Finite Group Databasebeta

← C2×#14361 #520659

Subgroups — C2×#14361 #520659

Order 512.

9390 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#121C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic, complemented
3C22×#388C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C22×#385C211yesmaximal, characteristic, complemented
7C22×#380C211yesmaximal, characteristic, complemented
8#14361C2116yesmaximal, direct product factor
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic, complemented
13C2×#1438C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C24×D4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C25×C4C2211yescharacteristic
22C22×#121—28no—
23C22×#121—28no—
24C22×#121C4116yescomplemented
25C22×#121C2218yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41C23×C22⋊C4C2211yescharacteristic
42C23×C22⋊C4C2211yescharacteristic
43C23×C42C2211yescharacteristic
44C2×#390—28no—
45C2×#390C2218yescomplemented
46C2×#388—28no—
47C2×#388C2218yescomplemented
48C2×#386—28no—
49C2×#386—28no—
50C2×#386C2218yescomplemented
51C2×#386C2218yescomplemented
52C2×#385—28no—
53C2×#385C2218yescomplemented
54C2×#380—28no—
55C2×#380C2218yescomplemented
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68#1441C2218yescomplemented
69#1439C2218yescomplemented
70#1439C2218yescomplemented
71#1438C2218yescomplemented
72#1438C2218yescomplemented
73#1438C2218yescomplemented
74#1436C2218yescomplemented
75C22⋊#95C2218yescomplemented
76C26C2311yescharacteristic
77C26C2311yescharacteristic
78C26C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—24no—
86C23×D4—24no—
87C23×D4—24no—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—24no—
91C23×D4—42no—
92C23×D4—42no—
93C23×D4—42no—
94C23×D4—42no—
95C23×D4—42no—
96C23×D4—42no—
97C23×D4C2×C418yes—
98C23×D4C2×C418yes—
99C23×D4C2×C418yescomplemented
100C23×D4C2314yes—
101C23×D4C2314yes—
102C23×D4C2314yes—
103C24×C4—24no—
104C24×C4—24no—
105C24×C4—24no—
106C24×C4—24no—
107C24×C4—24no—
108C24×C4—24no—
109C24×C4—24no—
110C24×C4—42no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4—42no—
114C24×C4—42no—
115C24×C4—42no—
116C24×C4C2×C418yescomplemented
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126C24×C4C2314yes—
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2314yes—
131C2×#121—2128no—
132C2×#121—232no—
133C2×#121—232no—
134C2×#121C2×C4164yescomplemented
135C22×C4⋊C4—24no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—42no—
144C22×C4⋊C4—42no—
145C22×C4⋊C4—42no—
146C22×C4⋊C4C2×C418yescomplemented
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2314yes—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—24no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—24no—
164C22×C22⋊C4—24no—
165C22×C22⋊C4—24no—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—42no—
168C22×C22⋊C4—42no—
169C22×C22⋊C4—42no—
170C22×C22⋊C4—42no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4—42no—
174C22×C22⋊C4—42no—
175C22×C22⋊C4—42no—
176C22×C22⋊C4—42no—
177C22×C22⋊C4—42no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4C2×C418yes—
186C22×C22⋊C4C2×C418yescomplemented
187C22×C22⋊C4D418yes—
188C22×C22⋊C4D418yes—
189C22×C22⋊C4D418yescomplemented
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2314yes—
194C22×C22⋊C4C2314yes—
195C22×C22⋊C4C2314yes—
196C22×C22⋊C4C2314yes—
197C22×C22⋊C4C2314yes—
198C22×C22⋊C4C2314yes—
199C22×C22⋊C4C2314yes—
