Finite Group Databasebeta

← C2×#15416 #608952

Subgroups — C2×#15416 #608952

Order 512.

5298 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×#390C211yesmaximal, characteristic
3C22×#388C211yesmaximal, characteristic, complemented
4C22×#387C211yesmaximal, characteristic, complemented
5#15416C2116yesmaximal, direct product factor
6C2×#1445C211yesmaximal, characteristic, complemented
7C2×#1440C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, 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×#1436C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊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×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#397—28no—
37C2×#397C2218yescomplemented
38C2×#390—28no—
39C2×#390C2218yes—
40C2×#388—28no—
41C2×#388C2218yescomplemented
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#1445C2218yescomplemented
61#1440C2218yescomplemented
62#1439C2218yescomplemented
63#1439C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1438C2218yes—
67#1438C2218yes—
68#1437C2218yescomplemented
69#1436C2218yescomplemented
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⋊C4D418yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
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—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⋊C4C2314yes—
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—24no—
160C22×C42—24no—
161C22×C42—42no—
162C22×C42—42no—
163C22×C42—42no—
164C22×C42C2314yes—
165C22×C42C2314yes—
166#397—232no—
167#390—232no—
168#388—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×#95D418yescomplemented
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—
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—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×C4C2×D414yes—
330C23×C4C2×D414yes—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4C2×D414yes—
334C23×C4C2×D414yes—
335C23×C4#4114yes—
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—416no—
366C2×C4⋊C4—416no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4C2×D4116yes—
369C2×C22⋊C4—232no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
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—28no—
389C2×C22⋊C4—28no—
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—416no—
407C2×C22⋊C4—416no—
408C2×C22⋊C4—416no—
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×C42—28no—
418C2×C42—28no—
419C2×C42—28no—
420C2×C42—44no—
421C2×C42—44no—
422C2×C42—44no—
423C2×C42—416no—
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#95C2×D4116yescomplemented
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×D412yes—
540C24C22×D412yes—
541C24C2×#4114yes—
542C24C2×#4114yes—
543C24C2×#4112yes—
544C24C2×#4112yes—
545C24C2×#4112yes—
546C24C2×#4112yes—
547C24C2×#4112yes—
548C24C2×#4112yes—
549C24C2×#4112yes—
550C24H(5,𝔽2)12yes—
551C24H(5,𝔽2)12yes—
552C24H(5,𝔽2)12yes—
553C24H(5,𝔽2)12yes—
554C24H(5,𝔽2)12yes—
555C242−1+412yes—
556C24C2511yescharacteristic
557C2×D4—232no—
558C2×D4—416no—
559C2×D4—416no—
560C2×D4—416no—
561C2×D4—416no—
562C2×D4—416no—
563C2×D4—4128no—
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—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
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—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#123116yes—
736C22×C4C22×D414yes—
737C22×C4C22×D414yes—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C22×D414yes—
741C22×C4C22×D414yes—
742C22×C4C2×#4114yes—
743C22×C4C2×#4114yes—
744C22×C4C2×#4114yes—
745C22×C4C2×#4114yes—
746C22×C4C2×#4114yes—
747C4⋊C4—232no—
748C4⋊C4—416no—
749C4⋊C4—416no—
750C4⋊C4—416no—
751C22⋊C4—232no—
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—
763C42—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—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
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—416no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—416no—
835C23—416no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—416no—
847C23—416no—
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#52514yes—
868C23#52914yes—
869C23#52914yes—
870C23#53214yes—
871C23#53514yes—
872C23#53714yes—
873C23#53814yes—
874C23#53814yes—
875C23#53814yes—
876C23#53814yes—
877C23#53914yes—
878C23#54014yes—
879C23#54214yes—
880C23D4214yes—
881C23#54614yes—
882C23#54614yes—
883C23#54614yes—
884C23#54814yes—
885C23#55014yes—
886C23#55014yes—
887C23#55114yes—
888C23#55114yes—
