Finite Group Databasebeta

← #360234

Subgroups — #360234

Order 512.

3186 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊C4C211yesmaximal, characteristic
2C2×#1923C212yesmaximal, complemented
3C2×#1797C211yesmaximal, characteristic, complemented
4C2×#1779C211yesmaximal, characteristic
5C2×#1779C211yesmaximal, characteristic
6C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
7#11147C212yesmaximal, complemented
8#11042C212yesmaximal, complemented
9#10921C212yesmaximal, complemented
10#10712C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C25×C4C2211yescharacteristic
13C23×C22⋊C4C411yescharacteristic
14C23×C22⋊C4C411yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×C4⋊C8C2212yescomplemented
18C22×C22⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×C22⋊C8C2212yes—
23C22×C22⋊C8C2212yes—
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C4×C8C2212yescomplemented
27C2×C4×C22⋊C4—28no—
28C2×C4×C22⋊C4C411yescharacteristic
29C2×C4×C22⋊C4C411yescharacteristic
30C2×C4×C22⋊C4C411yescharacteristic
31C2×C4×C22⋊C4C411yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C22×#95C411yescharacteristic
37C22×#95C411yescharacteristic
38#1923—28no—
39#1797—24no—
40#1779—24no—
41#1779—24no—
42C4×C22⋊C8—24no—
43C2×#336C2212yescomplemented
44C2×#336C2212yescomplemented
45C2×#336C2212yescomplemented
46C2×#336C2212yescomplemented
47C2×#336C2212yescomplemented
48C2×#336C2212yescomplemented
49C26C2×C411yescharacteristic
50C24×C4—24no—
51C24×C4—24no—
52C24×C4—22no—
53C24×C4—22no—
54C24×C4—22no—
55C24×C4—22no—
56C24×C4—22no—
57C24×C4—22no—
58C24×C4—42no—
59C24×C4—42no—
60C24×C4C2×C411yescharacteristic
61C24×C4C2×C411yescharacteristic
62C24×C4C2×C411yescharacteristic
63C24×C4C2×C411yescharacteristic
64C24×C4C2×C411yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8C2312yes—
71C23×C8C2312yes—
72C23×C8C2312yes—
73C23×C8C2312yes—
74C22×C22⋊C4—24no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—24no—
79C22×C22⋊C4C818yescomplemented
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C22⋊C4C2×C411yescharacteristic
85C22×C22⋊C4C2×C411yescharacteristic
86C22×C22⋊C4C2×C411yescharacteristic
87C22×C22⋊C4C2×C411yescharacteristic
88C22×C42—22no—
89C22×C42—22no—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—24no—
93C22×C42—24no—
94C22×C42—42no—
95C22×C42—42no—
96C22×C42C2×C411yescharacteristic
97C22×C42C2×C411yescharacteristic
98C22×C42C2×C411yescharacteristic
99C22×C42C2×C411yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×C4⋊C8—24no—
105C2×C4⋊C8—24no—
106C2×C4⋊C8—42no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—24no—
113C2×C22⋊C8—24no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—24no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—24no—
122C2×C22⋊C8—24no—
123C2×C22⋊C8—24no—
124C2×C22⋊C8—24no—
125C2×C22⋊C8—42no—
126C2×C22⋊C8—42no—
127C2×C22⋊C8—42no—
128C2×C22⋊C8—42no—
129C2×C22⋊C8D414yes—
130C2×C22⋊C8D414yes—
131C2×C4×C8—24no—
132C2×C4×C8—24no—
133C2×C4×C8—42no—
134C4×C22⋊C4—24no—
135C4×C22⋊C4—24no—
136C4×C22⋊C4—24no—
137C4×C22⋊C4—24no—
138C4×C22⋊C4—24no—
139C4×C22⋊C4—24no—
140C4×C22⋊C4—24no—
141C4×C22⋊C4D418yes—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152#336—24no—
153#336—24no—
154#336—24no—
155#336—24no—
156#336—42no—
157#336—42no—
158C25—22no—
159C25—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—41no—
169C25—41no—
170C25—41no—
171C25—41no—
172C25C2×C814yes—
173C25C22×C411yescharacteristic
174C25C22×C411yescharacteristic
175C25C22×C411yescharacteristic
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—216no—
181C23×C4—216no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—41no—
233C23×C4—41no—
234C23×C4—41no—
235C23×C4—41no—
236C23×C4—41no—
237C23×C4—41no—
238C23×C4—41no—
239C23×C4—41no—
240C23×C4—41no—
241C23×C4—41no—
242C23×C4—41no—