200C22×C22⋊C4C2314yes—
201C22×C22⋊C4C2314yes—
202C22×C22⋊C4C2314yes—
203C22×C42—24no—
204C22×C42—24no—
205C22×C42—42no—
206C22×C42C2314yes—
207#390—232no—
208#388—232no—
209#386—232no—
210#386—232no—
211#385—232no—
212#380—232no—
213C2×#95—24no—
214C2×#95—24no—
215C2×#95—24no—
216C2×#95—24no—
217C2×#95—24no—
218C2×#95—24no—
219C2×#95—24no—
220C2×#95—24no—
221C2×#95—24no—
222C2×#95—42no—
223C2×#95—42no—
224C2×#95D418yescomplemented
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25—22no—
247C25—22no—
248C25—22no—
249C25—22no—
250C25—22no—
251C25—22no—
252C25—22no—
253C25—22no—
254C25—22no—
255C25—22no—
256C25—22no—
257C25—22no—
258C25—22no—
259C25—22no—
260C25—22no—
261C25—22no—
262C25—22no—
263C25—22no—
264C25—22no—
265C25—22no—
266C25—22no—
267C25—22no—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—22no—
272C25—22no—
273C25—22no—
274C25—22no—
275C25C22×C414yes—
276C25C22×C414yes—
277C25C22×C414yes—
278C25C2×D414yes—
279C25C2×D414yes—
280C25C2×D414yes—
281C25#4114yes—
282C25C2412yes—
283C25C2412yes—
284C25C2412yes—
285C25C2411yescharacteristic
286C22×D4—232no—
287C22×D4—232no—
288C22×D4—232no—
289C22×D4—232no—
290C22×D4—28no—
291C22×D4—28no—
292C22×D4—28no—
293C22×D4—28no—
294C22×D4—28no—
295C22×D4—28no—
296C22×D4—28no—
297C22×D4—28no—
298C22×D4—232no—
299C22×D4—232no—
300C22×D4—28no—
301C22×D4—28no—
302C22×D4—28no—
303C22×D4—28no—
304C22×D4—416no—
305C22×D4—416no—
306C22×D4—416no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4—44no—
310C22×D4—44no—
311C22×D4—44no—
312C22×D4—44no—
313C22×D4—416no—
314C22×D4—416no—
315C22×D4—416no—
316C22×D4—416no—
317C22×D4—416no—
318C22×D4—416no—
319C22×D4—416no—
320C22×D4—416no—
321C22×D4—416no—
322C22×D4—416no—
323C22×D4—416no—
324C22×D4—416no—
325C22×D4C22×C4116yes—
326C22×D4C22×C4116yes—
327C22×D4C22×C4116yescomplemented
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—232no—
371C23×C4—232no—
372C23×C4—28no—
373C23×C4—28no—
374C23×C4—28no—
375C23×C4—28no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—28no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—28no—
406C23×C4—28no—
407C23×C4—416no—
408C23×C4—44no—
409C23×C4—44no—
410C23×C4—44no—
411C23×C4—44no—
412C23×C4—44no—
413C23×C4—44no—
414C23×C4—416no—
415C23×C4—416no—
416C23×C4—416no—
417C23×C4—416no—
418C23×C4—416no—
419C23×C4—416no—
420C23×C4—416no—
421C23×C4—416no—
422C23×C4—416no—
423C23×C4—416no—
424C23×C4—416no—
425C23×C4C22×C414yes—
426C23×C4C22×C414yes—
427C23×C4C22×C414yes—
428C23×C4C22×C414yes—
429C23×C4C22×C4116yescomplemented
430C23×C4C2×D414yes—
431C23×C4C2×D414yes—
432C23×C4C2×D414yes—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4C2×D414yes—
438C23×C4C2×D414yes—
439C23×C4#4114yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452#121—2256no—
453C2×C4⋊C4—232no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—28no—
458C2×C4⋊C4—28no—
459C2×C4⋊C4—28no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—28no—
462C2×C4⋊C4—44no—
463C2×C4⋊C4—44no—
464C2×C4⋊C4—44no—
465C2×C4⋊C4—416no—
466C2×C4⋊C4—416no—
467C2×C4⋊C4—416no—
468C2×C4⋊C4C22×C4116yescomplemented
469C2×C22⋊C4—232no—
470C2×C22⋊C4—28no—
471C2×C22⋊C4—28no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—28no—
477C2×C22⋊C4—28no—
478C2×C22⋊C4—28no—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—416no—
487C2×C22⋊C4—44no—
488C2×C22⋊C4—44no—
489C2×C22⋊C4—44no—
490C2×C22⋊C4—44no—
491C2×C22⋊C4—44no—
