Finite Group Databasebeta

← C22×#61707 #72315620

Subgroups — C22×#61707 #72315620

Order 1024.

78613 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3496C211yesmaximal, characteristic, complemented
2C23×#553C211yesmaximal, characteristic, complemented
3C2×#61707C2196yesmaximal, direct product factor
4C22×#3345C218yesmaximal, complemented
5C22×#3318C218yesmaximal, complemented
6C22×#3234C212yesmaximal, complemented
7C22×#3192C212yesmaximal, complemented
8C22×#3186C212yesmaximal, complemented
9C22×#3109C212yesmaximal, complemented
10C23×#481C212yesmaximal, complemented
11C22×#3094C212yesmaximal, complemented
12C22×#2973C211yesmaximal, characteristic, complemented
13C23×H(5,𝔽2)—21no—
14C2×#3496—224no—
15C2×#3496C22148yescomplemented
16C22×#553—224no—
17C22×#553—24no—
18C22×#553C2218yescomplemented
19C22×#553C22148yescomplemented
20C22×#547C2214yescomplemented
21C22×#546—24no—
22C22×D42C2214yescomplemented
23C22×#537—21no—
24C22×#534—21no—
25C22×#534—21no—
26C22×#532C2212yes—
27C23×#126—21no—
28C23×#125C2211yescharacteristic, complemented
29C23×#123—21no—
30C23×#121—21no—
31C23×#121C2212yes—
32C23×#121C2212yes—
33C23×#121C2211yescharacteristic, complemented
34C23×#121C2211yescharacteristic, complemented
35C23×C4×D4—21no—
36C23×C4×D4C2211yescharacteristic
37C23×C4×D4C2211yescharacteristic, complemented
38C23×#117C2211yescharacteristic, complemented
39C24×C4⋊C4C2211yescharacteristic, complemented
40#61707C2211024yesdirect product factor
41C2×#3345C221384yescomplemented
42C2×#3318C221384yescomplemented
43C2×#3234C22196yescomplemented
44C2×#3192C22196yescomplemented
45C2×#3186C22196yescomplemented
46C22×#501C2214yescomplemented
47C22×#490C2214yescomplemented
48C2×#3109C22196yescomplemented
49C2×#3094C22196yescomplemented
50C22×#481C2214yescomplemented
51C22×#481C2214yescomplemented
52C22×#481C2218yescomplemented
53C22×#481C2214yescomplemented
54C22×#481C22196yescomplemented
55C22×#482C2218yescomplemented
56C22×#480C2214yescomplemented
57C22×#480C2214yescomplemented
58C22×#478C2218yescomplemented
59C22×#476C2214yescomplemented
60C22×#469C2218yescomplemented
61C22×#466C2218yescomplemented
62C22×#459C2214yescomplemented
63C22×#447C2214yescomplemented
64C22×#447C2214yescomplemented
65C22×#447C2214yescomplemented
66C2×#2973C22148yescomplemented
67C22×#442C2218yescomplemented
68C22×#435C2218yescomplemented
69C22×#432C2212yescomplemented
70C22×#428C2214yescomplemented
71C23×#106C2214yescomplemented
72C22×#418C2214yescomplemented
73C23×#102C2214yescomplemented
74C22×#407C2212yescomplemented
75C23×C22⋊C8C2212yescomplemented
76C22×H(5,𝔽2)—248no—
77C22×H(5,𝔽2)—432no—
78C23×#41—24no—
79C23×#41—22no—
80C24×D4—22no—
81C24×D4—22no—
82C24×D4—21no—
83C24×D4—21no—
84C24×D4—24no—
85C24×D4D411yescharacteristic
86C24×D4C2312yes—
87C24×D4C2312yes—
88C24×D4C2311yescharacteristic
89C25×C4—21no—
90C25×C4—21no—
91C25×C4C2311yescharacteristic
92C25×C4C2311yescharacteristic
93C23×D8C2318yes—
94C23×M16C2314yes—
95C24×C8C2314yes—
96#3496—2384no—
97#3496C231256yescomplemented
98C2×#553—296no—
99C2×#553—2192no—
100C2×#553—2384no—
101C2×#553C231192yescomplemented
102C2×#553C231256yescomplemented
103C2×#547—248no—
104C2×#547C23196yescomplemented
105C2×#546—2192no—
106C2×D42—248no—
107C2×D42C23196yescomplemented
108C2×#537—248no—
109C2×#534—248no—
110C2×#534—248no—
111C2×#532—224no—
112C2×#532C23148yes—
