Finite Group Databasebeta

← C151×#14815 #50319740

Subgroups — C151×#14815 #50319740

Order 38656.

2278 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C151C212yesmaximal, complemented
2C2×#394×C151C212yesmaximal, complemented
3C2×#392×C151C211yesmaximal, characteristic
4C2×#390×C151C212yesmaximal, complemented
5C2×#390×C151C211yesmaximal, characteristic, complemented
6C2×#388×C151C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
8#1444×C151C211yesmaximal, characteristic, complemented
9#1439×C151C211yesmaximal, characteristic, complemented
10#1438×C151C211yesmaximal, characteristic, complemented
11#1437×C151C212yesmaximal, complemented
12C23×D4×C151C2212yes—
13C23×D4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2212yes—
16C22×C4⋊C4×C151C2212yes—
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2211yescharacteristic
20C22×C22⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2212yes—
25C22×C22⋊C4×C151C2212yes—
26C22×C22⋊C4×C151C2211yescharacteristic
27C22×C42×C151C2212yes—
28C22×C42×C151C2211yescharacteristic
29#396×C151—28no—
30#394×C151—28no—
31#392×C151—24no—
32#390×C151—28no—
33#390×C151—24no—
34#388×C151—24no—
35C4×C4⋊C4×C151—24no—
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2211yescharacteristic
40C2×#95×C151C2211yescharacteristic
41C2×#95×C151C2211yescharacteristic
42C25×C151C2311yescharacteristic
43C25×C151C2312yes—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—24no—
47C22×D4×C151—24no—
48C22×D4×C151—24no—
49C22×D4×C151—22no—
50C22×D4×C151—24no—
51C22×D4×C151—24no—
52C22×D4×C151—24no—
53C22×D4×C151—42no—
54C22×D4×C151—42no—
55C22×D4×C151—42no—
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C23×C4×C151C2312yes—
59C23×C4×C151C2312yes—
60C23×C4×C151C2311yescharacteristic
61C23×C4×C151C2311yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C23×C4×C151C2312yes—
64C23×C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151—24no—
66C2×C4⋊C4×C151—24no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—24no—
71C2×C4⋊C4×C151—24no—
72C2×C4⋊C4×C151—42no—
73C2×C4⋊C4×C151—42no—
74C2×C4⋊C4×C151D418yescomplemented
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—24no—
82C2×C22⋊C4×C151—24no—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—24no—
85C2×C22⋊C4×C151—24no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—24no—
88C2×C22⋊C4×C151—24no—
89C2×C22⋊C4×C151—24no—
90C2×C22⋊C4×C151—24no—
91C2×C22⋊C4×C151—24no—
92C2×C22⋊C4×C151—22no—
93C2×C22⋊C4×C151—24no—
94C2×C22⋊C4×C151—24no—
95C2×C22⋊C4×C151—24no—
96C2×C22⋊C4×C151—24no—
97C2×C22⋊C4×C151—42no—
98C2×C22⋊C4×C151—42no—
99C2×C22⋊C4×C151—42no—
100C2×C22⋊C4×C151D414yescomplemented
101C2×C42×C151—22no—
102C2×C42×C151—22no—
103C2×C42×C151—24no—
104C2×C42×C151—24no—
105C2×C42×C151—42no—
106C2×C42×C151D414yescomplemented
107#95×C151—22no—
108#95×C151—22no—
109#95×C151—22no—
110#95×C151—24no—
111#95×C151—24no—
112#95×C151D414yes—
113C24×C151—21no—
114C24×C151—22no—
115C24×C151—22no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—22no—
119C24×C151—21no—
120C24×C151—22no—
121C24×C151—21no—
122C24×C151—22no—
123C24×C151—22no—
124C24×C151—21no—
125C24×C151—22no—
126C24×C151—22no—
127C24×C151—22no—
128C24×C151—22no—
129C24×C151—22no—
130C24×C151—22no—
131C24×C151—22no—
132C24×C151—22no—
133C24×C151—21no—
134C24×C151—22no—
135C24×C151—21no—
136C24×C151—22no—
137C24×C151C2×D412yes—
138C24×C151#4114yes—
139C24×C151C2411yescharacteristic
140C2×D4×C151—28no—
141C2×D4×C151—216no—
142C2×D4×C151—48no—
143C2×D4×C151—48no—
144C2×D4×C151—48no—
145C2×D4×C151—48no—
146C2×D4×C151—48no—
147C2×D4×C151—48no—
148C2×D4×C151—44no—
149C2×D4×C151—48no—
150C2×D4×C151—44no—
151C2×D4×C151—48no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—21no—
165C22×C4×C151—22no—
