Finite Group Databasebeta

← #1007454

Subgroups — #1007454

Order 512.

2762 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2602C212yesmaximal, complemented
2C2×#2458C212yesmaximal, complemented
3#17107C211yesmaximal, characteristic, complemented
4#17083C211yesmaximal, characteristic
5#16541C212yesmaximal, complemented
6#16374C212yesmaximal, complemented
7#16276C212yesmaximal, complemented
8#15778C211yesmaximal, characteristic, complemented
9#15569C211yesmaximal, characteristic, complemented
10#15443C212yesmaximal, complemented
11#15428C212yesmaximal, complemented
12#15084C211yesmaximal, characteristic, complemented
13#14980C212yesmaximal, complemented
14#14760C212yesmaximal, complemented
15#14529C212yesmaximal, complemented
16#14199C212yesmaximal, complemented
17#14174C211yesmaximal, characteristic, complemented
18#14143C212yesmaximal, complemented
19C4×#394C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#2602—216no—
24#2458—216no—
25C2×#399C2212yes—
26C2×#398C2212yes—
27C2×#397C2212yes—
28C2×#395C2211yescharacteristic
29C2×#394C2211yescharacteristic
30C2×#394C2212yes—
31C2×#394C2212yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#393C2212yes—
35C2×#393C2212yes—
36C2×#392C2212yes—
37C2×#392C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#389C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#387C2212yes—
51C2×#387C2212yes—
52C2×#387C2212yes—
53C2×#386C2212yes—
54C2×#385C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59#1446C2211yescharacteristic
60#1445C2212yes—
61#1444C2211yescharacteristic
62#1444C2211yescharacteristic
63#1443C2212yes—
64#1442C2211yescharacteristic
65#1442C2211yescharacteristic
66#1441C2211yescharacteristic
67#1441C2212yes—
68#1441C2212yes—
69#1441C2211yescharacteristic
70#1441C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1438C2211yescharacteristic
88#1438C2211yescharacteristic
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1438C2211yescharacteristic
94#1437C2212yes—
95#1437C2212yes—
96#1437C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103C4⋊#95C2212yes—
104#1434C2211yescharacteristic
105#1434C2212yes—
106#1434C2211yescharacteristic
107#1434C2212yes—
108C4×#95C2211yescharacteristic
109C23×Q8C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C23×D4C2312yes—
112C23×D4C2312yes—
113C23×D4C2311yescharacteristic
114C24×C4C2312yes—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—44no—
118C2×C4×Q8—28no—
119C2×C4×Q8—42no—
120C2×C4×D4—28no—
121C2×C4×D4—42no—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
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×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165#399—28no—
166#398—28no—
167#397—28no—
168#395—24no—
169#394—28no—
170#394—24no—
171#394—28no—
172#394—28no—
173#394—28no—
174#393—28no—
175#393—28no—
176#392—28no—
177#392—44no—
178#390—28no—
179#390—28no—
180#390—42no—
181#389—28no—
182#388—28no—
183#388—28no—
184#388—28no—
185#388—28no—
186#388—28no—
187#388—28no—
188#388—28no—
189#387—28no—
190#387—28no—
191#387—28no—
192#387—44no—
193#386—28no—
194#385D4116yescomplemented
195C4×C4⋊C4—42no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—44no—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2311yescharacteristic
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C25C2412yes—
238C25C2412yes—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—41no—
242C22×Q8—42no—
243C22×Q8—41no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—41no—
252C22×D4—41no—
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—41no—
262C22×D4—41no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2×D418yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#123—432no—
293C4×Q8—416no—
294C4×D4—416no—
295C2×C4⋊C4—24no—
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—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
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—41no—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4#4114yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
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—24no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
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—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⋊C4C2×D418yes—
399C2×C22⋊C4C2×D418yes—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—42no—
412C2×C42—41no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419#95—24no—
420#95—24no—
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—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—22no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—22no—
438#95—24no—
439#95—42no—
440#95—42no—
441#95—41no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—41no—
446#95—42no—
447#95—41no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—41no—
452#95—41no—
453#95—42no—
454#95C2×D418yes—
455#95C2×D418yes—
456#95#4114yes—
457C24—22no—
458C24—22no—
459C24—22no—
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—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24C22×D414yes—
487C24C2511yescharacteristic
488C2×Q8—44no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—44no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C2×D4—82no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—84no—
512C2×D4—84no—
513C2×D4—82no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—84no—
517C22×C4—21no—
518C22×C4—21no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
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—21no—
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—216no—
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—21no—
589C22×C4—22no—
590C22×C4—21no—
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—21no—
611C22×C4—22no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D414yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C4⋊C4—82no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—84no—
663C22⋊C4—84no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C22⋊C4—84no—
667C42—44no—
668C42—48no—
669C42—44no—
670C42—44no—
671C42—84no—
672C42—84no—
673C42—84no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
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—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23C23×D412yes—
745C23C22×#4111yescharacteristic
746C23C22×#4111yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)11yescharacteristic
749C23#58511yescharacteristic
750C23#58512yes—
751C23#58512yes—
752C23#58511yescharacteristic
753C23#58512yes—
754C23#58511yescharacteristic
755Q8—416no—
756D4—416no—
757D4—816no—
758D4—816no—
759D4—88no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
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—41no—
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—816no—
867C2×C4D4214yes—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22#344912yes—
899C22#346011yescharacteristic
900C22C2×D4211yescharacteristic
901C22D4×#4112yes—
902C22D4×#4112yes—
903C22#348011yescharacteristic
904C22#348512yes—
905C22#348712yes—
906C22#349612yes—
907C22#350511yescharacteristic
908C22#350611yescharacteristic
909C22#351012yes—
910C22#351411yescharacteristic
911C22#352412yes—
912C22#352911yescharacteristic
913C22#353312yes—
914C22#353411yescharacteristic
915C22#354011yescharacteristic
916C22#354511yescharacteristic
917C22#356612yes—
918C22#356612yes—
919C22#356612yes—
920C22#356711yescharacteristic
921C4—24no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—42no—
927C4—42no—
928C4—44no—
929C4—42no—
930C4—44no—
931C4—42no—
932C4—42no—
933C4—82no—
934C4—82no—
935C4—81no—
936C4—82no—
937C4—82no—
938C2—84no—
939C2—162no—
940C2#3983611yescharacteristic
941C2#3994312yes—
942C2#4141612yes—
943C2#4240511yescharacteristic
944C2#4301711yescharacteristic
945C2#4392512yes—
946C2#4632211yescharacteristic
947C2#5209611yescharacteristic
948C2#5270811yescharacteristic
949C2#5900111yescharacteristic
950C2#5917512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#17083C2
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×#2602C2semidirect
2. C2×#2458C2semidirect
3. #17107C2semidirect
5. #16541C2semidirect
6. #16374C2semidirect
7. #16276C2semidirect
8. #15778C2semidirect
9. #15569C2semidirect
10. #15443C2semidirect
11. #15428C2semidirect
12. #15084C2semidirect
13. #14980C2semidirect
14. #14760C2semidirect
15. #14529C2semidirect
16. #14199C2semidirect
17. #14174C2semidirect
18. #14143C2semidirect
19. C4×#394C2semidirect
194. #385D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26022
C2×#24582
#171072
#170832
#165412
#163742
#162762
#157782
#155692
#154432
#154282
#150842
#149802
#147602
#145292
#141992
#141742
#141432
C4×#3942