113C22×C4⋊Q8C2312yes—
114C22×#127C2312yes—
115C22×#126—28no—
116C22×#126—248no—
117C22×#125—22no—
118C22×#125—212no—
119C22×#125C2314yes—
120C22×#125C23124yescomplemented
121C22×#124—22no—
122C22×#123—28no—
123C22×#123—248no—
124C22×#123—24no—
125C22×#123—24no—
126C22×C22⋊Q8—24no—
127C22×#121—28no—
128C22×#121—248no—
129C22×#121—224no—
130C22×#121—224no—
131C22×#121—22no—
132C22×#121—22no—
133C22×#121—22no—
134C22×#121—22no—
135C22×#121—22no—
136C22×#121—212no—
137C22×#121—22no—
138C22×#121—212no—
139C22×#121—22no—
140C22×#121—24no—
141C22×#121C2314yes—
142C22×#121C2314yes—
143C22×#121C2314yes—
144C22×#121C2314yes—
145C22×#121C23148yes—
146C22×#121C23148yes—
147C22×#121C2314yes—
148C22×#121C23124yescomplemented
149C22×#121C23124yescomplemented
150C22×#120—24no—
151C22×#120—24no—
152C22×C4×D4—22no—
153C22×C4×D4—212no—
154C22×C4×D4—22no—
155C22×C4×D4—28no—
156C22×C4×D4—248no—
157C22×C4×D4D4124yes—
158C22×C4×D4D414yes—
159C22×C4×D4C2314yes—
160C22×C4×D4C2314yes—
161C22×C4×D4C23124yes—
162C22×C4×D4C2314yes—
163C22×C4×D4C23124yescomplemented
164C22×#117—22no—
165C22×#117—212no—
166C22×#117C2314yes—
167C22×#117C23124yescomplemented
168C23×C4⋊C4—21no—
169C23×C4⋊C4—22no—
170C23×C4⋊C4—212no—
171C23×C4⋊C4—21no—
172C23×C4⋊C4—21no—
173C23×C4⋊C4D411yescharacteristic
174C23×C4⋊C4C2311yescharacteristic
175C23×C4⋊C4C2312yes—
176C23×C4⋊C4C2311yescharacteristic
177C23×C4⋊C4C2311yescharacteristic
178C23×C4⋊C4C2314yes—
179C23×C4⋊C4C2312yes—
180C23×C4⋊C4C23124yescomplemented
181C23×C22⋊C4—21no—
182C23×C22⋊C4—21no—
183C23×C22⋊C4—21no—
184C23×C22⋊C4—22no—
185C23×C22⋊C4—22no—
186C23×C22⋊C4—21no—
187C23×C22⋊C4D411yescharacteristic
188C23×C22⋊C4D411yescharacteristic
189C23×C42—21no—
190C23×C42C2311yescharacteristic
191#3345C2312048yescomplemented
192#3318C2312048yescomplemented
193#3234C231512yescomplemented
194#3192C231512yescomplemented
195#3186C231512yescomplemented
196C2×#501C23196yescomplemented
197C2×#490C23196yescomplemented
198#3109C231512yescomplemented
199#3094C231512yescomplemented
200C2×#481C23196yescomplemented
201C2×#481C231192yescomplemented
202C2×#481C23196yescomplemented
203C2×#481C23196yescomplemented
204C2×#481C231512yescomplemented
205C2×#482C231192yescomplemented
206C2×#480C23196yescomplemented
207C2×#480C23196yescomplemented
208C2×#478C231192yescomplemented
209C2×#476C23196yescomplemented
210C2×#469C231192yescomplemented
211C2×#466C231192yescomplemented
212C2×#459C23196yescomplemented
213C2×#447C23196yescomplemented
214C2×#447C23196yescomplemented
215C2×#447C23196yescomplemented
216#2973C231256yescomplemented
217C2×#442C231192yescomplemented
218C2×#435C231192yescomplemented
219C2×#432C23148yescomplemented
220C2×#428C23196yescomplemented
221C22×#107C2318yes—
222C22×#106C2318yes—
223C22×#106C2318yes—
224C22×#106C23196yescomplemented
225C22×C4⋊C8C2314yes—
226C2×#418C23196yescomplemented
227C22×#102C2318yes—
228C22×#102C2318yes—
229C22×#102C2318yes—
230C22×#102C2318yes—
231C22×#102C23196yescomplemented
232C2×#407C23148yescomplemented
233C22×C22⋊C8C2314yes—
234C22×C22⋊C8C2314yes—
235C22×C22⋊C8C2314yes—
236C22×C22⋊C8C23148yescomplemented
237C22×#97C2314yes—
238C26—21no—
239C26—22no—
240C26—22no—
241C26C2×D411yescharacteristic
242C26C2×D411yescharacteristic
243C2×H(5,𝔽2)—2256no—
244C2×H(5,𝔽2)—4768no—
245C22×#41—296no—
246C22×#41—248no—
247C22×#41—432no—
248C22×#41—464no—
249C23×Q8—22no—
250C23×D4—216no—