243C23×C4—41no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—48no—
247C23×C4—48no—
248C23×C4—48no—
249C23×C4—48no—
250C23×C4—48no—
251C23×C4—48no—
252C23×C4—48no—
253C23×C4—48no—
254C23×C4—48no—
255C23×C4—48no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4C2×C814yes—
261C23×C4C2×C814yes—
262C23×C4M1614yes—
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C411yescharacteristic
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C2×D414yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4#4114yes—
278C23×C4#4112yes—
279C23×C4#4112yes—
280C23×C4#4112yes—
281C23×C4#4112yes—
282C23×C4C2411yescharacteristic
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8C2×D414yes—
310C22×C8C2×D414yes—
311C2×C22⋊C4—232no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—232no—
329C2×C22⋊C4C22⋊C414yes—
330C2×C22⋊C4C22⋊C414yes—
331C2×C22⋊C4C2×C814yes—
332C2×C22⋊C4C2×C814yes—
333C2×C22⋊C4C2×C814yes—
334C2×C22⋊C4C2×C814yes—
335C2×C22⋊C4M1614yes—
336C2×C22⋊C4M1614yes—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—48no—
360C2×C42—48no—
361C2×C42—48no—
362C2×C42—48no—
363C2×C42—41no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42C2×D414yes—
368C2×C42C2×D414yes—
369C4⋊C8—48no—
370C22⋊C8—28no—
371C22⋊C8—28no—
372C22⋊C8—48no—
373C22⋊C8—48no—
374C22⋊C8—48no—
375C22⋊C8—48no—
376C22⋊C8—44no—
377C22⋊C8—44no—
378C4×C8—48no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95C22⋊C414yes—
386#95C22⋊C414yes—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—28no—
396C24—28no—
397C24—28no—
398C24—28no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24C2×C22⋊C412yes—
455C24#11712yes—
456C24#11712yes—
457C24C4×D412yes—
458C24C4×D412yes—
459C24C22×C812yes—
460C24C22×C812yes—
461C24C22×C812yes—
462C24C2×M1612yes—
463C24C2×M1612yes—
464C24C2×M1612yes—
465C24#13112yes—
466C24#13112yes—
467C24C23×C411yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4C2×C22⋊C412yes—
624C22×C4C2×C22⋊C412yes—
625C22×C4C2×C22⋊C412yes—
626C22×C4C2×C22⋊C412yes—
627C22×C4C2×C22⋊C412yes—
628C22×C4#11712yes—
629C22×C4#11712yes—
630C22×C4C4×D412yes—
631C22×C4C4×D412yes—
632C22×C4#12114yes—
633C22×C4#12314yes—
634C22×C4#12414yes—
635C22×C4#12614yes—
636C22×C4C22×C812yes—
637C22×C4C22×C812yes—
638C22×C4C22×C812yes—
639C22×C4C22×C812yes—
640C22×C4C2×M1612yes—
641C22×C4C2×M1612yes—
642C22×C4C2×M1612yes—
643C22×C4C2×M1612yes—
644C22×C4C2×M1612yes—
645C22×C4C2×M1612yes—
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D412yes—
649C22×C4C2×#4111yescharacteristic
650C22×C4C2×#4111yescharacteristic
651C22×C4C2×#4111yescharacteristic
652C22×C4C2×#4112yes—
653C22×C4C2×#4111yescharacteristic
654C22×C4H(5,𝔽2)12yes—
655C22×C4H(5,𝔽2)12yes—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—24no—
660C2×C8—24no—
661C2×C8—24no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—42no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—42no—
670C2×C8—42no—
671C2×C8—42no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8—42no—
683C2×C8—42no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4C22⋊C8116yescomplemented
692C42—24no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—44no—
697C42—44no—
698C42—44no—
699C42—44no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—232no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—416no—
770C23—416no—
771C23—416no—
772C23—416no—
773C23—416no—
774C23—416no—
775C23—416no—
776C23—416no—
777C23—416no—
778C23—416no—
779C23—416no—
780C23—416no—
781C23—416no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—416no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#38814yes—
816C23C2×C22⋊C814yes—
817C23#43114yes—
818C23#43114yes—
819C23#43314yes—
820C23C8×D414yes—
821C23C8×D414yes—
822C23#43514yes—
823C23#43614yes—
824C23C22×C22⋊C411yescharacteristic
825C23C2×#11711yescharacteristic
