Finite Group Databasebeta

← #368680

Subgroups — #368680

Order 512.

2356 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3C2×#1870C211yesmaximal, characteristic, complemented
4C2×#1870C211yesmaximal, characteristic, complemented
5C2×#1870C211yesmaximal, characteristic, complemented
6C2×#1869C211yesmaximal, characteristic, complemented
7C2×#1728C211yesmaximal, characteristic, complemented
8#11202C211yesmaximal, characteristic, complemented
9#11147C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10964C211yesmaximal, characteristic, complemented
12#10922C211yesmaximal, characteristic, complemented
13#10875C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×#121C411yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#435—24no—
25C2×#435—24no—
26C2×#435—24no—
27C22×C4⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37C22×#97C2211yescharacteristic
38C4×#121—24no—
39C4×#121—24no—
40C2×#390C411yescharacteristic
41C2×#389C411yescharacteristic
42C2×#388C411yescharacteristic
43C2×#388C411yescharacteristic
44C2×#386C411yescharacteristic
45C2×#386C411yescharacteristic
46C2×#380C411yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50#1870—24no—
51#1870—24no—
52#1870—24no—
53#1869—24no—
54#1728—24no—
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C23×D4C2×C411yescharacteristic
70C23×D4C2×C411yescharacteristic
71C23×D4C2×C411yescharacteristic
72C24×C4C2×C411yescharacteristic
73C24×C4C2×C411yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—41no—
87C22×M16—41no—
88C22×M16—41no—
89C22×M16—41no—
90C22×M16D414yescomplemented
91C23×C8—22no—
92C23×C8—22no—
93C23×C8—22no—
94C23×C8—22no—
95C23×C8—22no—
96C23×C8—41no—
97C23×C8—41no—
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—24no—
109C2×C4×D4—22no—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—22no—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—41no—
124C2×C4×D4—41no—
125C2×C4×D4D414yes—
126C2×C4×D4D414yes—
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C4⋊C4C2×C411yescharacteristic
129C22×C4⋊C4C2×C411yescharacteristic
130C22×C4⋊C4C2×C411yescharacteristic
131C22×C4⋊C4C2×C411yescharacteristic
132C22×C22⋊C4C2×C411yescharacteristic
133C22×C22⋊C4C2×C411yescharacteristic
134C22×C22⋊C4C2×C411yescharacteristic
135C22×C22⋊C4C2×C411yescharacteristic
136C22×C22⋊C4C2×C411yescharacteristic
137C22×C22⋊C4C2×C411yescharacteristic
138C22×C22⋊C4C2×C411yescharacteristic
139C22×C22⋊C4C2×C411yescharacteristic
140C22×C22⋊C4C2×C411yescharacteristic
141C22×C22⋊C4C2×C411yescharacteristic
142C22×C42—22no—
143C22×C42—22no—
144C22×C42—22no—
145C22×C42—22no—
146C22×C42—41no—
147C22×C42—41no—
148C22×C42C2×C411yescharacteristic
149C22×C42C2×C411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#435—232no—
155C2×C4⋊C8—22no—
156C2×C4⋊C8—22no—
157C2×C4⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—22no—
161C2×C22⋊C8—22no—
162C2×C22⋊C8—22no—
163C2×C22⋊C8—22no—
164C2×C22⋊C8—22no—
165C2×C22⋊C8—22no—
166C2×C22⋊C8—22no—
167C2×C22⋊C8—22no—
168C2×C22⋊C8—22no—
169C2×C22⋊C8—22no—
170C2×C22⋊C8—22no—
171C2×C22⋊C8—22no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—22no—
175C2×C22⋊C8—22no—
176C2×C22⋊C8—22no—
177C2×C22⋊C8—22no—
178C2×C22⋊C8—41no—
179C2×C22⋊C8—41no—
180C2×C22⋊C8—41no—
181C2×C22⋊C8—41no—
182C2×C22⋊C8—41no—
183C2×C22⋊C8—41no—
184C2×C22⋊C8D414yescomplemented
185C2×#97—22no—
