Finite Group Databasebeta

← #649192

Subgroups — #649192

Order 512.

3542 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2436C211yesmaximal, characteristic
2C2×#2422C211yesmaximal, characteristic
3C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#124C211yesmaximal, characteristic, complemented
5#15697C214yesmaximal, complemented
6#15291C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic
10#15217C211yesmaximal, characteristic, complemented
11#14797C214yesmaximal, complemented
12#14703C211yesmaximal, characteristic, complemented
13#14096C214yesmaximal, complemented
14#14027C211yesmaximal, characteristic, complemented
15#14026C211yesmaximal, characteristic, complemented
16#13978C211yesmaximal, characteristic, complemented
17#13926C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#123C2212yes—
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28#2436—28no—
29#2422—28no—
30C2×#397C2212yes—
31C2×#394C2212yes—
32C2×#393C2214yes—
33Q8×C22⋊C4—28no—
34C4×#124—28no—
35C2×#391C2212yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#388C2214yes—
51C2×#386C2214yes—
52C2×#385C2212yes—
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2214yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1446C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1437C2212yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2212yes—
84C4⋊#95C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90#1434C2212yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C23×Q8C2311yescharacteristic
105C23×D4C2311yescharacteristic
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C2×#124—24no—
111C2×#124—24no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—42no—
115C2×#124D418yes—
116C2×#123—28no—
117C2×#123—216no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—42no—
126C2×C4×Q8—42no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4—42no—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#397—28no—
166#394—28no—
167#393—216no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—28no—
176#391—28no—
177#391—42no—
178#390—24no—
179#390—24no—
180#390—42no—
181#389—24no—
182#388—216no—
183#388—28no—
184#386—216no—
185#385—28no—
186#384—24no—
187#382—24no—
188#382—42no—
189#380—24no—
190#380—24no—
191#380—28no—
192C4×C4⋊C4—42no—
193C4×C22⋊C4—28no—
194C4×C22⋊C4—216no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—42no—
197C4×C22⋊C4D418yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C43—24no—
227C25C2412yes—
228C25C2411yescharacteristic
229C22×Q8—232no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—24no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—42no—
246C22×Q8—42no—
247C22×Q8—416no—
248C22×Q8—416no—
249C22×Q8—416no—
250C22×Q8—416no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8C2×D414yes—
254C22×Q8#4114yes—
255C22×Q8#4114yes—
256C22×Q8#4114yes—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—28no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4C2×D414yes—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—28no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—44no—
287C23×C4C2×D414yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305#124—232no—
306#124—416no—
307#123—432no—
308#121—416no—
309C4×Q8—416no—
310C4×Q8—416no—
311C4×D4—416no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
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—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4C2×D4116yes—
375C2×C22⋊C4C2×D414yes—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4#4118yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—28no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—28no—
424#95—44no—
425#95—44no—
426#95—42no—
427#95—42no—
428#95—44no—
429#95—44no—
430#95—42no—
431#95—42no—
432#95—44no—
433#95—44no—
434#95C2×D414yes—
435#95C2×D414yes—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—22no—
451C24—22no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24C22×D414yes—
456C24C22×D412yes—
457C24C2×#4114yes—
458C24C2511yescharacteristic
459C2×Q8—216no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—48no—
470C2×Q8—48no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—48no—
474C2×Q8—4128no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8#123116yescomplemented
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—48no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—84no—
492C2×D4—88no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—216no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
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—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
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—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
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—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—48no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—48no—
591C22×C4—84no—
592C22×C4—88no—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C42−1+414yes—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C22⋊C4—232no—
625C22⋊C4—44no—
626C22⋊C4—48no—
627C22⋊C4—416no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—88no—
637C22⋊C4#124116yescomplemented
638C42—28no—
639C42—28no—
640C42—28no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—48no—
645C42—44no—
646C42—44no—
647C42—44no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—28no—
664C23—28no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
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—44no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23C2×#12414yes—
694C23C23×D411yescharacteristic
695C23C23×D411yescharacteristic
696C23C22×#4111yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4112yes—
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)11yescharacteristic
702C23C2×2−1+412yes—
703C23#58512yes—
704C23#58512yes—
705Q8—232no—
706Q8—432no—
707Q8—416no—
708D4—416no—
709D4—816no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—432no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
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—416no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—816no—
804C2×C4C2×#12318yes—
805C2×C4C2×#12314yes—
806C2×C4#52514yes—
807C2×C4C2×#12414yes—
808C2×C4C2×#12414yes—
809C2×C4#53814yes—
810C2×C4D4214yes—
811C2×C4#54614yes—
812C2×C4#54614yes—
813C2×C4#55114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—42no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—48no—
828C22—44no—
829C22—48no—
830C22—82no—
831C22—84no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22—82no—
836C22C22×#12311yescharacteristic
837C22C2×#52511yescharacteristic
838C22C22×#12411yescharacteristic
839C22#344911yescharacteristic
840C22C2×#53811yescharacteristic
841C22C2×D4211yescharacteristic
842C22C2×#54611yescharacteristic
843C22C2×#54611yescharacteristic
844C22D4×#4112yes—
845C22C2×#55111yescharacteristic
846C22#348012yes—
847C22#348012yes—
848C22#348212yes—
849C22#348912yes—
850C22#349911yescharacteristic
851C22#350011yescharacteristic
852C22#351412yes—
853C22#351612yes—
854C22#351812yes—
855C22#352012yes—
856C22#352412yes—
857C22#355112yes—
858C22#355412yes—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—42no—
866C4—44no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4#241818yes—
876C2—44no—
877C2—84no—
878C2C2×#241811yescharacteristic
879C2#3495511yescharacteristic
880C2#3566911yescharacteristic
881C2D4×#12411yescharacteristic
882C2#3630311yescharacteristic
883C2#3643212yes—
884C2#3768011yescharacteristic
885C2#3894811yescharacteristic
886C2#3924212yes—
887C2#5904312yes—
888C2#5948912yes—
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
3. C2×Q8×C22⋊C4C2semidirect
4. C2×C4×#124C2semidirect
5. #15697C2semidirect
6. #15291C2semidirect
7. #15240C2semidirect
8. #15233C2semidirect
10. #15217C2semidirect
11. #14797C2semidirect
12. #14703C2semidirect
13. #14096C2semidirect
14. #14027C2semidirect
15. #14026C2semidirect
16. #13978C2semidirect
17. #13926C2semidirect
18. #13922C2semidirect
19. C4×#388C2semidirect
480. C2×Q8#123semidirect
637. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#24362
C2×#24222
C2×Q8×C22⋊C42
C2×C4×#1242
#156972
#152912
#152402
#152332
#152192
#152172
#147972
#147032
#140962
#140272
#140262
#139782
#139262
#139222
C4×#3882