Finite Group Databasebeta

← C151×#24914 #50329839

Subgroups — C151×#24914 #50329839

Order 38656.

982 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×#448×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic, complemented
3#2420×C151C211yesmaximal, characteristic
4Q8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#2097×C151C211yesmaximal, characteristic, complemented
6#2076×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic
9#1935×C151C211yesmaximal, characteristic, complemented
10#1924×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1877×C151C211yesmaximal, characteristic, complemented
13#1865×C151C211yesmaximal, characteristic, complemented
14#1805×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23#448×C151—24no—
24#440×C151—24no—
25C2×#107×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39#397×C151—21no—
40#394×C151—21no—
41#391×C151—21no—
42#391×C151—21no—
43#391×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#386×C151—21no—
48#382×C151C2211yescharacteristic
49#381×C151—21no—
50#380×C151—21no—
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53C4×C22⋊C4×C151—21no—
54C4×C22⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151—21no—
62C22×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—22no—
65C22×Q8×C151—22no—
66C22×Q8×C151—41no—
67C22×Q8×C151—41no—
68C22×Q8×C151C2311yescharacteristic
69C22×Q8×C151C2311yescharacteristic
70C22×D4×C151—21no—
71C22×D4×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—22no—
79C2×SD16×C151—41no—
80C2×SD16×C151D414yes—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85#121×C151—22no—
86#121×C151—41no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—41no—
90C4×Q8×C151—41no—
91C4×D4×C151—22no—
92C4×D4×C151—41no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#107×C151—22no—
114#106×C151—41no—
115C4⋊C8×C151—41no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#102×C151—22no—
123#102×C151—41no—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—41no—
126#97×C151—22no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140C2×Q8×C151—24no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—42no—
150C2×Q8×C151—42no—
151C2×Q8×C151—44no—
152C2×Q8×C151—44no—
153C2×Q8×C151—44no—
154C2×Q8×C151—44no—
155C2×Q8×C151C2×D412yes—
156C2×Q8×C151#4112yes—
157C2×Q8×C151#4112yes—
158C2×Q8×C151#4112yes—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—81no—
167C2×D4×C151C2×D412yes—
168C22×C4×C151—21no—
169C22×C4×C151—24no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—42no—
183C22×C4×C151—42no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—81no—
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193SD16×C151—28no—
194SD16×C151—44no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151C2×D412yes—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—42no—
218C4⋊C4×C151—42no—
219C4⋊C4×C151—81no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—41no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—81no—
226C22⋊C4×C151—81no—
227C22⋊C4×C151—81no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—42no—
233C42×C151—42no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—22no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151#13712yes—
248C23×C151C22×D411yescharacteristic
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—22no—
253Q8×C151—22no—
254Q8×C151—48no—
255Q8×C151—41no—
256Q8×C151—41no—
257Q8×C151#12314yes—
258D4×C151—22no—
259D4×C151—22no—
260D4×C151—41no—
261D4×C151—41no—
262D4×C151—84no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—21no—
267C2×C4×C151—22no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—48no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—84no—
305C2×C4×C151C22×D411yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151C2×#4111yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C2×C4×C151H(5,𝔽2)11yescharacteristic
311C8×C151—22no—
312C8×C151—41no—
313C8×C151—41no—
314C8×C151—41no—
315C22×C151—22no—
316C22×C151—22no—
317C22×C151—22no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—42no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—81no—
326C22×C151—81no—
327C22×C151—81no—
328C22×C151—81no—
329C22×C151#52511yescharacteristic
330C22×C151D4211yescharacteristic
331C22×C151#54611yescharacteristic
332C22×C151C2×#13711yescharacteristic
333C22×C151#57511yescharacteristic
334C22×C151#57711yescharacteristic
335C22×C151#57711yescharacteristic
336C4×C151—24no—
337C4×C151—41no—
338C4×C151—42no—
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—41no—
342C4×C151—41no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151—81no—
348C4×C151C2×#12311yescharacteristic
349C4×C151#53811yescharacteristic
350C4×C151#54611yescharacteristic
351C4×C151#55111yescharacteristic
352C2×C151—42no—
353C2×C151—82no—
354C2×C151#241811yescharacteristic
355C2×C151#311711yescharacteristic
356C2×C151#312611yescharacteristic
357C2×C151#326611yescharacteristic
358C2×C151#327511yescharacteristic
359C2×C151#332011yescharacteristic
360C2×C151#332111yescharacteristic
361#24914C15111yesmaximal, characteristic, direct product factor, Sylow
362C151#2491411yescharacteristic, direct product factor, Sylow
363C2×#448C2×C15111yescharacteristic
364C2×#440C2×C15111yescharacteristic, complemented
365#2420C2×C15111yescharacteristic
366Q8×C22⋊C4C2×C15111yescharacteristic, complemented
367#2097C2×C15111yescharacteristic, complemented
368#2076C2×C15111yescharacteristic, complemented
369#2055C2×C15111yescharacteristic, complemented
370#2034C2×C15111yescharacteristic
371#1935C2×C15111yescharacteristic, complemented
372#1924C2×C15111yescharacteristic, complemented
373#1880C2×C15111yescharacteristic, complemented
