Finite Group Databasebeta

← #873740

Subgroups — #873740

Order 512.

3068 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic, complemented
3C2×#2491C211yesmaximal, characteristic
4C2×#2429C211yesmaximal, characteristic, complemented
5#16370C214yesmaximal, complemented
6#15781C214yesmaximal, complemented
7#15362C214yesmaximal, complemented
8#15243C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15222C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic
13#15191C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14421C214yesmaximal, complemented
16#14155C211yesmaximal, characteristic, complemented
17#14051C211yesmaximal, characteristic, complemented
18#14026C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2212yes—
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2850—28no—
31#2568—28no—
32#2491—28no—
33#2429—28no—
34C2×#400C2214yes—
35C2×#398C2212yes—
36C2×#396C2212yes—
37C2×#394C2212yes—
38C2×#393C2212yes—
39C2×#391C2214yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2212yes—
52C2×#389C2211yescharacteristic
53C2×#388C2214yes—
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#386C2214yes—
57C2×#385C2212yes—
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1446C2214yes—
67#1445C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2212yes—
83#1436C2214yes—
84#1436C2212yes—
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2312yes—
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×#124—24no—
109C2×#124—28no—
110C2×#124—216no—
111C2×#124—24no—
112C2×#124—42no—
113C2×#124—42no—
114C2×#124—42no—
115C2×#124—42no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—42no—
121C2×C22⋊Q8—42no—
122C2×#121—24no—
123C2×#121—24no—
124C2×#121—42no—
125C2×C4×Q8—24no—
126C2×C4×Q8—24no—
127C2×C4×Q8—42no—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C42—24no—
158C22×C42—42no—
159C22×C42—42no—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169#400—216no—
170#398—28no—
171#396—28no—
172#394—28no—
173#393—28no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—216no—
179#391—42no—
180#391—42no—
181#391—42no—
182#390—24no—
183#390—24no—
184#390—24no—
185#390—42no—
186#389—24no—
187#389—28no—
188#388—28no—
189#388—216no—
190#388—28no—
191#386—216no—
192#385—28no—
193#382—24no—
194#382D418yes—
195#380—24no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—42no—
199C4×C22⋊C4—42no—
200C4×C22⋊C4D418yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2314yes—
227C25C2412yes—
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—28no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—42no—
246C22×Q8—44no—
247C22×Q8#4114yes—
248C22×D4—24no—
249C22×D4—28no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—42no—
259C22×D4—44no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4C2×D414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C4⋊Q8—416no—
292C4⋊Q8—416no—
293#124—416no—
294#124—416no—
295#124—432no—
296C22⋊Q8—416no—
297C22⋊Q8—416no—
298#121—416no—
299C4×Q8—416no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4#4118yes—
379C2×C42—22no—
380C2×C42—22no—
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—24no—
390C2×C42—22no—
391C2×C42—28no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—28no—
410#95—28no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—44no—
420#95—44no—
421#95—42no—
422#95—44no—
423#95—44no—
424#95—42no—
425#95—42no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95C2×D414yes—
430#95C2×D414yes—
431#95C2×D4116yes—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—24no—
451C24—24no—
452C24C22×D412yes—
453C24C2×#4114yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—48no—
459C2×Q8—416no—
460C2×Q8—48no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—84no—
473C2×Q8—88no—
474C2×D4—48no—
475C2×D4—416no—
476C2×D4—48no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—84no—
485C2×D4—88no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
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—24no—
544C22×C4—22no—
545C22×C4—24no—
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—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—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4C22×D414yes—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C42−1+414yes—
600C22×C42−1+412yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—84no—
628C22⋊C4—88no—
629C22⋊C4#124116yescomplemented
630C42—28no—
631C42—28no—
632C42—28no—
633C42—48no—
634C42—48no—
635C42—48no—
636C42—44no—
637C42—44no—
638C42—44no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—42no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C2×#12414yes—
685C23C23×D411yescharacteristic
686C23C23×D411yescharacteristic
687C23C22×#4112yes—
688C23C22×#4111yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)11yescharacteristic
691C23C2×H(5,𝔽2)11yescharacteristic
692C23C2×2−1+411yescharacteristic
693C23C2×2−1+412yes—
694C23#58512yes—
695C23#58512yes—
696Q8—416no—
697Q8—816no—
698Q8—88no—
699D4—816no—
700D4—88no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—28no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—432no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—416no—
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—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4C2×#12414yes—
796C2×C4C2×#12414yes—
797C2×C4#53514yes—
798C2×C4#53714yes—
799C2×C4#53814yes—
800C2×C4D4214yes—
801C2×C4#54614yes—
802C2×C4#54814yes—
803C2×C4#56214yes—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—44no—
809C22—42no—
810C22—44no—
811C22—42no—
812C22—44no—
813C22—44no—
814C22—42no—
815C22—82no—
816C22—82no—
817C22—84no—
818C22—82no—
819C22—84no—
820C22—82no—
821C22—82no—
822C22—84no—
823C22—84no—
824C22—82no—
825C22—82no—
826C22C22×#12411yescharacteristic
827C22C2×#53511yescharacteristic
828C22C2×#53711yescharacteristic
829C22#344911yescharacteristic
830C22C2×#53811yescharacteristic
831C22C2×D4211yescharacteristic
832C22C2×#54611yescharacteristic
833C22C2×#54811yescharacteristic
834C22D4×#4112yes—
835C22#348212yes—
836C22#348912yes—
837C22#349911yescharacteristic
838C22#350011yescharacteristic
839C22#350612yes—
840C22#350712yes—
841C22#351412yes—
842C22#352012yes—
843C22#352412yes—
844C22C2×#56211yescharacteristic
845C22#354012yes—
846C22#354112yes—
847C22#355412yes—
848C22#355512yes—
849C4—24no—
850C4—24no—
851C4—44no—
852C4—42no—
853C4—44no—
854C4—42no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—42no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4#267618yes—
866C2—44no—
867C2—162no—
868C2#3518011yescharacteristic
869C2D4×#12411yescharacteristic
870C2#3630311yescharacteristic
871C2#3738911yescharacteristic
872C2#3768011yescharacteristic
873C2#3809511yescharacteristic
874C2#3986312yes—
875C2#4021812yes—
876C2#4561912yes—
877C2C2×#267611yescharacteristic
878C2#5908212yes—
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×#2568C2semidirect
4. C2×#2429C2semidirect
5. #16370C2semidirect
6. #15781C2semidirect
7. #15362C2semidirect
8. #15243C2semidirect
9. #15236C2semidirect
10. #15222C2semidirect
11. #15217C2semidirect
13. #15191C2semidirect
14. #14702C2semidirect
15. #14421C2semidirect
16. #14155C2semidirect
17. #14051C2semidirect
18. #14026C2semidirect
19. C4×#385C2semidirect
629. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#25682
C2×#24912
C2×#24292
#163702
#157812
#153622
#152432
#152362
#152222
#152172
#152152
#151912
#147022
#144212
#141552
#140512
#140262
C4×#3852