Finite Group Databasebeta

← C2×#13980 #514262

Subgroups — C2×#13980 #514262

Order 512.

6738 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#387C211yesmaximal, characteristic, complemented
2C22×#385C211yesmaximal, characteristic
3C22×#380C211yesmaximal, characteristic
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5C23×#95C211yesmaximal, characteristic
6#13980C2116yesmaximal, direct product factor
7C2×#1445C211yesmaximal, characteristic, complemented
8C2×#1443C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1441C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#387—28no—
31C2×#387C2218yescomplemented
32C2×#385C4116yescomplemented
33C2×#385C2218yes—
34C2×#380—28no—
35C2×#380C2218yes—
36C2×C4×C22⋊C4—28no—
37C2×C4×C22⋊C4C2218yes—
38C22×#95—28no—
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2218yes—
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1445C2218yescomplemented
63#1443C2218yescomplemented
64#1442C2218yescomplemented
65#1441C2218yescomplemented
66#1436C2218yescomplemented
67#1436C2218yescomplemented
68#1434C2218yescomplemented
69C22⋊#95C2218yes—
70C22⋊#95C2218yes—
71C22⋊#95C2218yes—
72C26C2311yescharacteristic
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—24no—
79C24×C4—24no—
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4—42no—
92C24×C4C2×C418yes—
93C24×C4Q818yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2314yes—
107C24×C4C2314yes—
108C24×C4C2314yes—
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2×C418yescomplemented
122C22×C4⋊C4C2×C418yescomplemented
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4C2×C418yes—
137C22×C22⋊C4C2×C418yes—
138C22×C22⋊C4D418yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—42no—
148C22×C42—42no—
149C22×C42C2314yes—
150C22×C42C2314yes—
151#387—232no—
152#385C2×C4164yescomplemented
153#380—232no—
154C4×C22⋊C4—232no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—232no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95C2×C418yescomplemented
176C2×#95C2×C418yescomplemented
177C2×#95D418yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
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—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25C22×C414yes—
209C25C2×D414yes—
210C25C2×Q814yes—
211C25#4114yes—
212C25#4114yes—
213C25#4114yes—
214C25#4114yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—232no—
226C23×C4—232no—
227C23×C4—232no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—28no—
254C23×C4—28no—
255C23×C4—28no—
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—232no—
294C23×C4—232no—
295C23×C4—28no—
296C23×C4—28no—
297C23×C4—28no—
298C23×C4—28no—
299C23×C4—28no—
300C23×C4—28no—
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—28no—
310C23×C4—28no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—416no—
318C23×C4—416no—
319C23×C4—44no—
320C23×C4—44no—
321C23×C4—44no—
322C23×C4—44no—
323C23×C4—44no—
324C23×C4—44no—
325C23×C4—416no—
326C23×C4—416no—
327C23×C4—416no—
328C23×C4—416no—
329C23×C4—416no—
330C23×C4—416no—
331C23×C4—416no—
332C23×C4—416no—
333C23×C4—416no—
334C23×C4—416no—
335C23×C4—416no—
336C23×C4—416no—
337C23×C4—416no—
338C23×C4—416no—
339C23×C4C22×C414yes—
340C23×C4C22×C414yes—
341C23×C4C22×C414yes—
342C23×C4C22×C414yes—
343C23×C4C22×C414yes—
344C23×C4C22×C4116yes—
345C23×C4C22×C414yes—
346C23×C4C2×D414yes—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2×D414yes—
350C23×C4C2×D414yes—
351C23×C4C2×Q814yes—
352C23×C4C2×Q8116yes—
353C23×C4C2×Q814yes—
354C23×C4#4114yes—
355C23×C4#4114yes—
356C23×C4#4114yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C2×C4⋊C4—232no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—416no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4C22×C4116yescomplemented
386C2×C4⋊C4C22×C4116yescomplemented
387C2×C22⋊C4—232no—
388C2×C22⋊C4—232no—
389C2×C22⋊C4—232no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—416no—
400C2×C22⋊C4C22×C4116yes—
