Finite Group Databasebeta

← C151×#25890 #50330815

Subgroups — C151×#25890 #50330815

Order 38656.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#488×C151C211yesmaximal, characteristic, complemented
3C2×#478×C151C211yesmaximal, characteristic, complemented
4#2562×C151C211yesmaximal, characteristic, complemented
5#2036×C151C211yesmaximal, characteristic, complemented
6#2035×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1983×C151C211yesmaximal, characteristic, complemented
10#1954×C151C211yesmaximal, characteristic, complemented
11#1788×C151C211yesmaximal, characteristic, complemented
12#1788×C151C211yesmaximal, characteristic, complemented
13#1786×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15C4×#102×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18#546×C151—24no—
19#546×C151—24no—
20C2×#125×C151C2211yescharacteristic, complemented
21C2×#124×C151C2211yescharacteristic
22C2×#123×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×#121×C151—21no—
25C2×#121×C151C2211yescharacteristic
26C2×#120×C151—21no—
27C2×C4×D4×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29C22×C22⋊C4×C151—21no—
30#488×C151—24no—
31#478×C151—24no—
32C2×#107×C151C2211yescharacteristic, complemented
33C2×#106×C151C2211yescharacteristic, complemented
34C2×C4⋊C8×C151C2211yescharacteristic, complemented
35C2×#103×C151C2211yescharacteristic, complemented
36C2×#103×C151C2211yescharacteristic, complemented
37C2×#103×C151C2211yescharacteristic, complemented
38C2×#103×C151C2211yescharacteristic, complemented
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C22⋊C8×C151C2211yescharacteristic, complemented
50C2×C22⋊C8×C151C2211yescharacteristic, complemented
51C2×C4×C8×C151C2211yescharacteristic, complemented
52#400×C151—21no—
53#394×C151—21no—
54#388×C151—21no—
55#388×C151—21no—
56#380×C151C2211yescharacteristic
57#380×C151C2211yescharacteristic
58#380×C151C2211yescharacteristic, complemented
59#380×C151C2211yescharacteristic, complemented
60C4×C4⋊C4×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63C25×C151—21no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C22×Q8×C151C2311yescharacteristic
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151D411yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C23×C4×C151—21no—
84C23×C4×C151—21no—
85C23×C4×C151C2311yescharacteristic
86C23×C4×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91#125×C151—22no—
92#125×C151—22no—
93#124×C151—22no—
94#124×C151D414yes—
95#123×C151—28no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—22no—
98#121×C151—28no—
99#121×C151—22no—
100#121×C151—22no—
101#120×C151—28no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151D414yes—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C22⋊C4×C151—28no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151D411yescharacteristic
126C2×C22⋊C4×C151D411yescharacteristic
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#106×C151—22no—
131C4⋊C8×C151—22no—
132#103×C151—22no—
133#103×C151—22no—
134#103×C151—41no—
135#103×C151—41no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—41no—
143#102×C151—41no—
144C22⋊C8×C151—41no—
145C22⋊C8×C151—41no—
146C22⋊C8×C151—41no—
147C22⋊C8×C151—41no—
148C4×C8×C151—22no—
149#95×C151—21no—
150#95×C151—21no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151—24no—
156C24×C151—21no—
157C24×C151—42no—
158C24×C151—42no—
159C24×C151—42no—
160C24×C151—42no—
161C24×C151—81no—
162C24×C151—81no—
163C24×C151C2×D411yescharacteristic
164C24×C151C2×D411yescharacteristic
165#41×C151—44no—
166#41×C151—44no—
167#41×C151—44no—
168#41×C151—44no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151C2×D412yes—
175C2×D4×C151—24no—
176C2×D4×C151—24no—
177C2×D4×C151—22no—
