Finite Group Databasebeta

← #1423496

Subgroups — #1423496

Order 512.

2586 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2491C211yesmaximal, characteristic
2C2×#2365C211yesmaximal, characteristic, complemented
3#16071C212yesmaximal, complemented
4#15840C212yesmaximal, complemented
5#15785C212yesmaximal, complemented
6#15696C212yesmaximal, complemented
7#15499C212yesmaximal, complemented
8#15456C212yesmaximal, complemented
9#15112C211yesmaximal, characteristic, complemented
10#15084C211yesmaximal, characteristic, complemented
11#14875C212yesmaximal, complemented
12#14799C212yesmaximal, complemented
13#14420C211yesmaximal, characteristic, complemented
14#14418C212yesmaximal
15#14240C211yesmaximal, characteristic, complemented
16#14225C211yesmaximal, characteristic, complemented
17#14125C212yesmaximal, complemented
18#14115C212yesmaximal, complemented
19#14026C212yesmaximal, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2212yes—
24#2491—28no—
25C2×#399C2211yescharacteristic
26C2×#399C2212yes—
27C2×#399C2212yes—
28C2×#397C2211yescharacteristic
29C2×#397C2212yes—
30C2×#394C2212yes—
31C2×#393C2212yes—
32#2365—28no—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#389C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#380C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54#1446C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1445C2211yescharacteristic
59#1445C2211yescharacteristic
60#1444C2211yescharacteristic
61#1444C2212yes—
62#1444C2212yes—
63#1442C2212yes—
64#1442C2211yescharacteristic
65#1442C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2211yescharacteristic
80#1439C2211yescharacteristic
81#1439C2212yes—
82#1438C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100C4⋊#95C2212yes—
101C4⋊#95C2212yes—
102#1434C2211yescharacteristic
103#1434C2212yes—
104#1434C2212yes—
105#1434C2211yescharacteristic
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C4×#95C2212yes—
109C23×Q8C2312yes—
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×C4⋊Q8—28no—
114C2×C4⋊Q8D418yes—
115C2×#124—28no—
116C2×#124—28no—
117C2×#124—44no—
118C2×#121—24no—
119C2×#121—28no—
120C2×C4×Q8—28no—
121C2×C4×Q8—44no—
122C2×C4×Q8—44no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
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×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#399—24no—
167#399—44no—
168#399—44no—
169#397—24no—
170#397—44no—
171#394—28no—
172#393—28no—
173#391—28no—
174#391—44no—
175#390—24no—
176#390—24no—
177#390—44no—
178#390—44no—
179#389—28no—
180#388—28no—
181#388—28no—
182#388—44no—
183#388—44no—
184#388—44no—
185#387—28no—
186#387—28no—
187#387—28no—
188#380—24no—
189C4×C4⋊C4—28no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193C4×C22⋊C4—24no—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
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×#95C2311yescharacteristic
234C25C2412yes—
235C25C2411yescharacteristic
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8C2×D418yes—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—41no—
252C22×D4—41no—
253C22×D4—42no—
254C22×D4—42no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—42no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C4⋊Q8—232no—
278#124—432no—
279#121—416no—
280C4×Q8—432no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
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⋊C4C2×D418yes—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4C2×D414yes—
321C2×C4⋊C4#4118yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
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—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
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—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
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#4114yes—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42C2×D414yes—
404#95—22no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—24no—
421#95—22no—
422#95—24no—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
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#4114yes—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24C2×#4112yes—
470C24C2511yescharacteristic
471C2×Q8—216no—
472C2×Q8—216no—
473C2×Q8—48no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—48no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—84no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
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—22no—
542C22×C4—22no—
543C22×C4—21no—
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—22no—
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—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C42−1+414yes—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—216no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4—84no—
616C4⋊C4#123116yes—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C42—28no—
638C42—48no—
639C42—48no—
640C42—48no—
641C42—44no—
642C42—48no—
643C42—48no—
644C42—84no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
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—
703C23C23×D411yescharacteristic
704C23C22×#4112yes—
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)12yes—
710C23C2×2−1+412yes—
711C23#58511yescharacteristic
712C23#58512yes—
713C23#58511yescharacteristic
714Q8—432no—
715D4—816no—
716D4—88no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
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—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—88no—
821C2×C4C2×#12314yes—
822C2×C4C2×#12318yes—
823C2×C4#54614yes—
824C2×C4#55014yes—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—82no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22C22×#12311yescharacteristic
852C22C2×#54611yescharacteristic
853C22C2×#55011yescharacteristic
854C22#348011yescharacteristic
855C22#348112yes—
856C22#348212yes—
857C22#348411yescharacteristic
858C22#348611yescharacteristic
859C22#348711yescharacteristic
860C22#348711yescharacteristic
861C22#349412yes—
862C22#350611yescharacteristic
863C22#351012yes—
864C22#351012yes—
865C22#351411yescharacteristic
866C22#351512yes—
867C22#351912yes—
868C22#352212yes—
869C22#354112yes—
870C22#354212yes—
871C22#354611yescharacteristic
872C22#355412yes—
873C22#356112yes—
874C4—24no—
875C4—24no—
876C4—28no—
877C4—24no—
878C4—42no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—44no—
883C4—81no—
884C4—81no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C2—82no—
892C2—162no—
893C2#3567911yescharacteristic
894C2#3623611yescharacteristic
895C2#3648311yescharacteristic
896C2#4419512yes—
897C2#4432712yes—
898C2#4493311yescharacteristic
899C2#4533511yescharacteristic
900C2#4980412yes—
901C2#5201111yescharacteristic
902C2#5904911yescharacteristic
903C2#5979712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2365C2semidirect
3. #16071C2semidirect
4. #15840C2semidirect
5. #15785C2semidirect
6. #15696C2semidirect
7. #15499C2semidirect
8. #15456C2semidirect
9. #15112C2semidirect
10. #15084C2semidirect
11. #14875C2semidirect
12. #14799C2semidirect
13. #14420C2semidirect
15. #14240C2semidirect
16. #14225C2semidirect
17. #14125C2semidirect
18. #14115C2semidirect
19. #14026C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24912
C2×#23652
#160712
#158402
#157852
#156962
#154992
#154562
#151122
#150842
#148752
#147992
#144202
#144182
#142402
#142252
#141252
#141152
#140262