Finite Group Databasebeta

← #649230

Subgroups — #649230

Order 512.

3238 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2429C211yesmaximal, characteristic, complemented
3C2×#2361C211yesmaximal, characteristic
4C2×C4×#124C211yesmaximal, characteristic, complemented
5#15719C214yesmaximal, complemented
6#15413C214yesmaximal, complemented
7#15243C211yesmaximal, characteristic, complemented
8#15222C211yesmaximal, characteristic, complemented
9#15215C211yesmaximal, characteristic
10#15215C211yesmaximal, characteristic
11#14819C214yesmaximal, complemented
12#14703C211yesmaximal, characteristic, complemented
13#14155C211yesmaximal, characteristic, complemented
14#14139C211yesmaximal, characteristic, complemented
15#14051C211yesmaximal, characteristic, complemented
16#14027C211yesmaximal, characteristic, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13886C214yesmaximal, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2212yes—
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2503—28no—
31#2429—28no—
32C2×#400C2214yes—
33C2×#398C2212yes—
34C2×#396C2212yes—
35#2361—28no—
36C4×#124—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#388C2214yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#381C2214yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2214yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1445C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2212yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89#1434C2214yes—
90#1434C2212yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—42no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124—42no—
110C2×#124—42no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—42no—
123C2×C4×D4—24no—
124C2×C4×D4—28no—
125C2×C4×D4—216no—
126C2×C4×D4—24no—
127C2×C4×D4—42no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#400—216no—
170#398—28no—
171#396—28no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—42no—
179#390—24no—
180#390—24no—
181#390—42no—
182#389—24no—
183#389—24no—
184#389—28no—
185#388—28no—
186#388—28no—
187#388—28no—
188#388—216no—
189#386—28no—
190#385—28no—
191#382—24no—
192#382D418yescomplemented
193#381—216no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—42no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—216no—
198C4×C22⋊C4—42no—
199C4×C22⋊C4D418yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2314yes—
225C2×#95C2311yescharacteristic
226C43—24no—
227C25C2412yes—
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8#4114yes—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—44no—
254C22×D4#4114yes—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—28no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—28no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C4⋊Q8—416no—
290#124—232no—
291#124—416no—
292C22⋊Q8—416no—
293C22⋊Q8—416no—
294#121—232no—
295C4×Q8—416no—
296C4×D4—416no—
297C4×D4—432no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—416no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4#4114yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
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—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—42no—
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—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C22⋊C4#4118yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—28no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—42no—
424#95—42no—
425#95—44no—
426#95—42no—
427#95—42no—
428#95—44no—
429#95C2×D4116yes—
430#95C2×D414yes—
431#95C2×D414yes—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24C22×D412yes—
452C24C2×#4114yes—
453C24C2×#4114yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
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×D4—216no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—22no—
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—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
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—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—48no—
566C22×C4—416no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—84no—
576C22×C4—88no—
577C22×C4—84no—
578C22×C4—88no—
579C22×C4C22×D414yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C42−1+414yes—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—48no—
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—44no—
612C4⋊C4—44no—
613C22⋊C4—216no—
614C22⋊C4—232no—
615C22⋊C4—44no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—84no—
625C22⋊C4—88no—
626C22⋊C4#124116yescomplemented
627C42—28no—
628C42—28no—
629C42—28no—
630C42—48no—
631C42—48no—
632C42—48no—
633C42—48no—
634C42—44no—
635C42—44no—
636C42—44no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—28no—
653C23—28no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
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—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23C2×#12414yes—
683C23C23×D411yescharacteristic
684C23C23×D411yescharacteristic
685C23C22×#4111yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4111yescharacteristic
688C23C22×#4112yes—
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)11yescharacteristic
691C23C2×2−1+412yes—
692C23#58512yes—
693C23#58512yes—
694Q8—416no—
695Q8—88no—
696D4—432no—
697D4—416no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—416no—
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—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—816no—
792C2×C4—816no—
793C2×C4#52514yes—
794C2×C4#52514yes—
795C2×C4C2×#12414yes—
796C2×C4C2×#12414yes—
797C2×C4#53814yes—
798C2×C4D4214yes—
799C2×C4#54614yes—
800C2×C4#55014yes—
801C2×C4#55314yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—44no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—48no—
815C22—44no—
816C22—44no—
817C22—48no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—84no—
822C22—84no—
823C22—82no—
824C22C2×#52511yescharacteristic
825C22C2×#52511yescharacteristic
826C22C22×#12411yescharacteristic
827C22#344911yescharacteristic
828C22C2×#53811yescharacteristic
829C22C2×D4211yescharacteristic
830C22C2×#54611yescharacteristic
831C22C2×#55011yescharacteristic
832C22D4×#4112yes—
833C22C2×#55311yescharacteristic
834C22#347512yes—
835C22#347512yes—
836C22#348212yes—
837C22#348912yes—
838C22#349911yescharacteristic
839C22#350011yescharacteristic
840C22#351412yes—
841C22#351512yes—
842C22#351612yes—
843C22#352012yes—
844C22#352412yes—
845C22#355112yes—
846C22#355412yes—
847C4—24no—
848C4—24no—
849C4—44no—
850C4—42no—
851C4—42no—
852C4—44no—
853C4—42no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4#245618yes—
864C2—44no—
865C2—84no—
866C2C2×#245611yescharacteristic
867C2#3494611yescharacteristic
868C2#3562211yescharacteristic
869C2D4×#12411yescharacteristic
870C2#3623012yes—
871C2#3630311yescharacteristic
872C2#3768011yescharacteristic
873C2#3894811yescharacteristic
874C2#3900012yes—
875C2#5905912yes—
876C2#5955612yes—
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×#2503C2semidirect
2. C2×#2429C2semidirect
4. C2×C4×#124C2semidirect
5. #15719C2semidirect
6. #15413C2semidirect
7. #15243C2semidirect
8. #15222C2semidirect
11. #14819C2semidirect
12. #14703C2semidirect
13. #14155C2semidirect
14. #14139C2semidirect
15. #14051C2semidirect
16. #14027C2semidirect
17. #13978C2semidirect
18. #13886C2semidirect
19. C4×#388C2semidirect
192. #382D4semidirect
626. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24292
C2×#23612
C2×C4×#1242
#157192
#154132
#152432
#152222
#152152
#148192
#147032
#141552
#141392
#140512
#140272
#139782
#138862
C4×#3882