Finite Group Databasebeta

← C22×#5490 #11702109

Subgroups — C22×#5490 #11702109

Order 768.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#67C211yesmaximal, characteristic, complemented
2C23×#235C211yesmaximal, characteristic, complemented
3C23×C3×C22⋊C4C211yesmaximal, characteristic, complemented
4C22×#953C211yesmaximal, characteristic, complemented
5C22×#929C211yesmaximal, characteristic, complemented
6C22×#930C211yesmaximal, characteristic, complemented
7C22×C4×#67C211yesmaximal, characteristic, complemented
8C2×#5490C2148yesmaximal, direct product factor
9C22×#883C211yesmaximal, characteristic, complemented
10C22×#884C211yesmaximal, characteristic, complemented
11C22×#884C211yesmaximal, characteristic, complemented
12C22×#882C211yesmaximal, characteristic, complemented
13C22×D3×C22⋊C4C211yesmaximal, characteristic, complemented
14C22×#885C211yesmaximal, characteristic, complemented
15C22×#878C211yesmaximal, characteristic, complemented
16C22×#67⋊C4C211yesmaximal, characteristic, complemented
17C22×#546—31nomaximal, Sylow
18C26×C3C2211yescharacteristic
19C25×D3C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic, complemented
21C24×C3×C4C2211yescharacteristic, complemented
22C23×#67—216no—
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C23×#67C2211yescharacteristic
26C23×#67C2211yescharacteristic
27C23×#67C2211yescharacteristic
28C23×#67C22124yescomplemented
29C23×#67C2211yescharacteristic, complemented
30C23×#67C2211yescharacteristic, complemented
31C24×Dic3C2211yescharacteristic
32C22×#235—216no—
33C22×#235C22124yescomplemented
34C23×D12C2211yescharacteristic, complemented
35C23×D12C2211yescharacteristic, complemented
36C23×C4×D3C2211yescharacteristic, complemented
37C23×C4×D3C2211yescharacteristic, complemented
38C23×C4×D3C2211yescharacteristic, complemented
39C23×Dic6C2211yescharacteristic, complemented
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C22124yescomplemented
43C22×C3×C22⋊C4C2211yescharacteristic, complemented
44C22×C3×C22⋊C4C2211yescharacteristic, complemented
45C2×#953C22124yescomplemented
46C22×#217C2211yescharacteristic
47C22×#217C2211yescharacteristic, complemented
48C22×#217C2211yescharacteristic, complemented
49C2×#930C22124yescomplemented
50C2×#929C22124yescomplemented
51C2×C4×#67C22124yescomplemented
52C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
54C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
55C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
56C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
57C22×C4⋊Dic3C2211yescharacteristic, complemented
58C22×Dic3⋊C4C2211yescharacteristic, complemented
59C22×Dic3⋊C4C2211yescharacteristic, complemented
60C22×Dic3⋊C4C2211yescharacteristic, complemented
61C22×C4×Dic3C2211yescharacteristic, complemented
62C2×#885C22124yescomplemented
63#5490C221256yesdirect product factor
64C2×#884C22124yescomplemented
65C2×#884C22124yescomplemented
66C2×#883C22124yescomplemented
67C2×#882C22124yescomplemented
68C2×#67⋊C4C22124yescomplemented
