Finite Group Databasebeta

← C2×#16275 #610754

Subgroups — C2×#16275 #610754

Order 512.

5166 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#387C211yesmaximal, characteristic, complemented
5#16275C2116yesmaximal, direct product factor
6C2×#1441C211yesmaximal, characteristic, complemented
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1439C211yesmaximal, characteristic, complemented
15C2×#1438C211yesmaximal, characteristic
16C2×#1436C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#397—28no—
37C2×#397C2218yescomplemented
38C2×#394—28no—
39C2×#394C2218yes—
40C2×#390—28no—
41C2×#390C2218yes—
42C2×#387—28no—
43C2×#387C2218yescomplemented
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1441C2218yescomplemented
61#1441C2218yescomplemented
62#1440C2218yescomplemented
63#1440C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1436C2218yescomplemented
71C26C2311yescharacteristic
72C26C2311yescharacteristic
73C23×D4—24no—
74C23×D4—24no—
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—42no—
79C23×D4—42no—
80C23×D4C2314yes—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4D418yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4D418yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C42—24no—
163C22×C42—24no—
164C22×C42—42no—
165C22×C42C2314yes—
166#397—232no—
167#394—232no—
168#390—232no—
169#387—232no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95—42no—
183C2×#95—42no—
184C2×#95—42no—
185C2×#95—42no—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25C2×D414yes—
231C25#4114yes—
232C25C2412yes—
233C25C2412yes—
234C25C2411yescharacteristic
235C22×D4—232no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—416no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4—416no—
247C22×D4—416no—
248C22×D4—416no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4C2×D414yes—
334C23×C4C2×D414yes—
335C23×C4C2×D414yes—
336C23×C4#4114yes—
337C23×C4#4114yes—
338C23×C4#4114yes—
339C23×C4#4114yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C2×C4⋊C4—232no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—416no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—416no—
371C2×C4⋊C4—416no—
372C2×C4⋊C4C2×D4116yes—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—416no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—416no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4—416no—
412C2×C22⋊C4—416no—
413C2×C22⋊C4—416no—
414C2×C22⋊C4—416no—
415C2×C22⋊C4—416no—
416C2×C22⋊C4—416no—
417C2×C22⋊C4—416no—
418C2×C22⋊C4—416no—
419C2×C22⋊C4—416no—
420C2×C22⋊C4C2×D4116yes—
421C2×C42—28no—
422C2×C42—28no—
423C2×C42—44no—
424C2×C42—416no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441C24—28no—
442C24—28no—
443C24—28no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24C22×D414yes—
540C24C22×D412yes—
541C24C22×D412yes—
542C24C2×#4114yes—
543C24C2×#4112yes—
544C24C2×#4112yes—
545C24C2×#4112yes—
546C24C2×#4112yes—
547C24C2×#4112yes—
548C24H(5,𝔽2)12yes—
549C24H(5,𝔽2)12yes—
550C24H(5,𝔽2)12yes—
551C24H(5,𝔽2)12yes—
552C24H(5,𝔽2)12yes—
553C24H(5,𝔽2)12yes—
554C242−1+412yes—
555C242−1+412yes—
556C24C2511yescharacteristic
557C2×D4—232no—
558C2×D4—416no—
559C2×D4—416no—
560C2×D4—416no—
561C2×D4—416no—
562C2×D4—4128no—
563C2×D4—416no—
564C2×D4—416no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
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—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
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—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4#123116yes—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C22×D414yes—
741C22×C4C22×D414yes—
742C22×C4C22×D414yes—
743C22×C4C2×#4114yes—
744C22×C4C2×#4114yes—
745C22×C4C2×#4114yes—
746C22×C4C2×#4114yes—
747C4⋊C4—232no—
748C4⋊C4—416no—
749C4⋊C4—416no—
750C4⋊C4—416no—
751C4⋊C4—416no—
752C22⋊C4—416no—
753C22⋊C4—416no—
754C22⋊C4—416no—
755C22⋊C4—416no—
756C22⋊C4—416no—
757C22⋊C4—416no—
758C22⋊C4—416no—
759C22⋊C4—416no—
760C22⋊C4—416no—
761C22⋊C4—416no—
762C22⋊C4—416no—
763C22⋊C4—416no—
764C42—416no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—416no—
780C23—416no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—416no—
786C23—416no—
787C23—416no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—416no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—416no—
832C23—416no—
833C23—42no—
834C23—42no—
835C23—416no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—416no—
849C23—88no—
850C23—88no—
851C23—88no—
852C23—88no—
853C23—88no—
854C23—88no—
855C23—88no—
856C23—88no—
857C23—88no—
858C23—88no—
859C23—88no—
860C23—88no—
861C23—88no—
862C23—88no—
863C23—88no—
864C23—88no—
