Finite Group Databasebeta

← #195922

Subgroups — #195922

Order 512.

1730 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#431C211yesmaximal, characteristic, complemented
2C2×#2290C211yesmaximal, characteristic
3#20714C211yesmaximal, characteristic, complemented
4C2×#1458C212yesmaximal, complemented
5#9082C212yesmaximal, complemented
6#9081C212yesmaximal, complemented
7#9080C212yesmaximal, complemented
8#9079C212yesmaximal
9#7906C212yesmaximal, complemented
10C22×C4×D4C411yescharacteristic
11C22×#117C2211yescharacteristic
12C23×C42C2211yescharacteristic
13C2×#431—21no—
14C2×#431—21no—
15C2×#431—28no—
16C2×#431C2212yes—
17C2×#431C2212yes—
18C2×#431C2212yes—
19C22×C4⋊C8—21no—
20C22×C22⋊C8C2212yes—
21C22×C4×C8—21no—
22#2290—21no—
23#2290—21no—
24#2290—21no—
25#2290—21no—
26#2290—21no—
27#2290—21no—
28#2290—21no—
29#2290—21no—
30C2×#388C411yescharacteristic
31C2×#388C2211yescharacteristic
32C2×#387C411yescharacteristic
33C2×#387C2211yescharacteristic
34C2×#386C411yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#385C411yescharacteristic
37C2×#385C2211yescharacteristic
38C2×C4×C4⋊C4C411yescharacteristic
39C2×C4×C22⋊C4C411yescharacteristic
40C2×C4×C22⋊C4C411yescharacteristic
41C2×#376C2211yescharacteristic
42#1817C2212yes—
43#1797—21no—
44#1797—21no—
45#1779C2212yes—
46C4×C22⋊C8—21no—
47C4×C22⋊C8—21no—
48#1458—28no—
49C2×#324C2214yes—
50C2×#323C2214yes—
51#1280C2214yes—
52#1280C2214yes—
53C23×D4C2×C411yescharacteristic
54C24×C4C2×C411yescharacteristic
55C24×C4C2×C411yescharacteristic
56C24×C4C2×C411yescharacteristic
57C24×C4C2311yescharacteristic
58C23×C8—22no—
59C2×C4×D4—21no—
60C2×C4×D4—21no—
61C2×C4×D4—21no—
62C2×C4×D4—21no—
63C2×C4×D4—24no—
64C2×C4×D4C818yescomplemented
65C2×#117—24no—
66C2×#117—21no—
67C2×#117—21no—
68C2×#117—21no—
69C2×#117—21no—
70C2×#117—24no—
71C22×C4⋊C4C2×C411yescharacteristic
72C22×C4⋊C4C2×C411yescharacteristic
73C22×C4⋊C4C2×C411yescharacteristic
74C22×C4⋊C4C2×C411yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C22⋊C4C2×C411yescharacteristic
77C22×C22⋊C4C2×C411yescharacteristic
78C22×C22⋊C4C2×C411yescharacteristic
79C22×C22⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2311yescharacteristic
84C22×C42—24no—
85C22×C42—24no—
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101#431—28no—
102#431—28no—
103#431—24no—
104#431—28no—
105#431—24no—
106#431—24no—
107#431D418yescomplemented
108C2×C4⋊C8—28no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—28no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8C2314yes—
117C2×C22⋊C8C2314yes—
118C2×C4×C8—28no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8—22no—
122#388—21no—
123#388—21no—
124#388—21no—
125#388—21no—
126#388—21no—
127#388—21no—
128#388—21no—
129#388—21no—
130#387—21no—
131#387—21no—
132#387—21no—
133#387—21no—
134#387—21no—
135#387—21no—
136#387—21no—
137#387—21no—
138#386—21no—
139#386—21no—
140#386—21no—
141#386—21no—
142#386—21no—
143#386—21no—
144#386—21no—
145#386—21no—
146#385—21no—
147#385—21no—
148#385—21no—
149#385—21no—
150#385—21no—
151#385—21no—
152#385—21no—
153#385—21no—
154C4×C4⋊C4—21no—
155C4×C4⋊C4—21no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4—21no—
166#376—21no—
167#376—21no—
168#376—21no—
169#376—21no—
170C2×#95C2×C411yescharacteristic
171C2×#95C2×C411yescharacteristic
172C2×#95C2×C411yescharacteristic
173C2×#95C2×C411yescharacteristic
174C2×#95C2×C411yescharacteristic
