Finite Group Databasebeta

← C151×#24034 #50328959

Subgroups — C151×#24034 #50328959

Order 38656.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2C2×#482×C151C211yesmaximal, characteristic, complemented
3C2×#416×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic, complemented
5#2041×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1865×C151C211yesmaximal, characteristic, complemented
12#1863×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19#550×C151—24no—
20#550×C151—24no—
21C2×#127×C151—21no—
22C2×#127×C151C2211yescharacteristic
23C2×#121×C151—21no—
24C2×#121×C151—21no—
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×D4×C151—21no—
29C2×C4×D4×C151C2211yescharacteristic
30C2×#117×C151C2211yescharacteristic
31#482×C151—24no—
32C2×#107×C151C2211yescharacteristic
33C2×#106×C151C2211yescharacteristic
34#416×C151—24no—
35C2×#103×C151C2211yescharacteristic
36C2×#103×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
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
50#397×C151—21no—
51#394×C151—21no—
52#389×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#388×C151—21no—
55#387×C151—21no—
56#380×C151C2211yescharacteristic
57#380×C151C2211yescharacteristic
58#380×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—41no—
71C2×#41×C151—41no—
72C2×#41×C151—41no—
73C2×#41×C151—41no—
74C2×#41×C151D414yes—
75C22×Q8×C151C2311yescharacteristic
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151D411yescharacteristic
83C22×D4×C151C2311yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C22×C8×C151—22no—
90C22×C8×C151—41no—
91C22×C8×C151—41no—
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C22×C8×C151C2311yescharacteristic
95C22×C8×C151C2311yescharacteristic
96#127×C151—28no—
97#127×C151—22no—
98#127×C151—22no—
99#121×C151—28no—
100#121×C151—28no—
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151D414yes—
105C4×Q8×C151—22no—
106C4×Q8×C151—22no—
107C4×D4×C151—28no—
108C4×D4×C151—22no—
109C4×D4×C151—22no—
110#117×C151—22no—
111#117×C151—22no—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151D411yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151D411yescharacteristic
128C2×C22⋊C4×C151D411yescharacteristic
129C2×C42×C151—21no—
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#106×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—22no—
137#103×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—
144#102×C151—41no—
145#102×C151—41no—
146C22⋊C8×C151—22no—
147C22⋊C8×C151—41no—
148C22⋊C8×C151—41no—
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—21no—
156C24×C151C2×D411yescharacteristic
157C24×C151C2×D411yescharacteristic
158#41×C151—28no—
159#41×C151—44no—
160#41×C151—44no—
161#41×C151—44no—
162#41×C151—44no—
163#41×C151—44no—
164#41×C151—44no—
165#41×C151—44no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151—21no—
169C2×Q8×C151C2×D412yes—
170C2×Q8×C151#4112yes—
171C2×Q8×C151#4112yes—
172C2×D4×C151—24no—
173C2×D4×C151—24no—
174C2×D4×C151—22no—
175C2×D4×C151—24no—
176C2×D4×C151—24no—
177C2×D4×C151—24no—
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—21no—
189C2×D4×C151—21no—
190C2×D4×C151—41no—
191C2×D4×C151—42no—
192C2×D4×C151—42no—
193C2×D4×C151—42no—
194C2×D4×C151—42no—
195C2×D4×C151—42no—
196C2×D4×C151—42no—
197C2×D4×C151—81no—
198C2×D4×C151—81no—
199C2×D4×C151—81no—
200C2×D4×C151—81no—
201C2×D4×C151—81no—
202C2×D4×C151—81no—
203C2×D4×C151C2×D412yes—
204C2×D4×C151C2×D412yes—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—24no—
211C22×C4×C151—21no—
212C22×C4×C151—24no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
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—42no—
226C22×C4×C151—42no—
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D412yes—
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2411yescharacteristic
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—
244C2×C8×C151—21no—
245C2×C8×C151—21no—
246C2×C8×C151—44no—
247C4⋊C4×C151—24no—
248C4⋊C4×C151—22no—
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—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—42no—
259C4⋊C4×C151—81no—
260C4⋊C4×C151C2×D412yes—
261C22⋊C4×C151—24no—
262C22⋊C4×C151—22no—
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—24no—
270C42×C151—21no—
271C42×C151—21no—
272C42×C151—42no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—22no—
280C23×C151—22no—
281C23×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—41no—
289C23×C151—41no—
290C23×C151—41no—