186C2×#97—22no—
187C2×#97—22no—
188#390—24no—
189#389—24no—
190#388—24no—
191#388—24no—
192#386—24no—
193#386—24no—
194#380—24no—
195C4×C4⋊C4—22no—
196C4×C4⋊C4—22no—
197C4×C22⋊C4—22no—
198C4×C22⋊C4—22no—
199C4×C22⋊C4—22no—
200C4×C22⋊C4—22no—
201C2×#95C2×C411yescharacteristic
202C2×#95C2×C411yescharacteristic
203C2×#95C2×C411yescharacteristic
204C2×#95C2×C411yescharacteristic
205C2×#95C2×C411yescharacteristic
206C2×#95C2×C411yescharacteristic
207#336—22no—
208#336—22no—
209#336—22no—
210#336—22no—
211#336—22no—
212#336—22no—
213#336—22no—
214#336—22no—
215#336—22no—
216#336—22no—
217#336—22no—
218#336—41no—
219#336—41no—
220#336D414yescomplemented
221C25C22×C411yescharacteristic
222C25C22×C411yescharacteristic
223C25C22×C411yescharacteristic
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—41no—
238C22×D4—41no—
239C22×D4—41no—
240C22×D4—41no—
241C22×D4—41no—
242C22×D4—41no—
243C22×D4C22⋊C414yes—
244C22×D4M1614yescomplemented
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4—41no—
290C23×C4—41no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4C22×C411yescharacteristic
294C23×C4C22×C411yescharacteristic
295C23×C4C22×C411yescharacteristic
296C23×C4C22×C411yescharacteristic
297C23×C4C22×C411yescharacteristic
298C23×C4C22×C411yescharacteristic
299C23×C4C22×C411yescharacteristic
300C23×C4C22×C411yescharacteristic
301C23×C4C22×C411yescharacteristic
302C23×C4C22×C411yescharacteristic
303C23×C4C22×C411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D412yes—
309C23×C4C2×D412yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4C2411yescharacteristic
313C2×M16—28no—
314C2×M16—28no—
315C2×M16—28no—
316C2×M16—44no—
317C2×M16—44no—
318C2×M16—44no—
319C2×M16—44no—
320C2×M16—44no—
321C2×M16—44no—
322C2×M16—44no—
323C2×M16—44no—
324C2×M16—44no—
325C2×M16—44no—
326C2×M16—44no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—28no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—44no—
377C22×C8—44no—
378C22×C8—44no—
379C22×C8—44no—
380C22×C8—44no—
381C22×C8—44no—
382C22×C8C2×D412yes—
383C22×C8C2×D412yes—
384C22×C8C2×D412yes—
385C22×C8C2×D412yes—
386C22×C8C2×D412yes—
387C22×C8C2×D412yes—
388C22×C8#4112yes—
389C22×C8#4112yes—
390#121—232no—
391C4×D4—28no—
392C4×D4—28no—
393C4×D4—28no—
394C4×D4—28no—
395C4×D4—44no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—44no—
399C4×D4—44no—
400C4×D4—44no—
401C4×D4—44no—
402C4×D4—44no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4C22⋊C414yes—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4C22⋊C414yes—
446C2×C22⋊C4C22⋊C414yes—
447C2×C22⋊C4M1614yescomplemented
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—44no—
473C2×C42—44no—
474C2×C42—44no—
475C2×C42—44no—
476C2×C42—41no—
477C2×C42—41no—
478C2×C42C2×D412yes—
479C2×C42C2×D412yes—
480C2×C42C2×D412yes—
481C2×C42#4112yes—
482C4⋊C8—28no—
483C22⋊C8—28no—
484C22⋊C8—28no—
485C22⋊C8—44no—
486C22⋊C8—44no—
487C22⋊C8—44no—
488C22⋊C8—44no—
489C22⋊C8—44no—
490C22⋊C8—44no—
491C22⋊C8—44no—
492#97—28no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×C22⋊C412yes—
538C24C2×C22⋊C412yes—
539C24C4×D412yes—
540C24C4×D412yes—
541C24C2×M1612yes—
542C24C2×M1612yes—
543C24C2×M1612yes—
544C24C23×C411yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—44no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—28no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—44no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C2×C22⋊C412yes—