69C2×D3×C22⋊C4C22124yescomplemented
70C2×#878C22124yescomplemented
71C23×#41—31no—
72C24×D4—31no—
73C2×#546—348no—
74C22×#124—31no—
75C22×#123—31no—
76C22×#123—31no—
77C22×C22⋊Q8—31no—
78C22×#121—31no—
79C22×#121—31no—
80C22×#121—31no—
81C22×#120—31no—
82C22×#120—31no—
83C22×C4×D4—31no—
84C22×C4×D4—31no—
85C23×C22⋊C4—31no—
86C23×C22⋊C4D311yescharacteristic, complemented
87C25×C3—28no—
88C25×C3—28no—
89C25×C3—44no—
90C25×C3C2311yescharacteristic
91C25×C3C23112yes—
92C25×C3C2311yescharacteristic
93C25×C3C2311yescharacteristic
94C24×D3—28no—
95C24×D3—28no—
96C24×D3—44no—
97C24×D3C2311yescharacteristic
98C24×D3C2311yescharacteristic
99C24×D3C23112yes—
100C24×D3C2311yescharacteristic
101C23×C3×C4—28no—
102C23×C3×C4—44no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C23112yescomplemented
108C23×C3×C4C23112yescomplemented
109C22×#67—28no—
110C22×#67—28no—
111C22×#67—28no—
112C22×#67—28no—
113C22×#67—2192no—
114C22×#67—28no—
115C22×#67—44no—
116C22×#67D4116yescomplemented
117C22×#67C23112yes—
118C22×#67C23112yes—
119C22×#67C23112yes—
120C22×#67C23112yes—
121C22×#67C23112yes—
122C22×#67C23164yescomplemented
123C22×#67C23112yescomplemented
124C22×#67C23112yescomplemented
125C23×Dic3—28no—
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C23112yes—
130C23×Dic3C2311yescharacteristic
131C23×Dic3C2311yescharacteristic
132C2×#235—2192no—
133C2×#235C23164yescomplemented
134C22×D12—28no—
135C22×D12—44no—
136C22×D12C23112yescomplemented
137C22×D12C23112yescomplemented
138C22×C4×D3—28no—
139C22×C4×D3—28no—
140C22×C4×D3—44no—
141C22×C4×D3C23112yescomplemented
142C22×C4×D3C23112yescomplemented
143C22×C4×D3C23112yescomplemented
144C22×Dic6—28no—
145C22×Dic6C23112yescomplemented
146C2×C3×C22⋊C4C23112yes—
147C2×C3×C22⋊C4C23112yes—
148C2×C3×C22⋊C4C23164yescomplemented
149C2×C3×C22⋊C4C23112yescomplemented
150C2×C3×C22⋊C4C23112yescomplemented
151#953C23164yescomplemented
152C2×#217C23112yes—
153C2×#217C23112yescomplemented
154C2×#217C23112yescomplemented
155#930C23164yescomplemented
156#929C23164yescomplemented
157C4×#67C23164yescomplemented
158C2×(C2×D3)⋊C4C23112yescomplemented
159C2×(C2×D3)⋊C4C23112yescomplemented
160C2×(C2×D3)⋊C4C23112yescomplemented
161C2×(C2×D3)⋊C4C23112yescomplemented
162C2×(C2×D3)⋊C4C23112yescomplemented
163C2×C4⋊Dic3C23112yescomplemented
164C2×Dic3⋊C4C23112yescomplemented
165C2×Dic3⋊C4C23112yescomplemented
166C2×Dic3⋊C4C23112yescomplemented
167C2×C4×Dic3C23112yescomplemented
168#885C23164yescomplemented
169#884C23164yescomplemented
170#884C23164yescomplemented
171#883C23164yescomplemented
172#882C23164yescomplemented
173#67⋊C4C23164yescomplemented
174D3×C22⋊C4C23164yescomplemented
175#878C23164yescomplemented
176C26—31no—
177C26C2×D311yescharacteristic
178C22×#41—324no—
179C22×#41—616no—
180C23×Q8—31no—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—324no—
186C23×D4—31no—
187C23×D4—31no—
188C23×D4—31no—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—616no—
192C24×C4—31no—
193C24×C4—31no—
194C24×C4—31no—
195C24×C4—31no—
