Finite Group Databasebeta

← C22×#17362 #72308838

Subgroups — C22×#17362 #72308838

Order 1024.

64765 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D4C211yesmaximal, characteristic
2C23×#407C212yesmaximal, complemented
3C2×#17362C2148yesmaximal, direct product factor
4C22×#1465C214yesmaximal, complemented
5C22×#1463C212yesmaximal, complemented
6C22×#1462C212yesmaximal, complemented
7C22×#1459C214yesmaximal, complemented
8C25×D4C411yescharacteristic
9C26×C4C411yescharacteristic
10C26×C4C2211yescharacteristic
11C24×M16—22no—
12C23×C4×D4—22no—
13C23×C4×D4—22no—
14C23×C4×D4—22no—
15C23×C4×D4—224no—
16C23×C4×D4—22no—
17C23×C4×D4C4124yes—
18C23×C4×D4C412yes—
19C23×C4×D4C412yes—
20C23×C4×D4C2212yes—
21C23×C4×D4C2212yes—
22C23×C4×D4C22124yes—
23C24×C4⋊C4C2211yescharacteristic
24C24×C22⋊C4C411yescharacteristic
25C24×C22⋊C4C2211yescharacteristic
26C24×C42C411yescharacteristic
27C22×#407—22no—
28C22×#407—224no—
29C22×#407—22no—
30C22×#407C2214yes—
31C22×#407C2214yescomplemented
32C22×#407C22148yescomplemented
33C23×C22⋊C8—22no—
34C23×C22⋊C8C2214yescomplemented
35#17362C221256yesdirect product factor
36C2×#1465C22196yescomplemented
37C2×#1463C22148yescomplemented
38C2×#1462C22148yescomplemented
39C2×#1459C22196yescomplemented
40C22×#324C2218yescomplemented
41C22×#323C2218yescomplemented
42C27C2×C411yescharacteristic
43C27C2×C411yescharacteristic
44C24×D4—22no—
45C24×D4—22no—
46C24×D4—212no—
47C24×D4—232no—
48C24×D4C2×C4124yes—
49C24×D4C2×C412yes—
50C24×D4C2×C412yes—
51C25×C4—212no—
52C25×C4—21no—
53C25×C4—21no—
54C25×C4—21no—
55C25×C4—21no—
56C25×C4—416no—
57C25×C4—416no—
58C25×C4C2×C411yescharacteristic
59C25×C4C2×C411yescharacteristic
60C25×C4C2×C411yescharacteristic
61C25×C4C2×C4124yes—
62C25×C4C2×C412yes—
63C25×C4C2×C412yes—
64C25×C4C2×C411yescharacteristic
65C25×C4C2×C4112yes—
66C25×C4C2×C411yescharacteristic
67C25×C4C2×C411yescharacteristic
68C25×C4D412yes—
69C25×C4D412yes—
70C25×C4D412yes—
71C25×C4D4124yes—
72C25×C4D412yes—
73C25×C4C2311yescharacteristic
74C25×C4C2311yescharacteristic
75C25×C4C2311yescharacteristic
76C25×C4C23112yes—
77C23×M16—24no—
78C23×M16—24no—
79C23×M16—248no—
80C23×M16—432no—
81C24×C8—24no—
82C22×C4×D4—248no—
83C22×C4×D4—24no—
84C22×C4×D4—24no—
85C22×C4×D4—248no—
86C22×C4×D4—248no—
87C22×C4×D4—248no—
88C22×C4×D4—24no—
89C22×C4×D4—224no—
90C22×C4×D4—2192no—
91C22×C4×D4—224no—
92C22×C4×D4—24no—
93C22×C4×D4—24no—
94C22×C4×D4—248no—
95C22×C4×D4—24no—
96C22×C4×D4—224no—
