Finite Group Databasebeta

← C22×#25042 #72307378

Subgroups — C22×#25042 #72307378

Order 1024.

21205 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#466C211yesmaximal, characteristic
2C23×#442C211yesmaximal, characteristic, complemented
3C22×#2420C211yesmaximal, characteristic, complemented
4C22×#2422C211yesmaximal, characteristic, complemented
5C2×#25042C2148yesmaximal, direct product factor
6C22×#2073C211yesmaximal, characteristic, complemented
7C22×#2071C211yesmaximal, characteristic, complemented
8C22×#2034C211yesmaximal, characteristic, complemented
9C22×#2033C211yesmaximal, characteristic, complemented
10C22×#1972C211yesmaximal, characteristic, complemented
11C22×#1944C211yesmaximal, characteristic, complemented
12C22×#1864C211yesmaximal, characteristic, complemented
13C22×#1862C211yesmaximal, characteristic, complemented
14C22×#1847C211yesmaximal, characteristic, complemented
15C22×#1807C211yesmaximal, characteristic, complemented
16C22×#1752C211yesmaximal, characteristic, complemented
17C24×D8C2211yescharacteristic
18C25×C8C2211yescharacteristic
19C23×#123—21no—
20C23×#121C2211yescharacteristic
21C23×#121C2211yescharacteristic
22C23×C4×D4C2211yescharacteristic
23C23×C4×D4C2211yescharacteristic
24C22×#466—216no—
25C22×#466C22124yes—
26C22×#442—216no—
27C22×#442C22124yescomplemented
28C23×#107C2211yescharacteristic
29C23×#107C2211yescharacteristic
30C23×#106C2211yescharacteristic
31C23×#106C2211yescharacteristic
32C23×#106C2211yescharacteristic
33C23×#102C2211yescharacteristic
34C23×#102C2211yescharacteristic
35C23×#102C2211yescharacteristic
36C23×#102C2211yescharacteristic
37C23×#102C2211yescharacteristic
38C23×#102C2211yescharacteristic
39C23×C22⋊C8C2211yescharacteristic
40C23×#97C2211yescharacteristic
41C23×#97C2211yescharacteristic
42C2×#2420—212no—
43C2×#2420C22124yescomplemented
44C2×#2422—212no—
45C2×#2422C22124yescomplemented
46C22×#397—21no—
47C22×#397—21no—
48C22×#394—21no—
49C22×#394—21no—
50C22×#390C2211yescharacteristic
51C22×#390C2211yescharacteristic
52C22×#389C2211yescharacteristic
53C22×#389C2211yescharacteristic
54C22×#386—21no—
55C22×#385—21no—
56C22×#384C2211yescharacteristic
57C22×#382C2211yescharacteristic
58C22×#381—21no—
59C22×#380C2211yescharacteristic
60C22×#380C2211yescharacteristic
61C22×C4×C22⋊C4C2211yescharacteristic
62#25042C221256yesdirect product factor
63C2×#2073C22124yescomplemented
64C2×#2071C22124yescomplemented
65C2×#2034C22124yescomplemented
66C2×#2033C22124yescomplemented
67C2×#1972C22124yescomplemented
68C2×#1944C22124yescomplemented
69C2×#1864C22124yescomplemented
70C2×#1862C22124yescomplemented
71C2×#1847C22124yescomplemented
72C2×#1807C22124yescomplemented
73C2×#1752C22124yescomplemented
74C22×#340C2211yescharacteristic
75C22×#340C2211yescharacteristic
76C22×#340C2211yescharacteristic
77C22×#340C2211yescharacteristic
78C22×#336C2211yescharacteristic
79C22×#336C2211yescharacteristic
80C24×D4—21no—
81C24×D4—21no—
82C24×D4C2311yescharacteristic
83C24×D4C2311yescharacteristic
