Finite Group Databasebeta

← C2×#15451 #608990

Subgroups — C2×#15451 #608990

Order 512.

5822 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic, complemented
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5#15451C2116yesmaximal, direct product factor
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1443C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1438C211yesmaximal, characteristic
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊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×C42C2211yescharacteristic
34C2×#397—28no—
35C2×#397C2218yescomplemented
36C2×#388—28no—
37C2×#388C2218yescomplemented
38C2×#386—28no—
39C2×#386C2218yes—
40C2×#385—28no—
41C2×#385C2218yescomplemented
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
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#1443C2218yescomplemented
61#1443C2218yescomplemented
62#1441C2218yescomplemented
63#1440C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1438C2218yes—
67#1438C2218yes—
68#1437C2218yescomplemented
69#1436C2218yescomplemented
70C22⋊#95C2218yescomplemented
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×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—42no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2314yes—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4D418yescomplemented
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—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
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⋊C4D418yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
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×C42—24no—
159C22×C42—42no—
160C22×C42—42no—
161C22×C42C2314yes—
162#397—232no—
163#388—232no—
164#386—232no—
165#385—232no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
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—42no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95—42no—
183C2×#95—42no—
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—
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—
228C25C2×D414yes—
229C25#4114yes—
230C25#4114yes—
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—28no—
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×C4—22no—
332C23×C4—28no—
333C23×C4—28no—
334C23×C4—44no—
335C23×C4—44no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—416no—
339C23×C4—416no—
340C23×C4—416no—
341C23×C4—416no—
342C23×C4—416no—
343C23×C4—416no—
344C23×C4—416no—
345C23×C4C2×D414yes—
346C23×C4C2×D414yes—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2×D414yes—
350C23×C4#4114yes—
351C23×C4#4114yes—
352C23×C4#4114yes—
353C23×C4#4114yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—416no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—416no—
377C2×C4⋊C4—416no—
378C2×C4⋊C4C2×D4116yescomplemented
379C2×C22⋊C4—232no—
380C2×C22⋊C4—232no—
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—28no—
389C2×C22⋊C4—28no—
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—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—416no—
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—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
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⋊C4—416no—
421C2×C22⋊C4—416no—
422C2×C22⋊C4C2×D4116yes—
423C2×C42—28no—
424C2×C42—44no—
425C2×C42—44no—
426C2×C42—416no—
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—28no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
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—28no—
462C24—28no—
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—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
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—
539C24—44no—
540C24#126116yes—
541C24C22×D414yes—
542C24C22×D412yes—
543C24C22×D412yes—
544C24C2×#4114yes—
545C24C2×#4114yes—
546C24C2×#4114yes—
547C24C2×#4112yes—
548C24C2×#4112yes—
549C24C2×#4112yes—
550C24C2×#4112yes—
551C24C2×#4112yes—
552C24C2×#4112yes—
553C24C2×#4112yes—
554C24H(5,𝔽2)12yes—
555C24H(5,𝔽2)12yes—
556C24H(5,𝔽2)12yes—
557C24H(5,𝔽2)12yes—
558C24H(5,𝔽2)12yes—
559C242−1+412yes—
560C24C2511yescharacteristic
561C2×D4—232no—
562C2×D4—416no—
563C2×D4—416no—
564C2×D4—416no—
565C2×D4—416no—
566C2×D4—416no—
567C2×D4—4128no—
568C2×D4—416no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
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—28no—
594C22×C4—28no—
595C22×C4—28no—
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—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—416no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—4128no—
685C22×C4—416no—
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—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4C22×D414yes—
751C22×C4C22×D414yes—
752C22×C4C22×D414yes—
753C22×C4C22×D414yes—
754C22×C4C22×D414yes—
755C22×C4C2×#4114yes—
756C22×C4C2×#4114yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C4⋊C4—416no—
760C4⋊C4—416no—
761C4⋊C4—416no—
762C22⋊C4—232no—
763C22⋊C4—232no—
764C22⋊C4—416no—
765C22⋊C4—416no—
766C22⋊C4—416no—
767C22⋊C4—416no—
768C22⋊C4—416no—
769C22⋊C4—416no—
770C22⋊C4—416no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C42—416no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—232no—
793C23—232no—
794C23—232no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—416no—
803C23—416no—
804C23—42no—
805C23—416no—
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—416no—
819C23—42no—