166C22×C4×C151—21no—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—21no—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—21no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—21no—
179C22×C4×C151—22no—
180C22×C4×C151—22no—
181C22×C4×C151—21no—
182C22×C4×C151—22no—
183C22×C4×C151—22no—
184C22×C4×C151—22no—
185C22×C4×C151—21no—
186C22×C4×C151—22no—
187C22×C4×C151—22no—
188C22×C4×C151—21no—
189C22×C4×C151—22no—
190C22×C4×C151—22no—
191C22×C4×C151—21no—
192C22×C4×C151C2×D414yes—
193C22×C4×C151C2×D412yes—
194C22×C4×C151C2×D412yes—
195C22×C4×C151C2×D412yes—
196C22×C4×C151C2×D412yes—
197C22×C4×C151C2×D414yes—
198C22×C4×C151C2×D414yes—
199C22×C4×C151C2×D412yes—
200C22×C4×C151C2×D412yes—
201C22×C4×C151C2×D414yes—
202C22×C4×C151#4112yes—
203C22×C4×C151#4112yes—
204C22×C4×C151#4114yes—
205C4⋊C4×C151—216no—
206C4⋊C4×C151—48no—
207C4⋊C4×C151—44no—
208C4⋊C4×C151—44no—
209C22⋊C4×C151—28no—
210C22⋊C4×C151—48no—
211C22⋊C4×C151—48no—
212C22⋊C4×C151—48no—
213C22⋊C4×C151—44no—
214C22⋊C4×C151—48no—
215C22⋊C4×C151—48no—
216C22⋊C4×C151—44no—
217C22⋊C4×C151—48no—
218C42×C151—28no—
219C42×C151—48no—
220C23×C151—22no—
221C23×C151—24no—
222C23×C151—24no—
223C23×C151—24no—
224C23×C151—24no—
225C23×C151—24no—
226C23×C151—22no—
227C23×C151—24no—
228C23×C151—24no—
229C23×C151—22no—
230C23×C151—24no—
231C23×C151—24no—
232C23×C151—42no—
233C23×C151—41no—
234C23×C151—42no—
235C23×C151—42no—
236C23×C151—42no—
237C23×C151—42no—
238C23×C151—41no—
239C23×C151—42no—
240C23×C151—42no—
241C23×C151—42no—
242C23×C151—42no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—42no—
246C23×C151—42no—
247C23×C151—42no—
248C23×C151—42no—
249C23×C151—41no—
250C23×C151—42no—
251C23×C151—41no—
252C23×C151—42no—
253C23×C151—42no—
254C23×C151—42no—
255C23×C151—42no—
256C23×C151—42no—
257C23×C151—42no—
258C23×C151—42no—
259C23×C151—42no—
260C23×C151—42no—
261C23×C151—42no—
262C23×C151—42no—
263C23×C151—42no—
264C23×C151—42no—
265C23×C151—42no—
266C23×C151—42no—
267C23×C151—41no—
268C23×C151—42no—
269C23×C151—42no—
270C23×C151—42no—
271C23×C151—42no—
272C23×C151—42no—
273C23×C151—42no—
274C23×C151—42no—
275C23×C151—42no—
276C23×C151—41no—
277C23×C151—42no—
278C23×C151C22×D411yescharacteristic
279C23×C151C22×D411yescharacteristic
280C23×C151C22×D411yescharacteristic
281C23×C151C22×D412yes—
282C23×C151C2×#4112yes—
283C23×C151C2×#4111yescharacteristic
284C23×C151C2×#4111yescharacteristic
285C23×C151C2×#4112yes—
286C23×C151H(5,𝔽2)12yes—
287C23×C151H(5,𝔽2)11yescharacteristic
288C23×C1512−1+411yescharacteristic
289D4×C151—416no—
290D4×C151—432no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—24no—
294C2×C4×C151—22no—
295C2×C4×C151—24no—
296C2×C4×C151—22no—
297C2×C4×C151—24no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—24no—
301C2×C4×C151—22no—
302C2×C4×C151—24no—
303C2×C4×C151—24no—
304C2×C4×C151—24no—
305C2×C4×C151—24no—
306C2×C4×C151—24no—
307C2×C4×C151—22no—
308C2×C4×C151—22no—
309C2×C4×C151—24no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—24no—
313C2×C4×C151—24no—
314C2×C4×C151—24no—
315C2×C4×C151—24no—
316C2×C4×C151—42no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—42no—
323C2×C4×C151—41no—
324C2×C4×C151—42no—
325C2×C4×C151—42no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—42no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—42no—
332C2×C4×C151—42no—
333C2×C4×C151—41no—
334C2×C4×C151—42no—
335C2×C4×C151—42no—
336C2×C4×C151—42no—
337C2×C4×C151—42no—
338C2×C4×C151—42no—
339C2×C4×C151—42no—
340C2×C4×C151#12114yes—
341C2×C4×C151#12114yes—
342C2×C4×C151#12118yes—
343C2×C4×C151#12714yes—
344C22×C151—42no—
345C22×C151—44no—
346C22×C151—44no—
347C22×C151—42no—
348C22×C151—44no—
349C22×C151—44no—
350C22×C151—44no—
351C22×C151—44no—
352C22×C151—44no—