84C25×C4—21no—
85C25×C4—21no—
86C25×C4C2311yescharacteristic
87C23×D8—28no—
88C23×D8—28no—
89C23×D8D4116yes—
90C23×D8C23112yes—
91C24×C8—28no—
92C24×C8—28no—
93C24×C8—28no—
94C24×C8C23112yes—
95C24×C8C2311yescharacteristic
96C24×C8C2311yescharacteristic
97C24×C8C2311yescharacteristic
98C24×C8C2311yescharacteristic
99C22×#123—224no—
100C22×#123—416no—
101C22×#121—26no—
102C22×#121—26no—
103C22×#121—28no—
104C22×#121—28no—
105C22×#121—44no—
106C22×#121—44no—
107C22×#121C23112yes—
108C22×#121C23112yes—
109C22×C4×D4—26no—
110C22×C4×D4—26no—
111C22×C4×D4—28no—
112C22×C4×D4—28no—
113C22×C4×D4—44no—
114C22×C4×D4—44no—
115C22×C4×D4C23112yes—
116C22×C4×D4C23112yes—
117C23×C4⋊C4—21no—
118C23×C4⋊C4—21no—
119C23×C4⋊C4—21no—
120C23×C4⋊C4—21no—
121C23×C4⋊C4C2311yescharacteristic
122C23×C4⋊C4C2311yescharacteristic
123C23×C4⋊C4C2311yescharacteristic
124C23×C4⋊C4C2311yescharacteristic
125C23×C4⋊C4C2311yescharacteristic
126C23×C4⋊C4C2311yescharacteristic
127C23×C22⋊C4—21no—
128C23×C22⋊C4—21no—
129C23×C22⋊C4—21no—
130C23×C22⋊C4—21no—
131C23×C22⋊C4—21no—
132C23×C22⋊C4—21no—
133C23×C22⋊C4—21no—
134C23×C22⋊C4—21no—
135C23×C22⋊C4—21no—
136C23×C22⋊C4—21no—
137C23×C22⋊C4D411yescharacteristic
138C23×C22⋊C4D411yescharacteristic
139C23×C42C2311yescharacteristic
140C23×C42C2311yescharacteristic
141C2×#466—2192no—
142C2×#466C23164yes—
143C2×#442—2192no—
144C2×#442C23164yescomplemented
145C22×#107—28no—
146C22×#107—44no—
147C22×#107C23112yes—
148C22×#107C23112yes—
149C22×#106—28no—
150C22×#106—28no—
151C22×#106—44no—
152C22×#106C23112yes—
153C22×#106C23112yes—
154C22×#106C23112yes—
155C22×#102—28no—
156C22×#102—28no—
157C22×#102—28no—
158C22×#102—28no—
159C22×#102—28no—
160C22×#102—28no—
161C22×#102C23112yes—
162C22×#102C23112yes—
163C22×#102C23112yes—
164C22×#102C23112yes—
165C22×#102C23112yes—
166C22×#102C23112yes—
167C22×C22⋊C8—28no—
168C22×C22⋊C8C23112yes—
169C22×#97—28no—
170C22×#97—28no—
171C22×#97C23112yes—
172C22×#97C23112yes—
173#2422—296no—
174#2422C23164yescomplemented
175#2420—296no—
176#2420C23164yescomplemented
177C2×#397—224no—
178C2×#397—224no—
179C2×#394—224no—
180C2×#394—224no—
181C2×#390—26no—
182C2×#390—26no—
183C2×#390C23112yes—
184C2×#390C23112yes—
185C2×#389—26no—
186C2×#389—26no—
187C2×#389C23112yes—
188C2×#389C23112yes—
189C2×#386—224no—
190C2×#385—224no—
191C2×#384—26no—
192C2×#384C23112yes—
193C2×#382—26no—
194C2×#382C23112yes—
195C2×#381—224no—
196C2×#380—26no—
197C2×#380—26no—
198C2×#380C23112yes—
199C2×#380C23112yes—
200C2×C4×C22⋊C4D4112yes—
201C2×C4×C22⋊C4C23112yes—
202C22×#95—21no—
203C22×#95—21no—
204C22×#95—21no—
205C22×#95—21no—
206C22×#95—21no—
207C22×#95—21no—
208C22×#95D411yescharacteristic
209C22×#95D411yescharacteristic
210#2073C23164yescomplemented
211#2071C23164yescomplemented
212#2034C23164yescomplemented
213#2033C23164yescomplemented
214#1972C23164yescomplemented
215#1944C23164yescomplemented
216#1864C23164yescomplemented
217#1862C23164yescomplemented
218#1847C23164yescomplemented
219#1807C23164yescomplemented
