Finite Group Databasebeta

← #873907

Subgroups — #873907

Order 512.

3468 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2862C211yesmaximal, characteristic, complemented
2C2×#2491C211yesmaximal, characteristic
3C2×#2436C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic, complemented
5#16375C214yesmaximal, complemented
6#15772C214yesmaximal, complemented
7#15391C214yesmaximal, complemented
8#15243C211yesmaximal, characteristic, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic
13#15191C211yesmaximal, characteristic, complemented
14#14708C211yesmaximal, characteristic, complemented
15#14421C214yesmaximal, complemented
16#14155C211yesmaximal, characteristic, complemented
17#14003C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×#124C2212yes—
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30#2862—28no—
31#2491—28no—
32#2436—28no—
33#2434—28no—
34C2×#395C2212yes—
35C2×#395C2212yes—
36C2×#394C2212yes—
37C2×#393C2214yes—
38C2×#393C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2214yes—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#386C2214yes—
57C2×#385C2212yes—
58C2×#385C2212yes—
59C2×#382C2214yes—
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1446C2214yes—
69#1446C2214yes—
70#1445C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1438C2214yes—
83#1437C2212yes—
84#1437C2214yes—
85#1437C2214yes—
86#1436C2212yes—
87C4⋊#95C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91#1434C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C23×Q8C2312yes—
107C23×D4C2311yescharacteristic
108C23×D4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—42no—
120C2×#124—24no—
121C2×#124—24no—
122C2×#124—28no—
123C2×#124—216no—
124C2×#124—24no—
125C2×#124—42no—
126C2×#124—42no—
127C2×#124—42no—
128C2×#124—42no—
129C2×#124—42no—
130C2×#124—42no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—42no—
133C2×C22⋊Q8—42no—
134C2×#121—24no—
135C2×#121—24no—
136C2×#121—42no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#395—28no—
173#395—28no—
174#394—28no—
175#393—216no—
176#393—28no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—216no—
184#391—42no—
185#391—42no—
186#391—42no—
187#391—42no—
188#391D418yes—
189#390—24no—
190#390—24no—
191#390—42no—
192#388—28no—
193#388—28no—
194#386—216no—
195#385—28no—
196#385—28no—
197#382—216no—
198#382—42no—
199#380—24no—
200C4×C4⋊C4—24no—
201C4×C4⋊C4—42no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4—42no—
204C4×C22⋊C4D418yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2311yescharacteristic
230C2×#95C2314yes—
231C2×#95C2311yescharacteristic
232C43—24no—
233C25C2412yes—
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—24no—
247C22×Q8—28no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—42no—
261C22×Q8—42no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8—44no—
266C22×Q8—416no—
267C22×Q8—416no—
268C22×Q8—416no—
269C22×Q8—416no—
270C22×Q8—416no—
271C22×Q8—416no—
272C22×Q8—416no—
273C22×Q8C2×D414yes—
274C22×Q8#4114yes—
275C22×D4—24no—
276C22×D4—28no—
277C22×D4—22no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—42no—
286C22×D4—44no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×D414yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C4⋊Q8—416no—
319C4⋊Q8—416no—
320C4⋊Q8—416no—
321#124—416no—
322#124—416no—
323#124—416no—
324#124—432no—
325C22⋊Q8—416no—
326#121—416no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×D414yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4#4118yes—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—28no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—42no—
421C2×C42C2×D414yes—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—28no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—42no—
439#95—44no—
440#95—44no—
441#95—42no—
442#95—42no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95C2×D414yes—
449#95C2×D414yes—
450#95C2×D4116yes—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24C22×D412yes—
472C24C2×#4114yes—
473C24C2511yescharacteristic
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—416no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—4128no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—84no—
507C2×Q8—88no—
508C2×D4—48no—
509C2×D4—416no—
510C2×D4—48no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—84no—
519C2×D4—88no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
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—24no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
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—24no—
580C22×C4—24no—
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—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4112yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+414yes—
636C22×C42−1+414yes—
637C4⋊C4—28no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C22⋊C4—28no—
649C22⋊C4—48no—
650C22⋊C4—416no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—416no—
654C22⋊C4—48no—
655C22⋊C4—416no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—84no—
661C22⋊C4—88no—
662C22⋊C4#124116yescomplemented
663C42—216no—
664C42—28no—
665C42—28no—
666C42—28no—
667C42—48no—
668C42—48no—
669C42—44no—
670C42—44no—
671C42—44no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
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—44no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C2×#12414yes—
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C22×#4112yes—
721C23C22×#4111yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×2−1+412yes—
727C23C2×2−1+412yes—
728C23#58512yes—
729Q8—432no—
730Q8—416no—
731Q8—416no—
732Q8—816no—
733Q8—88no—
734D4—816no—
735D4—88no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—416no—
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—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4C2×#12414yes—
832C2×C4C2×#12414yes—
833C2×C4#53514yes—
834C2×C4#53514yes—
835C2×C4#53614yes—
836C2×C4#53814yes—
837C2×C4D4214yes—
838C2×C4#54614yes—
839C2×C4#54614yes—
840C2×C4H(3,𝔽4)14yes—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—84no—
858C22—84no—
859C22—82no—
860C22—82no—
861C22—84no—
862C22—84no—
863C22C22×#12411yescharacteristic
864C22C2×#53511yescharacteristic
865C22C2×#53511yescharacteristic
866C22C2×#53611yescharacteristic
867C22C2×#53811yescharacteristic
868C22C2×D4211yescharacteristic
869C22C2×#54611yescharacteristic
870C22C2×#54611yescharacteristic
871C22D4×#4112yes—
872C22#348212yes—
873C22#348612yes—
874C22#349911yescharacteristic
875C22#350011yescharacteristic
876C22#351112yes—
877C22#351112yes—
878C22#351412yes—
879C22#351812yes—
880C22#352012yes—
881C22C2×H(3,𝔽4)11yescharacteristic
882C22#354712yes—
883C22#355212yes—
884C22#355412yes—
885C22#356112yes—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4#267018yes—
903C2—44no—
904C2—162no—
905C2#3528911yescharacteristic
906C2D4×#12411yescharacteristic
907C2#3630311yescharacteristic
908C2#3739111yescharacteristic
909C2#3767511yescharacteristic
910C2#3895811yescharacteristic
911C2#3985412yes—
912C2#4009812yes—
913C2#4604312yes—
914C2C2×#267011yescharacteristic
915C2#5910012yes—
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
1. C2×#2862C2semidirect
4. C2×#2434C2semidirect
5. #16375C2semidirect
6. #15772C2semidirect
7. #15391C2semidirect
8. #15243C2semidirect
9. #15243C2semidirect
10. #15236C2semidirect
11. #15217C2semidirect
13. #15191C2semidirect
14. #14708C2semidirect
15. #14421C2semidirect
16. #14155C2semidirect
17. #14003C2semidirect
18. #13922C2semidirect
19. C4×#388C2semidirect
662. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#28622
C2×#24912
C2×#24362
C2×#24342
#163752
#157722
#153912
#152432
#152362
#152172
#152152
#151912
#147082
#144212
#141552
#140032
#139222
C4×#3882