Finite Group Databasebeta

← #4414208

Subgroups — #4414208

Order 512.

2610 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2826C211yesmaximal, characteristic, complemented
2C2×C4×#123C211yesmaximal, characteristic, complemented
3#16668C211yesmaximal, characteristic, complemented
4#16660C211yesmaximal, characteristic, complemented
5#16654C212yesmaximal, complemented
6#16495C212yesmaximal, complemented
7#16491C212yesmaximal, complemented
8#16355C212yesmaximal, complemented
9#16346C212yesmaximal, complemented
10#14859C212yesmaximal, complemented
11#14807C211yesmaximal, characteristic, complemented
12#14805C212yesmaximal, complemented
13#14764C212yesmaximal, complemented
14#14749C212yesmaximal, complemented
15#14746C212yesmaximal, complemented
16#14722C211yesmaximal, characteristic
17#14696C212yesmaximal, complemented
18#14669C211yesmaximal, characteristic, complemented
19#14621C212yesmaximal, complemented
20C22×#123C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2826—28no—
25C2×#400C2212yes—
26C2×#399C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#397C2212yes—
29C2×#396C2212yes—
30C2×#394C2212yes—
31C2×#394C2212yes—
32C2×#394C2211yescharacteristic
33C2×#392C2212yes—
34C2×#392C2211yescharacteristic
35C4×#123—28no—
36C2×#389C2211yescharacteristic
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2211yescharacteristic
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54#1445C2212yes—
55#1445C2212yes—
56#1444C2212yes—
57#1443C2212yes—
58#1443C2212yes—
59#1443C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2211yescharacteristic
70#1441C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2211yescharacteristic
81#1439C2212yes—
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1439C2211yescharacteristic
86#1439C2212yes—
87#1439C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1438C2212yes—
94#1438C2212yes—
95#1438C2212yes—
96#1437C2212yes—
97#1437C2212yes—
98#1437C2212yes—
99#1437C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1434C2211yescharacteristic
104#1434C2212yes—
105#1434C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C23×D4C2311yescharacteristic
112C23×D4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×#123—24no—
118C2×#123—24no—
119C2×#123—24no—
120C2×#121—44no—
121C2×#121—42no—
122C2×C4×D4—24no—
123C2×C4×D4—42no—
124C2×C4×D4—42no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C42—24no—
161C22×C42—42no—
162C22×C42—42no—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167#400—28no—
168#399—24no—
169#399—42no—
170#397—28no—
171#396—28no—
172#394—28no—
173#394—28no—
174#394—42no—
175#392—28no—
176#392—24no—
177#389—42no—
178#388—28no—
179#388—44no—
180#388—44no—
181#388—44no—
182#387—28no—
183#387—44no—
184#386—28no—
185#386—24no—
186#386—28no—
187#386—44no—
188#385—44no—
189#385—44no—
190#385D418yescomplemented
191#381—24no—
192C4×C4⋊C4—28no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4—28no—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
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×#95C2312yes—
235C25C2412yes—
236C25C2411yescharacteristic
237C25C2411yescharacteristic
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—41no—
246C22×D4—41no—
247C22×D4—41no—
248C22×D4—41no—
249C22×D4—42no—
250C22×D4—41no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—41no—
263C22×D4#4114yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—41no—
275C23×C4—41no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—42no—
284C23×C4C2×D414yes—
285C23×C4#4114yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302#123—232no—
303#121—416no—
304C4×D4—416no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
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—41no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4C2×D418yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
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⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4C2×D414yes—
407C2×C22⋊C4C2×D414yes—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—41no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—416no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—24no—
429#95—22no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—42no—
436#95—42no—
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#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—41no—
459#95—41no—
460#95C2×D418yes—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24C22×D412yes—
495C24C2×#4112yes—
496C24C2×#4112yes—
497C24C2×#4112yes—
498C24C2511yescharacteristic
499C2×D4—28no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—82no—
512C2×D4—84no—
513C2×D4—84no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4—84no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4—82no—
521C2×D4—84no—
522C2×D4—84no—
523C2×D4—84no—
524C2×D4—84no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
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—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
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—44no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—48no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—82no—
641C22×C4—84no—
642C22×C4C22×D412yes—
643C22×C4C22×D414yes—
644C22×C4C22×D412yes—
645C22×C4C22×D414yes—
646C22×C4C2×#4114yes—
647C22×C4C2×#4112yes—
648C22×C4H(5,𝔽2)12yes—
649C22×C4H(5,𝔽2)14yes—
650C22×C4H(5,𝔽2)12yes—
651C4⋊C4—216no—
652C4⋊C4—48no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—48no—
657C4⋊C4—82no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C4⋊C4—84no—
661C4⋊C4—84no—
662C22⋊C4—216no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—44no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—84no—
682C22⋊C4—84no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C22⋊C4—84no—
686C42—48no—
687C42—48no—
688C42—48no—
689C42—44no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23#52514yes—
771C23C23×D411yescharacteristic
772C23C22×#4111yescharacteristic
773C23C22×#4111yescharacteristic
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)12yes—
777C23#58512yes—
778C23#58512yes—
779C23#58511yescharacteristic
780C23#58511yescharacteristic
781C23#58512yes—
782D4—416no—
783D4—88no—
784D4—816no—
785D4—816no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—416no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
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—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
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—88no—
893C2×C4#56014yes—
894C22—28no—
895C22—24no—
896C22—44no—
897C22—42no—
898C22—44no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—82no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22C2×#52511yescharacteristic
932C22#345512yes—
933C22#345911yescharacteristic
934C22#345911yescharacteristic
935C22#346012yes—
936C22#348411yescharacteristic
937C22#348512yes—
938C22#348711yescharacteristic
939C22#348812yes—
940C22#350511yescharacteristic
941C22#350511yescharacteristic
942C22#351412yes—
943C22#352112yes—
944C22C2×#56011yescharacteristic
945C22#352912yes—
946C22#352911yescharacteristic
947C22#353311yescharacteristic
948C22#353412yes—
949C22#353912yes—
950C22#354011yescharacteristic
951C22#356212yes—
952C22#356612yes—
953C22#356612yes—
954C4—24no—
955C4—44no—
956C4—42no—
957C4—44no—
958C4—42no—
959C4—42no—
960C4—44no—
961C4—42no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4—82no—
968C4—82no—
969C4—82no—
970C2—44no—
971C2—82no—
972C2—162no—
973C2#3498711yescharacteristic
974C2#3509512yes—
975C2#3667711yescharacteristic
976C2#3747312yes—
977C2#3749111yescharacteristic
978C2#4544111yescharacteristic
979C2#4545511yescharacteristic
980C2#4569111yescharacteristic
981C2#4569711yescharacteristic
982C2#4576612yes—
983C2#4586512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14722C2
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×#2826C2semidirect
2. C2×C4×#123C2semidirect
3. #16668C2semidirect
4. #16660C2semidirect
5. #16654C2semidirect
6. #16495C2semidirect
7. #16491C2semidirect
8. #16355C2semidirect
9. #16346C2semidirect
10. #14859C2semidirect
11. #14807C2semidirect
12. #14805C2semidirect
13. #14764C2semidirect
14. #14749C2semidirect
15. #14746C2semidirect
17. #14696C2semidirect
18. #14669C2semidirect
19. #14621C2semidirect
190. #385D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28262
C2×C4×#1232
#166682
#166602
#166542
#164952
#164912
#163552
#163462
#148592
#148072
#148052
#147642
#147492
#147462
#147222
#146962
#146692
#146212