220#1752C23164yescomplemented
221C2×#340C23112yes—
222C2×#340C23112yes—
223C2×#340C23112yes—
224C2×#340C23112yes—
225C2×#336C23112yes—
226C2×#336C23112yes—
227C26—21no—
228C26—21no—
229C26C2×D411yescharacteristic
230C23×D4—212no—
231C23×D4—212no—
232C23×D4—23no—
233C23×D4—23no—
234C23×D4—24no—
235C23×D4—24no—
236C23×D4—24no—
237C23×D4—24no—
238C23×D4—24no—
239C23×D4—24no—
240C23×D4—24no—
241C23×D4—24no—
242C23×D4—24no—
243C23×D4—24no—
244C23×D4—48no—
245C23×D4—48no—
246C23×D4—48no—
247C23×D4—48no—
248C23×D4—84no—
249C23×D4—84no—
250C23×D4C2×D418yes—
251C23×D4C2×D418yes—
252C23×D4C2416yes—
253C23×D4C2416yes—
254C24×C4—24no—
255C24×C4—24no—
256C24×C4—24no—
257C24×C4—24no—
258C24×C4—24no—
259C24×C4—24no—
260C24×C4—21no—
261C24×C4—21no—
262C24×C4—21no—
263C24×C4—21no—
264C24×C4—21no—
265C24×C4—21no—
266C24×C4—212no—
267C24×C4—212no—
268C24×C4—48no—
269C24×C4—48no—
270C24×C4—48no—
271C24×C4—48no—
272C24×C4—84no—
273C24×C4—84no—
274C24×C4C2×D416yes—
275C24×C4C2×D411yescharacteristic
276C24×C4C2×D411yescharacteristic
277C24×C4C2×D411yescharacteristic
278C24×C4C2×D411yescharacteristic
279C24×C4C2×D411yescharacteristic
280C24×C4C2416yes—
281C24×C4C2411yescharacteristic
282C22×D8—2128no—
283C22×D8—248no—
284C22×D8—248no—
285C22×D8C2×D4196yes—
286C22×D8C24116yes—
287C23×C8—24no—
288C23×C8—24no—
289C23×C8—24no—
290C23×C8—24no—
291C23×C8—24no—
292C23×C8—24no—
293C23×C8—24no—
294C23×C8—24no—
295C23×C8—248no—
296C23×C8—248no—
297C23×C8—248no—
298C23×C8—464no—
299C23×C8C2×D418yes—
300C23×C8#4118yes—
301C23×C8#4118yes—
302C23×C8#4118yes—
303C23×C8C24116yes—
304C23×C8C2416yes—
305C23×C8C2416yes—
306C23×C8C2416yes—
307C23×C8C2416yes—
308C2×#123—264no—
309C2×#123—4192no—
310C2×#121—224no—
311C2×#121—224no—
312C2×#121—248no—
313C2×#121—248no—
314C2×#121—424no—
315C2×#121—424no—
316C2×#121—448no—
317C2×#121—448no—
318C2×#121C24116yes—
319C2×#121C24116yes—
320C2×C4×D4—248no—
321C2×C4×D4—248no—
322C2×C4×D4—224no—
323C2×C4×D4—224no—
324C2×C4×D4—424no—
325C2×C4×D4—424no—
326C2×C4×D4—448no—
327C2×C4×D4—448no—
328C2×C4×D4C24116yes—
329C2×C4×D4C24116yes—
330C22×C4⋊C4—24no—
331C22×C4⋊C4—24no—
332C22×C4⋊C4—24no—
333C22×C4⋊C4—24no—
334C22×C4⋊C4—24no—
335C22×C4⋊C4—24no—
336C22×C4⋊C4—24no—
337C22×C4⋊C4—24no—
338C22×C4⋊C4—24no—
339C22×C4⋊C4—24no—
340C22×C4⋊C4—24no—
341C22×C4⋊C4—24no—
342C22×C4⋊C4—212no—
343C22×C4⋊C4—212no—
344C22×C4⋊C4—23no—
345C22×C4⋊C4—23no—
346C22×C4⋊C4—23no—
347C22×C4⋊C4—23no—
348C22×C4⋊C4—23no—
349C22×C4⋊C4—23no—
350C22×C4⋊C4—212no—
351C22×C4⋊C4—212no—
352C22×C4⋊C4—48no—
353C22×C4⋊C4—48no—
354C22×C4⋊C4—84no—
355C22×C4⋊C4—84no—
356C22×C4⋊C4C2416yes—
357C22×C4⋊C4C2416yes—
358C22×C4⋊C4C2416yes—
359C22×C4⋊C4C2416yes—
360C22×C4⋊C4C2416yes—
361C22×C4⋊C4C2416yes—
362C22×C22⋊C4—28no—
363C22×C22⋊C4—212no—
364C22×C22⋊C4—212no—
365C22×C22⋊C4—212no—
366C22×C22⋊C4—212no—
367C22×C22⋊C4—212no—
368C22×C22⋊C4—212no—
369C22×C22⋊C4—212no—
370C22×C22⋊C4—212no—
371C22×C22⋊C4—212no—
372C22×C22⋊C4—212no—
373C22×C22⋊C4—44no—
374C22×C22⋊C4—48no—