492C2×C22⋊C4—44no—
493C2×C22⋊C4—44no—
494C2×C22⋊C4—44no—
495C2×C22⋊C4—44no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4—44no—
498C2×C22⋊C4—44no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—44no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4—44no—
503C2×C22⋊C4—44no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4—416no—
506C2×C22⋊C4—416no—
507C2×C22⋊C4—416no—
508C2×C22⋊C4—416no—
509C2×C22⋊C4—416no—
510C2×C22⋊C4—416no—
511C2×C22⋊C4—416no—
512C2×C22⋊C4—416no—
513C2×C22⋊C4—416no—
514C2×C22⋊C4—416no—
515C2×C22⋊C4C22⋊C4164yescomplemented
516C2×C22⋊C4C22×C4116yes—
517C2×C22⋊C4C22×C4116yescomplemented
518C2×C22⋊C4C2×D4116yes—
519C2×C22⋊C4C2×D4116yes—
520C2×C22⋊C4C2×D4116yescomplemented
521C2×C42—28no—
522C2×C42—28no—
523C2×C42—44no—
524C2×C42—416no—
525#95—28no—
526#95—28no—
527#95—28no—
528#95—28no—
529#95—28no—
530#95—28no—
531#95—28no—
532#95—28no—
533#95—28no—
534#95—44no—
535#95—44no—
536#95C2×D4116yescomplemented
537C24—28no—
538C24—28no—
539C24—28no—
540C24—28no—
541C24—28no—
542C24—28no—
543C24—28no—
544C24—28no—
545C24—28no—
546C24—28no—
547C24—28no—
548C24—28no—
549C24—28no—
550C24—28no—
551C24—28no—
552C24—28no—
553C24—28no—
554C24—28no—
555C24—28no—
556C24—28no—
557C24—28no—
558C24—28no—
559C24—28no—
560C24—28no—
561C24—28no—
562C24—28no—
563C24—28no—
564C24—28no—
565C24—28no—
566C24—28no—
567C24—28no—
568C24—28no—
569C24—28no—
570C24—28no—
571C24—28no—
572C24—28no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—28no—
598C24—28no—
599C24—28no—
600C24—28no—
601C24—28no—
602C24—28no—
603C24—28no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—44no—
619C24—44no—
620C24—44no—
621C24—44no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—44no—
642C24—44no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24C2×C22⋊C4116yes—
679C24C4×D4116yes—
680C24C23×C414yes—
681C24C23×C414yes—
682C24C23×C414yes—
683C24C23×C412yes—
684C24C22×D414yes—
685C24C22×D414yes—
686C24C22×D414yes—
687C24C22×D412yes—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C2×#4114yes—
692C24C2×#4112yes—
693C24C2×#4112yes—
694C24H(5,𝔽2)12yes—
695C24H(5,𝔽2)12yes—
696C24H(5,𝔽2)12yes—
697C24H(5,𝔽2)12yes—
698C24H(5,𝔽2)12yes—
699C24H(5,𝔽2)12yes—
700C242−1+412yes—
701C242−1+412yes—
702C24C2511yescharacteristic
703C2×D4—232no—
704C2×D4—232no—
705C2×D4—232no—
706C2×D4—232no—
707C2×D4—232no—
708C2×D4—232no—
709C2×D4—416no—
710C2×D4—416no—
711C2×D4—416no—
712C2×D4—4128no—
713C2×D4—4128no—
714C2×D4—416no—
715C2×D4—416no—
716C2×D4—416no—
717C2×D4—416no—
718C2×D4—416no—
719C2×D4—416no—
720C2×D4—416no—
721C2×D4—416no—
722C2×D4—4128no—
723C2×D4—416no—
724C2×D4—416no—
725C2×D4—416no—
726C2×D4—416no—
727C22×C4—28no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—232no—
803C22×C4—232no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—416no—
833C22×C4—4128no—
834C22×C4—416no—
835C22×C4—416no—
836C22×C4—416no—
837C22×C4—416no—
838C22×C4—416no—
839C22×C4—416no—
840C22×C4—416no—
841C22×C4—416no—
842C22×C4—416no—
843C22×C4—416no—
844C22×C4—4128no—
845C22×C4—416no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4C2×C22⋊C4116yes—
895C22×C4C2×C22⋊C4116yes—
896C22×C4C4×D4116yes—
897C22×C4C23×C414yes—
898C22×C4C23×C414yes—
899C22×C4C23×C414yes—
900C22×C4C23×C414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D414yes—
905C22×C4C22×D414yes—
906C22×C4C22×D414yes—
907C22×C4C22×D414yes—
908C22×C4C22×D414yes—
