Finite Group Databasebeta

← #609872

Subgroups — #609872

Order 512.

3250 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2396C211yesmaximal, characteristic, complemented
2C2×#2297C211yesmaximal, characteristic
3#15884C211yesmaximal, characteristic, complemented
4#15857C212yesmaximal, complemented
5#15854C211yesmaximal, characteristic, complemented
6#15820C211yesmaximal, characteristic, complemented
7#15775C212yesmaximal, complemented
8#15662C211yesmaximal, characteristic, complemented
9#15471C212yesmaximal, complemented
10#15468C212yesmaximal, complemented
11#15413C212yesmaximal, complemented
12#15399C212yesmaximal, complemented
13C4×#397C212yesmaximal, complemented
14C4×#393C212yesmaximal, complemented
15#13851C212yesmaximal
16#13842C212yesmaximal, complemented
17C4×#381C212yesmaximal, complemented
18C4×#388C212yesmaximal, complemented
19#13761C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2396—28no—
25C2×#400C2211yescharacteristic
26C2×#399C2211yescharacteristic
27C2×#398C2212yes—
28C2×#397C2212yes—
29C2×#396C2212yes—
30C2×#395C2211yescharacteristic
31C2×#393C2212yes—
32C2×#393C2211yescharacteristic
33#2297—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×C4×C4⋊C4C2212yes—
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×#376C2211yescharacteristic
55C2×C43C2211yescharacteristic
56#1446C2212yes—
57#1446C2212yes—
58#1446C2212yes—
59#1445C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1438C2212yes—
81#1438C2212yes—
82#1438C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1437C2212yes—
87#1437C2211yescharacteristic
88#1437C2212yes—
89#1437C2211yescharacteristic
90#1437C2212yes—
91#1436C2211yescharacteristic
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2211yescharacteristic
96#1434C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C22×#41—24no—
110C22×#41—28no—
111C22×#41—28no—
112C22×#41—42no—
113C22×#41—42no—
114C23×Q8C2311yescharacteristic
115C23×Q8C2311yescharacteristic
116C23×D4C2312yes—
117C23×D4C2311yescharacteristic
118C24×C4C2312yes—
119C24×C4C2312yes—
120C24×C4C2311yescharacteristic
121C2×C4×Q8—24no—
122C2×C4×Q8—42no—
123C2×C4×Q8—42no—
124C2×#117—42no—
125C2×#117—42no—
126C2×#117D418yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C42—24no—
153C22×C42—28no—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#400—24no—
167#399—24no—
168#398—28no—
169#397—28no—
170#396—28no—
171#395—24no—
172#393—24no—
173#393—28no—
174#391—24no—
175#391—24no—
176#390—24no—
177#390—24no—
178#388—28no—
179#388—28no—
180#386—28no—
181#386—28no—
182#381—28no—
183#381—28no—
184C4×C4⋊C4—28no—
185C4×C4⋊C4—24no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—44no—
193C4×C22⋊C4—44no—
194#376—42no—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
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×#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×#95C2311yescharacteristic
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C43—42no—
239C25C2412yes—
240C25C2411yescharacteristic
241C2×#41—232no—
242C2×#41—432no—
243C2×#41—432no—
244C2×#41—416no—
245C2×#41—416no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—41no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8—41no—
255C22×Q8—41no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—22no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—42no—
267C22×D4—42no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D414yes—
285C23×C4#4118yes—
286C23×C4#4118yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C4×Q8—416no—
305#117—416no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4C2×D414yes—
326C2×C4⋊C4C2×D414yes—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
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—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—41no—
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⋊C4C2×D414yes—
380C2×C22⋊C4C2×D414yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—41no—
407C2×C42—42no—
408C2×C42—41no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—416no—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—22no—
422#95—22no—
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—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—41no—
449#95—42no—
450#95—41no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95#4118yescomplemented
456#95#4118yescomplemented
457C24—22no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—21no—
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—
478C24C22×D412yes—
479C24C2×#4114yes—
480C24C2×#4114yes—
481C24C2511yescharacteristic
482#41—4128no—
483C2×Q8—28no—
484C2×Q8—48no—
485C2×Q8—44no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—48no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×D4—28no—
494C2×D4—216no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—44no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—44no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—216no—
511C22×C4—216no—
512C22×C4—216no—
513C22×C4—22no—
514C22×C4—22no—
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—22no—
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—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
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—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—216no—
572C22×C4—216no—
573C22×C4—216no—
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—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—48no—
612C22×C4#124116yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4114yes—
623C22×C4C2×#4114yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C22⋊C4—216no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
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—
656C42—28no—
657C42—28no—
658C42—44no—
659C42—48no—
660C42—44no—
661C42—48no—
662C42—44no—
663C42—44no—
664C42—48no—
665C42—48no—
666C42—48no—
667C42—48no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
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—
723C23C2×#12414yes—
724C23C23×D411yescharacteristic
725C23C22×#4112yes—
726C23C22×#4112yes—
727C23C22×#4112yes—
728C23C22×#4112yes—
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23#58512yes—
732C23#58512yes—
733Q8—416no—
734Q8—416no—
735D4—416no—
736D4—432no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—232no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—432no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
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—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—432no—
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#52514yes—
842C2×C4C2×#12414yes—
843C2×C4C2×#12414yes—
844C2×C4#53414yes—
845C2×C4#55118yes—
846C2×C4#55118yes—
847C22—24no—
848C22—28no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22C2×#52511yescharacteristic
872C22C22×#12411yescharacteristic
873C22#344412yes—
874C22#344412yes—
875C22C2×#53411yescharacteristic
876C22#345512yes—
877C22#345512yes—
878C22#346012yes—
879C22#346012yes—
880C22D4×#4112yes—
881C22D4×#4112yes—
882C22C2×#55112yes—
883C22C2×#55112yes—
884C22#347512yes—
885C22#347512yes—
886C22#347512yes—
887C22#348012yes—
888C22#348111yescharacteristic
889C22#348311yescharacteristic
890C22#352911yescharacteristic
891C22#352911yescharacteristic
892C4—24no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4—42no—
897C4—42no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4#256118yes—
909C2—44no—
910C2—84no—
911C2#3474112yes—
912C2#3481312yes—
913C2C2×#256111yescharacteristic
914C2#3486112yes—
915C2#3487112yes—
916C2#5216511yescharacteristic
917C2#5216711yescharacteristic
918C2#5219712yes—
919C2#5220312yes—
subgroupG/H
centerC23×C4C24
commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2396C2semidirect
3. #15884C2semidirect
4. #15857C2semidirect
5. #15854C2semidirect
6. #15820C2semidirect
7. #15775C2semidirect
8. #15662C2semidirect
9. #15471C2semidirect
10. #15468C2semidirect
11. #15413C2semidirect
12. #15399C2semidirect
13. C4×#397C2semidirect
14. C4×#393C2semidirect
16. #13842C2semidirect
17. C4×#381C2semidirect
18. C4×#388C2semidirect
19. #13761C2semidirect
455. #95#41semidirect
456. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#23962
C2×#22972
#158842
#158572
#158542
#158202
#157752
#156622
#154712
#154682
#154132
#153992
C4×#3972
C4×#3932
#138512
#138422
C4×#3812
C4×#3882
#137612