375C22×C22⋊C4—48no—
376C22×C22⋊C4—48no—
377C22×C22⋊C4—48no—
378C22×C22⋊C4—48no—
379C22×C22⋊C4—48no—
380C22×C22⋊C4—48no—
381C22×C22⋊C4—84no—
382C22×C22⋊C4—84no—
383C22×C22⋊C4—84no—
384C22×C22⋊C4C2×D4112yes—
385C22×C22⋊C4C2×D4112yes—
386C22×C42—24no—
387C22×C42—24no—
388C22×C42—24no—
389C22×C42—24no—
390C22×C42C2×D416yes—
391C22×C42C2×D416yes—
392C22×C42C2416yes—
393C22×C42C2416yes—
394#466—2256no—
395#442—2256no—
396C2×#107—248no—
397C2×#107—424no—
398C2×#107C24116yes—
399C2×#107C24116yes—
400C2×#106—248no—
401C2×#106—248no—
402C2×#106—424no—
403C2×#106C24116yes—
404C2×#106C24116yes—
405C2×#106C24116yes—
406C2×#102—248no—
407C2×#102—248no—
408C2×#102—248no—
409C2×#102—248no—
410C2×#102—248no—
411C2×#102—248no—
412C2×#102C24116yes—
413C2×#102C24116yes—
414C2×#102C24116yes—
415C2×#102C24116yes—
416C2×#102C24116yes—
417C2×#102C24116yes—
418C2×C22⋊C8—248no—
419C2×C22⋊C8C24116yes—
420C2×#97—248no—
421C2×#97—248no—
422C2×#97C24116yes—
423C2×#97C24116yes—
424#397—264no—
425#397—264no—
426#394—264no—
427#394—264no—
428#390—224no—
429#390—224no—
430#390C24116yes—
431#390C24116yes—
432#389—224no—
433#389—224no—
434#389C24116yes—
435#389C24116yes—
436#386—264no—
437#385—264no—
438#384—224no—
439#384C24116yes—
440#382—224no—
441#382C24116yes—
442#381—264no—
443#380—224no—
444#380—224no—
445#380C24116yes—
446#380C24116yes—
447C4×C22⋊C4C2×D4148yes—
448C4×C22⋊C4C24116yes—
449C2×#95—212no—
450C2×#95—212no—
451C2×#95—212no—
452C2×#95—212no—
453C2×#95—212no—
454C2×#95—212no—
455C2×#95C2×D4112yes—
456C2×#95C2×D4112yes—
457#340C24116yes—
458#340C24116yes—
459#340C24116yes—
460#340C24116yes—
461#336C24116yes—
462#336C24116yes—
463C25—24no—
464C25—24no—
465C25—24no—
466C25—24no—
467C25—24no—
468C25—24no—
469C25—28no—
470C25—28no—
471C25—26no—
472C25—26no—
473C25—44no—
474C25—44no—
475C25—44no—
476C25—44no—
477C25—44no—
478C25—44no—
479C25—44no—
480C25—44no—
481C25—44no—
482C25—44no—
483C25—44no—
484C25—44no—
485C25AGL(1,ℤ/8)18yes—
486C25C22×D416yes—
487C25C22×D411yescharacteristic
488C22×D4—216no—
489C22×D4—216no—
490C22×D4—232no—
491C22×D4—232no—
492C22×D4—224no—
493C22×D4—224no—
494C22×D4—232no—
495C22×D4—232no—
496C22×D4—26no—
497C22×D4—26no—
498C22×D4—212no—
499C22×D4—212no—
500C22×D4—212no—
501C22×D4—212no—
502C22×D4—212no—
503C22×D4—212no—
504C22×D4—212no—
505C22×D4—212no—
506C22×D4—212no—
507C22×D4—212no—
508C22×D4—448no—
509C22×D4—448no—
510C22×D4—448no—
511C22×D4—448no—
512C22×D4—412no—
513C22×D4—412no—
514C22×D4—416no—
515C22×D4—416no—
516C22×D4—412no—
517C22×D4—412no—
518C22×D4—416no—
519C22×D4—416no—
520C22×D4—824no—
521C22×D4—824no—
522C22×D4—864no—
523C22×D4—864no—
524C22×D4C22×D4124yes—
525C22×D4C22×D4124yes—
526C22×D4C2514yes—
527C22×D4C2514yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—24no—
535C23×C4—24no—
536C23×C4—24no—
537C23×C4—24no—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—212no—
547C23×C4—212no—
548C23×C4—212no—
549C23×C4—212no—
550C23×C4—212no—
551C23×C4—212no—
552C23×C4—26no—
553C23×C4—26no—
554C23×C4—26no—