725C22×C4C2×C22⋊C412yes—
726C22×C4C2×C22⋊C412yes—
727C22×C4C2×C22⋊C412yes—
728C22×C4C4×D412yes—
729C22×C4C4×D412yes—
730C22×C4C4×D412yes—
731C22×C4C4×D412yes—
732C22×C4#12014yes—
733C22×C4#12114yes—
734C22×C4#12114yes—
735C22×C4#12314yes—
736C22×C4C2×M1612yes—
737C22×C4C2×M1612yes—
738C22×C4C2×M1612yes—
739C22×C4#13112yes—
740C22×C4#13112yes—
741C22×C4C22×D411yescharacteristic
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D411yescharacteristic
745C22×C4C22×D411yescharacteristic
746C22×C4C2×#4111yescharacteristic
747C22×C4C2×#4111yescharacteristic
748C22×C4C2×#4111yescharacteristic
749C22×C4C2×#4111yescharacteristic
750C22×C4C2×#4111yescharacteristic
751C22×C4H(5,𝔽2)11yescharacteristic
752C22×C4H(5,𝔽2)11yescharacteristic
753C22×C4H(5,𝔽2)11yescharacteristic
754C22×C42−1+411yescharacteristic
755M16—416no—
756M16—416no—
757C2×C8—22no—
758C2×C8—22no—
759C2×C8—22no—
760C2×C8—22no—
761C2×C8—22no—
762C2×C8—22no—
763C2×C8—22no—
764C2×C8—22no—
765C2×C8—22no—
766C2×C8—22no—
767C2×C8—22no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—416no—
779C2×C8—41no—
780C2×C8—41no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8—41no—
784C2×C8—41no—
785C2×C8—41no—
786C2×C8—41no—
787C2×C8—41no—
788C2×C8—41no—
789C2×C8—41no—
790C2×C8—41no—
791C2×C8—41no—
792C2×C8—41no—
793C2×C8—41no—
794C2×C8—41no—
795C2×C8—41no—
796C2×C8—41no—
797C2×C8—41no—
798C2×C8—41no—
799C2×C8—41no—
800C2×C8—41no—
801C2×C8—41no—
802C2×C8—41no—
803C2×C8—41no—
804C2×C8—41no—
805C2×C8—41no—
806C2×C8—41no—
807C2×C8—41no—
808C2×C8—41no—
809C2×C8—41no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8#12114yescomplemented
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—22no—
837C42—44no—
838C42—44no—
839C42—41no—
840C42—41no—
841C42—41no—
842C42—41no—
843C42—41no—
844C42—41no—
845C42—41no—
846C42—41no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23#38614yes—
951C23#40714yes—
952C23C22×C22⋊C411yescharacteristic
953C23C2×C4×D411yescharacteristic
954C23C2×C4×D411yescharacteristic
955C23C2×C4×D411yescharacteristic
956C23C4×#4111yescharacteristic
957C23#51811yescharacteristic
958C23#52011yescharacteristic
959C23C22×M1611yescharacteristic
960C23C22×M1611yescharacteristic
961C23C2×#13111yescharacteristic
962C23C2×#13111yescharacteristic
963C23#56811yescharacteristic
964C23#56811yescharacteristic
965C23#56811yescharacteristic
966C23#56811yescharacteristic
967D4—416no—
968D4—416no—
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—416no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—81no—
1064C2×C4—81no—
1065C2×C4—81no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—81no—
1069C2×C4—81no—
1070C2×C4—81no—
1071C2×C4#38614yes—
1072C2×C4#43514yescomplemented
1073C2×C4C2×#12011yescharacteristic
1074C2×C4C2×#12111yescharacteristic
1075C2×C4C2×#12111yescharacteristic
1076C2×C4C2×#12111yescharacteristic
1077C2×C4C2×#12311yescharacteristic
1078C2×C4#52511yescharacteristic
1079C2×C4#52911yescharacteristic
1080C2×C4#53211yescharacteristic
1081C2×C4#53411yescharacteristic
1082C2×C4#53711yescharacteristic
1083C2×C4#53811yescharacteristic
1084C2×C4#53911yescharacteristic
1085C2×C4D4211yescharacteristic
1086C2×C4D4211yescharacteristic
1087C2×C4D4211yescharacteristic