251C23×D4—24no—
252C23×D4—24no—
253C23×D4—24no—
254C23×D4—248no—
255C23×D4—248no—
256C23×D4—24no—
257C23×D4—224no—
258C23×D4—24no—
259C23×D4—224no—
260C23×D4—296no—
261C23×D4—22no—
262C23×D4—26no—
263C23×D4—21no—
264C23×D4—22no—
265C23×D4—22no—
266C23×D4—212no—
267C23×D4—212no—
268C23×D4—22no—
269C23×D4—48no—
270C23×D4—416no—
271C23×D4—416no—
272C23×D4—464no—
273C23×D4—432no—
274C23×D4—416no—
275C23×D4—432no—
276C23×D4—88no—
277C23×D4C2×D414yes—
278C23×D4C2×D4124yes—
279C23×D4C2414yes—
280C23×D4C2412yes—
281C23×D4C24124yes—
282C23×D4C24124yes—
283C23×D4C24112yes—
284C24×C4—21no—
285C24×C4—21no—
286C24×C4—22no—
287C24×C4—22no—
288C24×C4—21no—
289C24×C4—24no—
290C24×C4—224no—
291C24×C4—24no—
292C24×C4—24no—
293C24×C4—224no—
294C24×C4—48no—
295C24×C4—48no—
296C24×C4—88no—
297C24×C4—88no—
298C24×C4C2×D411yescharacteristic
299C24×C4C2×D411yescharacteristic
300C24×C4C2×D411yescharacteristic
301C24×C4C2×D411yescharacteristic
302C24×C4C2×D412yes—
303C24×C4C2×D412yes—
304C24×C4C2×D4112yes—
305C24×C4C2×D4112yes—
306C24×C4C2411yescharacteristic
307C24×C4C2412yes—
308C24×C4C2412yes—
309C24×C4C24112yes—
310C24×C4C24112yes—
311C22×D8—432no—
312C22×D8C24196yes—
313C22×M16—416no—
314C22×M16C24148yes—
315C23×C8—416no—
316C23×C8C2418yes—
317C23×C8C24148yes—
318#553—2768no—
319#553—21024no—
320#553C241512yescomplemented
321#547—2384no—
322#547C241256yescomplemented
323#546—21024no—
324D42—2384no—
325D42C241256yescomplemented
326#537—2256no—
327#534—2256no—
328#534—2256no—
329#532—2192no—
330#532C241128yes—
331C2×C4⋊Q8—212no—
332C2×C4⋊Q8C24124yes—
333C2×#127—212no—
334C2×#127C24124yes—
335C2×#126—2192no—
336C2×#126—2256no—
337C2×#125—224no—
338C2×#125—248no—
339C2×#125—296no—
340C2×#125C24148yes—
341C2×#125C24164yescomplemented
342C2×#124—248no—
343C2×#123—2192no—
344C2×#123—2256no—
345C2×#123—296no—
346C2×#123—296no—
347C2×C22⋊Q8—296no—
348C2×#121—2192no—
349C2×#121—2256no—
350C2×#121—224no—
351C2×#121—248no—
352C2×#121—248no—
353C2×#121—224no—
354C2×#121—224no—
355C2×#121—248no—
356C2×#121—248no—
357C2×#121—224no—
358C2×#121—224no—
359C2×#121—2192no—
360C2×#121—2192no—
361C2×#121—248no—
362C2×#121—296no—
363C2×#121—248no—
364C2×#121—296no—
365C2×#121—248no—
366C2×#121—296no—
367C2×#121C24148yes—
368C2×#121C24148yes—
369C2×#121C24148yes—
370C2×#121C241128yes—
371C2×#121C24148yes—
372C2×#121C24148yes—
373C2×#121C241128yes—
374C2×#121C24164yescomplemented
375C2×#121C24164yescomplemented
376C2×#120—296no—
377C2×#120—296no—
378C2×C4×D4—2192no—
379C2×C4×D4—2256no—
380C2×C4×D4—224no—
381C2×C4×D4—248no—
382C2×C4×D4—296no—
383C2×C4×D4—248no—
384C2×C4×D4—224no—
385C2×C4×D4C2×D4148yes—
386C2×C4×D4C2×D4196yes—
387C2×C4×D4C2×D41192yes—
388C2×C4×D4C24148yes—
389C2×C4×D4C24148yes—
390C2×C4×D4C24148yes—
391C2×C4×D4C24164yes—
392C2×C4×D4C24164yescomplemented
393C2×#117—224no—
394C2×#117—248no—
395C2×#117—296no—
396C2×#117C24148yes—
397C2×#117C24164yescomplemented
398C22×C4⋊C4—26no—
399C22×C4⋊C4—21no—
400C22×C4⋊C4—26no—
401C22×C4⋊C4—21no—
402C22×C4⋊C4—24no—
403C22×C4⋊C4—224no—
404C22×C4⋊C4—224no—
405C22×C4⋊C4—248no—
406C22×C4⋊C4—296no—
407C22×C4⋊C4—24no—
408C22×C4⋊C4—224no—
409C22×C4⋊C4—24no—
410C22×C4⋊C4—224no—
411C22×C4⋊C4—26no—
412C22×C4⋊C4—21no—
413C22×C4⋊C4—22no—
414C22×C4⋊C4—22no—
415C22×C4⋊C4—212no—
416C22×C4⋊C4—212no—
417C22×C4⋊C4—22no—
418C22×C4⋊C4C2×D414yes—
419C22×C4⋊C4C2×D4124yes—
420C22×C4⋊C4C24112yes—