555C23×C4—26no—
556C23×C4—26no—
557C23×C4—26no—
558C23×C4—216no—
559C23×C4—216no—
560C23×C4—448no—
561C23×C4—448no—
562C23×C4—448no—
563C23×C4—448no—
564C23×C4—416no—
565C23×C4—416no—
566C23×C4—416no—
567C23×C4—416no—
568C23×C4—44no—
569C23×C4—44no—
570C23×C4—44no—
571C23×C4—44no—
572C23×C4—44no—
573C23×C4—44no—
574C23×C4—44no—
575C23×C4—44no—
576C23×C4—44no—
577C23×C4—44no—
578C23×C4—44no—
579C23×C4—44no—
580C23×C4—44no—
581C23×C4—44no—
582C23×C4—44no—
583C23×C4—44no—
584C23×C4—44no—
585C23×C4—44no—
586C23×C4—824no—
587C23×C4—824no—
588C23×C4—864no—
589C23×C4—864no—
590C23×C4C22×D416yes—
591C23×C4C22×D416yes—
592C23×C4C22×D416yes—
593C23×C4C22×D416yes—
594C23×C4C22×D416yes—
595C23×C4C22×D4112yes—
596C23×C4C22×D414yes—
597C23×C4C22×D413yes—
598C23×C4C2×#4114yes—
599C23×C4C2×#4114yes—
600C23×C4C2×#4114yes—
601C23×C4H(5,𝔽2)14yes—
602C23×C42−1+414yes—
603C23×C4C2514yes—
604C23×C4C2513yes—
605C2×D8—2384no—
606C2×D8—232no—
607C2×D8—232no—
608C2×D8C22×D4164yes—
609C22×C8—232no—
610C22×C8—212no—
611C22×C8—212no—
612C22×C8—212no—
613C22×C8—212no—
614C22×C8—212no—
615C22×C8—212no—
616C22×C8—212no—
617C22×C8—212no—
618C22×C8—232no—
619C22×C8—232no—
620C22×C8—232no—
621C22×C8—416no—
622C22×C8—416no—
623C22×C8—4192no—
624C22×C8#123164yescomplemented
625C22×C8C22×D4124yes—
626C22×C8C2×#41124yes—
627C22×C8C2×#41124yes—
628C22×C8C2×#41124yes—
629C22×C8C2514yes—
630C22×C8C2514yes—
631C22×C8C2514yes—
632C22×C8C2514yes—
633#123—4256no—
634#121—232no—
635#121—232no—
636#121—416no—
637#121—416no—
638#121—496no—
639#121—496no—
640C4×D4—232no—
641C4×D4—232no—
642C4×D4—416no—
643C4×D4—416no—
644C4×D4—496no—
645C4×D4—496no—
646C2×C4⋊C4—212no—
647C2×C4⋊C4—212no—
648C2×C4⋊C4—212no—
649C2×C4⋊C4—212no—
650C2×C4⋊C4—212no—
651C2×C4⋊C4—212no—
652C2×C4⋊C4—212no—
653C2×C4⋊C4—212no—
654C2×C4⋊C4—212no—
655C2×C4⋊C4—212no—
656C2×C4⋊C4—212no—
657C2×C4⋊C4—212no—
658C2×C4⋊C4—216no—
659C2×C4⋊C4—216no—
660C2×C4⋊C4—26no—
661C2×C4⋊C4—26no—
662C2×C4⋊C4—26no—
663C2×C4⋊C4—26no—
664C2×C4⋊C4—26no—
665C2×C4⋊C4—26no—
666C2×C4⋊C4—216no—
667C2×C4⋊C4—216no—
668C2×C4⋊C4—448no—
669C2×C4⋊C4—448no—
670C2×C4⋊C4—412no—
671C2×C4⋊C4—412no—
672C2×C4⋊C4—412no—
673C2×C4⋊C4—412no—
674C2×C4⋊C4—412no—
675C2×C4⋊C4—412no—
676C2×C4⋊C4—824no—
677C2×C4⋊C4—824no—
678C2×C4⋊C4C2514yes—
679C2×C4⋊C4C2514yes—
680C2×C4⋊C4C2514yes—
681C2×C4⋊C4C2514yes—
682C2×C4⋊C4C2514yes—
683C2×C4⋊C4C2514yes—
684C2×C22⋊C4—248no—
685C2×C22⋊C4—216no—
686C2×C22⋊C4—216no—
687C2×C22⋊C4—216no—
688C2×C22⋊C4—216no—
689C2×C22⋊C4—216no—
690C2×C22⋊C4—216no—
691C2×C22⋊C4—216no—
692C2×C22⋊C4—216no—
693C2×C22⋊C4—216no—
694C2×C22⋊C4—216no—
695C2×C22⋊C4—424no—
696C2×C22⋊C4—448no—
697C2×C22⋊C4—448no—
698C2×C22⋊C4—448no—
699C2×C22⋊C4—448no—
700C2×C22⋊C4—448no—
701C2×C22⋊C4—448no—
702C2×C22⋊C4—448no—
703C2×C22⋊C4—824no—
704C2×C22⋊C4—824no—
705C2×C22⋊C4—824no—
706C2×C22⋊C4C22×D4116yes—
707C2×C22⋊C4C22×D4116yes—
708C2×C42—224no—
709C2×C42—224no—
710C2×C42—212no—
711C2×C42—212no—
712C2×C42—212no—
713C2×C42—212no—
714C2×C42C22×D4112yes—