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#12012yes—
301C23×C151C22×D411yescharacteristic
302Q8×C151—22no—
303Q8×C151—22no—
304Q8×C151—22no—
305Q8×C151#12314yes—
306D4×C151—22no—
307D4×C151—22no—
308D4×C151—22no—
309D4×C151—22no—
310D4×C151—48no—
311D4×C151—44no—
312D4×C151—48no—
313D4×C151—48no—
314D4×C151—41no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151—41no—
318D4×C151—84no—
319D4×C151—84no—
320D4×C151—84no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—22no—
324C2×C4×C151—22no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—22no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—48no—
340C2×C4×C151—48no—
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#12012yes—
360C2×C4×C151#13512yes—
361C2×C4×C151C22×D411yescharacteristic
362C2×C4×C151C22×D411yescharacteristic
363C2×C4×C151C2×#4111yescharacteristic
364C2×C4×C151C2×#4111yescharacteristic
365C2×C4×C151H(5,𝔽2)11yescharacteristic
366C2×C4×C151H(5,𝔽2)11yescharacteristic
367C8×C151—41no—
368C8×C151—41no—
369C8×C151—41no—
370C8×C151—41no—
371C22×C151—22no—
372C22×C151—22no—
373C22×C151—22no—
374C22×C151—41no—
375C22×C151—41no—
376C22×C151—41no—
377C22×C151—41no—
378C22×C151—42no—
379C22×C151—42no—
380C22×C151—41no—
381C22×C151—41no—
382C22×C151—42no—
383C22×C151—42no—
384C22×C151—41no—
385C22×C151—42no—
386C22×C151—42no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—81no—
392C22×C151—81no—
393C22×C151—81no—
394C22×C151—81no—
395C22×C151—81no—
396C22×C151—81no—
397C22×C151—81no—
398C22×C151—81no—
399C22×C151C2×#12011yescharacteristic
400C22×C151#54611yescharacteristic
401C22×C151#54611yescharacteristic
402C22×C151C2×#13511yescharacteristic
403C22×C151#57511yescharacteristic
404C22×C151#57611yescharacteristic
405C22×C151#57711yescharacteristic
406C4×C151—22no—
407C4×C151—24no—
408C4×C151—22no—
409C4×C151—41no—
410C4×C151—41no—
411C4×C151—42no—
412C4×C151—81no—
413C4×C151—81no—
414C4×C151—81no—
415C4×C151—81no—
416C4×C151C2×#12311yescharacteristic
417C4×C151#53411yescharacteristic
418C4×C151#54611yescharacteristic
419C4×C151#54611yescharacteristic
420C2×C151—42no—
421C2×C151—81no—
422C2×C151—82no—
423C2×C151—82no—
424C2×C151#240511yescharacteristic
425C2×C151#300211yescharacteristic
426C2×C151#301211yescharacteristic
427C2×C151#330411yescharacteristic
428C2×C151#330511yescharacteristic
429C2×C151#330911yescharacteristic
430C2×C151#331711yescharacteristic
431#24034C15111yesmaximal, characteristic, direct product factor, Sylow
432C151#2403411yescharacteristic, direct product factor, Sylow
433C2×#550C2×C15111yescharacteristic
434C2×#482C2×C15111yescharacteristic, complemented
435C2×#416C2×C15111yescharacteristic, complemented
436#2485C2×C15111yescharacteristic, complemented
437#2041C2×C15111yescharacteristic, complemented
438#2041C2×C15111yescharacteristic, complemented
439#2034C2×C15111yescharacteristic, complemented
440#2033C2×C15111yescharacteristic, complemented
441#1893C2×C15111yescharacteristic, complemented
442#1869C2×C15111yescharacteristic, complemented
443#1865C2×C15111yescharacteristic, complemented
444#1863C2×C15111yescharacteristic, complemented
445#1788C2×C15111yescharacteristic, complemented
446#1788C2×C15111yescharacteristic, complemented
447#1788C2×C15111yescharacteristic, complemented
448C22×#41C22×C15111yescharacteristic
449C22×#41C22×C15111yescharacteristic
450C23×C8C22×C15111yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C15111yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C15111yescharacteristic
458C2×#121C22×C15111yescharacteristic
459C2×C4×Q8C22×C15111yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C15111yescharacteristic
462C2×#117C22×C15111yescharacteristic
463#482—24no—
464C2×#107C22×C15111yescharacteristic
465C2×#106C22×C15111yescharacteristic
466#416—24no—
467C2×#103C22×C15111yescharacteristic
468C2×#103C22×C15111yescharacteristic
469C2×#103C22×C15111yescharacteristic
470C2×#103C22×C15111yescharacteristic
471C2×#102C22×C15111yescharacteristic
472C2×#102C22×C15111yescharacteristic
473C2×#102C22×C15111yescharacteristic
474C2×#102C22×C15111yescharacteristic
475C2×#102C22×C15111yescharacteristic
476C2×#102C22×C15111yescharacteristic
477C2×#102C22×C15111yescharacteristic
478C2×#102C22×C15111yescharacteristic
479C2×C22⋊C8C22×C15111yescharacteristic
480C2×C22⋊C8C22×C15111yescharacteristic
481C2×C22⋊C8C22×C15111yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C15111yescharacteristic
485#389C22×C15111yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C15111yescharacteristic