421C22×C4⋊C4C24124yes—
422C22×C4⋊C4C24112yes—
423C22×C4⋊C4C24112yes—
424C22×C4⋊C4C24148yes—
425C22×C4⋊C4C24124yes—
426C22×C4⋊C4C2412yes—
427C22×C4⋊C4C2412yes—
428C22×C4⋊C4C2412yes—
429C22×C4⋊C4C2414yes—
430C22×C4⋊C4C24164yescomplemented
431C22×C22⋊C4—24no—
432C22×C22⋊C4—224no—
433C22×C22⋊C4—24no—
434C22×C22⋊C4—24no—
435C22×C22⋊C4—224no—
436C22×C22⋊C4—24no—
437C22×C22⋊C4—224no—
438C22×C22⋊C4—24no—
439C22×C22⋊C4—24no—
440C22×C22⋊C4—24no—
441C22×C22⋊C4—248no—
442C22×C22⋊C4—248no—
443C22×C22⋊C4—224no—
444C22×C22⋊C4—24no—
445C22×C22⋊C4C2×D414yes—
446C22×C22⋊C4C2×D4124yes—
447C22×C22⋊C4C2×D414yes—
448C22×C22⋊C4C2×D4124yes—
449C22×C42—24no—
450C22×C42—224no—
451C22×C42C2×D412yes—
452C22×C42C2×D4112yes—
453C22×C42C2412yes—
454C22×C42C24112yes—
455#501C241256yescomplemented
456#490C241256yescomplemented
457#482C241512yescomplemented
458#481C241512yescomplemented
459#481C241256yescomplemented
460#481C241256yescomplemented
461#481C241256yescomplemented
462#480C241256yescomplemented
463#480C241256yescomplemented
464#478C241512yescomplemented
465#476C241256yescomplemented
466#469C241512yescomplemented
467#466C241512yescomplemented
468#459C241256yescomplemented
469#447C241256yescomplemented
470#447C241256yescomplemented
471#447C241256yescomplemented
472#442C241512yescomplemented
473#435C241512yescomplemented
474#432C241128yescomplemented
475#428C241256yescomplemented
476C2×#107C24196yes—
477C2×#106C24196yes—
478C2×#106C24196yes—
479C2×#106C241256yescomplemented
480C2×C4⋊C8C24148yes—
481#418C241256yescomplemented
482C2×#102C24196yes—
483C2×#102C24196yes—
484C2×#102C24196yes—
485C2×#102C24196yes—
486C2×#102C241256yescomplemented
487#407C241128yescomplemented
488C2×C22⋊C8C24148yes—
489C2×C22⋊C8C24148yes—
490C2×C22⋊C8C24148yes—
491C2×C22⋊C8C241128yescomplemented
492C2×#97C24148yes—
493C25—28no—
494C25—212no—
495C25—22no—
496C25—24no—
497C25—224no—
498C25—224no—
499C25—44no—
500C25—44no—
501C25—44no—
502C25—44no—
503C25—48no—
504C25—48no—
505C25—416no—
506C25—48no—
507C25—416no—
508C25—88no—
509C25—88no—
510C25—88no—
511C25—88no—
512C25AGL(1,ℤ/8)116yes—
513C25C22×D412yes—
514C25C22×D412yes—
515C25C22×D411yescharacteristic
516C25C22×D4112yes—
517C25C22×D4112yes—
518H(5,𝔽2)—42048no—
519C2×#41—2256no—
520C2×#41—2128no—
521C2×#41—4384no—
522C2×#41—4768no—
523C22×Q8—224no—
524C22×Q8—416no—
525C22×D4—232no—
526C22×D4—2192no—
527C22×D4—248no—
528C22×D4—264no—
529C22×D4—248no—
530C22×D4—248no—
531C22×D4—248no—
532C22×D4—2128no—
533C22×D4—2128no—
534C22×D4—248no—
535C22×D4—264no—
536C22×D4—2256no—
537C22×D4—212no—
538C22×D4—224no—
539C22×D4—26no—
540C22×D4—212no—
541C22×D4—224no—
542C22×D4—224no—
543C22×D4—224no—
544C22×D4—224no—
545C22×D4—248no—
546C22×D4—248no—
547C22×D4—216no—
548C22×D4—232no—
549C22×D4—448no—
550C22×D4—496no—
551C22×D4—496no—
552C22×D4—48no—
553C22×D4—448no—
554C22×D4—416no—
555C22×D4—4768no—
556C22×D4—432no—
557C22×D4—4384no—
558C22×D4—432no—
559C22×D4—4192no—
560C22×D4—432no—
561C22×D4—432no—
562C22×D4—4384no—
563C22×D4—848no—
564C22×D4—848no—
565C22×D4—88no—
566C22×D4—88no—
567C22×D4—88no—
568C22×D4—816no—
569C22×D4—896no—
570C22×D4C22×D4148yes—
571C22×D4C22×D4164yes—
572C22×D4C25112yes—
573C22×D4C25124yes—
574C22×D4C25116yes—
575C22×D4C25132yes—
576C22×D4C25132yes—
577C23×C4—28no—
578C23×C4—216no—
579C23×C4—216no—
580C23×C4—28no—
581C23×C4—212no—
582C23×C4—212no—
583C23×C4—212no—