1088C2×C4#54611yescharacteristic
1089C2×C4#54611yescharacteristic
1090C2×C4#54611yescharacteristic
1091C2×C4#54611yescharacteristic
1092C2×C4#54611yescharacteristic
1093C2×C4#54611yescharacteristic
1094C2×C4#54711yescharacteristic
1095C2×C4#54711yescharacteristic
1096C2×C4#54711yescharacteristic
1097C2×C4#54811yescharacteristic
1098C2×C4#55311yescharacteristic
1099C2×C4#55311yescharacteristic
1100C2×C4#55311yescharacteristic
1101C8—24no—
1102C8—42no—
1103C8—42no—
1104C8—42no—
1105C8—42no—
1106C8—42no—
1107C8—81no—
1108C8—81no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22C2×#38611yescharacteristic
1155C22C4×#12111yescharacteristic
1156C22#232511yescharacteristic
1157C22D4×C22⋊C411yescharacteristic
1158C22#233911yescharacteristic
1159C22#236111yescharacteristic
1160C22#236411yescharacteristic
1161C22C2×#40711yescharacteristic
1162C22#287911yescharacteristic
1163C22#288011yescharacteristic
1164C22#288011yescharacteristic
1165C22C2×#43511yescharacteristic
1166C22#293011yescharacteristic
1167C22#293111yescharacteristic
1168C22#293211yescharacteristic
1169C22#293311yescharacteristic
1170C22D4×M1611yescharacteristic
1171C22D4×M1611yescharacteristic
1172C22D4×M1611yescharacteristic
1173C22D4×M1611yescharacteristic
1174C22D4×M1611yescharacteristic
1175C22#293511yescharacteristic
1176C22#293511yescharacteristic
1177C22#296511yescharacteristic
1178C22#296711yescharacteristic
1179C22#296911yescharacteristic
1180C22#297011yescharacteristic
1181C22#297311yescharacteristic
1182C22#297411yescharacteristic
1183C22#297611yescharacteristic
1184C22#297811yescharacteristic
1185C22#298911yescharacteristic
1186C22#299011yescharacteristic
1187C22#299311yescharacteristic
1188C22#299511yescharacteristic
1189C4—24no—
1190C4—24no—
1191C4—42no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—81no—
1200C4#241011yescharacteristic
1201C4#241611yescharacteristic
1202C4#242411yescharacteristic
1203C4#242511yescharacteristic
1204C4#243011yescharacteristic
1205C4#244311yescharacteristic
1206C4#244411yescharacteristic
1207C4#254311yescharacteristic
1208C2—44no—
1209C2—44no—
1210C2—82no—
1211C2#1402311yescharacteristic
1212C2#2089811yescharacteristic
1213C2#2090011yescharacteristic
1214C2#2148611yescharacteristic
1215C2#2149011yescharacteristic
1216C2#2217011yescharacteristic
1217C2#2217411yescharacteristic
1218C2#2239911yescharacteristic
1219C2#2240011yescharacteristic
1220C2#2247111yescharacteristic
1221C2#2247211yescharacteristic
1222C2#2298611yescharacteristic
1223C2#2298811yescharacteristic
1224C2#2311811yescharacteristic
1225C2#2311911yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC22×#121C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#435C2semidirect
3. C2×#1870C2semidirect
4. C2×#1870C2semidirect
5. C2×#1870C2semidirect
6. C2×#1869C2semidirect
7. C2×#1728C2semidirect
8. #11202C2semidirect
9. #11147C2semidirect
10. #11042C2semidirect
11. #10964C2semidirect
12. #10922C2semidirect
13. #10875C2semidirect
14. #10714C2semidirect
15. #10712C2semidirect
90. C22×M16D4semidirect
184. C2×C22⋊C8D4semidirect
220. #336D4semidirect
244. C22×D4M16semidirect
447. C2×C22⋊C4M16semidirect
813. C2×C8#121semidirect
1072. C2×C4#435semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×C4×#1212
C2×#18702
C2×#18692
C2×#17282
#112022
#111472
#110422
#109642
#109222
#108752
#107142
#107122