175C2×#95C2×C411yescharacteristic
176C2×#95C2×C411yescharacteristic
177C2×#95C2×C411yescharacteristic
178C2×#95C2311yescharacteristic
179C2×#95C2311yescharacteristic
180#336—22no—
181#336—22no—
182#324—28no—
183#323—28no—
184C25C22×C411yescharacteristic
185C25C22×C411yescharacteristic
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—22no—
189C22×D4—42no—
190C22×D4—42no—
191C22×D4C2×C814yes—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—22no—
199C23×C4—24no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4C22⋊C411yescharacteristic
207C23×C4C22⋊C411yescharacteristic
208C23×C4C22⋊C411yescharacteristic
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22⋊C411yescharacteristic
211C23×C4C22⋊C411yescharacteristic
212C23×C4C22⋊C411yescharacteristic
213C23×C4C22⋊C411yescharacteristic
214C23×C4C2×C814yes—
215C23×C4C2×C814yescomplemented
216C23×C4M1614yes—
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2411yescharacteristic
234C22×C8—28no—
235C22×C8—24no—
236C22×C8—24no—
237C22×C8—44no—
238C22×C8—44no—
239C4×D4—28no—
240C4×D4—28no—
241C4×D4—28no—
242C4×D4—28no—
243#117—42no—
244#117—42no—
245#117—44no—
246#117—44no—
247#117—42no—
248#117—42no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4C2×C814yescomplemented
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4C2×C814yes—
292C2×C22⋊C4C2×C814yescomplemented
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—24no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42C22⋊C411yescharacteristic
319C2×C42C22⋊C411yescharacteristic
320C2×C42C22⋊C411yescharacteristic
321C2×C42C22⋊C411yescharacteristic
322C2×C42C22⋊C411yescharacteristic
323C2×C42C22⋊C411yescharacteristic
324C2×C42C22⋊C411yescharacteristic
325C2×C42C22⋊C411yescharacteristic
326C2×C42C2×C814yescomplemented
327C2×C42C2×D411yescharacteristic
328C2×C42C2×D411yescharacteristic
329C2×C42C2×D411yescharacteristic
330C2×C42C2×D411yescharacteristic
331C2×C42C2×D414yes—
332C2×C42C2×D411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42#4114yes—
337C4⋊C8—28no—
338C4⋊C8—28no—
339C4⋊C8—44no—
340C22⋊C8—28no—
341C22⋊C8—24no—
342C22⋊C8—24no—
343C22⋊C8—24no—
344C22⋊C8—44no—
345C22⋊C8—44no—
346C22⋊C8C2×D418yes—
347C4×C8—28no—
348C4×C8—28no—
349C4×C8—44no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—21no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24C2×C22⋊C411yescharacteristic
385C24C2×C22⋊C411yescharacteristic
386C24C22×C812yes—
387C24C22×C812yes—
388C24C2×M1612yes—
389C24C23×C411yescharacteristic
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—48no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—48no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—216no—
416C22×C4—216no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—216no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—48no—
466C22×C4—416no—
467C22×C4—48no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—48no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4C22⋊C814yes—
486C22×C4C22⋊C814yes—
487C22×C4C22⋊C814yes—
488C22×C4C22⋊C814yes—
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C4×D414yes—
500C22×C4C4×D414yes—
501C22×C4C22×C812yes—
502C22×C4C22×C812yes—
503C22×C4C22×C812yes—
504C22×C4C22×C812yes—
505C22×C4C22×C812yes—
506C22×C4C2×M1612yes—
507C22×C4C2×M1612yes—
508C22×C4#13114yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D412yes—
512C22×C4C2×#4112yes—