196C24×C4C2×D311yescharacteristic, complemented
197C24×C4C2×D311yescharacteristic, complemented
198#546—3256no—
199C2×#124—324no—
200C2×#123—324no—
201C2×#123—324no—
202C2×C22⋊Q8—324no—
203C2×#121—324no—
204C2×#121—324no—
205C2×#121—324no—
206C2×#120—324no—
207C2×#120—324no—
208C2×C4×D4—324no—
209C2×C4×D4—324no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—324no—
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D3124yescomplemented
226C22×C22⋊C4C2×D311yescharacteristic, complemented
227C22×C22⋊C4C2×D311yescharacteristic, complemented
228C22×C42—31no—
229C24×C3—24no—
230C24×C3—24no—
231C24×C3—24no—
232C24×C3—24no—
233C24×C3—248no—
234C24×C3—24no—
235C24×C3—24no—
236C24×C3—248no—
237C24×C3—24no—
238C24×C3—424no—
239C24×C3—464no—
240C24×C3C2×D418yes—
241C24×C3#4118yescomplemented
242C24×C3C2416yes—
243C24×C3C24116yes—
244C24×C3C2416yes—
245C24×C3C2416yes—
246C24×C3C2411yescharacteristic
247C23×D3—24no—
248C23×D3—24no—
249C23×D3—24no—
250C23×D3—24no—
251C23×D3—24no—
252C23×D3—24no—
253C23×D3—248no—
254C23×D3—24no—
255C23×D3—24no—
256C23×D3—248no—
257C23×D3—424no—
258C23×D3—464no—
259C23×D3C2×D418yes—
260C23×D3C2416yes—
261C23×D3C2416yes—
262C23×D3C24116yes—
263C23×D3C2416yes—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—248no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—424no—
270C22×C3×C4C2416yes—
271C22×C3×C4C2416yes—
272C22×C3×C4C2416yes—
273C22×C3×C4C2416yes—
274C22×C3×C4C24116yescomplemented
275C22×C3×C4C24116yescomplemented
276C2×#67—248no—
277C2×#67—248no—
278C2×#67—248no—
279C2×#67—248no—
280C2×#67—2256no—
281C2×#67—248no—
282C2×#67—424no—
283C2×#67C2×D4196yescomplemented
284C2×#67C24116yes—
285C2×#67C24116yes—
286C2×#67C24116yes—
287C2×#67C24116yes—
288C2×#67C24116yes—
289C2×#67C24116yescomplemented
290C2×#67C24116yescomplemented
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—24no—
295C22×Dic3—248no—
296C22×Dic3C2×D418yes—
297C22×Dic3C24116yes—
298C22×Dic3C2416yes—
299C22×Dic3C2416yes—
300C22×Dic3C2416yes—
301C22×Dic3C2416yes—
302C22×Dic3C2416yes—
303#235—2256no—
304C2×D12—248no—
305C2×D12—424no—
306C2×D12C24116yescomplemented
307C2×D12C24116yescomplemented
308C2×C4×D3—248no—
309C2×C4×D3—248no—
310C2×C4×D3—424no—
311C2×C4×D3C24116yescomplemented
312C2×C4×D3C24116yescomplemented
313C2×C4×D3C24116yescomplemented
314C2×Dic6—248no—
315C2×Dic6C24116yescomplemented
316C3×C22⋊C4C24116yes—
317C3×C22⋊C4C24116yes—
318C3×C22⋊C4C24116yescomplemented
319C3×C22⋊C4C24116yescomplemented
320#217C24116yes—
321#217C24116yescomplemented
322#217C24116yescomplemented
323(C2×D3)⋊C4C24116yescomplemented
324(C2×D3)⋊C4C24116yescomplemented
325(C2×D3)⋊C4C24116yescomplemented
326(C2×D3)⋊C4C24116yescomplemented
327(C2×D3)⋊C4C24116yescomplemented
328C4⋊Dic3C24116yescomplemented
329Dic3⋊C4C24116yescomplemented
330Dic3⋊C4C24116yescomplemented
331Dic3⋊C4C24116yescomplemented
332C4×Dic3C24116yescomplemented
333C25—28no—
334C25—28no—
335C25—31no—
336C25—31no—
337C25—31no—
338C25—312no—
339C25—44no—
340C25—68no—
341C25—68no—
342C25—124no—
