Finite Group Databasebeta

← C151×#24017 #50328942

Subgroups — C151×#24017 #50328942

Order 38656.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C151C211yesmaximal, characteristic
2C2×#485×C151C211yesmaximal, characteristic, complemented
3C2×#482×C151C211yesmaximal, characteristic, complemented
4#2311×C151C211yesmaximal, characteristic, complemented
5#2036×C151C211yesmaximal, characteristic, complemented
6#2035×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1874×C151C211yesmaximal, characteristic, complemented
10#1872×C151C211yesmaximal, characteristic, complemented
11#1853×C151C211yesmaximal, characteristic, complemented
12#1852×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1780×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18#537×C151—24no—
19#537×C151—24no—
20C2×C22⋊Q8×C151—21no—
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×#121×C151—21no—
24C2×#121×C151—21no—
25C2×#121×C151—21no—
26C2×#121×C151C2211yescharacteristic
27C2×#121×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C22×C4⋊C4×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#485×C151—24no—
32#482×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C22⋊C8×C151C2211yescharacteristic
50C2×C22⋊C8×C151C2211yescharacteristic
51#391×C151—21no—
52#390×C151—21no—
53#386×C151—21no—
54#386×C151—21no—
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#380×C151C2211yescharacteristic
58#380×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×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—22no—
71C2×#41×C151—41no—
72C2×#41×C151—41no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C22×Q8×C151D411yescharacteristic
76C22×Q8×C151C2311yescharacteristic
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151D411yescharacteristic
81C22×D4×C151D411yescharacteristic
82C22×D4×C151D411yescharacteristic
83C22×D4×C151C2311yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C22⋊Q8×C151—28no—
95C22⋊Q8×C151—22no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151D414yes—
99#121×C151—28no—
100#121×C151—28no—
101#121×C151—28no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—22no—
105#121×C151D414yes—
106#117×C151—22no—
107#117×C151—22no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—22no—
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—41no—
115C2×C4⋊C4×C151—41no—
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C42×C151—21no—
132#107×C151—22no—
133#107×C151—22no—
134#106×C151—22no—
135#106×C151—22no—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—41no—
139#103×C151—41no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—41no—
143#102×C151—41no—
144C22⋊C8×C151—22no—
145C22⋊C8×C151—22no—
146C22⋊C8×C151—22no—
147C22⋊C8×C151—22no—
148C22⋊C8×C151—41no—
149C22⋊C8×C151—41no—
150#95×C151—21no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151C2×D411yescharacteristic
156C24×C151C2×D411yescharacteristic
157C24×C151C2×D411yescharacteristic
158#41×C151—44no—
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—22no—
167C2×Q8×C151—22no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—41no—
174C2×Q8×C151C2×D412yes—
175C2×D4×C151—24no—
176C2×D4×C151—22no—
177C2×D4×C151—22no—
178C2×D4×C151—22no—
179C2×D4×C151—22no—
180C2×D4×C151—24no—
181C2×D4×C151—24no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—41no—
190C2×D4×C151—41no—
191C2×D4×C151—41no—
192C2×D4×C151—42no—
193C2×D4×C151—42no—
194C2×D4×C151—81no—
195C2×D4×C151—81no—
196C2×D4×C151—81no—
197C2×D4×C151—81no—
198C2×D4×C151C2×D412yes—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—24no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—24no—
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—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—42no—
223C22×C4×C151—42no—
224C22×C4×C151—42no—
225C22×C4×C151—81no—
226C22×C4×C151—81no—
227C22×C4×C151—81no—
228C22×C4×C151—81no—
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D412yes—
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151#4112yes—
235C22×C4×C151#4112yes—
236C22×C4×C151C2411yescharacteristic
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—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C4⋊C4×C151—24no—
250C4⋊C4×C151—24no—
251C4⋊C4×C151—24no—
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—21no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—42no—