584C23×C4—224no—
585C23×C4—224no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—24no—
589C23×C4—22no—
590C23×C4—248no—
591C23×C4—264no—
592C23×C4—248no—
593C23×C4—248no—
594C23×C4—264no—
595C23×C4—448no—
596C23×C4—448no—
597C23×C4—448no—
598C23×C4—448no—
599C23×C4—48no—
600C23×C4—48no—
601C23×C4—44no—
602C23×C4—44no—
603C23×C4—44no—
604C23×C4—432no—
605C23×C4—48no—
606C23×C4—48no—
607C23×C4—416no—
608C23×C4—48no—
609C23×C4—416no—
610C23×C4—816no—
611C23×C4—816no—
612C23×C4—896no—
613C23×C4—896no—
614C23×C4C22×D4112yes—
615C23×C4C22×D4112yes—
616C23×C4C22×D416yes—
617C23×C4C22×D4112yes—
618C23×C4C22×D412yes—
619C23×C4C22×D412yes—
620C23×C4C22×D411yescharacteristic
621C23×C4C22×D412yes—
622C23×C4C22×D412yes—
623C23×C4C22×D4112yes—
624C23×C4C22×D4112yes—
625C23×C4C22×D4124yes—
626C23×C4C22×D4124yes—
627C23×C4C22×D4112yes—
628C23×C4C22×D4148yes—
629C23×C4C22×D4148yes—
630C23×C4C25112yes—
631C23×C4C2516yes—
632C23×C4C25112yes—
633C23×C4C25116yes—
634C23×C4C25116yes—
635C23×C4C2511yescharacteristic
636C2×D8—4192no—
637C2×D8C251128yes—
638C2×M16—496no—
639C2×M16C25164yes—
640C22×C8—232no—
641C22×C8—496no—
642C22×C8C25148yes—
643C22×C8C25164yes—
644C4⋊Q8—248no—
645C4⋊Q8C25132yes—
646#127—248no—
647#127C25132yes—
648#126—2512no—
649#125—296no—
650#125—2128no—
651#125C25164yes—
652#124—2128no—
653#123—2512no—
654#123—2256no—
655#123—2256no—
656C22⋊Q8—2256no—
657#121—2512no—
658#121—296no—
659#121—2128no—
660#121—2128no—
661#121—296no—
662#121—296no—
663#121—2128no—
664#121—2128no—
665#121—296no—
666#121—296no—
667#121—2128no—
668#121—2128no—
669#121—2128no—
670#121—2256no—
671#121C25164yes—
672#121C25164yes—
673#121C25164yes—
674#121C25164yes—
675#121C25164yes—
676#120—2256no—
677#120—2256no—
678C4×D4—2512no—
679C4×D4—296no—
680C4×D4—2128no—
681C4×D4—2128no—
682C4×D4—296no—
683C4×D4C22×D41192yes—
684C4×D4C22×D41256yes—
685C4×D4C25164yes—
686C4×D4C25164yes—
687C4×D4C25164yes—
688#117—296no—
689#117—2128no—
690#117C25164yes—
691C2×C4⋊C4—212no—
692C2×C4⋊C4—224no—
693C2×C4⋊C4—26no—
694C2×C4⋊C4—212no—
695C2×C4⋊C4—224no—
696C2×C4⋊C4—26no—
697C2×C4⋊C4—248no—
698C2×C4⋊C4—296no—
699C2×C4⋊C4—264no—
700C2×C4⋊C4—2128no—
701C2×C4⋊C4—212no—
702C2×C4⋊C4—248no—
703C2×C4⋊C4—264no—
704C2×C4⋊C4—248no—
705C2×C4⋊C4—264no—
706C2×C4⋊C4—212no—
707C2×C4⋊C4—224no—
708C2×C4⋊C4—26no—
709C2×C4⋊C4—224no—
710C2×C4⋊C4—224no—
711C2×C4⋊C4—248no—
712C2×C4⋊C4—248no—
713C2×C4⋊C4—224no—
714C2×C4⋊C4C22×D4148yes—
715C2×C4⋊C4C22×D4164yes—
716C2×C4⋊C4C25112yes—
717C2×C4⋊C4C25112yes—
718C2×C4⋊C4C25124yes—
719C2×C4⋊C4C25116yes—
720C2×C4⋊C4C25116yes—
721C2×C4⋊C4C25164yes—
722C2×C4⋊C4C25112yes—
723C2×C4⋊C4C25116yes—
724C2×C4⋊C4C25132yes—
725C2×C4⋊C4C25132yes—
726C2×C22⋊C4—248no—
727C2×C22⋊C4—264no—
728C2×C22⋊C4—248no—
729C2×C22⋊C4—248no—
730C2×C22⋊C4—264no—
731C2×C22⋊C4—248no—
732C2×C22⋊C4—264no—
733C2×C22⋊C4—248no—
734C2×C22⋊C4—248no—
735C2×C22⋊C4—248no—
736C2×C22⋊C4—2128no—
737C2×C22⋊C4—2128no—
738C2×C22⋊C4—264no—
739C2×C22⋊C4—248no—
740C2×C22⋊C4C22×D4148yes—
741C2×C22⋊C4C22×D4164yes—
742C2×C22⋊C4C22×D4148yes—
743C2×C22⋊C4C22×D4164yes—
744C2×C42—248no—
745C2×C42—264no—
746C2×C42C22×D4124yes—
747C2×C42C22×D4112yes—
748C2×C42C22×D4148yes—
749C2×C42C25112yes—
750C2×C42C25116yes—
751#107C251128yes—
752#106C251128yes—
753#106C251128yes—
754C4⋊C8C25164yes—
755#102C251128yes—
756#102C251128yes—
757#102C251128yes—
758#102C251128yes—