178C2×D4×C151—24no—
179C2×D4×C151—22no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—41no—
189C2×D4×C151—42no—
190C2×D4×C151—42no—
191C2×D4×C151—44no—
192C2×D4×C151—44no—
193C2×D4×C151—44no—
194C2×D4×C151—42no—
195C2×D4×C151—42no—
196C2×D4×C151—44no—
197C2×D4×C151—81no—
198C2×D4×C151—81no—
199C2×D4×C151C2×D412yes—
200C2×D4×C151C2×D412yes—
201C2×D4×C151#4112yes—
202C2×D4×C151#4112yes—
203C22×C4×C151—24no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—24no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—42no—
224C22×C4×C151—42no—
225C22×C4×C151—81no—
226C22×C4×C151—81no—
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2411yescharacteristic
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C4⋊C4×C151—24no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151—42no—
256C4⋊C4×C151—42no—
257C4⋊C4×C151C2×D412yes—
258C22⋊C4×C151—24no—
259C22⋊C4×C151—24no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—24no—
262C22⋊C4×C151—24no—
263C22⋊C4×C151—24no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—42no—
266C22⋊C4×C151—42no—
267C22⋊C4×C151—81no—
268C22⋊C4×C151—81no—
269C42×C151—81no—
270C42×C151C2×D412yes—
271C42×C151C2×D412yes—
272C23×C151—21no—
273C23×C151—22no—
274C23×C151—22no—
275C23×C151—22no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—22no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—48no—
290C23×C151—48no—
291C23×C151—41no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—84no—
302C23×C151—84no—
303C23×C151—84no—
304C23×C151—84no—
305C23×C151—84no—
306C23×C151#13512yes—
307C23×C151C22×D411yescharacteristic
308Q8×C151—22no—
309Q8×C151—22no—
310Q8×C151—41no—
311Q8×C151—41no—
312D4×C151—22no—
313D4×C151—22no—
314D4×C151—22no—
315D4×C151—22no—
316D4×C151—22no—
317D4×C151—44no—
318D4×C151—48no—
319D4×C151—48no—
320D4×C151—41no—
321D4×C151—41no—
322D4×C151—84no—
323D4×C151#12414yes—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—48no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—84no—
362C2×C4×C151#12012yes—
363C2×C4×C151#12012yes—
364C2×C4×C151C22×D411yescharacteristic
365C2×C4×C151C22×D411yescharacteristic
366C2×C4×C151C2×#4111yescharacteristic
367C2×C4×C151C2×#4111yescharacteristic
368C2×C4×C151H(5,𝔽2)11yescharacteristic
369C2×C4×C151H(5,𝔽2)11yescharacteristic
370C8×C151—41no—
371C8×C151—41no—
372C8×C151—41no—
373C8×C151—41no—
374C22×C151—24no—
375C22×C151—22no—
376C22×C151—22no—
377C22×C151—22no—
378C22×C151—41no—
379C22×C151—42no—
380C22×C151—42no—
381C22×C151—41no—
382C22×C151—42no—
383C22×C151—42no—
384C22×C151—41no—
385C22×C151—42no—
386C22×C151—41no—
387C22×C151—42no—
388C22×C151—41no—
389C22×C151—42no—
390C22×C151—41no—
391C22×C151—42no—
392C22×C151—41no—
393C22×C151—42no—
394C22×C151—41no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—41no—
398C22×C151—816no—
399C22×C151—81no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151C2×#12011yescharacteristic
404C22×C151#54611yescharacteristic
405C22×C151#54611yescharacteristic
406C22×C151C2×#13511yescharacteristic
407C22×C151#57511yescharacteristic
408C22×C151#57611yescharacteristic
409C22×C151#57711yescharacteristic
410C4×C151—22no—
411C4×C151—22no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—42no—
415C4×C151—42no—
416C4×C151—81no—
417C4×C151—81no—
418C4×C151—81no—
419C4×C151—81no—
420C4×C151C2×#12411yescharacteristic
421C4×C151#53511yescharacteristic
422C4×C151#54611yescharacteristic
423C4×C151#54611yescharacteristic
424C2×C151—42no—
425C2×C151—44no—
426C2×C151—81no—
427C2×C151—82no—
428C2×C151#243511yescharacteristic
429C2×C151#300211yescharacteristic
430C2×C151#301211yescharacteristic
431C2×C151#329611yescharacteristic
432C2×C151#329711yescharacteristic
433C2×C151#332211yescharacteristic
434C2×C151#332311yescharacteristic
