescharacteristic
641C2#1918×C15111yescharacteristic
642C2#1920×C15111yescharacteristic
643C2#1934×C15111yescharacteristic
644C2#1935×C15111yescharacteristic
645C2#2023×C15111yescharacteristic
646C2#2026×C15111yescharacteristic
647C2#2033×C15111yescharacteristic
648C2#2035×C15111yescharacteristic
649C2#2086×C15111yescharacteristic
650C2#2088×C15111yescharacteristic
651C2#2099×C15111yescharacteristic
652C2#2101×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C2×D4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
24. #340×C151C4semidirect
326. #11292C151direct (N × H)
327. C151#11292direct (N × H)
351. #340C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1512
C2×#340×C1512
C2×#336×C1512
C4⋊#95×C1512
#11292151