759C22⋊C8C25164yes—
760C22⋊C8C25164yes—
761C22⋊C8C25164yes—
762#97C25164yes—
763C24—24no—
764C24—28no—
765C24—24no—
766C24—28no—
767C24—28no—
768C24—28no—
769C24—28no—
770C24—248no—
771C24—216no—
772C24—212no—
773C24—224no—
774C24—232no—
775C24—232no—
776C24—424no—
777C24—424no—
778C24—464no—
779C24—424no—
780C24—424no—
781C24—448no—
782C24—448no—
783C24—496no—
784C24—48no—
785C24—416no—
786C24—48no—
787C24—416no—
788C24—416no—
789C24—448no—
790C24—48no—
791C24—496no—
792C24—832no—
793C24—848no—
794C24—848no—
795C24—848no—
796C24—848no—
797C24—864no—
798C24—1664no—
799C24—1664no—
800C24C2×AGL(1,ℤ/8)18yes—
801C24C2×AGL(1,ℤ/8)116yes—
802C24C2×AGL(1,ℤ/8)196yes—
803C24C23×D4112yes—
804C24C23×D4112yes—
805C24C23×D416yes—
806C24C23×D4116yes—
807C24C23×D4116yes—
808C24C23×D411yescharacteristic
809#41—4512no—
810#41—41024no—
811C2×Q8—232no—
812C2×Q8—496no—
813C2×D4—2192no—
814C2×D4—2256no—
815C2×D4—264no—
816C2×D4—264no—
817C2×D4—264no—
818C2×D4—264no—
819C2×D4—264no—
820C2×D4—216no—
821C2×D4—212no—
822C2×D4—224no—
823C2×D4—232no—
824C2×D4—232no—
825C2×D4—232no—
826C2×D4—232no—
827C2×D4—248no—
828C2×D4—296no—
829C2×D4—432no—
830C2×D4—464no—
831C2×D4—464no—
832C2×D4—448no—
833C2×D4—496no—
834C2×D4—496no—
835C2×D4—41024no—
836C2×D4—4192no—
837C2×D4—4512no—
838C2×D4—4192no—
839C2×D4—4256no—
840C2×D4—4192no—
841C2×D4—4192no—
842C2×D4—4512no—
843C2×D4—424no—
844C2×D4—448no—
845C2×D4—896no—
846C2×D4—896no—
847C2×D4—848no—
848C2×D4—848no—
849C2×D4—848no—
850C2×D4—896no—
851C2×D4—8128no—
852C2×D4C23×D4164yes—
853C2×D4C26116yes—
854C2×D4C2618yes—
855C22×C4—28no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—248no—
861C22×C4—248no—
862C22×C4—248no—
863C22×C4—224no—
864C22×C4—224no—
865C22×C4—248no—
866C22×C4—248no—
867C22×C4—216no—
868C22×C4—212no—
869C22×C4—216no—
870C22×C4—212no—
871C22×C4—224no—
872C22×C4—216no—
873C22×C4—212no—
874C22×C4—232no—
875C22×C4—232no—
876C22×C4—264no—
877C22×C4—264no—
878C22×C4—264no—
879C22×C4—496no—
880C22×C4—496no—
881C22×C4—432no—
882C22×C4—432no—
883C22×C4—448no—
884C22×C4—448no—
885C22×C4—424no—
886C22×C4—424no—
887C22×C4—424no—
888C22×C4—4192no—
889C22×C4—448no—
890C22×C4—448no—
891C22×C4—496no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—416no—
895C22×C4—448no—
896C22×C4—48no—
897C22×C4—496no—
898C22×C4—896no—
899C22×C4—896no—
900C22×C4—8128no—
901C22×C4—8128no—
902C22×C4C23×D4112yes—
903C22×C4C23×D416yes—
904C22×C4C23×D4112yes—
905C22×C4C23×D4112yes—
906C22×C4C23×D4112yes—
907C22×C4C23×D4116yes—
908C22×C4C23×D4112yes—
909C22×C4C23×D4124yes—
910C22×C4C23×D4124yes—
911C22×C4C23×D4116yes—
912C22×C4C23×D4116yes—
913C22×C4C23×D4116yes—
914C22×C4C23×D4132yes—
915C22×C4C23×D4132yes—
916C22×C4C23×D413yes—
917C22×C4#58518yes—
918C22×C4C2614yes—
919C22×C4C2618yes—
920C22×C4C2618yes—
921C22×C4C2613yes—
922D8—4128no—
923M16—464no—
924C2×C8—296no—
925C2×C8—464no—
926C2×C8C26132yes—
927C4⋊C4—216no—
928C4⋊C4—212no—
929C4⋊C4—216no—
930C4⋊C4—212no—
931C4⋊C4—264no—
932C4⋊C4—224no—
933C4⋊C4—264no—
934C4⋊C4—264no—
935C4⋊C4—216no—
936C4⋊C4—212no—
937C4⋊C4—232no—
938C4⋊C4—232no—
939C4⋊C4—232no—
940C4⋊C4C23×D4164yes—
941C4⋊C4C2618yes—
942C4⋊C4C2618yes—
943C4⋊C4C2618yes—
944C4⋊C4C26116yes—
945C22⋊C4—264no—
946C22⋊C4—264no—
947C22⋊C4—264no—
948C22⋊C4—264no—
949C22⋊C4—264no—
950C22⋊C4—264no—
951C22⋊C4—264no—
952C22⋊C4—264no—
953C22⋊C4C23×D4164yes—
954C22⋊C4C23×D4164yes—
