Finite Group Databasebeta

← #852966

Subgroups — #852966

Order 512.

3482 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2771C211yesmaximal, characteristic, complemented
2C22×#381C211yesmaximal, characteristic
3#16697C212yesmaximal, complemented
4#16675C211yesmaximal, characteristic, complemented
5#16668C211yesmaximal, characteristic, complemented
6#15953C212yesmaximal, complemented
7#15483C212yesmaximal, complemented
8#15469C212yesmaximal, complemented
9#15398C212yesmaximal, complemented
10#14820C211yesmaximal, characteristic
11#14767C212yesmaximal, complemented
12#14738C212yesmaximal, complemented
13#14734C211yesmaximal, characteristic
14#14693C212yesmaximal
15#14508C211yesmaximal, characteristic, complemented
16#14384C212yesmaximal, complemented
17#14131C212yesmaximal, complemented
18#14004C212yesmaximal, complemented
19#13991C212yesmaximal
20C25×C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2771—28no—
24C2×#400C2212yescomplemented
25C2×#400C2212yescomplemented
26C2×#399C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#397C2211yescharacteristic
30C2×#389C2212yescomplemented
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#387C2212yescomplemented
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#381—28no—
43C2×#381C2211yescharacteristic
44C2×#381C2212yes—
45C2×#381C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#381C2212yes—
48C2×#381C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C22×#95C2212yes—
55C22×#95C2212yes—
56#1445C2212yescomplemented
57#1445C2212yescomplemented
58#1445C2212yescomplemented
59#1444C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1442C2212yescomplemented
72#1442C2212yescomplemented
73#1441C2212yescomplemented
74#1441C2212yescomplemented
75#1441C2212yescomplemented
76#1441C2212yescomplemented
77#1441C2212yescomplemented
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2211yescharacteristic
85#1439C2212yes—
86#1439C2212yes—
87#1439C2211yescharacteristic
88#1439C2212yes—
89#1439C2211yescharacteristic
90#1437C2212yes—
91#1437C2212yes—
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96C4⋊#95C2212yescomplemented
97#1434C2212yescomplemented
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C24×C4—24no—
111C24×C4—24no—
112C24×C4—24no—
113C24×C4—42no—
114C24×C4—42no—
115C24×C4—42no—
116C24×C4—42no—
117C24×C4C2312yes—
118C24×C4C2312yes—
119C24×C4C2311yescharacteristic
120C24×C4C2312yes—
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2312yes—
163#400—28no—
164#400—28no—
165#399—24no—
166#399—42no—
167#397—24no—
168#397—42no—
169#389—28no—
170#388—28no—
171#388—44no—
172#387—28no—
173#385—28no—
174#385—28no—
175#385—28no—
176#385—28no—
177#385—44no—
178#385—44no—
179#385—44no—
180#385—44no—
181#381—24no—
182#381—24no—
183#381—24no—
184#381—28no—
185#381—28no—
186#381D418yes—
187#380—42no—
188#380—42no—
189#379—28no—
190#379—28no—
191C4×C22⋊C4—44no—
192C2×#95—28no—
193C2×#95—28no—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
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×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25—24no—
247C25—24no—
248C25—42no—
249C25—42no—
250C25#4114yes—
251C25C2411yescharacteristic
252C25C2411yescharacteristic
253C25C2411yescharacteristic
254C23×C4—232no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—41no—
286C23×C4—41no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4—416no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4C2×D414yes—
305C23×C4#4114yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—41no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
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—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—416no—
407C2×C22⋊C4—416no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4C2×D414yes—
414C2×C22⋊C4#4118yes—
415C2×C42—24no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—22no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—22no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
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#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—41no—
463#95—42no—
464#95—41no—
465#95C2×D418yes—
466#95C2×D418yes—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—216no—
497C24—48no—
498C24—48no—
499C24—48no—
500C24—48no—
501C24—48no—
502C24—48no—
503C24—48no—
504C24—48no—
505C24—48no—
506C24—48no—
507C24—44no—
508C24—44no—
509C24—48no—
510C24—44no—
511C24—44no—
512C24C22×D412yes—
513C24C2×#4112yes—
514C24C2×#4112yes—
515C24C2×#4112yes—
516C24C2×#4112yes—
517C24C2×#4114yes—
518C24H(5,𝔽2)12yes—
519C24H(5,𝔽2)12yes—
520C24H(5,𝔽2)12yes—
521C24H(5,𝔽2)12yes—
522C242−1+414yes—
523C24C2511yescharacteristic
524C22×C4—216no—
525C22×C4—216no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—22no—
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—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