820C23—416no—
821C23—416no—
822C23—416no—
823C23—416no—
824C23—416no—
825C23—416no—
826C23—42no—
827C23—42no—
828C23—416no—
829C23—416no—
830C23—416no—
831C23—42no—
832C23—416no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—416no—
858C23—42no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—42no—
864C23—42no—
865C23—88no—
866C23—88no—
867C23—88no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23—88no—
873C23#52514yes—
874C23#52514yes—
875C23#52514yes—
876C23C2×#12618yes—
877C23C2×#12614yes—
878C23#52914yes—
879C23#53214yes—
880C23#53414yes—
881C23#53414yes—
882C23#53814yes—
883C23#53814yes—
884C23#53814yes—
885C23#53814yes—
886C23#53914yes—
887C23#54214yes—
888C23#54214yes—
889C23D4214yes—
890C23#54614yes—
891C23#54614yes—
892C23#54614yes—
893C23#54714yes—
894C23#54814yes—
895C23#55014yes—
896C23#55114yes—
897C23#55114yes—
898C23#55114yes—
899C23#55114yes—
900C23#55214yes—
901C23#55314yes—
902C23#55314yes—
903C23#55314yes—
904C23#55314yes—
905C23#55314yes—
906C23#55914yes—
907C23#56014yes—
908C23#56214yes—
909C23C23×D411yescharacteristic
910C23C23×D411yescharacteristic
911C23C22×#4111yescharacteristic
912C23C22×#4111yescharacteristic
913C23C22×#4111yescharacteristic
914C23C22×#4111yescharacteristic
915C23C22×#4111yescharacteristic
916C23C22×#4111yescharacteristic
917C23C22×#4111yescharacteristic
918C23C2×H(5,𝔽2)11yescharacteristic
919C23C2×H(5,𝔽2)11yescharacteristic
920C23C2×H(5,𝔽2)11yescharacteristic
921C23C2×H(5,𝔽2)11yescharacteristic
922C23C2×H(5,𝔽2)11yescharacteristic
923C23C2×2−1+411yescharacteristic
924D4—464no—
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—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—464no—
953C2×C4—416no—
954C2×C4—416no—
955C2×C4—42no—
956C2×C4—416no—
957C2×C4—416no—
958C2×C4—416no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
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—416no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—416no—
991C2×C4—416no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—416no—
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—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—88no—
1027C2×C4—88no—
1028C2×C4—88no—
1029C2×C4—88no—
1030C22—28no—
1031C22—28no—
1032C22—28no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—464no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—82no—
1054C22—82no—
1055C22—832no—
1056C22—82no—
1057C22—82no—
1058C22—82no—
1059C22—82no—
1060C22—82no—
1061C22—82no—
1062C22#245618yes—
1063C22#246118yes—
1064C22#247018yes—
1065C22#248018yes—
1066C22#248118yes—
1067C22#251018yes—
1068C22#255418yes—
1069C22#260018yes—
1070C22#260218yes—
1071C22#266818yes—
1072C22#270818yes—
1073C22#273018yes—
1074C22#275118yes—
1075C22#275718yes—
1076C22#277818yes—
1077C22C2×#52511yescharacteristic
1078C22C2×#52511yescharacteristic
1079C22C2×#52511yescharacteristic
1080C22C22×#12611yescharacteristic
1081C22C2×#52911yescharacteristic
1082C22C2×#53211yescharacteristic
1083C22C2×#53411yescharacteristic
1084C22C2×#53411yescharacteristic
1085C22C2×#53811yescharacteristic
1086C22C2×#53811yescharacteristic
1087C22C2×#53811yescharacteristic
1088C22C2×#53811yescharacteristic
1089C22C2×#53911yescharacteristic
1090C22C2×#54211yescharacteristic
1091C22C2×#54211yescharacteristic
1092C22C2×D4211yescharacteristic
1093C22C2×#54611yescharacteristic
1094C22C2×#54611yescharacteristic
1095C22C2×#54611yescharacteristic
1096C22C2×#54711yescharacteristic
1097C22C2×#54811yescharacteristic
1098C22C2×#55011yescharacteristic
1099C22C2×#55111yescharacteristic
1100C22C2×#55111yescharacteristic
1101C22C2×#55111yescharacteristic
1102C22C2×#55111yescharacteristic
1103C22C2×#55211yescharacteristic
1104C22C2×#55311yescharacteristic
1105C22C2×#55311yescharacteristic
1106C22C2×#55311yescharacteristic
1107C22C2×#55311yescharacteristic
1108C22C2×#55311yescharacteristic
1109C22C2×#55911yescharacteristic
1110C22C2×#56011yescharacteristic
1111C22C2×#56211yescharacteristic
1112C4—44no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—44no—
1119C4—44no—
1120C4—44no—
1121C4—82no—
1122C4—82no—
1123C4—82no—
1124C4—82no—
1125C2—48no—
1126C2—84no—
1127C2#15451116yesdirect product factor
1128C2C2×#245611yescharacteristic
1129C2C2×#248011yescharacteristic
1130C2C2×#248111yescharacteristic
1131C2C2×#246111yescharacteristic
1132C2C2×#247011yescharacteristic
1133C2C2×#251011yescharacteristic
1134C2C2×#255411yescharacteristic
1135C2C2×#260011yescharacteristic
1136C2C2×#260211yescharacteristic
1137C2C2×#266811yescharacteristic
1138C2C2×#270811yescharacteristic
1139C2C2×#273011yescharacteristic
1140C2C2×#275111yescharacteristic
1141C2C2×#275711yescharacteristic
1142C2C2×#277811yescharacteristic
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
2. C22×#388C2semidirect
4. C22×#385C2semidirect
5. #15451C2direct (N × H)
6. C2×#1443C2semidirect
7. C2×#1443C2semidirect
8. C2×#1441C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
35. C2×#397C22semidirect
37. C2×#388C22semidirect
41. C2×#385C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1441C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
68. #1437C22semidirect
69. #1436C22semidirect
70. C22⋊#95C22semidirect
110. C22×C4⋊C4D4semidirect
378. C2×C4⋊C4C2×D4semidirect
1127. C2#15451direct (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×#3882
C22×#3862
C22×#3852
#154512
C2×#14432
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952