955C42—264no—
956C42C23×D4132yes—
957C42C23×D4124yes—
958C42C2618yes—
959C23—232no—
960C23—264no—
961C23—212no—
962C23—224no—
963C23—212no—
964C23—224no—
965C23—224no—
966C23—224no—
967C23—224no—
968C23—232no—
969C23—28no—
970C23—216no—
971C23—416no—
972C23—416no—
973C23—4192no—
974C23—416no—
975C23—416no—
976C23—432no—
977C23—432no—
978C23—464no—
979C23—432no—
980C23—424no—
981C23—448no—
982C23—448no—
983C23—432no—
984C23—424no—
985C23—424no—
986C23—448no—
987C23—464no—
988C23—896no—
989C23—832no—
990C23—832no—
991C23—832no—
992C23—832no—
993C23—8192no—
994C23—832no—
995C23—864no—
996C23—16192no—
997C23—16192no—
998C23#348514yes—
999C23C22×AGL(1,ℤ/8)124yes—
1000C23C22×AGL(1,ℤ/8)148yes—
1001C23C22×AGL(1,ℤ/8)164yes—
1002C23C22×AGL(1,ℤ/8)14yes—
1003C23#358514yes—
1004C23C24×D418yes—
1005C23C24×D418yes—
1006C23C24×D414yes—
1007C23C24×D413yes—
1008Q8—464no—
1009D4—2128no—
1010D4—216no—
1011D4—232no—
1012D4—432no—
1013D4—464no—
1014D4—4128no—
1015D4—4128no—
1016D4—4128no—
1017D4—4128no—
1018D4—424no—
1019D4—448no—
1020D4—832no—
1021D4—832no—
1022D4—832no—
1023D4—864no—
1024C2×C4—212no—
1025C2×C4—224no—
1026C2×C4—224no—
1027C2×C4—224no—
1028C2×C4—232no—
1029C2×C4—224no—
1030C2×C4—224no—
1031C2×C4—248no—
1032C2×C4—248no—
1033C2×C4—216no—
1034C2×C4—216no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—216no—
1039C2×C4—28no—
1040C2×C4—432no—
1041C2×C4—432no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—4128no—
1046C2×C4—432no—
1047C2×C4—432no—
1048C2×C4—464no—
1049C2×C4—448no—
1050C2×C4—432no—
1051C2×C4—424no—
1052C2×C4—464no—
1053C2×C4—424no—
1054C2×C4—424no—
1055C2×C4—864no—
1056C2×C4—864no—
1057C2×C4#3485112yes—
1058C2×C4C24×D418yes—
1059C2×C4C24×D414yes—
1060C2×C4C24×D418yes—
1061C2×C4C24×D418yes—
1062C2×C4C24×D418yes—
1063C2×C4C24×D413yes—
1064C2×C4C2×#585112yes—
1065C2×C4C2711yescharacteristic
1066C8—232no—
1067C22—24no—
1068C22—28no—
1069C22—24no—
1070C22—28no—
1071C22—248no—
1072C22—296no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—464no—
1077C22—448no—
1078C22—48no—
1079C22—416no—
1080C22—416no—
1081C22—48no—
1082C22—48no—
1083C22—416no—
1084C22—832no—
1085C22—864no—
1086C22—848no—
1087C22—896no—
1088C22—1664no—
1089C22—1664no—
1090C22#61707116yesdirect product factor
1091C22C2×#348516yes—
1092C22C23×AGL(1,ℤ/8)18yes—
1093C22C23×AGL(1,ℤ/8)116yes—
1094C22C23×AGL(1,ℤ/8)16yes—
1095C22C2×#358516yes—
1096C22C25×D411yescharacteristic
1097C4—24no—
1098C4—28no—
1099C4—28no—
1100C4—28no—
1101C4—28no—
1102C4—416no—
1103C4—48no—
1104C4—48no—
1105C4—48no—
1106C4C2×#348516yes—
1107C4C22×#58512yes—
1108C2—28no—
1109C2—216no—
1110C2—48no—
1111C2—88no—
1112C2—816no—
1113C2C2×#61707112yesdirect product factor
1114C2C22×#348511yescharacteristic
1115C2C24×AGL(1,ℤ/8)11yescharacteristic
1116C2C22×#358511yescharacteristic
subgroupG/H
center, socleC24C23×D4
commutator, Frattini, cosocleC2×C4C27
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#3496C2semidirect
2. C23×#553C2semidirect
3. C2×#61707C2direct (N × H)
4. C22×#3345C2semidirect
5. C22×#3318C2semidirect
6. C22×#3234C2semidirect
7. C22×#3192C2semidirect
8. C22×#3186C2semidirect
9. C22×#3109C2semidirect
10. C23×#481C2semidirect
11. C22×#3094C2semidirect
12. C22×#2973C2semidirect
15. C2×#3496C22semidirect
18. C22×#553C22semidirect
19. C22×#553C22semidirect
20. C22×#547C22semidirect
22. C22×D42C22semidirect