343C25C22×D311yescharacteristic
344C25C22×D3112yes—
345C25C22×D311yescharacteristic
346C25C22×D311yescharacteristic
347C2×#41—364no—
348C2×#41—6192no—
349C22×Q8—312no—
350C22×Q8—68no—
351C22×D4—316no—
352C22×D4—312no—
353C22×D4—312no—
354C22×D4—312no—
355C22×D4—312no—
356C22×D4—312no—
357C22×D4—312no—
358C22×D4—364no—
359C22×D4—312no—
360C22×D4—312no—
361C22×D4—312no—
362C22×D4—68no—
363C22×D4—68no—
364C22×D4—6192no—
365C22×D4—68no—
366C22×D4—68no—
367C22×D4—68no—
368C22×D4—68no—
369C22×D4—124no—
370C22×D4—124no—
371C23×C4—28no—
372C23×C4—31no—
373C23×C4—312no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—312no—
379C23×C4—312no—
380C23×C4—312no—
381C23×C4—44no—
382C23×C4—68no—
383C23×C4—68no—
384C23×C4—68no—
385C23×C4—124no—
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D3112yescomplemented
391C23×C4C22×D3112yescomplemented
392#124—364no—
393#123—364no—
394#123—364no—
395C22⋊Q8—364no—
396#121—364no—
397#121—364no—
398#121—364no—
399#120—364no—
400#120—364no—
401C4×D4—364no—
402C4×D4—364no—
403C2×C4⋊C4—312no—
404C2×C4⋊C4—312no—
405C2×C4⋊C4—312no—
406C2×C4⋊C4—312no—
407C2×C22⋊C4—312no—
408C2×C22⋊C4—312no—
409C2×C22⋊C4—312no—
410C2×C22⋊C4—312no—
411C2×C22⋊C4—312no—
412C2×C22⋊C4—312no—
413C2×C22⋊C4—312no—
414C2×C22⋊C4—312no—
415C2×C22⋊C4—364no—
416C2×C22⋊C4C22×D3112yes—
417C2×C22⋊C4C22×D3112yes—
418C2×C22⋊C4C22×D3164yescomplemented
419C2×C22⋊C4C22×D3112yescomplemented
420C2×C22⋊C4C22×D3112yescomplemented
421C2×C42—312no—
422C23×C3—232no—
423C23×C3—232no—
424C23×C3—212no—
425C23×C3—212no—
426C23×C3—212no—
427C23×C3—212no—
428C23×C3—232no—
429C23×C3—212no—
430C23×C3—212no—
431C23×C3—232no—
432C23×C3—212no—
433C23×C3—416no—
434C23×C3—4192no—
435C23×C3—416no—
436C23×C3C22×D4124yes—
437C23×C3C22×D414yes—
438C23×C3C2×#4114yes—
439C23×C3C2×#41124yescomplemented
440C23×C3H(5,𝔽2)14yes—
441C23×C3C2514yes—
442C23×C3C2514yes—
443C23×C3C2514yes—
444C23×C3C2513yes—
445C22×D3—232no—
446C22×D3—212no—
447C22×D3—212no—
448C22×D3—212no—
449C22×D3—212no—
450C22×D3—212no—
451C22×D3—212no—
452C22×D3—232no—
453C22×D3—212no—
454C22×D3—212no—
455C22×D3—232no—
456C22×D3—416no—
457C22×D3—4192no—
458C22×D3—416no—
459C22×D3—416no—
460C22×D3C22×D4124yes—
461C22×D3C2514yes—
462C22×D3C2514yes—
463C22×D3C2514yes—
464C2×C3×C4—212no—
465C2×C3×C4—212no—
466C2×C3×C4—232no—
467C2×C3×C4—212no—
468C2×C3×C4—212no—
469C2×C3×C4—416no—
470C2×C3×C4C2514yes—
471C2×C3×C4C2514yes—
472C2×C3×C4C2514yes—
473C2×C3×C4C2514yes—
474#67—232no—
475#67—232no—
476#67—232no—
477#67—232no—
478#67—232no—
479#67—416no—
480#67C22×D4164yescomplemented
481C2×Dic3—212no—
482C2×Dic3—212no—
483C2×Dic3—212no—
484C2×Dic3—212no—
485C2×Dic3—232no—
486C2×Dic3C22×D4124yes—
487C2×Dic3C2514yes—
488C2×Dic3C2514yes—
489C2×Dic3C2514yes—
490C2×Dic3C2514yes—
491C2×Dic3C2514yes—
492D12—232no—
493D12—416no—
494C4×D3—232no—
495C4×D3—232no—
496C4×D3—416no—
497Dic6—232no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—248no—
504C24—248no—
505C24—24no—
506C24—24no—
507C24—38no—
508C24—36no—
509C24—36no—
510C24—36no—