909C22×C4C22×D414yes—
910C22×C4C2×#4114yes—
911C4⋊C4—232no—
912C4⋊C4—416no—
913C4⋊C4—416no—
914C4⋊C4—416no—
915C22⋊C4—232no—
916C22⋊C4—416no—
917C22⋊C4—416no—
918C22⋊C4—416no—
919C22⋊C4—416no—
920C22⋊C4—416no—
921C22⋊C4—416no—
922C22⋊C4—416no—
923C22⋊C4—416no—
924C22⋊C4—416no—
925C22⋊C4—416no—
926C22⋊C4—416no—
927C22⋊C4C2×C22⋊C4164yescomplemented
928C42—416no—
929C23—232no—
930C23—232no—
931C23—232no—
932C23—232no—
933C23—232no—
934C23—232no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—416no—
979C23—416no—
980C23—416no—
981C23—416no—
982C23—416no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—416no—
987C23—416no—
988C23—416no—
989C23—416no—
990C23—416no—
991C23—416no—
992C23—416no—
993C23—416no—
994C23—416no—
995C23—416no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—416no—
1007C23—416no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—416no—
1015C23—416no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—416no—
1024C23—416no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—416no—
1035C23—416no—
1036C23—416no—
1037C23—416no—
1038C23—416no—
1039C23—416no—
1040C23—416no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—88no—
1070C23—88no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—88no—
1077C23C22×C22⋊C418yes—
1078C23C22×C22⋊C414yes—
1079C23C2×C4×D418yes—
1080C23C2×C4×D414yes—
1081C23C2×C4×D414yes—
1082C23#51814yes—
1083C23#51814yes—
1084C23#52014yes—
1085C23#52014yes—
1086C23#53414yes—
1087C23#53514yes—
1088C23#53514yes—
1089C23#53614yes—
1090C23#53714yes—
1091C23#53714yes—
1092C23#53714yes—
1093C23#53714yes—
1094C23#53814yes—
1095C23#53914yes—
1096C23#54014yes—
1097C23#54214yes—
1098C23D4214yes—
1099C23D4214yes—
1100C23D4214yes—
1101C23D4214yes—
1102C23D4214yes—
1103C23#54614yes—
1104C23#54614yes—
1105C23#54614yes—
1106C23#54614yes—
1107C23#54714yes—
1108C23#54814yes—
1109C23#55314yes—
1110C23#56014yes—
1111C23#56014yes—
1112C23#56214yes—
1113C23#56214yes—
1114C23C24×C411yescharacteristic
1115C23C23×D411yescharacteristic
1116C23C23×D411yescharacteristic
1117C23C23×D411yescharacteristic
1118C23C23×D411yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C22×#4111yescharacteristic
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23C2×H(5,𝔽2)11yescharacteristic
1123C23C2×H(5,𝔽2)11yescharacteristic
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×2−1+411yescharacteristic
1128C23C2×2−1+411yescharacteristic
1129D4—464no—
1130D4—464no—
1131D4—464no—
1132C2×C4—232no—
1133C2×C4—232no—
1134C2×C4—232no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—464no—
1169C2×C4—464no—
1170C2×C4—416no—
1171C2×C4—416no—
1172C2×C4—416no—
1173C2×C4—416no—
1174C2×C4—416no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—88no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—88no—
1227C2×C4C22×C22⋊C418yes—
1228C2×C4C22×C22⋊C418yes—
1229C2×C4C2×C4×D418yes—
1230C22—28no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—28no—
1235C22—28no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—464no—
1240C22—464no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—832no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22#231118yes—
1279C22#232418yes—
1280C22#232518yes—
1281C22D4×C22⋊C418yes—
1282C22D4×C22⋊C418yes—
1283C22#236118yes—
1284C22#237718yes—
1285C22#266918yes—
1286C22#267118yes—
1287C22#267218yes—
1288C22#267518yes—
1289C22#267618yes—
1290C22#268118yes—
