Finite Group Databasebeta

← #616311

Subgroups — #616311

Order 512.

3952 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic, complemented
3C2×#2416C211yesmaximal, characteristic
4C2×C42×D4C211yesmaximal, characteristic, complemented
5#15234C211yesmaximal, characteristic, complemented
6#15233C211yesmaximal, characteristic, complemented
7#15217C211yesmaximal, characteristic, complemented
8#15215C211yesmaximal, characteristic, complemented
9#15093C214yesmaximal, complemented
10#14968C214yesmaximal, complemented
11#14703C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14700C211yesmaximal, characteristic, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14137C211yesmaximal, characteristic, complemented
17#14023C214yesmaximal, complemented
18#13999C214yesmaximal, complemented
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2212yes—
25C22×#121C2211yescharacteristic
26C22×C4×D4C2212yes—
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32#2850—28no—
33#2417—28no—
34#2416—28no—
35C2×#398C2212yes—
36C2×#396C2212yes—
37C2×#396C2212yes—
38C2×#394C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2214yes—
50C2×#388C2214yes—
51C2×#386C2214yes—
52C2×#386C2214yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2214yes—
56C2×#382C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C42×D4—28no—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2212yes—
67C22×#95C2214yes—
68C2×C43C2211yescharacteristic
69#1443C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1437C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2214yes—
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C2×#124—24no—
107C2×#124—42no—
108C2×#124—42no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×#121—28no—
116C2×#121—216no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121—42no—
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4—28no—
128C2×C4×D4D418yes—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—42no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C42—24no—
166C22×C42—42no—
167C22×C42—42no—
168C22×C42—42no—
169C22×C42—42no—
170C22×C42D418yescomplemented
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179C22×C42C2312yes—
180#398—28no—
181#396—28no—
182#396—28no—
183#394—28no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—42no—
188#390—24no—
189#390—24no—
190#390—24no—
191#390—42no—
192#389—24no—
193#389—24no—
194#388—216no—
195#388—48no—
196#386—28no—
197#386—216no—
198#386—28no—
199#386—216no—
200#386—48no—
201#382—24no—
202#380—24no—
203#380—24no—
204#380—28no—
205C4×C4⋊C4—24no—
206C4×C4⋊C4—28no—
207C4×C22⋊C4—28no—
208C4×C22⋊C4—24no—
209C4×C22⋊C4—24no—
210C4×C22⋊C4—28no—
211C2×#95—48no—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C43—24no—
234C25C2412yes—
235C25C2411yescharacteristic
236C25C2411yescharacteristic
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—28no—
251C22×D4—28no—
252C22×D4—24no—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4C2×D414yes—
265C22×D4#4118yes—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—28no—
286C23×C4—28no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4C2×D414yes—
300C23×C4C2×D418yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4#4114yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320#124—416no—
321C22⋊Q8—416no—
322C22⋊Q8—416no—
323#121—416no—
324#121—432no—
325#121—416no—
326C4×D4—264no—
327C4×D4—232no—
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—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—416no—
362C2×C4⋊C4—416no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4#4114yes—
369C2×C4⋊C4#4114yes—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4#4118yes—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—416no—
434C2×C42—416no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441C2×C42C2×D414yes—
442C2×C42C2×D418yes—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—28no—
450#95—28no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—28no—
458#95—28no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—24no—
482C24—22no—
483C24—22no—
484C24—24no—
485C24—22no—
486C24—24no—
487C24—22no—
488C24—22no—
489C24—24no—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C22×D412yes—
493C24C2×#4114yes—
494C24C2×#4112yes—
495C24C2×#4114yes—
496C24C2×#4114yes—
497C24C2511yescharacteristic
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×D4—28no—
506C2×D4—216no—
507C2×D4—216no—
508C2×D4—28no—
509C2×D4—48no—
510C2×D4—416no—
511C2×D4—48no—
512C2×D4—416no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—416no—
516C2×D4—48no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—84no—
525C2×D4—88no—
526C2×D4#124116yescomplemented
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—216no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