353C22×C151—44no—
354C22×C151—42no—
355C22×C151—44no—
356C22×C151—82no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—82no—
360C22×C151—81no—
361C22×C151—82no—
362C22×C151—82no—
363C22×C151—82no—
364C22×C151—82no—
365C22×C151—82no—
366C22×C151—81no—
367C22×C151—82no—
368C22×C151—82no—
369C22×C151—82no—
370C22×C151C2×#12111yescharacteristic
371C22×C151C2×#12112yes—
372C22×C151C2×#12111yescharacteristic
373C22×C151#52511yescharacteristic
374C22×C151#52512yes—
375C22×C151#52912yes—
376C22×C151C2×#12711yescharacteristic
377C22×C151#53211yescharacteristic
378C22×C151#53212yes—
379C22×C151#53511yescharacteristic
380C22×C151#53711yescharacteristic
381C22×C151#53812yes—
382C22×C151#54212yes—
383C22×C151D4211yescharacteristic
384C22×C151D4212yes—
385C22×C151#54612yes—
386C22×C151#54612yes—
387C22×C151#54711yescharacteristic
388C22×C151#54811yescharacteristic
389C22×C151#54812yes—
390C22×C151#55012yes—
391C22×C151#55112yes—
392C22×C151#55311yescharacteristic
393C4×C151—24no—
394C4×C151—24no—
395C4×C151—24no—
396C4×C151—28no—
397C4×C151—44no—
398C4×C151—42no—
399C4×C151—81no—
400C4×C151—81no—
401C4×C151—82no—
402C2×C151—84no—
403C2×C151—82no—
404C2×C151#239211yescharacteristic
405C2×C151#241111yescharacteristic
406C2×C151#241611yescharacteristic
407C2×C151#242412yes—
408C2×C151#242612yes—
409C2×C151#246112yes—
410C2×C151#254011yescharacteristic
411C2×C151#254111yescharacteristic
412C2×C151#255412yes—
413C2×C151#266211yescharacteristic
414C2×C151#285611yescharacteristic
415#14815C15111yesmaximal, characteristic, direct product factor, Sylow
416C151#1481511yescharacteristic, direct product factor, Sylow
417C2×#396C2×C15112yescomplemented
418C2×#394C2×C15112yescomplemented
419C2×#392C2×C15111yescharacteristic
420C2×#390C2×C15111yescharacteristic, complemented
421C2×#390C2×C15112yescomplemented
422C2×#388C2×C15111yescharacteristic, complemented
423C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
424#1444C2×C15111yescharacteristic, complemented
425#1439C2×C15111yescharacteristic, complemented
426#1438C2×C15111yescharacteristic, complemented
427#1437C2×C15112yescomplemented
428C23×D4C22×C15112yes—
429C23×D4C22×C15111yescharacteristic
430C22×C4⋊C4C22×C15111yescharacteristic
431C22×C4⋊C4C22×C15112yes—
432C22×C4⋊C4C22×C15112yes—
433C22×C4⋊C4C22×C15111yescharacteristic
434C22×C22⋊C4C22×C15112yes—
435C22×C22⋊C4C22×C15111yescharacteristic
436C22×C22⋊C4C22×C15111yescharacteristic
437C22×C22⋊C4C22×C15112yes—
438C22×C22⋊C4C22×C15112yes—
439C22×C22⋊C4C22×C15112yes—
440C22×C22⋊C4C22×C15112yes—
441C22×C22⋊C4C22×C15112yes—
442C22×C22⋊C4C22×C15111yescharacteristic
443C22×C42C22×C15112yes—
444C22×C42C22×C15111yescharacteristic
445#396—28no—
446#394—28no—
447#392—24no—
448#390—28no—
449#390—24no—
450#388—24no—
451C4×C4⋊C4—24no—
452C2×#95C22×C15112yes—
453C2×#95C22×C15112yes—
454C2×#95C22×C15111yescharacteristic
455C2×#95C22×C15111yescharacteristic
456C2×#95C22×C15111yescharacteristic
457C2×#95C22×C15111yescharacteristic
458C25C23×C15112yes—
459C25C23×C15111yescharacteristic
460C22×D4—24no—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C23×C4C23×C15112yes—
473C23×C4C23×C15111yescharacteristic
474C23×C4C23×C15111yescharacteristic
475C23×C4C23×C15111yescharacteristic
476C23×C4C23×C15112yes—
477C23×C4C23×C15111yescharacteristic
478C23×C4C23×C15112yes—
479C23×C4C23×C15111yescharacteristic
480C23×C4C23×C15111yescharacteristic
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4D4×C15118yescomplemented
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4D4×C15114yescomplemented
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—24no—
520C2×C42—24no—
521C2×C42—42no—
522C2×C42D4×C15114yescomplemented
523#95—22no—
524#95—22no—
525#95—22no—
526#95—24no—
527#95—24no—