97C22×C4×D4—24no—
98C22×C4×D4—248no—
99C22×C4×D4—224no—
100C22×C4×D4—248no—
101C22×C4×D4—248no—
102C22×C4×D4—2192no—
103C22×C4×D4—24no—
104C22×C4×D4C2×C4124yes—
105C22×C4×D4C2×C4148yes—
106C22×C4×D4C2×C41192yes—
107C22×C4×D4C2×C4124yes—
108C22×C4×D4C2×C4148yes—
109C22×C4×D4C23124yes—
110C22×C4×D4C23124yes—
111C22×C4×D4C23164yes—
112C23×C4⋊C4—22no—
113C23×C4⋊C4—22no—
114C23×C4⋊C4—212no—
115C23×C4⋊C4C2×C4112yes—
116C23×C4⋊C4C2×C412yes—
117C23×C4⋊C4C2312yes—
118C23×C4⋊C4C23112yes—
119C23×C22⋊C4—22no—
120C23×C22⋊C4—22no—
121C23×C22⋊C4—212no—
122C23×C22⋊C4—22no—
123C23×C22⋊C4—22no—
124C23×C22⋊C4—212no—
125C23×C22⋊C4C2×C412yes—
126C23×C22⋊C4C2×C4124yes—
127C23×C22⋊C4C2×C412yes—
128C23×C22⋊C4C2×C4112yes—
129C23×C22⋊C4C2×C412yes—
130C23×C22⋊C4C2312yes—
131C23×C22⋊C4C23112yes—
132C23×C42—212no—
133C23×C42—21no—
134C23×C42—21no—
135C23×C42—21no—
136C23×C42—21no—
137C23×C42C2×C4124yes—
138C23×C42C2×C412yes—
139C23×C42C2×C412yes—
140C2×#407—224no—
141C2×#407—248no—
142C2×#407—248no—
143C2×#407—224no—
144C2×#407—2192no—
145C2×#407C23148yes—
146C2×#407C23148yescomplemented
147C2×#407C231128yescomplemented
148C22×C22⋊C8—24no—
149C22×C22⋊C8—24no—
150C22×C22⋊C8—248no—
151C22×C22⋊C8—24no—
152C22×C22⋊C8—224no—
153C22×C22⋊C8C2318yes—
154C22×C22⋊C8C23148yescomplemented
155#1465C231256yescomplemented
156#1463C231128yescomplemented
157#1462C231128yescomplemented
158#1459C231256yescomplemented
159C2×#324C23196yescomplemented
160C2×#323C23196yescomplemented
161C26—26no—
162C26—21no—
163C26—21no—
164C26—216no—
165C26—216no—
166C26—48no—
167C26—48no—
168C26—48no—
169C26—48no—
170C26C22⋊C412yes—
171C26C22⋊C412yes—
172C26C22⋊C4112yes—
173C26C22×C411yescharacteristic
174C26C22×C4112yes—
175C26C22×C411yescharacteristic
176C26C22×C4112yes—
177C26C22×C412yes—
178C26C22×C411yescharacteristic
179C23×D4—264no—
180C23×D4—264no—
181C23×D4—2384no—
182C23×D4—24no—
183C23×D4—248no—
184C23×D4—248no—
185C23×D4—296no—
186C23×D4—212no—
187C23×D4—24no—
188C23×D4—212no—
189C23×D4—216no—
190C23×D4—216no—
191C23×D4—2384no—
192C23×D4—216no—
193C23×D4M16132yescomplemented
194C23×D4C22×C4164yes—
195C23×D4C22×C4124yes—
196C23×D4C22×C4124yes—
197C24×C4—26no—
198C24×C4—21no—
199C24×C4—21no—
200C24×C4—216no—
201C24×C4—232no—
202C24×C4—216no—
203C24×C4—26no—
204C24×C4—21no—
205C24×C4—21no—
206C24×C4—26no—
207C24×C4—21no—
208C24×C4—21no—
209C24×C4—296no—
210C24×C4—212no—
211C24×C4—212no—
212C24×C4—224no—
213C24×C4—224no—
214C24×C4—224no—