513C2×C8—28no—
514C2×C8—416no—
515C2×C8—44no—
516C2×C8—44no—
517C2×C8—44no—
518C2×C8—44no—
519C2×C8—44no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—41no—
525C4⋊C4—42no—
526C4⋊C4—41no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—41no—
542C22⋊C4—42no—
543C22⋊C4—41no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C42—21no—
549C42—21no—
550C42—22no—
551C42—22no—
552C42—21no—
553C42—21no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—22no—
562C42—24no—
563C42—24no—
564C42—42no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42#12012yes—
569C42#12012yes—
570C42#12114yes—
571C42#12114yes—
572C42#12312yes—
573C42#12312yes—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—21no—
592C23—22no—
593C23—24no—
594C23—42no—
595C23—42no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—41no—
611C23—82no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23C2×C22⋊C812yes—
616C23C2×C22⋊C812yes—
617C23#41012yes—
618C23#41312yes—
619C23C22×C22⋊C411yescharacteristic
620C23C2×C4×D412yes—
621C23C23×C811yescharacteristic
622C23C22×M1611yescharacteristic
623C23C2×#13112yes—
624D4—48no—
625D4—48no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—28no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—24no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—48no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4#38612yes—
703C2×C4#38612yes—
704C2×C4#38612yes—
705C2×C4#38612yes—
706C2×C4C2×C22⋊C812yes—
707C2×C4C2×C22⋊C812yes—
708C2×C4C2×C22⋊C812yes—
709C2×C4C2×C22⋊C812yes—
710C2×C4#40812yes—
711C2×C4#40812yes—
712C2×C4#41012yes—
713C2×C4#41312yes—
714C2×C4C8×D418yes—
715C2×C4#43518yes—
716C2×C4C2×#12011yescharacteristic
717C2×C4C2×#12112yes—
718C2×C4C2×#12311yescharacteristic
719C8—48no—
720C8—84no—
721C22—22no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—48no—
739C22—48no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—84no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22#145814yescomplemented
754C22C2×#38611yescharacteristic
755C22C22×C22⋊C811yescharacteristic
756C22C2×#40811yescharacteristic
757C22C2×#41011yescharacteristic
758C22C2×#41011yescharacteristic
759C22C2×#41311yescharacteristic
760C22C2×#41311yescharacteristic
761C22C2×C8×D412yes—
762C22C2×#43512yes—
763C4—22no—
764C4—22no—
765C4—21no—
766C4—22no—
767C4—21no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—41no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4#186914yes—
782C4#186914yes—
783C2—22no—
784C2—22no—
785C2—24no—
786C2—42no—
787C2—82no—
788C2C2×#145811yescharacteristic
789C2#1734911yescharacteristic
790C2#1737611yescharacteristic
791C2#1738011yescharacteristic
792C2C2×#186911yescharacteristic
793C2#2098311yescharacteristic
794C2#2098911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC23C23×C8
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC23×D4C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#431C2semidirect
3. #20714C2semidirect
4. C2×#1458C2semidirect
5. #9082C2semidirect
6. #9081C2semidirect
7. #9080C2semidirect
9. #7906C2semidirect
64. C2×C4×D4C8semidirect
107. #431D4semidirect
215. C23×C4C2×C8semidirect
265. C2×C4⋊C4C2×C8semidirect
292. C2×C22⋊C4C2×C8semidirect
326. C2×C42C2×C8semidirect
753. C22#1458semidirect

Maximal subgroups

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

subgroupindex
C22×#4312
C2×#22902
#207142
C2×#14582
#90822
#90812
#90802
#90792
#79062