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—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—216no—
584C22×C4—28no—
585C22×C4—28no—
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—24no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—416no—
626C22×C4—416no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—48no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—88no—
637C22×C4—88no—
638C22×C4#121116yes—
639C22×C4C22×D414yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D414yes—
646C22×C4C22×D412yes—
647C22×C4C22×D412yes—
648C22×C4C2×#4114yes—
649C22×C4C2×#4114yes—
650C22×C4C2×#4114yes—
651C22×C4C2×#4114yes—
652C22×C4C2×#4112yes—
653C22×C4C2×#4114yes—
654C22×C4C2×#4112yes—
655C22×C4C2×#4112yes—
656C22×C4C2×#4112yes—
657C22×C4H(5,𝔽2)14yes—
658C22×C4H(5,𝔽2)12yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C42−1+414yes—
661C4⋊C4—216no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—84no—
675C22⋊C4—216no—
676C22⋊C4—28no—
677C22⋊C4—216no—
678C22⋊C4—28no—
679C22⋊C4—416no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—416no—
688C22⋊C4—84no—
689C22⋊C4—88no—
690C22⋊C4—84no—
691C42—216no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—48no—
696C42—48no—
697C42—44no—
698C42—44no—
699C42—48no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—22no—
719C23—24no—
720C23—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—44no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—42no—
757C23—42no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23C2×#12114yes—
764C23#52518yes—
765C23C2×#12414yes—
766C23C2×#12414yes—
767C23#52918yes—
768C23#53214yes—
769C23C23×D411yescharacteristic
770C23C23×D411yescharacteristic
771C23C22×#4111yescharacteristic
772C23C22×#4112yes—
773C23C22×#4112yes—
774C23C22×#4111yescharacteristic
775C23C22×#4111yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)12yes—
779C23C2×2−1+412yes—
780Q8—88no—
781D4—232no—
782D4—816no—
783D4—816no—
784D4—88no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—232no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—432no—
822C2×C4—432no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—416no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—816no—
876C2×C4—816no—
877C2×C4C2×#12114yes—
878C2×C4C2×#12114yes—
879C2×C4C2×#12414yes—
880C2×C4#53214yes—
881C2×C4#53414yes—
882C2×C4#53718yes—
883C2×C4#54614yes—
884C2×C4#54614yes—
885C2×C4#55314yes—
886C2×C4#55314yes—
887C22—24no—
888C22—28no—
889C22—24no—
890C22—24no—
891C22—28no—
892C22—24no—
893C22—28no—
894C22—24no—
895C22—24no—
896C22—28no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—44no—
902C22—42no—
903C22—42no—
904C22—44no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22—82no—
909C22—84no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—84no—
914C22—82no—
915C22—84no—
916C22—82no—
917C22—82no—
918C22—84no—
919C22#285018yes—
920C22C22×#12111yescharacteristic
921C22C2×#52512yes—
922C22C22×#12411yescharacteristic
923C22C2×#52912yes—
924C22C2×#53211yescharacteristic
925C22C2×#53211yescharacteristic
926C22C2×#53411yescharacteristic
927C22C2×#53712yes—
928C22C2×#54611yescharacteristic
929C22C2×#54611yescharacteristic
930C22C2×#55311yescharacteristic
931C22C2×#55311yescharacteristic
932C22#348112yes—
933C22#348112yes—
934C22#348212yes—
935C22#348212yes—
936C22#349811yescharacteristic
937C22#349911yescharacteristic
938C22#351112yes—
939C22#351912yes—
940C22#351912yes—
941C22#352012yes—
942C22#352012yes—
943C4—24no—
944C4—28no—
945C4—24no—
946C4—42no—
947C4—44no—
948C4—44no—
949C4—44no—
950C4—44no—
951C4—44no—
952C4—42no—
953C4—82no—
954C4—82no—
955C4—82no—
956C4—82no—
957C4—82no—
958C4#254318yes—
959C2—28no—
960C2—44no—
961C2—162no—
962C2C2×#254311yescharacteristic
963C2#3496412yes—
964C2#3507712yes—
965C2#3527311yescharacteristic
966C2#3628911yescharacteristic
967C2#3629212yes—
968C2#3630311yescharacteristic
969C2#3630512yes—
970C2#3636211yescharacteristic
971C2#3637611yescharacteristic
972C2C2×#285011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2850C2semidirect
2. C2×#2417C2semidirect
4. C2×C42×D4C2semidirect
5. #15234C2semidirect
6. #15233C2semidirect
7. #15217C2semidirect
8. #15215C2semidirect
9. #15093C2semidirect
10. #14968C2semidirect
11. #14703C2semidirect
12. #14702C2semidirect
13. #14700C2semidirect
14. #14698C2semidirect
15. #14139C2semidirect
16. #14137C2semidirect
17. #14023C2semidirect
18. #13999C2semidirect
19. C2×C4⋊#95C2semidirect
170. C22×C42D4semidirect
526. C2×D4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#24172
C2×#24162
C2×C42×D42
#152342
#152332
#152172
#152152
#150932
#149682
#147032
#147022
#147002
#146982
#141392
#141372
#140232
#139992
C2×C4⋊#952