Finite Group Databasebeta

← C2×#13999 #514291

Subgroups — C2×#13999 #514291

Order 512.

7998 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#386C211yesmaximal, characteristic
5C22×#380C211yesmaximal, characteristic, complemented
6C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C23×#95C211yesmaximal, characteristic, complemented
8#13999C2116yesmaximal, direct product factor
9C2×#1443C211yesmaximal, characteristic, complemented
10C2×#1442C211yesmaximal, characteristic, complemented
11C2×#1440C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C25×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×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#388—28no—
35C2×#388C2218yescomplemented
36C2×#386—28no—
37C2×#386—28no—
38C2×#386C4116yescomplemented
39C2×#386C2218yes—
40C2×#386C2218yes—
41C2×#386C2218yes—
42C2×#380—28no—
43C2×#380C2218yescomplemented
44C2×C4×C22⋊C4—28no—
45C2×C4×C22⋊C4C2218yescomplemented
46C22×#95—28no—
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
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2218yescomplemented
66#1443C2218yescomplemented
67#1442C2218yescomplemented
68#1440C2218yescomplemented
69#1439C2218yescomplemented
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72#1434C2218yescomplemented
73C22⋊#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4C2×C418yes—
83C23×D4C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—24no—
97C24×C4—42no—
98C24×C4—42no—
99C24×C4—42no—
100C24×C4—42no—
101C24×C4—42no—
102C24×C4—42no—
103C24×C4C2×C418yes—
104C24×C4D418yes—
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2314yes—
117C24×C4C2314yes—
118C24×C4C2314yes—
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4—42no—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
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⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4C2×C418yes—
153C22×C22⋊C4C2×C418yescomplemented
154C22×C22⋊C4C2×C418yescomplemented
155C22×C22⋊C4D418yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—24no—
169C22×C42—42no—
170C22×C42—42no—
171C22×C42C2314yes—
172C22×C42C2314yes—
173#388—232no—
174#386—232no—
175#386—232no—
176#386C2×C4164yescomplemented
177#380—232no—
178C4×C22⋊C4—232no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—232no—
193C2×#95—42no—
194C2×#95—42no—
195C2×#95C2×C418yescomplemented
196C2×#95C2×C418yescomplemented
197C2×#95D418yescomplemented
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
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—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25C22×C414yes—
239C25C22×C414yes—
240C25C2×D414yes—
241C25C2×D414yes—
242C25#4114yes—
243C25#4114yes—
244C25#4114yes—
245C25#4114yes—
246C25C2412yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C22×D4—232no—
250C22×D4—232no—
251C22×D4—232no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—28no—
257C22×D4—28no—
258C22×D4—416no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4C22×C4116yes—
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—232no—
272C23×C4—232no—
273C23×C4—232no—
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—28no—
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—28no—
297C23×C4—28no—
298C23×C4—28no—
299C23×C4—28no—
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×C4—22no—
332C23×C4—22no—
333C23×C4—232no—
334C23×C4—232no—
335C23×C4—28no—
336C23×C4—28no—
337C23×C4—28no—
338C23×C4—28no—
339C23×C4—28no—