489#380C22×C15111yescharacteristic
490#380C22×C15111yescharacteristic
491#340C22×C15111yescharacteristic
492#340C22×C15111yescharacteristic
493#336C22×C15111yescharacteristic
494#336C22×C15111yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C15114yes—
507C22×Q8C23×C15111yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C15111yescharacteristic
515C22×D4C23×C15111yescharacteristic
516C22×D4C23×C15111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C15111yescharacteristic
520C23×C4C23×C15111yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C15111yescharacteristic
525C22×C8C23×C15111yescharacteristic
526C22×C8C23×C15111yescharacteristic
527C22×C8C23×C15111yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C15114yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C15111yescharacteristic
548C2×C4⋊C4C23×C15111yescharacteristic
549C2×C4⋊C4C23×C15111yescharacteristic
550C2×C4⋊C4C23×C15111yescharacteristic
551C2×C4⋊C4C23×C15111yescharacteristic
552C2×C4⋊C4C23×C15111yescharacteristic
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⋊C4D4×C15111yescharacteristic
560C2×C22⋊C4D4×C15111yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C15111yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C15111yescharacteristic
589C24C2×D4×C15111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C15112yes—
602C2×Q8#41×C15112yes—
603C2×Q8#41×C15112yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C15112yes—
636C2×D4C2×D4×C15112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
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—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C15111yescharacteristic
660C22×C4C2×D4×C15111yescharacteristic
661C22×C4C2×D4×C15111yescharacteristic
662C22×C4C2×D4×C15112yes—
663C22×C4C2×D4×C15112yes—
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C24×C15111yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
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—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
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—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C15112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C15112yes—
733C23C22×D4×C15111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C15114yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
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#120×C15112yes—
792C2×C4#135×C15112yes—
793C2×C4C22×D4×C15111yescharacteristic
794C2×C4C22×D4×C15111yescharacteristic
795C2×C4C2×#41×C15111yescharacteristic
796C2×C4C2×#41×C15111yescharacteristic
797C2×C4H(5,𝔽2)×C15111yescharacteristic
798C2×C4H(5,𝔽2)×C15111yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C15111yescharacteristic
832C22#546×C15111yescharacteristic
833C22#546×C15111yescharacteristic
834C22C2×#135×C15111yescharacteristic
835C22#575×C15111yescharacteristic
836C22#576×C15111yescharacteristic
837C22#577×C15111yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C15111yescharacteristic
849C4#534×C15111yescharacteristic
850C4#546×C15111yescharacteristic
851C4#546×C15111yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2#2405×C15111yescharacteristic
857C2#3002×C15111yescharacteristic
858C2#3012×C15111yescharacteristic
859C2#3304×C15111yescharacteristic
860C2#3305×C15111yescharacteristic
861C2#3309×C15111yescharacteristic
862C2#3317×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#550×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×#482×C151C2semidirect
3. C2×#416×C151C2semidirect
4. #2485×C151C2semidirect
5. #2041×C151C2semidirect
6. #2041×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1893×C151C2semidirect
10. #1869×C151C2semidirect
11. #1865×C151C2semidirect
12. #1863×C151C2semidirect
13. #1788×C151C2semidirect
14. #1788×C151C2semidirect
15. #1788×C151C2semidirect
431. #24034C151direct (N × H)
432. C151#24034direct (N × H)
434. C2×#482C2×C151semidirect
435. C2×#416C2×C151semidirect
436. #2485C2×C151semidirect
437. #2041C2×C151semidirect
438. #2041C2×C151semidirect
439. #2034C2×C151semidirect
440. #2033C2×C151semidirect
441. #1893C2×C151semidirect
442. #1869C2×C151semidirect
443. #1865C2×C151semidirect
444. #1863C2×C151semidirect
445. #1788C2×C151semidirect
446. #1788C2×C151semidirect
447. #1788C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#482×C1512
C2×#416×C1512
#2485×C1512
#2041×C1512
#2034×C1512
#2033×C1512
#1893×C1512
#1869×C1512
#1865×C1512
#1863×C1512
#1788×C1512
#24034151