Finite Group Databasebeta

← #719413

Subgroups — #719413

Order 512.

4308 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic
2C2×#2501C211yesmaximal, characteristic, complemented
3C2×#2413C212yesmaximal, complemented
4C2×#2411C212yesmaximal, complemented
5C22×#399C211yesmaximal, characteristic, complemented
6C2×#2344C211yesmaximal, characteristic, complemented
7#17071C212yesmaximal, complemented
8#16811C212yesmaximal, complemented
9#15776C214yesmaximal, complemented
10#15765C214yesmaximal, complemented
11#15148C212yesmaximal, complemented
12#15084C212yesmaximal, complemented
13#15069C212yesmaximal, complemented
14#14911C212yesmaximal, complemented
15#14271C211yesmaximal, characteristic, complemented
16#13903C211yesmaximal, characteristic, complemented
17#13782C211yesmaximal, characteristic, complemented
18C22×#123C2211yescharacteristic
19C22×#123C2212yes—
20C22×#123C2212yes—
21C22×#123C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#120C2211yescharacteristic
24C22×#120C2211yescharacteristic
25C22×#117C2212yes—
26C23×C4⋊C4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30#2539—28no—
31#2501—28no—
32#2413—216no—
33#2411—216no—
34C2×#399—28no—
35C2×#399C2212yes—
36C2×#399C2212yes—
37C2×#399C2214yes—
38C2×#399C2212yes—
39C2×#399C2211yescharacteristic, complemented
40C2×#399C2211yescharacteristic, complemented
41C2×#399C2211yescharacteristic, complemented
42C2×#399C2211yescharacteristic, complemented
43C2×#398C2214yescomplemented
44C2×#396C2214yes—
45C2×#396C2214yescomplemented
46C2×#394C2214yes—
47C2×#392C2212yes—
48#2344—28no—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2214yes—
52C2×#390C2212yescomplemented
53C2×#389C2214yescomplemented
54C2×#389C2212yescomplemented
55C2×#388C2214yes—
56C2×#388C2214yescomplemented
57C2×#387C2214yescomplemented
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#385C2212yes—
61C2×#384C2212yescomplemented
62C2×#381C2212yes—
63C2×#381C2212yes—
64C2×#380C2211yescharacteristic
65C2×#379C2212yes—
66C2×C4×C4⋊C4C2212yescomplemented
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C22×#95C2211yescharacteristic
70#1445C2212yescomplemented
71#1444C2214yescomplemented
72#1444C2214yescomplemented
73#1439C2214yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2212yes—
77#1439C2214yescomplemented
78#1439C2212yescomplemented
79#1439C2214yescomplemented
80#1439C2212yescomplemented
81#1438C2214yes—
82#1438C2214yes—
83#1438C2212yescomplemented
84#1437C2214yes—
85#1436C2214yescomplemented
86C4⋊#95C2212yescomplemented
87#1434C2212yescomplemented
88C22⋊#95C2212yes—
89C26C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C2×#123—28no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—24no—
105C2×#123—24no—
106C2×#123—44no—
107C2×#123—44no—
108C2×#123—44no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#120—28no—
113C2×#120—24no—
114C2×#120—24no—
115C2×#120—44no—
116C2×#117—28no—
117C2×#117—28no—
118C2×#117—28no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—28no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4D418yescomplemented
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C22⋊C4—28no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—28no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—44no—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C42C2314yes—
169C22×C42C2312yes—
170C22×C42C2312yes—
171#399—216no—
172#399—28no—
173#399—28no—
174#399—24no—
175#399—24no—
176#399—24no—
177#399—24no—
178#399—28no—
179#398—216no—
180#396—216no—
181#396—216no—
182#394—216no—
183#392—28no—
184#390—216no—
185#390—28no—
186#390—28no—
187#390—28no—
188#389—216no—
189#389—28no—
190#388—216no—
191#388—216no—
192#387—216no—
193#386—28no—
194#386—28no—
195#385D4116yescomplemented
196#384—28no—
197#381—28no—
198#381—28no—
199#380—24no—
200#379—28no—
201C4×C4⋊C4—28no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4D418yes—
204C2×#95—24no—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C25—22no—
221C25—24no—
222C25—22no—
223C25—24no—
224C25—22no—
225C25—24no—
226C25—42no—
227C25—44no—
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C25C2412yes—
231C25C2411yescharacteristic
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—44no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D418yes—
273C23×C4C2×D418yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4#4114yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290#123—432no—
291#123—432no—
292#123—416no—
293#123—416no—
294#121—416no—
295#120—416no—
296#120—416no—
297#117—432no—
298C2×C4⋊C4—232no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—432no—
338C2×C4⋊C4C2×D418yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
341C2×C4⋊C4C2×D4116yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—432no—
395C2×C22⋊C4—416no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4C2×D418yes—
402C2×C22⋊C4C2×D414yes—
403C2×C22⋊C4C2×D418yes—
404C2×C42—28no—
405C2×C42—28no—
406C2×C42—28no—
407C2×C42—24no—
408C2×C42—44no—