528#95D4×C15114yes—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—22no—
551C24—21no—
552C24—22no—
553C24C2×D4×C15112yes—
554C24#41×C15114yes—
555C24C24×C15111yescharacteristic
556C2×D4—216no—
557C2×D4—28no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—48no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4C2×D4×C15114yes—
609C22×C4C2×D4×C15112yes—
610C22×C4C2×D4×C15112yes—
611C22×C4C2×D4×C15112yes—
612C22×C4C2×D4×C15112yes—
613C22×C4C2×D4×C15114yes—
614C22×C4C2×D4×C15114yes—
615C22×C4C2×D4×C15112yes—
616C22×C4C2×D4×C15112yes—
617C22×C4C2×D4×C15114yes—
618C22×C4#41×C15112yes—
619C22×C4#41×C15112yes—
620C22×C4#41×C15114yes—
621C4⋊C4—216no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C22⋊C4—28no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C42—28no—
635C42—48no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—42no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23C22×D4×C15111yescharacteristic
695C23C22×D4×C15111yescharacteristic
696C23C22×D4×C15111yescharacteristic
697C23C22×D4×C15112yes—
698C23C2×#41×C15112yes—
699C23C2×#41×C15111yescharacteristic
700C23C2×#41×C15111yescharacteristic
701C23C2×#41×C15112yes—
702C23H(5,𝔽2)×C15112yes—
703C23H(5,𝔽2)×C15111yescharacteristic
704C232−1+4×C15111yescharacteristic
705D4—416no—
706D4—432no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4#121×C15114yes—
757C2×C4#121×C15114yes—
758C2×C4#121×C15118yes—
759C2×C4#127×C15114yes—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—81no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22C2×#121×C15111yescharacteristic
787C22C2×#121×C15112yes—
788C22C2×#121×C15111yescharacteristic
789C22#525×C15111yescharacteristic
790C22#525×C15112yes—
791C22#529×C15112yes—
792C22C2×#127×C15111yescharacteristic
793C22#532×C15111yescharacteristic
794C22#532×C15112yes—
795C22#535×C15111yescharacteristic
796C22#537×C15111yescharacteristic
797C22#538×C15112yes—
798C22#542×C15112yes—
799C22D42×C15111yescharacteristic
800C22D42×C15112yes—
801C22#546×C15112yes—
802C22#546×C15112yes—
803C22#547×C15111yescharacteristic
804C22#548×C15111yescharacteristic
805C22#548×C15112yes—
806C22#550×C15112yes—
807C22#551×C15112yes—
808C22#553×C15111yescharacteristic
809C4—24no—
810C4—24no—
811C4—24no—
812C4—28no—
813C4—44no—
814C4—42no—
815C4—81no—
816C4—81no—
817C4—82no—
818C2—84no—
819C2—82no—
820C2#2392×C15111yescharacteristic
821C2#2411×C15111yescharacteristic
822C2#2416×C15111yescharacteristic
823C2#2424×C15112yes—
824C2#2426×C15112yes—
825C2#2461×C15112yes—
826C2#2540×C15111yescharacteristic
827C2#2541×C15111yescharacteristic
828C2#2554×C15112yes—
829C2#2662×C15111yescharacteristic
830C2#2856×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC2×#392×C151C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#396×C151C2semidirect
2. C2×#394×C151C2semidirect
4. C2×#390×C151C2semidirect
5. C2×#390×C151C2semidirect
6. C2×#388×C151C2semidirect
7. C2×C4×C4⋊C4×C151C2semidirect
8. #1444×C151C2semidirect
9. #1439×C151C2semidirect
10. #1438×C151C2semidirect
11. #1437×C151C2semidirect
74. C2×C4⋊C4×C151D4semidirect
100. C2×C22⋊C4×C151D4semidirect
106. C2×C42×C151D4semidirect
415. #14815C151direct (N × H)
416. C151#14815direct (N × H)
417. C2×#396C2×C151semidirect
418. C2×#394C2×C151semidirect
420. C2×#390C2×C151semidirect
421. C2×#390C2×C151semidirect
422. C2×#388C2×C151semidirect
423. C2×C4×C4⋊C4C2×C151semidirect
424. #1444C2×C151semidirect
425. #1439C2×C151semidirect
426. #1438C2×C151semidirect
427. #1437C2×C151semidirect
490. C2×C4⋊C4D4×C151semidirect
516. C2×C22⋊C4D4×C151semidirect
522. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1512
C2×#394×C1512
C2×#392×C1512
C2×#390×C1512
C2×#388×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#14815151