340C23×C4—28no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—28no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—28no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—44no—
362C23×C4—44no—
363C23×C4—44no—
364C23×C4—44no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4—416no—
370C23×C4—416no—
371C23×C4—416no—
372C23×C4—416no—
373C23×C4—416no—
374C23×C4—416no—
375C23×C4—416no—
376C23×C4—416no—
377C23×C4—416no—
378C23×C4—416no—
379C23×C4C22×C414yes—
380C23×C4C22×C414yes—
381C23×C4C22×C414yes—
382C23×C4C22×C414yes—
383C23×C4C22×C4116yes—
384C23×C4C22×C414yes—
385C23×C4C2×D414yes—
386C23×C4C2×D414yes—
387C23×C4C2×D414yes—
388C23×C4C2×D414yes—
389C23×C4C2×D4116yes—
390C23×C4C2×D414yes—
391C23×C4C2×D414yes—
392C23×C4C2×D414yes—
393C23×C4#4114yes—
394C23×C4#4114yes—
395C23×C4#4114yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C2×C4⋊C4—28no—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—28no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—416no—
416C2×C4⋊C4—416no—
417C2×C22⋊C4—232no—
418C2×C22⋊C4—232no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—232no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—416no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—416no—
447C2×C22⋊C4—416no—
448C2×C22⋊C4—416no—
449C2×C22⋊C4C22×C4116yes—
450C2×C22⋊C4C22×C4116yescomplemented
451C2×C22⋊C4C22×C4116yescomplemented
452C2×C22⋊C4C2×D4116yes—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—28no—
456C2×C42—28no—
457C2×C42—44no—
458C2×C42—44no—
459C2×C42—416no—
460C2×C42—416no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—28no—
470#95—28no—
471#95—28no—
472#95—28no—
473#95—28no—
474#95—44no—
475#95—44no—
476#95C22×C4116yescomplemented
477#95C22×C4116yescomplemented
478#95C2×D4116yescomplemented
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—28no—
499C24—28no—
500C24—28no—
501C24—28no—
502C24—28no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—28no—
516C24—28no—
517C24—28no—
518C24—28no—
519C24—28no—
520C24—28no—
521C24—28no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24#117116yes—
565C24C4×D4116yes—
566C24C4×D4116yes—
567C24#121116yes—
568C24#123116yes—
569C24#124116yes—
570C24#126116yes—
571C24C23×C414yes—
572C24C23×C414yes—
573C24C23×C412yes—
574C24C22×D414yes—
575C24C22×D414yes—
576C24C22×D412yes—
577C24C22×D412yes—
578C24C22×D412yes—
579C24C2×#4114yes—
580C24C2×#4114yes—
581C24C2×#4114yes—
582C24C2×#4114yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24C2×#4112yes—
587C24C2×#4112yes—
588C24C2×#4112yes—
589C24C2×#4112yes—
590C24H(5,𝔽2)12yes—
591C24H(5,𝔽2)12yes—
592C24H(5,𝔽2)12yes—
593C242−1+412yes—
594C24C2511yescharacteristic
595C2×D4—232no—
596C2×D4—232no—
597C2×D4—232no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—416no—
601C2×D4—416no—
602C2×D4—4128no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
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—232no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—28no—
628C22×C4—232no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—232no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
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—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—232no—
708C22×C4—232no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—4128no—
726C22×C4—4128no—
727C22×C4—416no—
728C22×C4—416no—
729C22×C4—416no—
730C22×C4—416no—
731C22×C4—416no—
732C22×C4—416no—
733C22×C4—416no—
734C22×C4—416no—
735C22×C4—416no—
736C22×C4—416no—
737C22×C4—416no—