374#1877C2×C15111yescharacteristic, complemented
375#1865C2×C15111yescharacteristic, complemented
376#1805C2×C15111yescharacteristic, complemented
377#1787C2×C15111yescharacteristic, complemented
378C23×Q8C22×C15111yescharacteristic
379C22×SD16C22×C15111yescharacteristic
380C22×SD16C22×C15111yescharacteristic
381C2×#121C22×C15111yescharacteristic
382C2×C4×Q8C22×C15111yescharacteristic
383C2×C4×Q8C22×C15111yescharacteristic
384C2×C4×D4C22×C15111yescharacteristic
385#448—24no—
386#440—24no—
387C2×#107C22×C15111yescharacteristic
388C2×#106C22×C15111yescharacteristic
389C2×C4⋊C8C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#103C22×C15111yescharacteristic
394C2×#103C22×C15111yescharacteristic
395C2×#103C22×C15111yescharacteristic
396C2×#102C22×C15111yescharacteristic
397C2×#102C22×C15111yescharacteristic
398C2×C22⋊C8C22×C15111yescharacteristic
399C2×C22⋊C8C22×C15111yescharacteristic
400C2×#97C22×C15111yescharacteristic
401#397—21no—
402#394—21no—
403#391—21no—
404#391—21no—
405#391C22×C15111yescharacteristic
406#391C22×C15111yescharacteristic
407#390C22×C15111yescharacteristic
408#389C22×C15111yescharacteristic
409#386—21no—
410#382C22×C15111yescharacteristic
411#381—21no—
412#380—21no—
413#380C22×C15111yescharacteristic
414#380C22×C15111yescharacteristic
415C4×C22⋊C4—21no—
416C4×C22⋊C4C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420#340C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422#336C22×C15111yescharacteristic
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—21no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—41no—
429C22×Q8—41no—
430C22×Q8C23×C15111yescharacteristic
431C22×Q8C23×C15111yescharacteristic
432C22×D4—21no—
433C22×D4C23×C15111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C15111yescharacteristic
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—41no—
442C2×SD16D4×C15114yes—
443C22×C8C23×C15111yescharacteristic
444C22×C8C23×C15111yescharacteristic
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447#121—22no—
448#121—41no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—41no—
452C4×Q8—41no—
453C4×D4—22no—
454C4×D4—41no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4C23×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C15111yescharacteristic
470C2×C22⋊C4D4×C15111yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C15111yescharacteristic
474C2×C42C23×C15111yescharacteristic
475#107—22no—
476#106—41no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#102—22no—
485#102—41no—
486C22⋊C8—22no—
487C22⋊C8—41no—
488#97—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C15111yescharacteristic
499#95D4×C15111yescharacteristic
500C24—21no—
501C24C2×D4×C15111yescharacteristic
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8C2×D4×C15112yes—
518C2×Q8#41×C15112yes—
519C2×Q8#41×C15112yes—
520C2×Q8#41×C15112yes—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4C2×D4×C15112yes—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4C2×D4×C15111yescharacteristic
550C22×C4C2×D4×C15111yescharacteristic
551C22×C4C2×D4×C15111yescharacteristic
552C22×C4C2×D4×C15111yescharacteristic
553C22×C4C2×D4×C15111yescharacteristic
554C22×C4C24×C15111yescharacteristic
555SD16—28no—
556SD16—44no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C2×D4×C15112yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C22⋊C4—22no—
583C22⋊C4—41no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—42no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23#137×C15112yes—
610C23C22×D4×C15111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—48no—
617Q8—41no—
618Q8—41no—
619Q8#123×C15114yes—
620D4—22no—
621D4—22no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—48no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4C22×D4×C15111yescharacteristic
668C2×C4C2×#41×C15111yescharacteristic
669C2×C4C2×#41×C15111yescharacteristic
670C2×C4C2×#41×C15111yescharacteristic
671C2×C4H(5,𝔽2)×C15111yescharacteristic
672C2×C4H(5,𝔽2)×C15111yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22#525×C15111yescharacteristic
692C22D42×C15111yescharacteristic
693C22#546×C15111yescharacteristic
694C22C2×#137×C15111yescharacteristic
695C22#575×C15111yescharacteristic
696C22#577×C15111yescharacteristic
697C22#577×C15111yescharacteristic
698C4—24no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#123×C15111yescharacteristic
711C4#538×C15111yescharacteristic
712C4#546×C15111yescharacteristic
713C4#551×C15111yescharacteristic
714C2—42no—
715C2—82no—
716C2#2418×C15111yescharacteristic
717C2#3117×C15111yescharacteristic
718C2#3126×C15111yescharacteristic
719C2#3266×C15111yescharacteristic
720C2#3275×C15111yescharacteristic
721C2#3320×C15111yescharacteristic
722C2#3321×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C151C2semidirect
4. Q8×C22⋊C4×C151C2semidirect
5. #2097×C151C2semidirect
6. #2076×C151C2semidirect
7. #2055×C151C2semidirect
9. #1935×C151C2semidirect
10. #1924×C151C2semidirect
11. #1880×C151C2semidirect
12. #1877×C151C2semidirect
13. #1865×C151C2semidirect
14. #1805×C151C2semidirect
15. #1787×C151C2semidirect
361. #24914C151direct (N × H)
362. C151#24914direct (N × H)
364. C2×#440C2×C151semidirect
366. Q8×C22⋊C4C2×C151semidirect
367. #2097C2×C151semidirect
368. #2076C2×C151semidirect
369. #2055C2×C151semidirect
371. #1935C2×C151semidirect
372. #1924C2×C151semidirect
373. #1880C2×C151semidirect
374. #1877C2×C151semidirect
375. #1865C2×C151semidirect
376. #1805C2×C151semidirect
377. #1787C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1512
C2×#440×C1512
#2420×C1512
Q8×C22⋊C4×C1512
#2097×C1512
#2076×C1512
#2055×C1512
#2034×C1512
#1935×C1512
#1924×C1512
#1880×C1512
#1877×C1512
#1865×C1512
#1805×C1512
#1787×C1512
#24914151