889C23#55114yes—
890C23#55114yes—
891C23#55214yes—
892C23#55314yes—
893C23#55314yes—
894C23#55314yes—
895C23#55614yes—
896C23#55914yes—
897C23#55914yes—
898C23#56014yes—
899C23#56214yes—
900C23C23×D411yescharacteristic
901C23C23×D411yescharacteristic
902C23C22×#4111yescharacteristic
903C23C22×#4111yescharacteristic
904C23C22×#4111yescharacteristic
905C23C22×#4111yescharacteristic
906C23C22×#4111yescharacteristic
907C23C22×#4111yescharacteristic
908C23C22×#4111yescharacteristic
909C23C2×H(5,𝔽2)11yescharacteristic
910C23C2×H(5,𝔽2)11yescharacteristic
911C23C2×H(5,𝔽2)11yescharacteristic
912C23C2×H(5,𝔽2)11yescharacteristic
913C23C2×H(5,𝔽2)11yescharacteristic
914C23C2×2−1+411yescharacteristic
915D4—464no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—232no—
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—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—416no—
952C2×C4—416no—
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—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—416no—
972C2×C4—416no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—416no—
981C2×C4—416no—
982C2×C4—416no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—416no—
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—42no—
1014C2×C4—42no—
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—832no—
1040C22—832no—
1041C22—82no—
1042C22—82no—
1043C22—82no—
1044C22—82no—
1045C22—82no—
1046C22—82no—
1047C22—82no—
1048C22—82no—
1049C22—82no—
1050C22—82no—
1051C22—82no—
1052C22#244518yes—
1053C22#244818yes—
1054C22#245618yes—
1055C22#246018yes—
1056C22#246718yes—
1057C22#248218yes—
1058C22#255718yes—
1059C22#259518yes—
1060C22#260118yes—
1061C22#267618yes—
1062C22#270518yes—
1063C22#271418yes—
1064C22#275118yes—
1065C22#278618yes—
1066C22#279718yes—
1067C22C22×#12311yescharacteristic
1068C22C2×#52511yescharacteristic
1069C22C2×#52511yescharacteristic
1070C22C2×#52911yescharacteristic
1071C22C2×#52911yescharacteristic
1072C22C2×#53211yescharacteristic
1073C22C2×#53511yescharacteristic
1074C22C2×#53711yescharacteristic
1075C22C2×#53811yescharacteristic
1076C22C2×#53811yescharacteristic
1077C22C2×#53811yescharacteristic
1078C22C2×#53811yescharacteristic
1079C22C2×#53911yescharacteristic
1080C22C2×#54011yescharacteristic
1081C22C2×#54211yescharacteristic
1082C22C2×D4211yescharacteristic
1083C22C2×#54611yescharacteristic
1084C22C2×#54611yescharacteristic
1085C22C2×#54611yescharacteristic
1086C22C2×#54811yescharacteristic
1087C22C2×#55011yescharacteristic
1088C22C2×#55011yescharacteristic
1089C22C2×#55111yescharacteristic
1090C22C2×#55111yescharacteristic
1091C22C2×#55111yescharacteristic
1092C22C2×#55111yescharacteristic
1093C22C2×#55211yescharacteristic
1094C22C2×#55311yescharacteristic
1095C22C2×#55311yescharacteristic
1096C22C2×#55311yescharacteristic
1097C22C2×#55611yescharacteristic
1098C22C2×#55911yescharacteristic
1099C22C2×#55911yescharacteristic
1100C22C2×#56011yescharacteristic
1101C22C2×#56211yescharacteristic
1102C4—28no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—82no—
1112C4—82no—
1113C4—82no—
1114C4—82no—
1115C2—84no—
1116C2—84no—
1117C2#15416116yesdirect product factor
1118C2C2×#245611yescharacteristic
1119C2C2×#246011yescharacteristic
1120C2C2×#246711yescharacteristic
1121C2C2×#244511yescharacteristic
1122C2C2×#244811yescharacteristic
1123C2C2×#248211yescharacteristic
1124C2C2×#255711yescharacteristic
1125C2C2×#259511yescharacteristic
1126C2C2×#260111yescharacteristic
1127C2C2×#267611yescharacteristic
1128C2C2×#270511yescharacteristic
1129C2C2×#271411yescharacteristic
1130C2C2×#275111yescharacteristic
1131C2C2×#278611yescharacteristic
1132C2C2×#279711yescharacteristic
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
3. C22×#388C2semidirect
4. C22×#387C2semidirect
5. #15416C2direct (N × H)
6. C2×#1445C2semidirect
7. C2×#1440C2semidirect
8. C2×#1439C2semidirect
9. C2×#1439C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×#1436C2semidirect
37. C2×#397C22semidirect
41. C2×#388C22semidirect
43. C2×#387C22semidirect
60. #1445C22semidirect
61. #1440C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
68. #1437C22semidirect
69. #1436C22semidirect
70. #1436C22semidirect
185. C2×#95D4semidirect
440. #95C2×D4semidirect
1117. C2#15416direct (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×#3902
C22×#3882
C22×#3872
#154162
C2×#14452
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362