Finite Group Databasebeta

← #764913

Subgroups — #764913

Order 512.

2950 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2569C211yesmaximal, characteristic, complemented
2C2×#2312C211yesmaximal, characteristic
3#16049C212yesmaximal, complemented
4#15866C212yesmaximal, complemented
5#15742C212yesmaximal, complemented
6#15675C212yesmaximal, complemented
7#15653C212yesmaximal, complemented
8#15620C212yesmaximal, complemented
9#15366C212yesmaximal, complemented
10#15365C212yesmaximal, complemented
11#14734C212yesmaximal
12#14726C212yesmaximal
13#14130C211yesmaximal, characteristic, complemented
14#14004C212yesmaximal, complemented
15#13980C212yesmaximal, complemented
16#13965C211yesmaximal, characteristic, complemented
17#13907C211yesmaximal, characteristic, complemented
18C2×#1439C211yesmaximal, characteristic
19#13775C211yesmaximal, characteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23#2569—28no—
24C2×#400C2212yescomplemented
25C2×#399C2212yes—
26C2×#399C2212yes—
27C2×#398C2212yescomplemented
28C2×#396C2212yes—
29C2×#396C2212yes—
30#2312—28no—
31C2×#389C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#389C2212yescomplemented
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#387C2212yescomplemented
39C2×#387C2212yescomplemented
40C2×#387C2212yescomplemented
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#379C2211yescharacteristic
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55C22×#95C2211yescharacteristic
56C22×#95C2212yes—
57#1445C2212yescomplemented
58#1444C2211yescharacteristic, complemented
59#1444C2212yescomplemented
60#1444C2212yescomplemented
61#1444C2212yescomplemented
62#1444C2211yescharacteristic, complemented
63#1443C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2211yescharacteristic, complemented
66#1442C2212yescomplemented
67#1442C2211yescharacteristic, complemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97C4⋊#95C2211yescharacteristic, complemented
98C4⋊#95C2211yescharacteristic, complemented
99C4⋊#95C2212yescomplemented
100C4⋊#95C2211yescharacteristic, complemented
101C4⋊#95C2212yescomplemented
102C4⋊#95C2212yescomplemented
103C4⋊#95C2211yescharacteristic, complemented
104#1434C2212yescomplemented
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2211yescharacteristic
109C26C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C22×C4⋊C4—24no—
115C22×C4⋊C4—44no—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—44no—
136C22×C22⋊C4—44no—
137C22×C22⋊C4—44no—
138C22×C22⋊C4Q818yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164#400—28no—
165#399—44no—
166#399—44no—
167#398—28no—
168#396—44no—
169#396—44no—
170#389—44no—
171#389—44no—
172#389—44no—
173#388—28no—
174#388—28no—
175#388—28no—
176#388—28no—
177#387—28no—
178#387—28no—
179#387—44no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—44no—
184#380—24no—
185#380—28no—
186#380—44no—
187#380D418yes—
188#379—28no—
189#379—24no—
190#379—24no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—28no—
194C2×#95—24no—
195C2×#95—44no—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C25—22no—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—42no—
243C25—42no—
244C25—42no—
245C25—42no—
246C25C2×Q814yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4C2×D414yes—
270C23×C4C2×Q814yes—
271C23×C4C2×Q814yes—
272C23×C4#4114yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—416no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4C2×D418yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—232no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—432no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4C2×D418yes—
398C2×C22⋊C4C2×Q818yes—
399C2×C22⋊C4C2×Q818yes—
400C2×C22⋊C4#4114yes—
401C2×C22⋊C4#4114yes—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415#95—24no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—22no—
424#95—22no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95C2×D414yes—
454#95C2×D414yes—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—28no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—28no—
475C24—28no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—84no—
487C24—82no—
488C24—82no—
489C24—84no—