263C4⋊C4×C151C2×D412yes—
264C4⋊C4×C151C2×D412yes—
265C22⋊C4×C151—24no—
266C22⋊C4×C151—24no—
267C22⋊C4×C151—24no—
268C22⋊C4×C151—24no—
269C22⋊C4×C151—42no—
270C22⋊C4×C151—81no—
271C22⋊C4×C151—81no—
272C22⋊C4×C151—81no—
273C22⋊C4×C151—81no—
274C42×C151—42no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—22no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151#12012yes—
302C23×C151#12312yes—
303C23×C151C22×D411yescharacteristic
304Q8×C151—22no—
305Q8×C151—22no—
306Q8×C151—44no—
307Q8×C151—41no—
308Q8×C151—41no—
309D4×C151—22no—
310D4×C151—22no—
311D4×C151—44no—
312D4×C151—44no—
313D4×C151—44no—
314D4×C151—48no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151—84no—
318D4×C151—84no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—22no—
324C2×C4×C151—22no—
325C2×C4×C151—22no—
326C2×C4×C151—22no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—21no—
332C2×C4×C151—22no—
333C2×C4×C151—22no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—48no—
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—84no—
361C2×C4×C151—84no—
362C2×C4×C151#12012yes—
363C2×C4×C151#12312yes—
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—22no—
375C22×C151—22no—
376C22×C151—22no—
377C22×C151—22no—
378C22×C151—22no—
379C22×C151—22no—
380C22×C151—41no—
381C22×C151—41no—
382C22×C151—41no—
383C22×C151—41no—
384C22×C151—41no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—42no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—42no—
396C22×C151—41no—
397C22×C151—42no—
398C22×C151—81no—
399C22×C151—81no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151C2×#12011yescharacteristic
403C22×C151C2×#12311yescharacteristic
404C22×C151#53411yescharacteristic
405C22×C151#57611yescharacteristic
406C22×C151#57711yescharacteristic
407C22×C151#57711yescharacteristic
408C22×C151#57811yescharacteristic
409C4×C151—22no—
410C4×C151—22no—
411C4×C151—41no—
412C4×C151—42no—
413C4×C151—42no—
414C4×C151—42no—
415C4×C151—81no—
416C4×C151—81no—
417C4×C151—81no—
418C4×C151—81no—
419C4×C151#54611yescharacteristic
420C4×C151#54611yescharacteristic
421C4×C151#54611yescharacteristic
422C4×C151#54611yescharacteristic
423C2×C151—42no—
424C2×C151—42no—
425C2×C151—81no—
426C2×C151—82no—
427C2×C151#240511yescharacteristic
428C2×C151#301211yescharacteristic
429C2×C151#301311yescharacteristic
430C2×C151#309811yescharacteristic
431C2×C151#309911yescharacteristic
432C2×C151#319811yescharacteristic
433C2×C151#320111yescharacteristic
434#24017C15111yesmaximal, characteristic, direct product factor, Sylow
435C151#2401711yescharacteristic, direct product factor, Sylow
436C2×#537C2×C15111yescharacteristic
437C2×#485C2×C15111yescharacteristic, complemented
438C2×#482C2×C15111yescharacteristic, complemented
439#2311C2×C15111yescharacteristic, complemented
440#2036C2×C15111yescharacteristic, complemented
441#2035C2×C15111yescharacteristic, complemented
442#2034C2×C15111yescharacteristic, complemented
443#2033C2×C15111yescharacteristic, complemented
444#1874C2×C15111yescharacteristic, complemented
445#1872C2×C15111yescharacteristic, complemented
446#1853C2×C15111yescharacteristic, complemented
447#1852C2×C15111yescharacteristic, complemented
448#1788C2×C15111yescharacteristic, complemented
449#1788C2×C15111yescharacteristic, complemented
450#1780C2×C15111yescharacteristic, complemented
451C22×#41C22×C15111yescharacteristic
452C22×#41C22×C15111yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C15111yescharacteristic
457C2×C22⋊Q8C22×C15111yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C15111yescharacteristic
462C2×#121C22×C15111yescharacteristic
463C2×#117C22×C15111yescharacteristic
464C22×C4⋊C4C22×C15111yescharacteristic
465C22×C4⋊C4C22×C15111yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C15111yescharacteristic
469C2×#107C22×C15111yescharacteristic
470C2×#106C22×C15111yescharacteristic
471C2×#106C22×C15111yescharacteristic
472C2×#103C22×C15111yescharacteristic
473C2×#103C22×C15111yescharacteristic
474C2×#103C22×C15111yescharacteristic
475C2×#103C22×C15111yescharacteristic
476C2×#102C22×C15111yescharacteristic
477C2×#102C22×C15111yescharacteristic
478C2×#102C22×C15111yescharacteristic
479C2×#102C22×C15111yescharacteristic
480C2×C22⋊C8C22×C15111yescharacteristic
481C2×C22⋊C8C22×C15111yescharacteristic