511C24—316no—
512C24—424no—
513C24—464no—
514C24—648no—
515C24—64no—
516C24—64no—
517C24—64no—
518C24—64no—
519C24—648no—
520C24—64no—
521C24—64no—
522C24—64no—
523C24—64no—
524C24—1224no—
525C24—1264no—
526C24#23518yescomplemented
527C24D3×D418yes—
528C24C23×D316yes—
529C24C23×D3116yes—
530C24C23×D316yes—
531C24C23×D316yes—
532C24C23×D311yescharacteristic
533#41—6256no—
534C2×Q8—316no—
535C2×Q8—648no—
536C2×D4—396no—
537C2×D4—316no—
538C2×D4—316no—
539C2×D4—316no—
540C2×D4—316no—
541C2×D4—316no—
542C2×D4—316no—
543C2×D4—316no—
544C2×D4—316no—
545C2×D4—316no—
546C2×D4—648no—
547C2×D4—648no—
548C2×D4—6256no—
549C2×D4—648no—
550C2×D4—648no—
551C2×D4—648no—
552C2×D4—648no—
553C2×D4—1224no—
554C2×D4—1224no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—248no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—38no—
561C22×C4—36no—
562C22×C4—36no—
563C22×C4—36no—
564C22×C4—36no—
565C22×C4—36no—
566C22×C4—316no—
567C22×C4—316no—
568C22×C4—316no—
569C22×C4—316no—
570C22×C4—424no—
571C22×C4—648no—
572C22×C4—648no—
573C22×C4—648no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—64no—
577C22×C4—64no—
578C22×C4—1224no—
579C22×C4C23×D316yes—
580C22×C4C23×D316yes—
581C22×C4C23×D316yes—
582C22×C4C23×D316yes—
583C22×C4C23×D3116yescomplemented
584C22×C4C23×D3116yescomplemented
585C4⋊C4—316no—
586C4⋊C4—316no—
587C4⋊C4—316no—
588C4⋊C4—316no—
589C22⋊C4—316no—
590C22⋊C4—316no—
591C22⋊C4—316no—
592C22⋊C4—316no—
593C22⋊C4—316no—
594C22⋊C4—316no—
595C22⋊C4—316no—
596C22⋊C4—316no—
597C22⋊C4C23×D3116yes—
598C22⋊C4C23×D3116yes—
599C22⋊C4C23×D3116yescomplemented
600C22⋊C4C23×D3116yescomplemented
601C42—316no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—248no—
607C22×C3—248no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—464no—
612C22×C3—424no—
613C22×C3#546116yescomplemented
614C22×C3C23×D418yes—
615C22×C3C23×D416yes—
616C22×C3C22×#4116yes—
617C22×C3C22×#4118yescomplemented
618C22×C3C2×H(5,𝔽2)16yes—
619C22×C3C2611yescharacteristic
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—248no—
623C2×D3—24no—
624C2×D3—24no—
625C2×D3—24no—
626C2×D3—24no—
627C2×D3—24no—
628C2×D3—24no—
629C2×D3—464no—
630C2×D3—424no—
631C2×D3—424no—
632C2×D3C23×D418yes—
633C3×C4—24no—
634C3×C4—24no—
635C3×C4—24no—
636C3×C4—24no—
637Dic3—24no—
638Dic3—24no—
639Dic3—24no—
640Dic3—24no—
641Dic3C23×D418yes—
642C23—212no—
643C23—212no—
644C23—212no—
645C23—212no—
646C23—232no—
647C23—232no—
648C23—212no—
649C23—232no—
650C23—232no—
651C23—212no—
652C23—212no—
653C23—324no—
654C23—34no—
655C23—34no—
656C23—34no—
657C23—416no—
658C23—4192no—
659C23—416no—
660C23—632no—
661C23—612no—
662C23—612no—
663C23—632no—
664C23—612no—
665C23—612no—
666C23—632no—
667C23—612no—
668C23—612no—
669C23—612no—
670C23—612no—
671C23—1216no—
672C23—12192no—
673C23—1216no—
674C23—1216no—
675C23C2×#23514yes—
676C23C2×#235124yescomplemented
677C23C2×D3×D4124yes—
678C23C2×D3×D414yes—
679C23#100414yes—
680C23C24×D314yes—
681C23C24×D314yes—
682C23C24×D314yes—
683C23C24×D313yes—
684Q8—632no—
685D4—364no—