1291C22#269118yes—
1292C22#270318yes—
1293C22C23×C22⋊C411yescharacteristic
1294C22C22×C4×D411yescharacteristic
1295C22C22×C4×D411yescharacteristic
1296C22C2×#51811yescharacteristic
1297C22C2×#51811yescharacteristic
1298C22C2×#52011yescharacteristic
1299C22C2×#52011yescharacteristic
1300C22C2×#53411yescharacteristic
1301C22C2×#53511yescharacteristic
1302C22C2×#53511yescharacteristic
1303C22C2×#53611yescharacteristic
1304C22C2×#53711yescharacteristic
1305C22C2×#53711yescharacteristic
1306C22C2×#53711yescharacteristic
1307C22C2×#53711yescharacteristic
1308C22C2×#53811yescharacteristic
1309C22C2×#53911yescharacteristic
1310C22C2×#54011yescharacteristic
1311C22C2×#54211yescharacteristic
1312C22C2×D4211yescharacteristic
1313C22C2×D4211yescharacteristic
1314C22C2×D4211yescharacteristic
1315C22C2×D4211yescharacteristic
1316C22C2×D4211yescharacteristic
1317C22C2×#54611yescharacteristic
1318C22C2×#54611yescharacteristic
1319C22C2×#54611yescharacteristic
1320C22C2×#54611yescharacteristic
1321C22C2×#54711yescharacteristic
1322C22C2×#54811yescharacteristic
1323C22C2×#55311yescharacteristic
1324C22C2×#56011yescharacteristic
1325C22C2×#56011yescharacteristic
1326C22C2×#56211yescharacteristic
1327C22C2×#56211yescharacteristic
1328C4—28no—
1329C4—28no—
1330C4—28no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—82no—
1337C4—82no—
1338C4—82no—
1339C4—82no—
1340C2—48no—
1341C2—48no—
1342C2—84no—
1343C2#14361116yesdirect product factor
1344C2C2×#231111yescharacteristic
1345C2C2×#232411yescharacteristic
1346C2C2×#232511yescharacteristic
1347C2C2×D4×C22⋊C411yescharacteristic
1348C2C2×D4×C22⋊C411yescharacteristic
1349C2C2×#236111yescharacteristic
1350C2C2×#237711yescharacteristic
1351C2C2×#266911yescharacteristic
1352C2C2×#267111yescharacteristic
1353C2C2×#267211yescharacteristic
1354C2C2×#267511yescharacteristic
1355C2C2×#267611yescharacteristic
1356C2C2×#268111yescharacteristic
1357C2C2×#269111yescharacteristic
1358C2C2×#270311yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC23×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#390C2semidirect
3. C22×#388C2semidirect
4. C22×#386C2semidirect
5. C22×#386C2semidirect
6. C22×#385C2semidirect
7. C22×#380C2semidirect
8. #14361C2direct (N × H)
9. C2×#1441C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1438C2semidirect
13. C2×#1438C2semidirect
14. C2×#1438C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
24. C22×#121C4semidirect
45. C2×#390C22semidirect
47. C2×#388C22semidirect
50. C2×#386C22semidirect
51. C2×#386C22semidirect
53. C2×#385C22semidirect
55. C2×#380C22semidirect
68. #1441C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1438C22semidirect
72. #1438C22semidirect
73. #1438C22semidirect
74. #1436C22semidirect
75. C22⋊#95C22semidirect
99. C23×D4C2×C4semidirect
116. C24×C4C2×C4semidirect
134. C2×#121C2×C4semidirect
146. C22×C4⋊C4C2×C4semidirect
186. C22×C22⋊C4C2×C4semidirect
189. C22×C22⋊C4D4semidirect
224. C2×#95D4semidirect
327. C22×D4C22×C4semidirect
429. C23×C4C22×C4semidirect
468. C2×C4⋊C4C22×C4semidirect
515. C2×C22⋊C4C22⋊C4semidirect
517. C2×C22⋊C4C22×C4semidirect
520. C2×C22⋊C4C2×D4semidirect
536. #95C2×D4semidirect
927. C22⋊C4C2×C22⋊C4semidirect
1343. C2#14361direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1212
C22×#3902
C22×#3882
C22×#3862
C22×#3852
C22×#3802
#143612
C2×#14412
C2×#14392
C2×#14382
C2×#14362
C2×C22⋊#952