738C22×C4—416no—
739C22×C4—416no—
740C22×C4—4128no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—416no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4C4×D4116yes—
793C22×C4#121116yes—
794C22×C4C23×C414yes—
795C22×C4C23×C414yes—
796C22×C4C23×C414yes—
797C22×C4C23×C414yes—
798C22×C4C23×C414yes—
799C22×C4C22×D414yes—
800C22×C4C22×D414yes—
801C22×C4C22×D414yes—
802C22×C4C22×D414yes—
803C22×C4C22×D414yes—
804C22×C4C22×D414yes—
805C22×C4C22×D414yes—
806C22×C4C2×#4114yes—
807C22×C4C2×#4114yes—
808C22×C4C2×#4114yes—
809C4⋊C4—416no—
810C4⋊C4—416no—
811C22⋊C4—232no—
812C22⋊C4—232no—
813C22⋊C4—232no—
814C22⋊C4—416no—
815C22⋊C4—416no—
816C22⋊C4—416no—
817C22⋊C4—416no—
818C22⋊C4—416no—
819C22⋊C4—416no—
820C42—416no—
821C42—416no—
822C23—232no—
823C23—232no—
824C23—232no—
825C23—232no—
826C23—232no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—232no—
834C23—24no—
835C23—232no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—232no—
858C23—232no—
859C23—232no—
860C23—232no—
861C23—232no—
862C23—232no—
863C23—232no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23—416no—
906C23—88no—
907C23—88no—
908C23—88no—
909C23—88no—
910C23—88no—
911C23—88no—
912C23—88no—
913C23—88no—
914C23#388164yescomplemented
915C23C2×#11718yes—
916C23C2×#11714yes—
917C23C2×C4×D418yes—
918C23C2×C4×D418yes—
919C23C2×C4×D414yes—
920C23C2×C4×D414yes—
921C23C2×C4×D414yes—
922C23C4×#4114yes—
923C23#51814yes—
924C23#52014yes—
925C23C2×#12118yes—
926C23C2×#12114yes—
927C23C2×#12114yes—
928C23C2×#12318yes—
929C23C2×#12314yes—
930C23#52514yes—
931C23C2×#12418yes—
932C23C2×#12414yes—
933C23C2×#12618yes—
934C23C2×#12614yes—
935C23#52914yes—
936C23#53214yes—
937C23#53414yes—
938C23#53714yes—
939C23#53814yes—
940C23#53914yes—
941C23D4214yes—
942C23#54614yes—
943C23#54614yes—
944C23#54614yes—
945C23#54614yes—
946C23#54714yes—
947C23#54814yes—
948C23#55114yes—
949C23#55114yes—
950C23#55114yes—
951C23#55114yes—
952C23#55214yes—
953C23#55214yes—
954C23#55314yes—
955C23#55314yes—
956C23#55314yes—
957C23C24×C411yescharacteristic
958C23C23×D411yescharacteristic
959C23C23×D411yescharacteristic
960C23C23×D411yescharacteristic
961C23C22×#4111yescharacteristic
962C23C22×#4111yescharacteristic
963C23C22×#4111yescharacteristic
964C23C22×#4111yescharacteristic
965C23C22×#4111yescharacteristic
966C23C22×#4111yescharacteristic
967C23C22×#4111yescharacteristic
968C23C2×H(5,𝔽2)11yescharacteristic
969C23C2×H(5,𝔽2)11yescharacteristic
970C23C2×H(5,𝔽2)11yescharacteristic
971C23C2×2−1+411yescharacteristic
972D4—464no—
973C2×C4—232no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—232no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—464no—
1015C2×C4—464no—
1016C2×C4—464no—
1017C2×C4—416no—
1018C2×C4—416no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—416no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—416no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—416no—
1060C2×C4—416no—
1061C2×C4—416no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—88no—
1077C2×C4—88no—
1078C2×C4C2×C4×D418yes—
1079C2×C4C2×#12118yes—
1080C22—28no—
1081C22—28no—
1082C22—28no—
1083C22—28no—
1084C22—28no—
1085C22—28no—
1086C22—28no—
1087C22—28no—
1088C22—28no—
1089C22—28no—
1090C22—2128no—
1091C22—28no—
1092C22—28no—
1093C22—28no—
1094C22—28no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—82no—
1103C22—82no—
1104C22—82no—
1105C22—82no—
1106C22—82no—
1107C22—832no—
1108C22—82no—
1109C22—82no—
1110C22—82no—
1111C22C2×#38818yes—