401C2×C22⋊C4C22×C4116yes—
402C2×C22⋊C4C2×D4116yes—
403C2×C42—28no—
404C2×C42—28no—
405C2×C42—28no—
406C2×C42—28no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42—416no—
410C2×C42—416no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95C22×C4116yescomplemented
431#95C22×C4116yescomplemented
432#95C2×D4116yes—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
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—28no—
456C24—28no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24#117116yes—
470C24C4×D4116yes—
471C24C4×Q8116yes—
472C24C22⋊Q8116yes—
473C24#123116yes—
474C24#125116yes—
475C24#126116yes—
476C24C23×C414yes—
477C24C23×C412yes—
478C24C22×D414yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C22×Q814yes—
482C24C22×Q812yes—
483C24C2×#4114yes—
484C24C2×#4114yes—
485C24C2×#4114yes—
486C24C2×#4114yes—
487C24C2×#4112yes—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24H(5,𝔽2)12yes—
495C24H(5,𝔽2)12yes—
496C24H(5,𝔽2)12yes—
497C242−1+412yes—
498C24C2511yescharacteristic
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—232no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—232no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—232no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
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—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—232no—
613C22×C4—232no—
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—416no—
629C22×C4—416no—
630C22×C4—4128no—
631C22×C4—4128no—
632C22×C4—416no—
633C22×C4—416no—
634C22×C4—416no—
635C22×C4—416no—
636C22×C4—416no—
637C22×C4—416no—
638C22×C4—416no—
639C22×C4—416no—
640C22×C4—416no—
641C22×C4—416no—
642C22×C4—416no—
643C22×C4—416no—
644C22×C4—416no—
645C22×C4—4128no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
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—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×C4C4×D4116yes—
702C22×C4C22⋊Q8116yes—
703C22×C4C23×C414yes—
704C22×C4C23×C414yes—
705C22×C4C23×C414yes—
706C22×C4C23×C414yes—
707C22×C4C23×C414yes—
708C22×C4C23×C414yes—
709C22×C4C22×D414yes—
710C22×C4C22×D414yes—
711C22×C4C22×D414yes—
712C22×C4C22×D414yes—
713C22×C4C22×D414yes—
714C22×C4C22×Q814yes—
715C22×C4C22×Q814yes—
716C22×C4C2×#4114yes—
717C22×C4C2×#4114yes—
718C22×C4C2×#4114yes—
719C4⋊C4—232no—
720C4⋊C4—416no—
721C4⋊C4—416no—
722C4⋊C4—416no—
723C22⋊C4—232no—
724C22⋊C4—232no—
725C22⋊C4—232no—
726C22⋊C4—416no—
727C42—416no—
728C42—416no—
729C23—232no—
730C23—232no—
731C23—232no—
732C23—232no—
733C23—232no—
734C23—232no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—232no—
748C23—232no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—232no—
757C23—232no—
758C23—232no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—232no—
769C23—232no—
770C23—232no—
771C23#387164yescomplemented
772C23C2×#11718yes—
773C23C2×#11714yes—
774C23C2×C4×D418yes—
775C23C2×C4×D414yes—
776C23C2×C4×D414yes—
777C23C2×C4×Q818yes—
778C23C2×C4×Q814yes—
779C23C4×#4114yes—
780C23#51814yes—
781C23#52014yes—
782C23C2×C22⋊Q818yes—
783C23C2×C22⋊Q814yes—
784C23C2×C22⋊Q814yes—
785C23C2×#12318yes—
786C23C2×#12314yes—
787C23#52514yes—
788C23C2×#12518yes—
789C23C2×#12514yes—
790C23C2×#12618yes—
791C23C2×#12614yes—
792C23#52914yes—
793C23#53314yes—
794C23#53814yes—
795C23#53914yes—
796C23#54314yes—
797C23#54414yes—
798C23D4214yes—
799C23#54614yes—
800C23#54614yes—
801C23#54614yes—
802C23#54614yes—
803C23#54714yes—
804C23#54814yes—
805C23#55114yes—
806C23#55114yes—
807C23#55114yes—
808C23#55114yes—
809C23#55214yes—
810C23#55214yes—
811C23#55314yes—
812C23#55314yes—
813C23#55314yes—
814C23C24×C411yescharacteristic
815C23C23×D411yescharacteristic
816C23C23×D411yescharacteristic
817C23C23×Q811yescharacteristic
818C23C22×#4111yescharacteristic
819C23C22×#4111yescharacteristic
820C23C22×#4111yescharacteristic
821C23C22×#4111yescharacteristic
822C23C22×#4111yescharacteristic
823C23C22×#4111yescharacteristic
824C23C22×#4111yescharacteristic