482C2×C22⋊C8C22×C15111yescharacteristic
483C2×C22⋊C8C22×C15111yescharacteristic
484C2×C22⋊C8C22×C15111yescharacteristic
485C2×C22⋊C8C22×C15111yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C15111yescharacteristic
491#380C22×C15111yescharacteristic
492#380C22×C15111yescharacteristic
493#380C22×C15111yescharacteristic
494#340C22×C15111yescharacteristic
495#340C22×C15111yescharacteristic
496#340C22×C15111yescharacteristic
497#340C22×C15111yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C15111yescharacteristic
511C22×Q8C23×C15111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C15111yescharacteristic
516C22×D4D4×C15111yescharacteristic
517C22×D4D4×C15111yescharacteristic
518C22×D4C23×C15111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C15111yescharacteristic
523C23×C4C23×C15111yescharacteristic
524C23×C4C23×C15111yescharacteristic
525C22×C8C23×C15111yescharacteristic
526C22×C8C23×C15111yescharacteristic
527C22×C8C23×C15111yescharacteristic
528C22×C8C23×C15111yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C15114yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C15114yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C15111yescharacteristic
552C2×C4⋊C4C23×C15111yescharacteristic
553C2×C4⋊C4C23×C15111yescharacteristic
554C2×C4⋊C4C23×C15111yescharacteristic
555C2×C4⋊C4C23×C15111yescharacteristic
556C2×C4⋊C4C23×C15111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C15111yescharacteristic
591C24C2×D4×C15111yescharacteristic
592C24C2×D4×C15111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C15112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C15112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
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—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4C2×D4×C15112yes—
667C22×C4C2×D4×C15112yes—
668C22×C4C2×D4×C15111yescharacteristic
669C22×C4#41×C15112yes—
670C22×C4#41×C15112yes—
671C22×C4C24×C15111yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C15112yes—
699C4⋊C4C2×D4×C15112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C15112yes—
737C23#123×C15112yes—
738C23C22×D4×C15111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
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—84no—
796C2×C4—84no—
797C2×C4#120×C15112yes—
798C2×C4#123×C15112yes—
799C2×C4C22×D4×C15111yescharacteristic
800C2×C4C22×D4×C15111yescharacteristic
801C2×C4C2×#41×C15111yescharacteristic
802C2×C4C2×#41×C15111yescharacteristic
803C2×C4H(5,𝔽2)×C15111yescharacteristic
804C2×C4H(5,𝔽2)×C15111yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C15111yescharacteristic
838C22C2×#123×C15111yescharacteristic
839C22#534×C15111yescharacteristic
840C22#576×C15111yescharacteristic
841C22#577×C15111yescharacteristic
842C22#577×C15111yescharacteristic
843C22#578×C15111yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C15111yescharacteristic
855C4#546×C15111yescharacteristic
856C4#546×C15111yescharacteristic
857C4#546×C15111yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2#2405×C15111yescharacteristic
863C2#3012×C15111yescharacteristic
864C2#3013×C15111yescharacteristic
865C2#3098×C15111yescharacteristic
866C2#3099×C15111yescharacteristic
867C2#3198×C15111yescharacteristic
868C2#3201×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C151C2semidirect
3. C2×#482×C151C2semidirect
4. #2311×C151C2semidirect
5. #2036×C151C2semidirect
6. #2035×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1874×C151C2semidirect
10. #1872×C151C2semidirect
11. #1853×C151C2semidirect
12. #1852×C151C2semidirect
13. #1788×C151C2semidirect
14. #1788×C151C2semidirect
15. #1780×C151C2semidirect
434. #24017C151direct (N × H)
435. C151#24017direct (N × H)
437. C2×#485C2×C151semidirect
438. C2×#482C2×C151semidirect
439. #2311C2×C151semidirect
440. #2036C2×C151semidirect
441. #2035C2×C151semidirect
442. #2034C2×C151semidirect
443. #2033C2×C151semidirect
444. #1874C2×C151semidirect
445. #1872C2×C151semidirect
446. #1853C2×C151semidirect
447. #1852C2×C151semidirect
448. #1788C2×C151semidirect
449. #1788C2×C151semidirect
450. #1780C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1512
C2×#485×C1512
C2×#482×C1512
#2311×C1512
#2036×C1512
#2035×C1512
#2034×C1512
#2033×C1512
#1874×C1512
#1872×C1512
#1853×C1512
#1852×C1512
#1788×C1512
#1780×C1512
#24017151