215C24×C4—22no—
216C24×C4—22no—
217C24×C4—224no—
218C24×C4—22no—
219C24×C4—22no—
220C24×C4—48no—
221C24×C4—496no—
222C24×C4—48no—
223C24×C4—416no—
224C24×C4—416no—
225C24×C4—4192no—
226C24×C4—48no—
227C24×C4—48no—
228C24×C4—496no—
229C24×C4—416no—
230C24×C4—48no—
231C24×C4—416no—
232C24×C4—4192no—
233C24×C4—416no—
234C24×C4—416no—
235C24×C4—416no—
236C24×C4—4192no—
237C24×C4—416no—
238C24×C4—416no—
239C24×C4—48no—
240C24×C4—48no—
241C24×C4C22⋊C411yescharacteristic
242C24×C4C22⋊C4112yes—
243C24×C4C22⋊C411yescharacteristic
244C24×C4C22⋊C4124yes—
245C24×C4C22⋊C412yes—
246C24×C4C22⋊C411yescharacteristic
247C24×C4C22⋊C412yes—
248C24×C4C22⋊C4124yes—
249C24×C4C22⋊C4124yes—
250C24×C4C22⋊C4196yes—
251C24×C4C22⋊C4112yes—
252C24×C4C22⋊C4112yes—
253C24×C4C22⋊C412yes—
254C24×C4C22⋊C4124yes—
255C24×C4C22⋊C412yes—
256C24×C4C22⋊C411yescharacteristic
257C24×C4C22×C4112yes—
258C24×C4C22×C4112yes—
259C24×C4C22×C411yescharacteristic
260C24×C4C22×C411yescharacteristic
261C24×C4C22×C412yes—
262C24×C4C22×C4112yes—
263C24×C4C22×C412yes—
264C24×C4C22×C4164yes—
265C24×C4C22×C4124yes—
266C24×C4C22×C4124yes—
267C24×C4C22×C4112yes—
268C24×C4C22×C412yes—
269C24×C4C22×C416yes—
270C24×C4C22×C411yescharacteristic
271C24×C4C22×C416yes—
272C24×C4C22×C4148yes—
273C24×C4C22×C4112yes—
274C24×C4C22×C416yes—
275C24×C4C22×C4112yes—
276C24×C4C2×D412yes—
277C24×C4C2×D412yes—
278C24×C4C2×D4124yes—
279C24×C4C2×D412yes—
280C24×C4C2×D412yes—
281C24×C4C2×D4124yes—
282C24×C4C2×D4112yes—
283C24×C4C2×D412yes—
284C24×C4C2×D412yes—
285C24×C4C2×D4112yes—
286C24×C4C2×D4124yes—
287C24×C4C2×D4112yes—
288C24×C4C2×D4196yes—
289C24×C4C2×D4124yes—
290C24×C4C2411yescharacteristic
291C24×C4C2416yes—
292C24×C4C2416yes—
293C24×C4C2416yes—
294C24×C4C24116yes—
295C22×M16—248no—
296C22×M16—248no—
297C22×M16—2128no—
298C22×M16—432no—
299C22×M16—432no—
300C22×M16—4384no—
301C23×C8—28no—
302C23×C8—248no—
303C23×C8—432no—
304C2×C4×D4—248no—
305C2×C4×D4—2384no—
306C2×C4×D4—296no—
307C2×C4×D4—296no—
308C2×C4×D4—248no—
309C2×C4×D4—248no—
310C2×C4×D4—296no—
311C2×C4×D4—2384no—
312C2×C4×D4—2384no—
313C2×C4×D4—2384no—
314C2×C4×D4—248no—
315C2×C4×D4—296no—
316C2×C4×D4—296no—
317C2×C4×D4—2192no—
318C2×C4×D4—296no—
319C2×C4×D4—2192no—
320C2×C4×D4—248no—
321C2×C4×D4—248no—
322C2×C4×D4—2128no—
323C2×C4×D4—248no—
324C2×C4×D4—296no—
325C2×C4×D4—248no—
326C2×C4×D4—2128no—
327C2×C4×D4—296no—
328C2×C4×D4—2128no—
329C2×C4×D4—2128no—
330C2×C4×D4C22×C4196yes—
331C2×C4×D4C22×C41128yes—