435#25890C15111yesmaximal, characteristic, direct product factor, Sylow
436C151#2589011yescharacteristic, direct product factor, Sylow
437C2×#546C2×C15111yescharacteristic
438C2×#488C2×C15111yescharacteristic, complemented
439C2×#478C2×C15111yescharacteristic, complemented
440#2562C2×C15111yescharacteristic, complemented
441#2036C2×C15111yescharacteristic, complemented
442#2035C2×C15111yescharacteristic, complemented
443#2034C2×C15111yescharacteristic, complemented
444#2033C2×C15111yescharacteristic, complemented
445#1983C2×C15111yescharacteristic, complemented
446#1954C2×C15111yescharacteristic, complemented
447#1788C2×C15111yescharacteristic, complemented
448#1788C2×C15111yescharacteristic, complemented
449#1786C2×C15111yescharacteristic, complemented
450#1786C2×C15111yescharacteristic, complemented
451C4×#102C2×C15111yescharacteristic, complemented
452C22×#41C22×C15111yescharacteristic
453C23×D4C22×C15111yescharacteristic
454#546—24no—
455#546—24no—
456C2×#125C22×C15111yescharacteristic, complemented
457C2×#124C22×C15111yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C15111yescharacteristic
460C2×#121—21no—
461C2×#121C22×C15111yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C15111yescharacteristic
464C2×C4×D4C22×C15111yescharacteristic
465C22×C22⋊C4—21no—
466#488—24no—
467#478—24no—
468C2×#107C22×C15111yescharacteristic, complemented
469C2×#106C22×C15111yescharacteristic, complemented
470C2×C4⋊C8C22×C15111yescharacteristic, complemented
471C2×#103C22×C15111yescharacteristic, complemented
472C2×#103C22×C15111yescharacteristic, complemented
473C2×#103C22×C15111yescharacteristic, complemented
474C2×#103C22×C15111yescharacteristic, complemented
475C2×#102C22×C15111yescharacteristic
476C2×#102C22×C15111yescharacteristic
477C2×#102C22×C15111yescharacteristic
478C2×#102C22×C15111yescharacteristic
479C2×#102C22×C15111yescharacteristic
480C2×#102C22×C15111yescharacteristic
481C2×#102C22×C15111yescharacteristic
482C2×#102C22×C15111yescharacteristic
483C2×C22⋊C8C22×C15111yescharacteristic
484C2×C22⋊C8C22×C15111yescharacteristic
485C2×C22⋊C8C22×C15111yescharacteristic, complemented
486C2×C22⋊C8C22×C15111yescharacteristic, complemented
487C2×C4×C8C22×C15111yescharacteristic, complemented
488#400—21no—
489#394—21no—
490#388—21no—
491#388—21no—
492#380C22×C15111yescharacteristic
493#380C22×C15111yescharacteristic
494#380C22×C15111yescharacteristic, complemented
495#380C22×C15111yescharacteristic, complemented
496C4×C4⋊C4C22×C15111yescharacteristic, complemented
497#340C22×C15111yescharacteristic, complemented
498#340C22×C15111yescharacteristic, complemented
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C15111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C15111yescharacteristic
517C22×D4C23×C15111yescharacteristic
518C22×D4C23×C15111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C15111yescharacteristic
522C23×C4C23×C15111yescharacteristic
523C22×C8C23×C15111yescharacteristic
524C22×C8C23×C15111yescharacteristic
525C22×C8C23×C15111yescharacteristic
526C22×C8C23×C15111yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C15114yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C15114yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C15111yescharacteristic
546C2×C4⋊C4C23×C15111yescharacteristic
547C2×C4⋊C4C23×C15111yescharacteristic
548C2×C4⋊C4C23×C15111yescharacteristic
549C2×C4⋊C4C23×C15111yescharacteristic
550C2×C4⋊C4C23×C15111yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C15111yescharacteristic
562C2×C22⋊C4D4×C15111yescharacteristic
563C2×C42—21no—
564C2×C42C23×C15111yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C15111yescharacteristic