409C2×C42—44no—
410C2×C42C2×D418yes—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—28no—
416#95—24no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—44no—
423#95—44no—
424#95C2×D418yes—
425#95C2×D4116yes—
426C24—22no—
427C24—24no—
428C24—22no—
429C24—28no—
430C24—22no—
431C24—24no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—24no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—416no—
457C24—48no—
458C24—48no—
459C24—416no—
460C24—48no—
461C24—44no—
462C24—44no—
463C24—48no—
464C24—44no—
465C24—44no—
466C24—48no—
467C24—88no—
468C24—84no—
469C24—84no—
470C24—88no—
471C24C22×D412yes—
472C24C22×D412yes—
473C24C22×D414yes—
474C24C2×#4112yes—
475C24H(5,𝔽2)14yes—
476C242−1+414yes—
477C24C2511yescharacteristic
478C2×D4—416no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—48no—
495C2×D4—84no—
496C2×D4—88no—
497C2×D4—84no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—88no—
501C2×D4—88no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—416no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—416no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4#121116yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D418yes—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C22×D414yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D418yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—216no—
597C4⋊C4—416no—
598C4⋊C4—416no—
599C4⋊C4—416no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—416no—
608C4⋊C4—48no—
609C22⋊C4—28no—
610C22⋊C4—216no—
611C22⋊C4—416no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4#127116yes—
631C42—48no—
632C42—48no—
633C42—416no—
634C23—24no—
635C23—28no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—28no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—28no—
644C23—28no—
645C23—24no—
646C23—28no—
647C23—24no—
648C23—24no—
649C23—28no—
650C23—432no—
651C23—416no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—832no—
703C23—816no—
704C23—816no—
705C23—88no—
706C23—816no—
707C23—88no—
708C23C2×#12114yes—
709C23C2×#12714yes—
710C23#53514yes—
711C23D4218yes—
712C23#55018yes—
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C23×D412yes—
716C23C22×#4111yescharacteristic
717C23C2×H(5,𝔽2)12yes—
718C23C2×2−1+412yes—
719C23#58514yes—
720C23#58512yes—
721D4—816no—
722D4—88no—
723D4—816no—
724D4—88no—
725D4—88no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—432no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—432no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—88no—
798C2×C4C2×#12114yes—
799C2×C4C2×#12114yes—
800C2×C4C2×#12718yes—
801C22—216no—
802C22—24no—
803C22—28no—
804C22—28no—
805C22—24no—
806C22—28no—
807C22—28no—
808C22—48no—
809C22—48no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—832no—
814C22—84no—
815C22—82no—
816C22—84no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—84no—
821C22—84no—
822C22—81no—
823C22—81no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22#254118yes—
837C22C22×#12111yescharacteristic
838C22C22×#12711yescharacteristic
839C22C2×#53511yescharacteristic
840C22#344912yes—
841C22C2×D4212yes—
842C22C2×#55012yes—
843C22#348514yes—
844C22#348512yes—
845C22#348611yescharacteristic
846C22#348711yescharacteristic
847C22#348914yes—
848C22#348912yes—
849C22#349112yes—
850C22#349512yes—
851C22#353314yes—
852C22#353514yes—
853C4—24no—
854C4—24no—
855C4—28no—
856C4—44no—
857C4—44no—
858C4—48no—
859C4—44no—
860C4—44no—
861C4—44no—
862C4—82no—
863C4—81no—
864C4—81no—
865C4—84no—
866C2—28no—
867C2—84no—
868C2—161no—
869C2—161no—
870C2C2×#254111yescharacteristic
871C2#3508911yescharacteristic
872C2#3566111yescharacteristic
873C2#3606012yes—
874C2#3765312yes—
875C2#3765512yes—
876C2#4140712yes—
877C2#4352814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2539C2
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×#2501C2semidirect
3. C2×#2413C2semidirect
4. C2×#2411C2semidirect
5. C22×#399C2semidirect
6. C2×#2344C2semidirect
7. #17071C2semidirect
8. #16811C2semidirect
9. #15776C2semidirect
10. #15765C2semidirect
11. #15148C2semidirect
12. #15084C2semidirect
13. #15069C2semidirect
14. #14911C2semidirect
15. #14271C2semidirect
16. #13903C2semidirect
17. #13782C2semidirect
39. C2×#399C22semidirect
40. C2×#399C22semidirect
41. C2×#399C22semidirect
42. C2×#399C22semidirect
43. C2×#398C22semidirect
45. C2×#396C22semidirect
52. C2×#390C22semidirect
53. C2×#389C22semidirect
54. C2×#389C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
61. C2×#384C22semidirect
66. C2×C4×C4⋊C4C22semidirect
70. #1445C22semidirect
71. #1444C22semidirect
72. #1444C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
83. #1438C22semidirect
85. #1436C22semidirect
86. C4⋊#95C22semidirect
87. #1434C22semidirect
124. C22×C4⋊C4D4semidirect
195. #385D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#25012
C2×#24132
C2×#24112
C22×#3992
C2×#23442
#170712
#168112
#157762
#157652
#151482
#150842
#150692
#149112
#142712
#139032
#137822