826C23C2×#11711yescharacteristic
827C23C2×C4×D411yescharacteristic
828C23C2×C4×D411yescharacteristic
829C23#51811yescharacteristic
830C23#51811yescharacteristic
831C23C23×C811yescharacteristic
832C23C22×M1611yescharacteristic
833C23C22×M1611yescharacteristic
834C23C22×M1611yescharacteristic
835C23C2×#13111yescharacteristic
836C23C2×#13111yescharacteristic
837C23#56811yescharacteristic
838C23#56811yescharacteristic
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—416no—
889C2×C4—416no—
890C2×C4—416no—
891C2×C4—416no—
892C2×C4—416no—
893C2×C4—416no—
894C2×C4—416no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4#38814yes—
932C2×C4C2×C22⋊C814yes—
933C2×C4C2×C22⋊C814yes—
934C2×C4#40714yes—
935C2×C4C2×#12111yescharacteristic
936C2×C4C2×#12311yescharacteristic
937C2×C4#52512yes—
938C2×C4#52512yes—
939C2×C4C2×#12411yescharacteristic
940C2×C4C2×#12611yescharacteristic
941C2×C4#53812yes—
942C2×C4#53812yes—
943C2×C4D4212yes—
944C2×C4D4212yes—
945C2×C4#54612yes—
946C2×C4#54612yes—
947C2×C4#54612yes—
948C2×C4#54612yes—
949C2×C4#55112yes—
950C2×C4#55112yes—
951C8—44no—
952C8—44no—
953C8—82no—
954C8—82no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22—464no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22#192318yescomplemented
1001C22#228011yescharacteristic
1002C22C2×#38811yescharacteristic
1003C22#231211yescharacteristic
1004C22D4×C22⋊C411yescharacteristic
1005C22D4×C22⋊C411yescharacteristic
1006C22#234211yescharacteristic
1007C22#234211yescharacteristic
1008C22C22×C22⋊C811yescharacteristic
1009C22C2×#40711yescharacteristic
1010C22#288011yescharacteristic
1011C22#288011yescharacteristic
1012C22C2×#43111yescharacteristic
1013C22C2×#43111yescharacteristic
1014C22C2×#43311yescharacteristic
1015C22#292011yescharacteristic
1016C22#292011yescharacteristic
1017C22#292111yescharacteristic
1018C22#292411yescharacteristic
1019C22#292411yescharacteristic
1020C22C2×C8×D411yescharacteristic
1021C22C2×C8×D411yescharacteristic
1022C22C2×#43511yescharacteristic
1023C22C2×#43611yescharacteristic
1024C22D4×M1611yescharacteristic
1025C22D4×M1611yescharacteristic
1026C22D4×M1611yescharacteristic
1027C22D4×M1611yescharacteristic
1028C22#297211yescharacteristic
1029C22#297211yescharacteristic
1030C22#297311yescharacteristic
1031C22#297411yescharacteristic
1032C22#297411yescharacteristic
1033C22#297411yescharacteristic
1034C22#297411yescharacteristic
1035C22#297511yescharacteristic
1036C4—24no—
1037C4—24no—
1038C4—24no—
1039C4—24no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4#241812yes—
1048C4#242412yes—
1049C4#247212yes—
1050C4#248012yes—
1051C2—28no—
1052C2—44no—
1053C2—44no—
1054C2#1387311yescharacteristic
1055C2#2071411yescharacteristic
1056C2#2071611yescharacteristic
1057C2C2×#192311yescharacteristic
1058C2#2104911yescharacteristic
1059C2#2190211yescharacteristic
1060C2#2190411yescharacteristic
1061C2D4×C22⋊C811yescharacteristic
1062C2D4×C22⋊C811yescharacteristic
1063C2#2239911yescharacteristic
1064C2#2240111yescharacteristic
1065C2#2255211yescharacteristic
1066C2#2255211yescharacteristic
1067C2#2255311yescharacteristic
1068C2#2255511yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC26C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#1923C2semidirect
3. C2×#1797C2semidirect
6. C2×C4×C22⋊C8C2semidirect
7. #11147C2semidirect
8. #11042C2semidirect
9. #10921C2semidirect
10. #10712C2semidirect
11. #10712C2semidirect
17. C22×C4⋊C8C22semidirect
26. C22×C4×C8C22semidirect
43. C2×#336C22semidirect
44. C2×#336C22semidirect
45. C2×#336C22semidirect
46. C2×#336C22semidirect
47. C2×#336C22semidirect
48. C2×#336C22semidirect
79. C22×C22⋊C4C8semidirect
691. C22⋊C4C22⋊C8semidirect
1000. C22#1923semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊C42
C2×#19232
C2×#17972
C2×#17792
C2×C4×C22⋊C82
#111472
#110422
#109212
#107122