686D4—632no—
687D4—632no—
688D4—632no—
689D4—632no—
690D4—632no—
691D4—632no—
692D4—1216no—
693D4—1216no—
694C2×C4—212no—
695C2×C4—212no—
696C2×C4—232no—
697C2×C4—212no—
698C2×C4—212no—
699C2×C4—324no—
700C2×C4—34no—
701C2×C4—34no—
702C2×C4—34no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—416no—
706C2×C4—632no—
707C2×C4—632no—
708C2×C4—632no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—1216no—
714C2×C4C24×D314yes—
715C2×C4C24×D314yes—
716C2×C4C24×D314yes—
717C2×C4C24×D314yes—
718C2×C3—28no—
719C2×C3—28no—
720C2×C3—44no—
721C2×C3C2×#546112yescomplemented
722C2×C3C24×D411yescharacteristic
723C2×C3C23×#4111yescharacteristic
724C2×C3C22×H(5,𝔽2)11yescharacteristic
725D3—28no—
726D3—44no—
727D3—44no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—248no—
733C22—248no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—38no—
738C22—464no—
739C22—424no—
740C22—64no—
741C22—64no—
742C22—648no—
743C22—64no—
744C22—64no—
745C22—64no—
746C22—64no—
747C22—64no—
748C22—64no—
749C22—1264no—
750C22—1224no—
751C22—1224no—
752C22#5490116yesdirect product factor
753C22C22×#23516yes—
754C22C22×#23518yescomplemented
755C22C22×D3×D418yes—
756C22C22×D3×D416yes—
757C22C2×#100416yes—
758C22C25×D311yescharacteristic
759C4—24no—
760C4—24no—
761C4—24no—
762C4—24no—
763C4—38no—
764C4—64no—
765C4—64no—
766C4—64no—
767C4—64no—
768C3C22×#54611yescharacteristic, complemented, Sylow
769C2—28no—
770C2—28no—
771C2—44no—
772C2—68no—
773C2—124no—
774C2—124no—
775C2C2×#5490112yesdirect product factor
776C2C23×#23511yescharacteristic
777C2C23×D3×D411yescharacteristic
778C2C22×#100411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC23×C3×C22⋊C4C2
socleC24×C3C24
hypercenterC23×C22⋊C4D3
hypocenterC3C22×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C24×#67C2semidirect
2. C23×#235C2semidirect
3. C23×C3×C22⋊C4C2semidirect
4. C22×#953C2semidirect
5. C22×#929C2semidirect
6. C22×#930C2semidirect
7. C22×C4×#67C2semidirect
8. C2×#5490C2direct (N × H)
9. C22×#883C2semidirect
10. C22×#884C2semidirect
11. C22×#884C2semidirect
12. C22×#882C2semidirect
13. C22×D3×C22⋊C4C2semidirect
14. C22×#885C2semidirect
15. C22×#878C2semidirect
16. C22×#67⋊C4C2semidirect
20. C24×C3×C4C22semidirect
21. C24×C3×C4C22semidirect
28. C23×#67C22semidirect
29. C23×#67C22semidirect
30. C23×#67C22semidirect
33. C22×#235C22semidirect
34. C23×D12C22semidirect
35. C23×D12C22semidirect
36. C23×C4×D3C22semidirect
37. C23×C4×D3C22semidirect
38. C23×C4×D3C22semidirect
39. C23×Dic6C22semidirect
42. C22×C3×C22⋊C4C22semidirect
43. C22×C3×C22⋊C4C22semidirect
44. C22×C3×C22⋊C4C22semidirect
45. C2×#953C22semidirect
47. C22×#217C22semidirect
48. C22×#217C22semidirect
49. C2×#930C22semidirect
50. C2×#929C22semidirect
51. C2×C4×#67C22semidirect
52. C22×(C2×D3)⋊C4C22semidirect
53. C22×(C2×D3)⋊C4C22semidirect
54. C22×(C2×D3)⋊C4C22semidirect
55. C22×(C2×D3)⋊C4C22semidirect
56. C22×(C2×D3)⋊C4C22semidirect
57. C22×C4⋊Dic3C22semidirect
58. C22×Dic3⋊C4C22semidirect
59. C22×Dic3⋊C4C22semidirect
