Finite Group Databasebeta

← #613900

Subgroups — #613900

Order 512.

4500 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2539C211yesmaximal, characteristic
3C2×#2413C212yesmaximal, complemented
4C2×#2411C212yesmaximal, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6C2×C4×#117C211yesmaximal, characteristic, complemented
7#15163C214yesmaximal, complemented
8#14910C212yesmaximal, complemented
9#14900C212yesmaximal, complemented
10#14870C212yesmaximal, complemented
11#14815C212yesmaximal, complemented
12#14700C214yesmaximal, complemented
13#14152C211yesmaximal, characteristic, complemented
14#13996C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13965C211yesmaximal, characteristic, complemented
17#13903C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C22×#120C2212yes—
22C22×#117C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2854—28no—
29#2539—28no—
30#2413—216no—
31#2411—216no—
32C2×#399C2212yes—
33C2×#398C2214yescomplemented
34C2×#396C2214yes—
35C2×#396C2214yescomplemented
36C2×#394C2214yes—
37C2×#392C2212yes—
38C2×#390C2214yes—
39C2×#390C2214yes—
40C2×#390C2214yes—
41C2×#390C2211yescharacteristic, complemented
42C2×#390C2211yescharacteristic, complemented
43C2×#389C2211yescharacteristic, complemented
44C2×#389C2211yescharacteristic, complemented
45C2×#389C2214yescomplemented
46C2×#388—28no—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#388C2214yes—
51C2×#388C2212yes—
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2214yescomplemented
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#385C2212yes—
59C2×#385C2212yes—
60C2×#381C2212yes—
61C2×#380C2211yescharacteristic
62C2×#379C2212yes—
63C4×#117—28no—
64C2×C4×C4⋊C4C2212yescomplemented
65C2×C4×C4⋊C4C2212yescomplemented
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×#376C2212yescomplemented
70C22×#95C2211yescharacteristic
71C22×#95C2211yescharacteristic
72C2×C43C2212yescomplemented
73#1445C2212yescomplemented
74#1445C2214yescomplemented
75#1444C2212yescomplemented
76#1444C2212yescomplemented
77#1439C2212yes—
78#1439C2214yes—
79#1439C2212yes—
80#1439C2214yescomplemented
81#1438C2214yes—
82#1438C2212yescomplemented
83#1437C2214yes—
84#1437C2214yes—
85#1437C2214yescomplemented
86#1437C2214yescomplemented
87C4⋊#95C2214yescomplemented
88C4⋊#95C2214yescomplemented
89C26C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2314yes—
92C23×D4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C2×#123—28no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—28no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#120—28no—
109C2×#120—28no—
110C2×#120—28no—
111C2×#117—28no—
112C2×#117—28no—
113C2×#117D4116yescomplemented
114C22×C4⋊C4—28no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4—24no—
128C22×C22⋊C4—28no—
129C22×C22⋊C4—28no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42D418yescomplemented
157C22×C42C2314yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2314yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165#399—28no—
166#398—216no—
167#396—216no—
168#396—216no—
169#394—216no—
170#392—28no—
171#390—216no—
172#390—24no—
173#390—24no—
174#390—216no—
175#390—216no—
176#389—24no—
177#389—24no—
178#389—216no—
179#388—28no—
180#388—28no—
181#388—216no—
182#388—216no—
183#388—28no—
184#388—28no—
185#388—28no—
186#388—28no—
187#386—28no—
188#386—28no—
189#386—28no—
190#385—28no—
191#385—28no—
192#381—28no—
193#380—24no—
194#379—28no—
195C4×C4⋊C4—28no—
196C4×C4⋊C4—28no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—28no—
199C4×C22⋊C4D418yes—
200#376—28no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C43—28no—
220C25—22no—
221C25—24no—
222C25—22no—
223C25—24no—
224C25—22no—
225C25—24no—
226C25—42no—
227C25—42no—
228C25—42no—
229C25C2412yes—
230C25C2412yes—
231C25C2411yescharacteristic
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—28no—
240C22×D4—22no—
241C22×D4—28no—
242C22×D4—28no—
243C22×D4—22no—
244C22×D4—28no—
245C22×D4—22no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—42no—
250C22×D4—42no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4C2×D414yes—
274C23×C4C2×D418yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2414yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2414yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293#123—432no—
294#123—432no—
295#121—416no—
296#120—432no—
297#117—264no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4C2×D4116yes—
328C2×C22⋊C4—232no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
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—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
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—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—416no—
377C2×C22⋊C4—416no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×D418yes—
383C2×C22⋊C4C2×D418yes—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4#4118yes—
386C2×C22⋊C4#4118yes—
387C2×C42—232no—
388C2×C42—28no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—28no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—28no—