332C2×C4×D4C22×C4196yes—
333C2×C4×D4C22×C41128yes—
334C2×C4×D4C24132yes—
335C2×C4×D4C24132yes—
336C22×C4⋊C4—224no—
337C22×C4⋊C4—24no—
338C22×C4⋊C4—248no—
339C22×C4⋊C4—224no—
340C22×C4⋊C4—212no—
341C22×C4⋊C4—24no—
342C22×C4⋊C4—224no—
343C22×C4⋊C4—212no—
344C22×C4⋊C4—224no—
345C22×C4⋊C4—248no—
346C22×C4⋊C4C22×C4148yes—
347C22×C4⋊C4C22×C4112yes—
348C22×C4⋊C4C22×C4124yes—
349C22×C4⋊C4C24112yes—
350C22×C4⋊C4C24116yes—
351C22×C22⋊C4—24no—
352C22×C22⋊C4—248no—
353C22×C22⋊C4—248no—
354C22×C22⋊C4—24no—
355C22×C22⋊C4—212no—
356C22×C22⋊C4—296no—
357C22×C22⋊C4—212no—
358C22×C22⋊C4—224no—
359C22×C22⋊C4—24no—
360C22×C22⋊C4—248no—
361C22×C22⋊C4—212no—
362C22×C22⋊C4—224no—
363C22×C22⋊C4—24no—
364C22×C22⋊C4—224no—
365C22×C22⋊C4—212no—
366C22×C22⋊C4—224no—
367C22×C22⋊C4—248no—
368C22×C22⋊C4C22×C4124yes—
369C22×C22⋊C4C22×C4164yes—
370C22×C22⋊C4C22×C4124yes—
371C22×C22⋊C4C22×C4148yes—
372C22×C22⋊C4C22×C4112yes—
373C22×C22⋊C4C22×C4124yes—
374C22×C22⋊C4C24112yes—
375C22×C22⋊C4C24116yes—
376C22×C42—224no—
377C22×C42—22no—
378C22×C42—22no—
379C22×C42—296no—
380C22×C42—224no—
381C22×C42—212no—
382C22×C42—224no—
383C22×C42—212no—
384C22×C42—22no—
385C22×C42—224no—
386C22×C42—22no—
387C22×C42C22×C4164yes—
388C22×C42C22×C4124yes—
389C22×C42C22×C4124yes—
390#407—296no—
391#407—2128no—
392#407—296no—
393#407—2128no—
394#407C24164yes—
395#407C24164yescomplemented
396C2×C22⋊C8—248no—
397C2×C22⋊C8—2128no—
398C2×C22⋊C8—248no—
399C2×C22⋊C8—224no—
400C2×C22⋊C8—296no—
401C2×C22⋊C8—248no—
402C2×C22⋊C8C24148yes—
403C2×C22⋊C8C24164yescomplemented
404#324C241128yescomplemented
405#323C241128yescomplemented
406C25—28no—
407C25—28no—
408C25—28no—
409C25—296no—
410C25—216no—
411C25—216no—
412C25—224no—
413C25—212no—
414C25—212no—
415C25—26no—
416C25—22no—
417C25—296no—
418C25—28no—
419C25—28no—
420C25—296no—
421C25—216no—
422C25—216no—
423C25—296no—
424C25—216no—
425C25—216no—
426C25—48no—
427C25—448no—
428C25—44no—
429C25—448no—
430C25—44no—
431C25—48no—
432C25—448no—
433C25—44no—
434C25—448no—
435C25—44no—
436C25—48no—
437C25—448no—
438C25—48no—
439C25—448no—
440C25—448no—
441C25—48no—
442C25—4256no—
443C25—4256no—
444C25—448no—
445C25—48no—
446C25—48no—
447C25—48no—
448C25C2×C22⋊C412yes—
449C25C2×C22⋊C416yes—
450C25C2×C22⋊C4124yes—
451C25C2×C22⋊C4124yes—
452C25C2×C22⋊C412yes—
453C25C2×C22⋊C411yescharacteristic
454C25C2×C22⋊C411yescharacteristic
455C25C2×C22⋊C416yes—
456C25C2×C22⋊C4148yes—
457C25C2×C22⋊C416yes—
458C25C2×M16116yes—