60. C22×Dic3⋊C4C22semidirect
61. C22×C4×Dic3C22semidirect
62. C2×#885C22semidirect
63. #5490C22direct (N × H)
64. C2×#884C22semidirect
65. C2×#884C22semidirect
66. C2×#883C22semidirect
67. C2×#882C22semidirect
68. C2×#67⋊C4C22semidirect
69. C2×D3×C22⋊C4C22semidirect
70. C2×#878C22semidirect
86. C23×C22⋊C4D3semidirect
107. C23×C3×C4C23semidirect
108. C23×C3×C4C23semidirect
116. C22×#67D4semidirect
122. C22×#67C23semidirect
123. C22×#67C23semidirect
124. C22×#67C23semidirect
133. C2×#235C23semidirect
136. C22×D12C23semidirect
137. C22×D12C23semidirect
141. C22×C4×D3C23semidirect
142. C22×C4×D3C23semidirect
143. C22×C4×D3C23semidirect
145. C22×Dic6C23semidirect
148. C2×C3×C22⋊C4C23semidirect
149. C2×C3×C22⋊C4C23semidirect
150. C2×C3×C22⋊C4C23semidirect
151. #953C23semidirect
153. C2×#217C23semidirect
154. C2×#217C23semidirect
155. #930C23semidirect
156. #929C23semidirect
157. C4×#67C23semidirect
158. C2×(C2×D3)⋊C4C23semidirect
159. C2×(C2×D3)⋊C4C23semidirect
160. C2×(C2×D3)⋊C4C23semidirect
161. C2×(C2×D3)⋊C4C23semidirect
162. C2×(C2×D3)⋊C4C23semidirect
163. C2×C4⋊Dic3C23semidirect
164. C2×Dic3⋊C4C23semidirect
165. C2×Dic3⋊C4C23semidirect
166. C2×Dic3⋊C4C23semidirect
167. C2×C4×Dic3C23semidirect
168. #885C23semidirect
169. #884C23semidirect
170. #884C23semidirect
171. #883C23semidirect
172. #882C23semidirect
173. #67⋊C4C23semidirect
174. D3×C22⋊C4C23semidirect
175. #878C23semidirect
196. C24×C4C2×D3semidirect
197. C24×C4C2×D3semidirect
225. C22×C22⋊C4C2×D3semidirect
226. C22×C22⋊C4C2×D3semidirect
227. C22×C22⋊C4C2×D3semidirect
241. C24×C3#41semidirect
274. C22×C3×C4C24semidirect
275. C22×C3×C4C24semidirect
283. C2×#67C2×D4semidirect
289. C2×#67C24semidirect
290. C2×#67C24semidirect
306. C2×D12C24semidirect
307. C2×D12C24semidirect
311. C2×C4×D3C24semidirect
312. C2×C4×D3C24semidirect
313. C2×C4×D3C24semidirect
315. C2×Dic6C24semidirect
318. C3×C22⋊C4C24semidirect
319. C3×C22⋊C4C24semidirect
321. #217C24semidirect
322. #217C24semidirect
323. (C2×D3)⋊C4C24semidirect
324. (C2×D3)⋊C4C24semidirect
325. (C2×D3)⋊C4C24semidirect
326. (C2×D3)⋊C4C24semidirect
327. (C2×D3)⋊C4C24semidirect
328. C4⋊Dic3C24semidirect
329. Dic3⋊C4C24semidirect
330. Dic3⋊C4C24semidirect
331. Dic3⋊C4C24semidirect
332. C4×Dic3C24semidirect
390. C23×C4C22×D3semidirect
391. C23×C4C22×D3semidirect
418. C2×C22⋊C4C22×D3semidirect
419. C2×C22⋊C4C22×D3semidirect
420. C2×C22⋊C4C22×D3semidirect
439. C23×C3C2×#41semidirect
480. #67C22×D4semidirect
526. C24#235semidirect
583. C22×C4C23×D3semidirect
584. C22×C4C23×D3semidirect
599. C22⋊C4C23×D3semidirect
600. C22⋊C4C23×D3semidirect
613. C22×C3#546semidirect
617. C22×C3C22×#41semidirect
676. C23C2×#235semidirect
721. C2×C3C2×#546semidirect
752. C22#5490direct (N × H)
754. C22C22×#235semidirect
768. C3C22×#546semidirect
775. C2C2×#5490direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#672
C23×#2352
C23×C3×C22⋊C42
C22×#9532
C22×#9292
C22×#9302
C22×C4×#672
C2×#54902
C22×#8832
C22×#8842
C22×#8822
C22×D3×C22⋊C42
C22×#8852
C22×#8782
C22×#67⋊C42
C22×#5463