490C24—82no—
491C24—82no—
492C24—84no—
493C24—84no—
494C24—84no—
495C24—84no—
496C24C22×D412yes—
497C24C22×Q814yes—
498C24C22×Q812yes—
499C24C2×#4112yes—
500C24C2×#4112yes—
501C24C2×#4112yes—
502C24H(5,𝔽2)12yes—
503C242−1+412yes—
504C24C2511yescharacteristic
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—82no—
614C22×C4—84no—
615C22×C4—82no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4C22⋊Q8116yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×Q814yes—
626C22×C4C22×Q812yes—
627C22×C4C22×Q812yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4H(5,𝔽2)14yes—
635C22×C4H(5,𝔽2)14yes—
636C4⋊C4—28no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—84no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C22⋊C4—216no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—216no—
657C22⋊C4—216no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—44no—
663C22⋊C4—48no—
664C22⋊C4—44no—
665C22⋊C4—84no—
666C22⋊C4—84no—
667C22⋊C4—84no—
668C22⋊C4—84no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C42—82no—
674C42—82no—
675C42—84no—
676C42—84no—
677C42—84no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—432no—
702C23—42no—
703C23—416no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—88no—
732C23—816no—
733C23—88no—
734C23—88no—
735C23—816no—
736C23—816no—
737C23—88no—
738C23—88no—
739C23—88no—
740C23C2×C22⋊Q814yes—
741C23#53314yes—
742C23#54414yes—
743C23#54714yes—
744C23#55014yes—
745C23#55214yes—
746C23#55314yes—
747C23C23×D411yescharacteristic
748C23C23×Q811yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4111yescharacteristic
751C23C22×#4111yescharacteristic
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)12yes—
754C23C2×H(5,𝔽2)12yes—
755C23C2×2−1+411yescharacteristic
756C23#58512yes—
757C23#58512yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—416no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—88no—
865C2×C4—816no—
866C2×C4—816no—
867C2×C4C2×C22⋊Q814yes—
868C2×C4C2×C22⋊Q814yes—
869C22—24no—
870C22—24no—
871C22—28no—
872C22—28no—
873C22—28no—
874C22—28no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—832no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22#244118yes—
896C22C22×C22⋊Q811yescharacteristic
897C22C2×#53311yescharacteristic
898C22C2×#54411yescharacteristic
899C22C2×#54711yescharacteristic
900C22C2×#55011yescharacteristic
901C22C2×#55211yescharacteristic
902C22C2×#55311yescharacteristic
903C22#348812yes—
904C22#349011yescharacteristic
905C22#349111yescharacteristic
906C22#349612yes—
907C22#350112yes—
908C22#350112yes—
909C22#350811yescharacteristic
910C22#351011yescharacteristic
911C22#351312yes—
912C22#351412yes—
913C22#351912yes—
914C22#352112yes—
915C22#353212yes—
916C22#353312yes—
917C22#354112yes—
918C22#354112yes—
919C4—24no—
920C4—24no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—44no—
928C4—42no—
929C4—44no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C2—28no—
937C2—84no—
938C2C2×#244111yescharacteristic
939C2#3535911yescharacteristic
940C2#3540212yes—
941C2#3551511yescharacteristic
942C2#3674812yes—
943C2#4391112yes—
944C2#4391312yes—
945C2#4396211yescharacteristic
946C2#4396411yescharacteristic
947C2#4408111yescharacteristic
948C2#4446511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2569C2semidirect
3. #16049C2semidirect
4. #15866C2semidirect
5. #15742C2semidirect
6. #15675C2semidirect
7. #15653C2semidirect
8. #15620C2semidirect
9. #15366C2semidirect
10. #15365C2semidirect
13. #14130C2semidirect
14. #14004C2semidirect
15. #13980C2semidirect
16. #13965C2semidirect
17. #13907C2semidirect
24. C2×#400C22semidirect
27. C2×#398C22semidirect
31. C2×#389C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
38. C2×#387C22semidirect
39. C2×#387C22semidirect
40. C2×#387C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. C4⋊#95C22semidirect
98. C4⋊#95C22semidirect
99. C4⋊#95C22semidirect
100. C4⋊#95C22semidirect
101. C4⋊#95C22semidirect
102. C4⋊#95C22semidirect
103. C4⋊#95C22semidirect
104. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25692
C2×#23122
#160492
#158662
#157422
#156752
#156532
#156202
#153662
#153652
#147342
#147262
#141302
#140042
#139802
#139652
#139072
C2×#14392
#137752