1112C22C2×#388116yescomplemented
1113C22C4×#12118yes—
1114C22#232518yes—
1115C22#235218yes—
1116C22#235318yes—
1117C22#235818yes—
1118C22#235918yes—
1119C22#241218yes—
1120C22#241618yes—
1121C22#247218yes—
1122C22#248118yes—
1123C22#248818yes—
1124C22#249818yes—
1125C22#251018yes—
1126C22#254318yes—
1127C22C22×#11711yescharacteristic
1128C22C22×C4×D411yescharacteristic
1129C22C22×C4×D411yescharacteristic
1130C22C22×C4×D411yescharacteristic
1131C22C2×C4×#4111yescharacteristic
1132C22C2×#51811yescharacteristic
1133C22C2×#52011yescharacteristic
1134C22C22×#12111yescharacteristic
1135C22C22×#12111yescharacteristic
1136C22C22×#12311yescharacteristic
1137C22C2×#52511yescharacteristic
1138C22C22×#12411yescharacteristic
1139C22C22×#12611yescharacteristic
1140C22C2×#52911yescharacteristic
1141C22C2×#53211yescharacteristic
1142C22C2×#53411yescharacteristic
1143C22C2×#53711yescharacteristic
1144C22C2×#53811yescharacteristic
1145C22C2×#53911yescharacteristic
1146C22C2×D4211yescharacteristic
1147C22C2×#54611yescharacteristic
1148C22C2×#54611yescharacteristic
1149C22C2×#54611yescharacteristic
1150C22C2×#54611yescharacteristic
1151C22C2×#54711yescharacteristic
1152C22C2×#54811yescharacteristic
1153C22C2×#55111yescharacteristic
1154C22C2×#55111yescharacteristic
1155C22C2×#55111yescharacteristic
1156C22C2×#55111yescharacteristic
1157C22C2×#55211yescharacteristic
1158C22C2×#55211yescharacteristic
1159C22C2×#55311yescharacteristic
1160C22C2×#55311yescharacteristic
1161C22C2×#55311yescharacteristic
1162C4—28no—
1163C4—28no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—44no—
1168C4—44no—
1169C4—44no—
1170C4—44no—
1171C4—44no—
1172C4—44no—
1173C4—82no—
1174C4—82no—
1175C2—216no—
1176C2—84no—
1177C2#13999116yesdirect product factor
1178C2C22×#38811yescharacteristic
1179C2C2×C4×#12111yescharacteristic
1180C2C2×#232511yescharacteristic
1181C2C2×#235211yescharacteristic
1182C2C2×#235311yescharacteristic
1183C2C2×#235811yescharacteristic
1184C2C2×#235911yescharacteristic
1185C2C2×#241211yescharacteristic
1186C2C2×#247211yescharacteristic
1187C2C2×#248111yescharacteristic
1188C2C2×#241611yescharacteristic
1189C2C2×#248811yescharacteristic
1190C2C2×#251011yescharacteristic
1191C2C2×#249811yescharacteristic
1192C2C2×#254311yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
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×#388C2semidirect
5. C22×#380C2semidirect
6. C22×C4×C22⋊C4C2semidirect
7. C23×#95C2semidirect
8. #13999C2direct (N × H)
9. C2×#1443C2semidirect
10. C2×#1442C2semidirect
11. C2×#1440C2semidirect
12. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1434C2semidirect
16. C2×C22⋊#95C2semidirect
35. C2×#388C22semidirect
38. C2×#386C4semidirect
43. C2×#380C22semidirect
45. C2×C4×C22⋊C4C22semidirect
65. C22×#95C22semidirect
66. #1443C22semidirect
67. #1442C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. #1434C22semidirect
73. C22⋊#95C22semidirect
153. C22×C22⋊C4C2×C4semidirect
154. C22×C22⋊C4C2×C4semidirect
176. #386C2×C4semidirect
195. C2×#95C2×C4semidirect
196. C2×#95C2×C4semidirect
197. C2×#95D4semidirect
450. C2×C22⋊C4C22×C4semidirect
451. C2×C22⋊C4C22×C4semidirect
476. #95C22×C4semidirect
477. #95C22×C4semidirect
478. #95C2×D4semidirect
914. C23#388semidirect
1112. C22C2×#388semidirect
1177. C2#13999direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3862
C22×#3802
C22×C4×C22⋊C42
C23×#952
#139992
C2×#14432
C2×#14422
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952