715C2×C42C22×D4112yes—
716C2×C42C2514yes—
717C2×C42C2514yes—
718#107—232no—
719#107—416no—
720#106—232no—
721#106—232no—
722#106—416no—
723#102—232no—
724#102—232no—
725#102—232no—
726#102—232no—
727#102—232no—
728#102—232no—
729C22⋊C8—232no—
730#97—232no—
731#97—232no—
732#95—216no—
733#95—216no—
734#95—216no—
735#95—216no—
736#95—216no—
737#95—216no—
738#95C22×D4116yes—
739#95C22×D4116yes—
740C24—232no—
741C24—232no—
742C24—212no—
743C24—212no—
744C24—212no—
745C24—232no—
746C24—212no—
747C24—212no—
748C24—212no—
749C24—24no—
750C24—24no—
751C24—224no—
752C24—224no—
753C24—416no—
754C24—416no—
755C24—416no—
756C24—416no—
757C24—412no—
758C24—412no—
759C24—432no—
760C24—432no—
761C24—412no—
762C24—412no—
763C24—432no—
764C24—432no—
765C24—432no—
766C24—432no—
767C24—412no—
768C24—412no—
769C24—412no—
770C24—412no—
771C24—412no—
772C24—412no—
773C24—412no—
774C24—412no—
775C24—816no—
776C24—816no—
777C24—816no—
778C24—816no—
779C24—816no—
780C24—816no—
781C24—816no—
782C24—816no—
783C24#53214yes—
784C24D4214yes—
785C24#54714yes—
786C24C2×AGL(1,ℤ/8)124yes—
787C24C2×AGL(1,ℤ/8)14yes—
788C24#57514yes—
789C24#57614yes—
790C24#57714yes—
791C24C23×D414yes—
792C24C23×D413yes—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—248no—
804C2×D4—248no—
805C2×D4—224no—
806C2×D4—224no—
807C2×D4—248no—
808C2×D4—248no—
809C2×D4—432no—
810C2×D4—432no—
811C2×D4—432no—
812C2×D4—432no—
813C2×D4—412no—
814C2×D4—412no—
815C2×D4—496no—
816C2×D4—496no—
817C2×D4—424no—
818C2×D4—424no—
819C2×D4—412no—
820C2×D4—412no—
821C2×D4—424no—
822C2×D4—424no—
823C2×D4—816no—
824C2×D4—816no—
825C2×D4—8192no—
826C2×D4—8192no—
827C2×D4C23×D418yes—
828C2×D4C23×D418yes—
829C22×C4—212no—
830C22×C4—212no—
831C22×C4—212no—
832C22×C4—212no—
833C22×C4—212no—
834C22×C4—212no—
835C22×C4—212no—
836C22×C4—212no—
837C22×C4—212no—
838C22×C4—212no—
839C22×C4—212no—
840C22×C4—212no—
841C22×C4—212no—
842C22×C4—212no—
843C22×C4—212no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—224no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—432no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—416no—
864C22×C4—416no—
865C22×C4—416no—
866C22×C4—416no—
867C22×C4—416no—
868C22×C4—424no—
869C22×C4—496no—
870C22×C4—424no—
871C22×C4—424no—
872C22×C4—424no—
873C22×C4—412no—
874C22×C4—412no—
875C22×C4—412no—
876C22×C4—412no—
877C22×C4—412no—
878C22×C4—412no—
879C22×C4—412no—
880C22×C4—412no—
881C22×C4—412no—
882C22×C4—412no—
883C22×C4—412no—
884C22×C4—412no—
885C22×C4—412no—
886C22×C4—412no—
887C22×C4—412no—
888C22×C4—412no—
889C22×C4—412no—
890C22×C4—412no—
891C22×C4—816no—
892C22×C4—816no—
893C22×C4—8192no—
894C22×C4—8192no—
895C22×C4—816no—
896C22×C4—816no—
897C22×C4—816no—
898C22×C4—816no—
899C22×C4—816no—
900C22×C4—816no—
901C22×C4C2×#123116yes—
902C22×C4#532112yes—
903C22×C4#542116yes—
904C22×C4D42112yes—
905C22×C4#547112yes—
906C22×C4#547116yes—
907C22×C4#553116yes—
908C22×C4C23×D414yes—
909C22×C4C23×D414yes—
910C22×C4C23×D414yes—
911C22×C4C23×D414yes—
912C22×C4C23×D414yes—