399C2×C42—24no—
400C2×C42—28no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—44no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42C2×D4116yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42C2×D418yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95C2×D418yes—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—28no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—416no—
455C24—48no—
456C24—48no—
457C24—416no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—48no—
465C24—48no—
466C24—84no—
467C24—84no—
468C24—88no—
469C24—88no—
470C24C22×D412yes—
471C24C22×D414yes—
472C24C22×D412yes—
473C24C2×#4114yes—
474C24C2×#4114yes—
475C24C2×#4112yes—
476C24C2511yescharacteristic
477C2×D4—416no—
478C2×D4—416no—
479C2×D4—416no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—416no—
490C2×D4—44no—
491C2×D4—88no—
492C2×D4—84no—
493C2×D4—84no—
494C2×D4—88no—
495C2×D4—88no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—88no—
580C22×C4#121116yes—
581C22×C4#127116yes—
582C22×C4C22×D412yes—
583C22×C4C22×D418yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D418yes—
588C22×C4C22×D418yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D414yes—
594C22×C4C22×D414yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4118yes—
599C22×C4C2×#4114yes—
600C4⋊C4—232no—
601C4⋊C4—416no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—88no—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—416no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4#121132yes—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—28no—
635C42—232no—
636C42—48no—
637C42—416no—
638C42—48no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—28no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—24no—
648C23—24no—
649C23—28no—
650C23—28no—
651C23—24no—
652C23—28no—
653C23—24no—
654C23—28no—
655C23—24no—
656C23—416no—
657C23—416no—
658C23—416no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—832no—
701C23—832no—
702C23—88no—
703C23—88no—
704C23—88no—
705C23—88no—
706C23C2×#12118yes—
707C23C2×#12114yes—
708C23C2×#12714yes—
709C23#53214yes—
710C23#53218yes—
711C23C23×D411yescharacteristic
712C23C23×D411yescharacteristic
713C23C23×D412yes—
714C23C22×#4111yescharacteristic
715C23C22×#4112yes—
716C23C22×#4112yes—
717C23#58512yes—
718C23#58512yes—
719C23#58512yes—
720D4—832no—
721D4—88no—
722D4—816no—
723C2×C4—232no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
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—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—88no—
798C2×C4—88no—
799C2×C4C2×#12114yes—
800C2×C4C2×#12114yes—
801C2×C4C2×#121116yes—
802C2×C4#52514yes—
803C2×C4C2×#12714yes—
804C2×C4C2×#12714yes—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—216no—
811C22—216no—
812C22—24no—
813C22—44no—
814C22—44no—
815C22—48no—
816C22—48no—
817C22—44no—
818C22—832no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—84no—
824C22—84no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—84no—
832C22—84no—
833C22—84no—
834C22—84no—
835C22—82no—
836C22#285618yes—
837C22C22×#12111yescharacteristic
838C22C22×#12112yes—
839C22C2×#52511yescharacteristic
840C22C22×#12711yescharacteristic
841C22C2×#53211yescharacteristic
842C22C2×#53212yes—
843C22#344911yescharacteristic
844C22#344911yescharacteristic
845C22#344911yescharacteristic
846C22D4×#4114yes—
847C22D4×#4112yes—
848C22#347514yes—
849C22#347512yes—
850C22#348512yes—
851C22#349112yes—
852C22#350014yes—
853C22#352114yes—
854C4—24no—
855C4—24no—
856C4—24no—
857C4—24no—
858C4—216no—
859C4—24no—
860C4—44no—
861C4—48no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C2—28no—
869C2—84no—
870C2—162no—
871C2#3473711yescharacteristic
872C2#3487711yescharacteristic
873C2#3493611yescharacteristic
874C2#3508911yescharacteristic
875C2#3514511yescharacteristic
876C2#3532911yescharacteristic
877C2#3621814yes—
878C2#3626714yes—
879C2C2×#285611yescharacteristic
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
1. C2×#2854C2semidirect
3. C2×#2413C2semidirect
4. C2×#2411C2semidirect
5. C22×#388C2semidirect
6. C2×C4×#117C2semidirect
7. #15163C2semidirect
8. #14910C2semidirect
9. #14900C2semidirect
10. #14870C2semidirect
11. #14815C2semidirect
12. #14700C2semidirect
13. #14152C2semidirect
14. #13996C2semidirect
15. #13995C2semidirect
16. #13965C2semidirect
17. #13903C2semidirect
33. C2×#398C22semidirect
35. C2×#396C22semidirect
41. C2×#390C22semidirect
42. C2×#390C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
64. C2×C4×C4⋊C4C22semidirect
65. C2×C4×C4⋊C4C22semidirect
69. C2×#376C22semidirect
72. C2×C43C22semidirect
73. #1445C22semidirect
74. #1445C22semidirect
75. #1444C22semidirect
76. #1444C22semidirect
80. #1439C22semidirect
82. #1438C22semidirect
85. #1437C22semidirect
86. #1437C22semidirect
87. C4⋊#95C22semidirect
88. C4⋊#95C22semidirect
113. C2×#117D4semidirect
156. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#25392
C2×#24132
C2×#24112
C22×#3882
C2×C4×#1172
#151632
#149102
#149002
#148702
#148152
#147002
#141522
#139962
#139952
#139652
#139032