459C25C2×M16116yescomplemented
460C25C23×C416yes—
461C25C23×C411yescharacteristic
462C25C23×C4116yes—
463C25C23×C416yes—
464C25C23×C4116yes—
465C25C23×C4112yes—
466C25C23×C416yes—
467C22×D4—2768no—
468C22×D4—2768no—
469C22×D4—21536no—
470C22×D4—2192no—
471C22×D4—264no—
472C22×D4—248no—
473C22×D4—2128no—
474C22×D4—2128no—
475C22×D4—248no—
476C22×D4—248no—
477C22×D4—248no—
478C22×D4—296no—
479C22×D4—296no—
480C22×D4—264no—
481C22×D4—2192no—
482C22×D4—2512no—
483C22×D4—296no—
484C22×D4C2×M161192yescomplemented
485C22×D4C23×C4132yes—
486C22×D4C23×C4132yes—
487C23×C4—296no—
488C23×C4—216no—
489C23×C4—216no—
490C23×C4—224no—
491C23×C4—212no—
492C23×C4—212no—
493C23×C4—26no—
494C23×C4—22no—
495C23×C4—28no—
496C23×C4—216no—
497C23×C4—28no—
498C23×C4—296no—
499C23×C4—216no—
500C23×C4—216no—
501C23×C4—2192no—
502C23×C4—296no—
503C23×C4—28no—
504C23×C4—28no—
505C23×C4—296no—
506C23×C4—28no—
507C23×C4—28no—
508C23×C4—216no—
509C23×C4—2192no—
510C23×C4—216no—
511C23×C4—224no—
512C23×C4—26no—
513C23×C4—212no—
514C23×C4—212no—
515C23×C4—22no—
516C23×C4—224no—
517C23×C4—26no—
518C23×C4—212no—
519C23×C4—212no—
520C23×C4—22no—
521C23×C4—248no—
522C23×C4—248no—
523C23×C4—264no—
524C23×C4—264no—
525C23×C4—264no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—264no—
529C23×C4—224no—
530C23×C4—224no—
531C23×C4—496no—
532C23×C4—448no—
533C23×C4—496no—
534C23×C4—4384no—
535C23×C4—448no—
536C23×C4—424no—
537C23×C4—448no—
538C23×C4—4192no—
539C23×C4—448no—
540C23×C4—424no—
541C23×C4—448no—
542C23×C4—496no—
543C23×C4—496no—
544C23×C4—448no—
545C23×C4—4384no—
546C23×C4—424no—
547C23×C4—424no—
548C23×C4—464no—
549C23×C4—48no—
550C23×C4—496no—
551C23×C4—48no—
552C23×C4—424no—
553C23×C4—44no—
554C23×C4—48no—
555C23×C4—48no—
556C23×C4—48no—
557C23×C4—496no—
558C23×C4—448no—
559C23×C4—44no—
560C23×C4—424no—
561C23×C4—4192no—
562C23×C4—416no—
563C23×C4—416no—
564C23×C4—4768no—
565C23×C4—496no—
566C23×C4—4192no—
567C23×C4—496no—
568C23×C4—4192no—
569C23×C4—496no—
570C23×C4—496no—
571C23×C4—4256no—
572C23×C4—448no—
573C23×C4—48no—
574C23×C4—448no—
575C23×C4—48no—
576C23×C4—48no—
577C23×C4—48no—
578C23×C4—4192no—
579C23×C4—416no—
580C23×C4—416no—
581C23×C4—448no—
582C23×C4—48no—
583C23×C4—448no—
584C23×C4—48no—
585C23×C4#99116yes—
586C23×C4C2×C22⋊C4112yes—
587C23×C4C2×C22⋊C412yes—
588C23×C4C2×C22⋊C4112yes—
589C23×C4C2×C22⋊C4196yes—
590C23×C4C2×C22⋊C4124yes—
591C23×C4C2×C22⋊C4124yes—
592C23×C4C2×C22⋊C4112yes—