825C23C2×H(5,𝔽2)11yescharacteristic
826C23C2×H(5,𝔽2)11yescharacteristic
827C23C2×H(5,𝔽2)11yescharacteristic
828C23C2×2−1+411yescharacteristic
829C2×C4—232no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—232no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—464no—
874C2×C4—464no—
875C2×C4—464no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—416no—
880C2×C4—416no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—416no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—416no—
907C2×C4—416no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—88no—
941C2×C4—88no—
942C2×C4C2×C4×D418yes—
943C2×C4C2×C22⋊Q818yes—
944C22—28no—
945C22—28no—
946C22—28no—
947C22—28no—
948C22—28no—
949C22—28no—
950C22—28no—
951C22—28no—
952C22—28no—
953C22—28no—
954C22—28no—
955C22—2128no—
956C22—28no—
957C22—28no—
958C22—28no—
959C22C2×#38718yes—
960C22C2×#387116yescomplemented
961C22C4×C22⋊Q818yes—
962C22#232918yes—
963C22#235218yes—
964C22#235318yes—
965C22#235818yes—
966C22#235918yes—
967C22#243718yes—
968C22#243818yes—
969C22#244218yes—
970C22#244318yes—
971C22#244418yes—
972C22#248018yes—
973C22#249318yes—
974C22#256918yes—
975C22C22×#11711yescharacteristic
976C22C22×C4×D411yescharacteristic
977C22C22×C4×D411yescharacteristic
978C22C22×C4×Q811yescharacteristic
979C22C2×C4×#4111yescharacteristic
980C22C2×#51811yescharacteristic
981C22C2×#52011yescharacteristic
982C22C22×C22⋊Q811yescharacteristic
983C22C22×C22⋊Q811yescharacteristic
984C22C22×#12311yescharacteristic
985C22C2×#52511yescharacteristic
986C22C22×#12511yescharacteristic
987C22C22×#12611yescharacteristic
988C22C2×#52911yescharacteristic
989C22C2×#53311yescharacteristic
990C22C2×#53811yescharacteristic
991C22C2×#53911yescharacteristic
992C22C2×#54311yescharacteristic
993C22C2×#54411yescharacteristic
994C22C2×D4211yescharacteristic
995C22C2×#54611yescharacteristic
996C22C2×#54611yescharacteristic
997C22C2×#54611yescharacteristic
998C22C2×#54611yescharacteristic
999C22C2×#54711yescharacteristic
1000C22C2×#54811yescharacteristic
1001C22C2×#55111yescharacteristic
1002C22C2×#55111yescharacteristic
1003C22C2×#55111yescharacteristic
1004C22C2×#55111yescharacteristic
1005C22C2×#55211yescharacteristic
1006C22C2×#55211yescharacteristic
1007C22C2×#55311yescharacteristic
1008C22C2×#55311yescharacteristic
1009C22C2×#55311yescharacteristic
1010C4—28no—
1011C4—28no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—82no—
1023C4—82no—
1024C2—216no—
1025C2#13980116yesdirect product factor
1026C2C22×#38711yescharacteristic
1027C2C2×C4×C22⋊Q811yescharacteristic
1028C2C2×#232911yescharacteristic
1029C2C2×#235211yescharacteristic
1030C2C2×#235311yescharacteristic
1031C2C2×#235811yescharacteristic
1032C2C2×#235911yescharacteristic
1033C2C2×#243711yescharacteristic
1034C2C2×#244311yescharacteristic
1035C2C2×#248011yescharacteristic
1036C2C2×#244411yescharacteristic
1037C2C2×#244211yescharacteristic
1038C2C2×#243811yescharacteristic
1039C2C2×#249311yescharacteristic
1040C2C2×#256911yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#387C2semidirect
6. #13980C2direct (N × H)
7. C2×#1445C2semidirect
8. C2×#1443C2semidirect
9. C2×#1442C2semidirect
10. C2×#1441C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×#1434C2semidirect
31. C2×#387C22semidirect
32. C2×#385C4semidirect
62. #1445C22semidirect
63. #1443C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1436C22semidirect
67. #1436C22semidirect
68. #1434C22semidirect
121. C22×C4⋊C4C2×C4semidirect
122. C22×C4⋊C4C2×C4semidirect
152. #385C2×C4semidirect
175. C2×#95C2×C4semidirect
176. C2×#95C2×C4semidirect
385. C2×C4⋊C4C22×C4semidirect
386. C2×C4⋊C4C22×C4semidirect
430. #95C22×C4semidirect
431. #95C22×C4semidirect
771. C23#387semidirect
960. C22C2×#387semidirect
1025. C2#13980direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3872
C22×#3852
C22×#3802
C22×C4×C22⋊C42
C23×#952
#139802
C2×#14452
C2×#14432
C2×#14422
C2×#14412
C2×#14362
C2×#14342
C2×C22⋊#952