865C23C2×#12314yes—
866C23#52514yes—
867C23#52914yes—
868C23#53414yes—
869C23#53514yes—
870C23#53714yes—
871C23#53714yes—
872C23#53814yes—
873C23#53814yes—
874C23#53814yes—
875C23#53814yes—
876C23#53814yes—
877C23#53914yes—
878C23#54014yes—
879C23#54014yes—
880C23#54014yes—
881C23#54214yes—
882C23#54214yes—
883C23#54214yes—
884C23D4214yes—
885C23#54614yes—
886C23#54614yes—
887C23#54614yes—
888C23#54714yes—
889C23#54814yes—
890C23#55014yes—
891C23#55114yes—
892C23#55214yes—
893C23#55314yes—
894C23#55614yes—
895C23#55914yes—
896C23#56014yes—
897C23#56214yes—
898C23#56214yes—
899C23#56314yes—
900C23C23×D411yescharacteristic
901C23C23×D411yescharacteristic
902C23C22×#4111yescharacteristic
903C23C22×#4111yescharacteristic
904C23C22×#4111yescharacteristic
905C23C22×#4111yescharacteristic
906C23C22×#4111yescharacteristic
907C23C2×H(5,𝔽2)11yescharacteristic
908C23C2×H(5,𝔽2)11yescharacteristic
909C23C2×H(5,𝔽2)11yescharacteristic
910C23C2×H(5,𝔽2)11yescharacteristic
911C23C2×H(5,𝔽2)11yescharacteristic
912C23C2×H(5,𝔽2)11yescharacteristic
913C23C2×2−1+411yescharacteristic
914C23C2×2−1+411yescharacteristic
915D4—464no—
916C2×C4—24no—
917C2×C4—232no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—416no—
942C2×C4—416no—
943C2×C4—42no—
944C2×C4—416no—
945C2×C4—416no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—416no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—416no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—88no—
1014C2×C4—88no—
1015C2×C4—88no—
1016C2×C4—88no—
1017C2×C4—88no—
1018C2×C4—88no—
1019C2×C4C2×#12318yes—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—44no—
1033C22—44no—
1034C22—82no—
1035C22—82no—
1036C22—82no—
1037C22—82no—
1038C22—82no—
1039C22—82no—
1040C22—82no—
1041C22—82no—
1042C22—82no—
1043C22—82no—
1044C22—82no—
1045C22—832no—
1046C22—832no—
1047C22—82no—
1048C22—82no—
1049C22—82no—
1050C22—82no—
1051C22—82no—
1052C22#241818yes—
1053C22#244818yes—
1054C22#246818yes—
1055C22#262418yes—
1056C22#263018yes—
1057C22#264818yes—
1058C22#267618yes—
1059C22#268218yes—
1060C22#270718yes—
1061C22#270918yes—
1062C22#271418yes—
1063C22#271518yes—
1064C22#275118yes—
1065C22#278618yes—
1066C22#283018yes—
1067C22C22×#12311yescharacteristic
1068C22C2×#52511yescharacteristic
1069C22C2×#52911yescharacteristic
1070C22C2×#53411yescharacteristic
1071C22C2×#53511yescharacteristic
1072C22C2×#53711yescharacteristic
1073C22C2×#53711yescharacteristic
1074C22C2×#53811yescharacteristic
1075C22C2×#53811yescharacteristic
1076C22C2×#53811yescharacteristic
1077C22C2×#53811yescharacteristic
1078C22C2×#53811yescharacteristic
1079C22C2×#53911yescharacteristic
1080C22C2×#54011yescharacteristic
1081C22C2×#54011yescharacteristic
1082C22C2×#54011yescharacteristic
1083C22C2×#54211yescharacteristic
1084C22C2×#54211yescharacteristic
1085C22C2×#54211yescharacteristic
1086C22C2×D4211yescharacteristic
1087C22C2×#54611yescharacteristic
1088C22C2×#54611yescharacteristic
1089C22C2×#54611yescharacteristic
1090C22C2×#54711yescharacteristic
1091C22C2×#54811yescharacteristic
1092C22C2×#55011yescharacteristic
1093C22C2×#55111yescharacteristic
1094C22C2×#55211yescharacteristic
1095C22C2×#55311yescharacteristic
1096C22C2×#55611yescharacteristic
1097C22C2×#55911yescharacteristic
1098C22C2×#56011yescharacteristic
1099C22C2×#56211yescharacteristic
1100C22C2×#56211yescharacteristic
1101C22C2×#56311yescharacteristic
1102C4—28no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—82no—
1110C4—82no—
1111C4—82no—
1112C4—82no—
1113C4—82no—
1114C4—82no—
1115C2—84no—
1116C2—84no—
1117C2#16275116yesdirect product factor
1118C2C2×#263011yescharacteristic
1119C2C2×#264811yescharacteristic
1120C2C2×#262411yescharacteristic
1121C2C2×#241811yescharacteristic
1122C2C2×#246811yescharacteristic
1123C2C2×#244811yescharacteristic
1124C2C2×#283011yescharacteristic
1125C2C2×#267611yescharacteristic
1126C2C2×#268211yescharacteristic
1127C2C2×#270711yescharacteristic
1128C2C2×#270911yescharacteristic
1129C2C2×#271411yescharacteristic
1130C2C2×#271511yescharacteristic
1131C2C2×#275111yescharacteristic
1132C2C2×#278611yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#397C2semidirect
4. C22×#387C2semidirect
5. #16275C2direct (N × H)
6. C2×#1441C2semidirect
7. C2×#1441C2semidirect
8. C2×#1440C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
14. C2×#1439C2semidirect
16. C2×#1436C2semidirect
37. C2×#397C22semidirect
43. C2×#387C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
70. #1436C22semidirect
1117. C2#16275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3972
C22×#3942
C22×#3902
C22×#3872
#162752
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14362