913C22×C4C23×D416yes—
914C22×C4C23×D413yes—
915C22×C4C22×#4116yes—
916C22×C4C22×#4116yes—
917C22×C4C22×#4116yes—
918C22×C4C2×H(5,𝔽2)16yes—
919C22×C4C2×2−1+416yes—
920C22×C4C2611yescharacteristic
921D8—2128no—
922C2×C8—24no—
923C2×C8—24no—
924C2×C8—248no—
925C2×C8—24no—
926C2×C8—24no—
927C2×C8—24no—
928C2×C8—24no—
929C2×C8—24no—
930C2×C8—24no—
931C2×C8—424no—
932C2×C8—424no—
933C2×C8—464no—
934C2×C8C2×#123196yescomplemented
935C2×C8C23×D418yes—
936C2×C8C22×#4118yes—
937C2×C8C22×#4118yes—
938C2×C8C22×#4118yes—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—432no—
952C4⋊C4—432no—
953C4⋊C4—412no—
954C4⋊C4—412no—
955C4⋊C4—412no—
956C4⋊C4—412no—
957C4⋊C4—412no—
958C4⋊C4—412no—
959C4⋊C4—816no—
960C4⋊C4—816no—
961C22⋊C4—232no—
962C22⋊C4—416no—
963C22⋊C4—432no—
964C22⋊C4—432no—
965C22⋊C4—432no—
966C22⋊C4—432no—
967C22⋊C4—432no—
968C22⋊C4—432no—
969C22⋊C4—432no—
970C22⋊C4—816no—
971C22⋊C4—816no—
972C22⋊C4—816no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—224no—
978C42—224no—
979C23—248no—
980C23—248no—
981C23—248no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—28no—
989C23—28no—
990C23—424no—
991C23—424no—
992C23—424no—
993C23—424no—
994C23—4128no—
995C23—448no—
996C23—448no—
997C23—448no—
998C23—448no—
999C23—44no—
1000C23—44no—
1001C23—44no—
1002C23—44no—
1003C23—44no—
1004C23—44no—
1005C23—44no—
1006C23—44no—
1007C23—448no—
1008C23—448no—
1009C23—44no—
1010C23—44no—
1011C23—44no—
1012C23—44no—
1013C23—824no—
1014C23—824no—
1015C23—824no—
1016C23—824no—
1017C23—824no—
1018C23—824no—
1019C23—824no—
1020C23—824no—
1021C23—8128no—
1022C23—8128no—
1023C23#2422116yes—
1024C23#3179116yes—
1025C23#3180116yes—
1026C23#3264116yes—
1027C23#3267116yes—
1028C23#3345116yes—
1029C23#3347116yes—
1030C23C2×#53216yes—
1031C23C2×D4216yes—
1032C23C2×#54716yes—
1033C23C22×AGL(1,ℤ/8)18yes—
1034C23C22×AGL(1,ℤ/8)16yes—
1035C23C2×#57516yes—
1036C23C2×#57616yes—
1037C23C2×#57716yes—
1038C23C24×D411yescharacteristic
1039D4—28no—
1040D4—28no—
1041D4—28no—
1042D4—28no—
1043D4—448no—
1044D4—448no—
1045D4—44no—
1046D4—44no—
1047D4—44no—
1048D4—44no—
1049D4—864no—
1050D4—864no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—424no—
1067C2×C4—424no—
1068C2×C4—424no—
1069C2×C4—424no—
1070C2×C4—424no—
1071C2×C4—448no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—864no—
1095C2×C4—864no—
1096C2×C4—824no—
1097C2×C4—824no—
1098C2×C4—824no—
1099C2×C4—824no—
1100C2×C4—824no—
1101C2×C4—824no—
1102C2×C4#2422148yes—
1103C2×C4C22×#123112yes—
1104C2×C4C2×#53216yes—
1105C2×C4C2×#542112yes—
1106C2×C4C2×D4216yes—
1107C2×C4C2×#54716yes—
1108C2×C4C2×#547112yes—
1109C2×C4C2×#553112yes—
1110C2×C4C24×D411yescharacteristic
1111C2×C4C23×#4111yescharacteristic
1112C2×C4C23×#4111yescharacteristic
1113C2×C4C23×#4111yescharacteristic
1114C2×C4C22×H(5,𝔽2)11yescharacteristic
1115C2×C4C22×2−1+411yescharacteristic
1116C8—28no—
1117C8—44no—
1118C8—44no—
1119C8C22×#123116yescomplemented
1120C22—28no—
1121C22—28no—
1122C22—28no—
1123C22—496no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—48no—