593C23×C4C2×C22⋊C4112yes—
594C23×C4C2×C22⋊C411yescharacteristic
595C23×C4C2×C22⋊C411yescharacteristic
596C23×C4C2×C22⋊C4148yes—
597C23×C4C2×C22⋊C416yes—
598C23×C4C2×C22⋊C4112yes—
599C23×C4C2×C22⋊C416yes—
600C23×C4C2×C22⋊C4112yes—
601C23×C4C2×C22⋊C4124yes—
602C23×C4C2×C22⋊C416yes—
603C23×C4C2×C22⋊C4112yes—
604C23×C4C2×C22⋊C4196yes—
605C23×C4C2×C22⋊C4196yes—
606C23×C4C2×C22⋊C4148yes—
607C23×C4C2×C22⋊C4124yes—
608C23×C4C2×C22⋊C4124yes—
609C23×C4C2×C22⋊C4148yes—
610C23×C4C2×C22⋊C4112yes—
611C23×C4C2×C22⋊C4124yes—
612C23×C4C2×C22⋊C4196yes—
613C23×C4C2×C22⋊C4112yes—
614C23×C4C2×C22⋊C4124yes—
615C23×C4C2×C22⋊C411yescharacteristic
616C23×C4C2×C22⋊C4112yes—
617C23×C4C2×C22⋊C411yescharacteristic
618C23×C4C2×M16116yescomplemented
619C23×C4C23×C4116yes—
620C23×C4C23×C4116yes—
621C23×C4C23×C416yes—
622C23×C4C23×C416yes—
623C23×C4C23×C4112yes—
624C23×C4C23×C4116yes—
625C23×C4C23×C4112yes—
626C23×C4C23×C4116yes—
627C23×C4C23×C4112yes—
628C23×C4C23×C4132yes—
629C23×C4C23×C4132yes—
630C23×C4C23×C4112yes—
631C23×C4C23×C413yes—
632C23×C4C23×C416yes—
633C23×C4C23×C4116yes—
634C23×C4C23×C4112yes—
635C23×C4C23×C4112yes—
636C23×C4C23×C4116yes—
637C23×C4C22×D412yes—
638C23×C4C22×D4112yes—
639C23×C4C22×D4112yes—
640C23×C4C22×D4112yes—
641C23×C4C22×D4132yes—
642C23×C4C22×D416yes—
643C23×C4C22×D4112yes—
644C23×C4C22×D4124yes—
645C23×C4C22×D4132yes—
646C23×C4C22×D4124yes—
647C23×C4C22×D4112yes—
648C23×C4C22×D4112yes—
649C23×C4C22×D4132yes—
650C23×C4C22×D4124yes—
651C23×C4C22×D4132yes—
652C23×C4C2513yes—
653C23×C4C2514yes—
654C23×C4C2514yes—
655C23×C4C2514yes—
656C2×M16—264no—
657C2×M16—264no—
658C2×M16—4192no—
659C2×M16—4192no—
660C2×M16—4512no—
661C22×C8—248no—
662C22×C8—264no—
663C22×C8—432no—
664C22×C8—4192no—
665C4×D4—2256no—
666C4×D4—2192no—
667C4×D4—2192no—
668C4×D4—2256no—
669C4×D4—2192no—
670C4×D4—2256no—
671C4×D4—2192no—
672C4×D4—2256no—
673C4×D4—264no—
674C4×D4—264no—
675C4×D4—264no—
676C4×D4—264no—
677C2×C4⋊C4—296no—
678C2×C4⋊C4—224no—
679C2×C4⋊C4—248no—
680C2×C4⋊C4—296no—
681C2×C4⋊C4—224no—
682C2×C4⋊C4—248no—
683C2×C4⋊C4—224no—
684C2×C4⋊C4—232no—
685C2×C4⋊C4—224no—
686C2×C4⋊C4—232no—
687C2×C4⋊C4C23×C4124yes—
688C2×C4⋊C4C23×C4132yes—
689C2×C4⋊C4C2518yes—
690C2×C22⋊C4—248no—
691C2×C22⋊C4—2128no—
692C2×C22⋊C4—2128no—
693C2×C22⋊C4—248no—
694C2×C22⋊C4—248no—
695C2×C22⋊C4—248no—
696C2×C22⋊C4—296no—
697C2×C22⋊C4—224no—
698C2×C22⋊C4—248no—
699C2×C22⋊C4—224no—
700C2×C22⋊C4—248no—
