Finite Group Databasebeta

← C2×#15399 #608934

Subgroups — C2×#15399 #608934

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×#399C211yesmaximal, characteristic, complemented
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C22×#381C211yesmaximal, characteristic, complemented
5#15399C2116yesmaximal, direct product factor
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, 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×#399—28no—
35C2×#399C2218yescomplemented
36C2×#388—28no—
37C2×#388C2218yescomplemented
38C2×#386—28no—
39C2×#386C2218yes—
40C2×#381—28no—
41C2×#381C2218yescomplemented
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#1442C2218yescomplemented
62#1442C2218yescomplemented
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—24no—
85C24×C4—24no—
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—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
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—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⋊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#399—232no—
163#388—232no—
164#386—232no—
165#381—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—42no—
178C2×#95—42no—
179C2×#95—42no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95—42no—
183C2×#95D418yescomplemented
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—232no—
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—28no—
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—28no—
306C23×C4—28no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—28no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—28no—
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—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—44no—
338C23×C4—44no—
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—28no—
371C2×C4⋊C4—28no—
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⋊C4—416no—
379C2×C22⋊C4—232no—
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—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—416no—
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—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
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⋊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—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95C2×D4116yescomplemented
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#124116yes—
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—4128no—
567C2×D4—416no—
568C2×D4—416no—
569C22×C4—232no—
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—28no—
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—22no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—4128no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—416no—
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—416no—
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—232no—
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—24no—
793C23—232no—
794C23—232no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—416no—
803C23—42no—
804C23—42no—
805C23—416no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—416no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—416no—
819C23—416no—
820C23—42no—
821C23—416no—
822C23—416no—
823C23—416no—
824C23—416no—
825C23—416no—
826C23—416no—
827C23—42no—
828C23—42no—
829C23—416no—
830C23—416no—
831C23—416no—
832C23—42no—
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×#12418yes—
877C23C2×#12414yes—
878C23#52914yes—
879C23#52914yes—
880C23#53414yes—
881C23#53514yes—
882C23#53814yes—
883C23#53914yes—
884C23#53914yes—
885C23#54014yes—
886C23#54014yes—
887C23#54014yes—
888C23#54214yes—
889C23D4214yes—
890C23#54614yes—
891C23#54614yes—
892C23#54614yes—
893C23#54714yes—
894C23#54714yes—
895C23#55014yes—
896C23#55114yes—
897C23#55114yes—
898C23#55114yes—
899C23#55114yes—
900C23#55114yes—
901C23#55114yes—
902C23#55114yes—
903C23#55214yes—
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—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—416no—
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—416no—
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—416no—
990C2×C4—416no—
991C2×C4—42no—
992C2×C4—416no—
993C2×C4—416no—
994C2×C4—416no—
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—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—464no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
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—832no—
1054C22—82no—
1055C22—82no—
1056C22—82no—
1057C22—82no—
1058C22—82no—
1059C22—82no—
1060C22—82no—
1061C22—82no—
1062C22#245518yes—
1063C22#245718yes—
1064C22#247118yes—
1065C22#247218yes—
1066C22#247918yes—
1067C22#248818yes—
1068C22#251618yes—
1069C22#256118yes—
1070C22#259818yes—
1071C22#267318yes—
1072C22#270118yes—
1073C22#270618yes—
1074C22#274318yes—
1075C22#274618yes—
1076C22#275218yes—
1077C22C2×#52511yescharacteristic
1078C22C2×#52511yescharacteristic
1079C22C2×#52511yescharacteristic
1080C22C22×#12411yescharacteristic
1081C22C2×#52911yescharacteristic
1082C22C2×#52911yescharacteristic
1083C22C2×#53411yescharacteristic
1084C22C2×#53511yescharacteristic
1085C22C2×#53811yescharacteristic
1086C22C2×#53911yescharacteristic
1087C22C2×#53911yescharacteristic
1088C22C2×#54011yescharacteristic
1089C22C2×#54011yescharacteristic
1090C22C2×#54011yescharacteristic
1091C22C2×#54211yescharacteristic
1092C22C2×D4211yescharacteristic
1093C22C2×#54611yescharacteristic
1094C22C2×#54611yescharacteristic
1095C22C2×#54611yescharacteristic
1096C22C2×#54711yescharacteristic
1097C22C2×#54711yescharacteristic
1098C22C2×#55011yescharacteristic
1099C22C2×#55111yescharacteristic
1100C22C2×#55111yescharacteristic
1101C22C2×#55111yescharacteristic
1102C22C2×#55111yescharacteristic
1103C22C2×#55111yescharacteristic
1104C22C2×#55111yescharacteristic
1105C22C2×#55111yescharacteristic
1106C22C2×#55211yescharacteristic
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#15399116yesdirect product factor
1128C2C2×#245511yescharacteristic
1129C2C2×#247211yescharacteristic
1130C2C2×#245711yescharacteristic
1131C2C2×#247911yescharacteristic
1132C2C2×#247111yescharacteristic
1133C2C2×#248811yescharacteristic
1134C2C2×#251611yescharacteristic
1135C2C2×#256111yescharacteristic
1136C2C2×#259811yescharacteristic
1137C2C2×#267311yescharacteristic
1138C2C2×#270111yescharacteristic
1139C2C2×#270611yescharacteristic
1140C2C2×#274311yescharacteristic
1141C2C2×#274611yescharacteristic
1142C2C2×#275211yescharacteristic
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×#399C2semidirect
2. C22×#388C2semidirect
4. C22×#381C2semidirect
5. #15399C2direct (N × H)
6. C2×#1443C2semidirect
7. C2×#1442C2semidirect
8. C2×#1442C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
35. C2×#399C22semidirect
37. C2×#388C22semidirect
41. C2×#381C22semidirect
60. #1443C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
68. #1437C22semidirect
69. #1436C22semidirect
70. C22⋊#95C22semidirect
183. C2×#95D4semidirect
444. #95C2×D4semidirect
1127. C2#15399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3992
C22×#3882
C22×#3862
C22×#3812
#153992
C2×#14432
C2×#14422
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952