28. C23×#125C22semidirect
33. C23×#121C22semidirect
34. C23×#121C22semidirect
37. C23×C4×D4C22semidirect
38. C23×#117C22semidirect
39. C24×C4⋊C4C22semidirect
40. #61707C22direct (N × H)
41. C2×#3345C22semidirect
42. C2×#3318C22semidirect
43. C2×#3234C22semidirect
44. C2×#3192C22semidirect
45. C2×#3186C22semidirect
46. C22×#501C22semidirect
47. C22×#490C22semidirect
48. C2×#3109C22semidirect
49. C2×#3094C22semidirect
50. C22×#481C22semidirect
51. C22×#481C22semidirect
52. C22×#481C22semidirect
53. C22×#481C22semidirect
54. C22×#481C22semidirect
55. C22×#482C22semidirect
56. C22×#480C22semidirect
57. C22×#480C22semidirect
58. C22×#478C22semidirect
59. C22×#476C22semidirect
60. C22×#469C22semidirect
61. C22×#466C22semidirect
62. C22×#459C22semidirect
63. C22×#447C22semidirect
64. C22×#447C22semidirect
65. C22×#447C22semidirect
66. C2×#2973C22semidirect
67. C22×#442C22semidirect
68. C22×#435C22semidirect
69. C22×#432C22semidirect
70. C22×#428C22semidirect
71. C23×#106C22semidirect
72. C22×#418C22semidirect
73. C23×#102C22semidirect
74. C22×#407C22semidirect
75. C23×C22⋊C8C22semidirect
97. #3496C23semidirect
101. C2×#553C23semidirect
102. C2×#553C23semidirect
104. C2×#547C23semidirect
107. C2×D42C23semidirect
120. C22×#125C23semidirect
148. C22×#121C23semidirect
149. C22×#121C23semidirect
163. C22×C4×D4C23semidirect
167. C22×#117C23semidirect
180. C23×C4⋊C4C23semidirect
191. #3345C23semidirect
192. #3318C23semidirect
193. #3234C23semidirect
194. #3192C23semidirect
195. #3186C23semidirect
196. C2×#501C23semidirect
197. C2×#490C23semidirect
198. #3109C23semidirect
199. #3094C23semidirect
200. C2×#481C23semidirect
201. C2×#481C23semidirect
202. C2×#481C23semidirect
203. C2×#481C23semidirect
204. C2×#481C23semidirect
205. C2×#482C23semidirect
206. C2×#480C23semidirect
207. C2×#480C23semidirect
208. C2×#478C23semidirect
209. C2×#476C23semidirect
210. C2×#469C23semidirect
211. C2×#466C23semidirect
212. C2×#459C23semidirect
213. C2×#447C23semidirect
214. C2×#447C23semidirect
215. C2×#447C23semidirect
216. #2973C23semidirect
217. C2×#442C23semidirect
218. C2×#435C23semidirect
219. C2×#432C23semidirect
220. C2×#428C23semidirect
224. C22×#106C23semidirect
226. C2×#418C23semidirect
231. C22×#102C23semidirect
232. C2×#407C23semidirect
236. C22×C22⋊C8C23semidirect
320. #553C24semidirect
322. #547C24semidirect
325. D42C24semidirect
341. C2×#125C24semidirect
374. C2×#121C24semidirect
375. C2×#121C24semidirect
392. C2×C4×D4C24semidirect
397. C2×#117C24semidirect
430. C22×C4⋊C4C24semidirect
455. #501C24semidirect
456. #490C24semidirect
457. #482C24semidirect
458. #481C24semidirect
459. #481C24semidirect
460. #481C24semidirect
461. #481C24semidirect
462. #480C24semidirect
463. #480C24semidirect
464. #478C24semidirect
465. #476C24semidirect
466. #469C24semidirect
467. #466C24semidirect
468. #459C24semidirect
469. #447C24semidirect
470. #447C24semidirect
471. #447C24semidirect
472. #442C24semidirect
473. #435C24semidirect
474. #432C24semidirect
475. #428C24semidirect
479. C2×#106C24semidirect
481. #418C24semidirect
486. C2×#102C24semidirect
487. #407C24semidirect
491. C2×C22⋊C8C24semidirect
1090. C22#61707direct (N × H)
1113. C2C2×#61707direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#34962
C23×#5532
C2×#617072
C22×#33452
C22×#33182
C22×#32342
C22×#31922
C22×#31862
C22×#31092
C23×#4812
C22×#30942
C22×#29732