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—21no—
568C22×C4—22no—
569C22×C4—21no—
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—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—48no—
643C22×C4—48no—
644C22×C4—4128no—
645C22×C4—48no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—48no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—84no—
661C22×C4—84no—
662C22×C4—84no—
663C22×C4—82no—
664C22×C4—82no—
665C22×C4—84no—
666C22×C4—84no—
667C22×C4C22×D412yes—
668C22×C4C22×D414yes—
669C22×C4C22×D414yes—
670C22×C4C22×D412yes—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C22×C4C2×#4114yes—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—84no—
679C4⋊C4—84no—
680C4⋊C4—84no—
681C4⋊C4—84no—
682C4⋊C4—84no—
683C4⋊C4—84no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C22⋊C4—216no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—48no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—84no—
704C22⋊C4—84no—
705C42—84no—
706C42—84no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—22no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—232no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—432no—
751C23—432no—
752C23—432no—
753C23—416no—
754C23—432no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—41no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—41no—
770C23—41no—
771C23—42no—
772C23—42no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—416no—
780C23#52514yes—
781C23#53814yes—
782C23#53814yes—
783C23#53918yes—
784C23#55218yes—
785C23#55914yes—
786C23#56314yes—
787C23C23×D411yescharacteristic
788C23C22×#4111yescharacteristic
789C23C22×#4111yescharacteristic
790C23C22×#4112yes—
791C23C2×H(5,𝔽2)11yescharacteristic
792C23C2×H(5,𝔽2)11yescharacteristic
793C23C2×H(5,𝔽2)11yescharacteristic
794C23C2×H(5,𝔽2)11yescharacteristic
795C23C2×2−1+412yes—
796C23#58512yes—
797C23#58512yes—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—432no—
818C2×C4—416no—
819C2×C4—416no—
820C2×C4—432no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
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—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
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—42no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—41no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—88no—
907C2×C4—816no—
908C2×C4—88no—
909C22—28no—
910C22—24no—
911C22—28no—
912C22—24no—
913C22—28no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—28no—
918C22—24no—
919C22—28no—
920C22—24no—
921C22—24no—
922C22—28no—
923C22—464no—
924C22—44no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—44no—
930C22—42no—
931C22—42no—
932C22—44no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—44no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22#277118yescomplemented
943C22C2×#52511yescharacteristic
944C22C2×#53811yescharacteristic
945C22C2×#53811yescharacteristic
946C22C2×#53912yes—
947C22D4×#4112yes—
948C22C2×#55212yes—
949C22#347512yes—
950C22C2×#55911yescharacteristic
951C22#348411yescharacteristic
952C22#348411yescharacteristic
953C22#348912yes—
954C22#349011yescharacteristic
955C22#349011yescharacteristic
956C22#349112yes—
957C22#349512yes—
958C22#351312yes—
959C22#351312yes—
960C22C2×#56311yescharacteristic
961C22#353312yes—
962C22#353311yescharacteristic
963C22#353311yescharacteristic
964C22#353512yes—
965C22#353512yes—
966C4—44no—
967C4—42no—
968C4—44no—
969C4—44no—
970C4—42no—
971C4—44no—
972C4—44no—
973C4—82no—
974C4—81no—
975C4—82no—
976C4—82no—
977C4—82no—
978C4—81no—
979C4—82no—
980C4—82no—
981C4—82no—
982C2—28no—
983C2—44no—
984C2—44no—
985C2#3498811yescharacteristic
986C2#3622312yes—
987C2#3697411yescharacteristic
988C2#3771212yes—
989C2#3790112yes—
990C2#3806512yes—
991C2#4545611yescharacteristic
992C2#4547411yescharacteristic
993C2C2×#277111yescharacteristic
994C2#5918911yescharacteristic
995C2#5936711yescharacteristic
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×#2771C2semidirect
3. #16697C2semidirect
4. #16675C2semidirect
5. #16668C2semidirect
6. #15953C2semidirect
7. #15483C2semidirect
8. #15469C2semidirect
9. #15398C2semidirect
11. #14767C2semidirect
12. #14738C2semidirect
15. #14508C2semidirect
16. #14384C2semidirect
17. #14131C2semidirect
18. #14004C2semidirect
24. C2×#400C22semidirect
25. C2×#400C22semidirect
30. C2×#389C22semidirect
33. C2×#387C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1444C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1442C22semidirect
72. #1442C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
77. #1441C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. C4⋊#95C22semidirect
97. #1434C22semidirect
942. C22#2771semidirect

Maximal subgroups

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

subgroupindex
C2×#27712
C22×#3812
#166972
#166752
#166682
#159532
#154832
#154692
#153982
#148202
#147672
#147382
#147342
#146932
#145082
#143842
#141312
#140042
#139912