600C24C2×D4×C15111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C15112yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C15112yes—
636C2×D4C2×D4×C15112yes—
637C2×D4#41×C15112yes—
638C2×D4#41×C15112yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C15111yescharacteristic
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4C2×D4×C15111yescharacteristic
667C22×C4C24×C15111yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C15112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C15112yes—
707C42C2×D4×C15112yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C15112yes—
743C23C22×D4×C15111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C15114yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C15112yes—
799C2×C4#120×C15112yes—
800C2×C4C22×D4×C15111yescharacteristic
801C2×C4C22×D4×C15111yescharacteristic
802C2×C4C2×#41×C15111yescharacteristic
803C2×C4C2×#41×C15111yescharacteristic
804C2×C4H(5,𝔽2)×C15111yescharacteristic
805C2×C4H(5,𝔽2)×C15111yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—24no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C15111yescharacteristic
840C22#546×C15111yescharacteristic
841C22#546×C15111yescharacteristic
842C22C2×#135×C15111yescharacteristic
843C22#575×C15111yescharacteristic
844C22#576×C15111yescharacteristic
845C22#577×C15111yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C15111yescharacteristic
857C4#535×C15111yescharacteristic
858C4#546×C15111yescharacteristic
859C4#546×C15111yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2#2435×C15111yescharacteristic
865C2#3002×C15111yescharacteristic
866C2#3012×C15111yescharacteristic
867C2#3296×C15111yescharacteristic
868C2#3297×C15111yescharacteristic
869C2#3322×C15111yescharacteristic
870C2#3323×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#488×C151C2semidirect
3. C2×#478×C151C2semidirect
4. #2562×C151C2semidirect
5. #2036×C151C2semidirect
6. #2035×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1983×C151C2semidirect
10. #1954×C151C2semidirect
11. #1788×C151C2semidirect
12. #1788×C151C2semidirect
13. #1786×C151C2semidirect
14. #1786×C151C2semidirect
15. C4×#102×C151C2semidirect
20. C2×#125×C151C22semidirect
32. C2×#107×C151C22semidirect
33. C2×#106×C151C22semidirect
34. C2×C4⋊C8×C151C22semidirect
35. C2×#103×C151C22semidirect
36. C2×#103×C151C22semidirect
37. C2×#103×C151C22semidirect
38. C2×#103×C151C22semidirect
49. C2×C22⋊C8×C151C22semidirect
50. C2×C22⋊C8×C151C22semidirect
51. C2×C4×C8×C151C22semidirect
58. #380×C151C22semidirect
59. #380×C151C22semidirect
60. C4×C4⋊C4×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
435. #25890C151direct (N × H)
436. C151#25890direct (N × H)
438. C2×#488C2×C151semidirect
439. C2×#478C2×C151semidirect
440. #2562C2×C151semidirect
441. #2036C2×C151semidirect
442. #2035C2×C151semidirect
443. #2034C2×C151semidirect
444. #2033C2×C151semidirect
445. #1983C2×C151semidirect
446. #1954C2×C151semidirect
447. #1788C2×C151semidirect
448. #1788C2×C151semidirect
449. #1786C2×C151semidirect
450. #1786C2×C151semidirect
451. C4×#102C2×C151semidirect
456. C2×#125C22×C151semidirect
468. C2×#107C22×C151semidirect
469. C2×#106C22×C151semidirect
470. C2×C4⋊C8C22×C151semidirect
471. C2×#103C22×C151semidirect
472. C2×#103C22×C151semidirect
473. C2×#103C22×C151semidirect
474. C2×#103C22×C151semidirect
485. C2×C22⋊C8C22×C151semidirect
486. C2×C22⋊C8C22×C151semidirect
487. C2×C4×C8C22×C151semidirect
494. #380C22×C151semidirect
495. #380C22×C151semidirect
496. C4×C4⋊C4C22×C151semidirect
497. #340C22×C151semidirect
498. #340C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1512
C2×#488×C1512
C2×#478×C1512
#2562×C1512
#2036×C1512
#2035×C1512
#2034×C1512
#2033×C1512
#1983×C1512
#1954×C1512
#1788×C1512
#1786×C1512
C4×#102×C1512
#25890151