1129C22—48no—
1130C22—48no—
1131C22—48no—
1132C22—48no—
1133C22—48no—
1134C22—896no—
1135C22—896no—
1136C22—84no—
1137C22—84no—
1138C22—84no—
1139C22—84no—
1140C22—84no—
1141C22—84no—
1142C22—84no—
1143C22—84no—
1144C22#25042164yesdirect product factor
1145C22C2×#2422112yes—
1146C22C2×#3179112yes—
1147C22C2×#3180112yes—
1148C22C2×#3264112yes—
1149C22C2×#3267112yes—
1150C22C2×#3345112yes—
1151C22C2×#3347112yes—
1152C22C22×#53211yescharacteristic
1153C22C22×D4211yescharacteristic
1154C22C22×#54711yescharacteristic
1155C22C23×AGL(1,ℤ/8)11yescharacteristic
1156C22C22×#57511yescharacteristic
1157C22C22×#57611yescharacteristic
1158C22C22×#57711yescharacteristic
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—84no—
1165C4—84no—
1166C4—84no—
1167C4—84no—
1168C4—84no—
1169C4—84no—
1170C4C2×#2422112yes—
1171C4C23×#12311yescharacteristic
1172C4C22×#54211yescharacteristic
1173C4C22×#54711yescharacteristic
1174C4C22×#55311yescharacteristic
1175C2—48no—
1176C2—88no—
1177C2—88no—
1178C2C2×#25042124yesdirect product factor
1179C2C22×#242211yescharacteristic
1180C2C22×#317911yescharacteristic
1181C2C22×#318011yescharacteristic
1182C2C22×#326411yescharacteristic
1183C2C22×#326711yescharacteristic
1184C2C22×#334511yescharacteristic
1185C2C22×#334711yescharacteristic
subgroupG/H
center, socleC25C22×D4
commutator, Frattini, cosocleC22×C4C26
prime radicalC23×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C22×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C23×#442C2semidirect
3. C22×#2420C2semidirect
4. C22×#2422C2semidirect
5. C2×#25042C2direct (N × H)
6. C22×#2073C2semidirect
7. C22×#2071C2semidirect
8. C22×#2034C2semidirect
9. C22×#2033C2semidirect
10. C22×#1972C2semidirect
11. C22×#1944C2semidirect
12. C22×#1864C2semidirect
13. C22×#1862C2semidirect
14. C22×#1847C2semidirect
15. C22×#1807C2semidirect
16. C22×#1752C2semidirect
27. C22×#442C22semidirect
43. C2×#2420C22semidirect
45. C2×#2422C22semidirect
62. #25042C22direct (N × H)
63. C2×#2073C22semidirect
64. C2×#2071C22semidirect
65. C2×#2034C22semidirect
66. C2×#2033C22semidirect
67. C2×#1972C22semidirect
68. C2×#1944C22semidirect
69. C2×#1864C22semidirect
70. C2×#1862C22semidirect
71. C2×#1847C22semidirect
72. C2×#1807C22semidirect
73. C2×#1752C22semidirect
144. C2×#442C23semidirect
174. #2422C23semidirect
176. #2420C23semidirect
210. #2073C23semidirect
211. #2071C23semidirect
212. #2034C23semidirect
213. #2033C23semidirect
214. #1972C23semidirect
215. #1944C23semidirect
216. #1864C23semidirect
217. #1862C23semidirect
218. #1847C23semidirect
219. #1807C23semidirect
220. #1752C23semidirect
624. C22×C8#123semidirect
934. C2×C8C2×#123semidirect
1119. C8C22×#123semidirect
1144. C22#25042direct (N × H)
1178. C2C2×#25042direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#4662
C23×#4422
C22×#24202
C22×#24222
C2×#250422
C22×#20732
C22×#20712
C22×#20342
C22×#20332
C22×#19722
C22×#19442
C22×#18642
C22×#18622
C22×#18472
C22×#18072
C22×#17522