701C2×C22⋊C4—296no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—232no—
704C2×C22⋊C4—224no—
705C2×C22⋊C4—232no—
706C2×C22⋊C4C23×C4132yes—
707C2×C22⋊C4C23×C4132yes—
708C2×C22⋊C4C23×C4124yes—
709C2×C22⋊C4C23×C4132yes—
710C2×C22⋊C4C2518yes—
711C2×C42—264no—
712C2×C42—224no—
713C2×C42—224no—
714C2×C42—264no—
715C2×C42—264no—
716C2×C42—248no—
717C2×C42—248no—
718C2×C42—264no—
719C2×C42—224no—
720C2×C42—224no—
721C2×C42C23×C4132yes—
722C2×C42C23×C4132yes—
723C22⋊C8—264no—
724C22⋊C8—264no—
725C22⋊C8—248no—
726C22⋊C8—264no—
727C22⋊C8C25132yes—
728C24—2128no—
729C24—224no—
730C24—24no—
731C24—24no—
732C24—224no—
733C24—24no—
734C24—224no—
735C24—24no—
736C24—28no—
737C24—224no—
738C24—24no—
739C24—224no—
740C24—24no—
741C24—28no—
742C24—224no—
743C24—2192no—
744C24—296no—
745C24—296no—
746C24—296no—
747C24—296no—
748C24—2192no—
749C24—224no—
750C24—28no—
751C24—248no—
752C24—216no—
753C24—296no—
754C24—28no—
755C24—296no—
756C24—28no—
757C24—216no—
758C24—216no—
759C24—212no—
760C24—212no—
761C24—264no—
762C24—224no—
763C24—224no—
764C24—264no—
765C24—412no—
766C24—448no—
767C24—496no—
768C24—412no—
769C24—412no—
770C24—432no—
771C24—412no—
772C24—412no—
773C24—448no—
774C24—496no—
775C24—412no—
776C24—464no—
777C24—412no—
778C24—432no—
779C24—412no—
780C24—4128no—
781C24—4128no—
782C24—424no—
783C24—432no—
784C24—464no—
785C24—424no—
786C24—432no—
787C24—496no—
788C24—424no—
789C24—448no—
790C24—4768no—
791C24—4768no—
792C24—4768no—
793C24—4768no—
794C24—496no—
795C24—424no—
796C24—448no—
797C24—464no—
798C24—464no—
799C24—4128no—
800C24—4128no—
801C24—448no—
802C24—48no—
803C24—448no—
804C24—48no—
805C24#407116yes—
806C24#407148yes—
807C24C2×#9918yes—
808C24#41318yes—
809C24C22×C22⋊C4112yes—
810C24C22×C22⋊C4112yes—
811C24C22×C22⋊C4132yes—
812C24C22×C22⋊C4132yes—
813C24C22×C22⋊C4112yes—
814C24C22×C22⋊C413yes—
815C24C22×C22⋊C416yes—
816C24C22×C22⋊C416yes—
817C24C22×C22⋊C4112yes—
818C24C22×C22⋊C4112yes—
819C24C22×C22⋊C411yescharacteristic
820C24C22×M1618yes—
821C24C22×M16148yes—
822C24C22×M16148yescomplemented
823C24C24×C414yes—
824C24C24×C413yes—
825C24C24×C414yes—
826C24C24×C418yes—
827C24C24×C414yes—
828C2×D4—21024no—
829C2×D4—21024no—
830C2×D4—2384no—
831C2×D4—2384no—
832C2×D4—2384no—
833C2×D4—2384no—
834C2×D4—264no—
835C2×D4—264no—
836C2×D4—264no—
837C2×D4—264no—
838C2×D4—264no—
839C2×D4C22×M161128yescomplemented
840C22×C4—2192no—
841C22×C4—296no—
842C22×C4—296no—
843C22×C4—248no—
844C22×C4—216no—
845C22×C4—28no—
846C22×C4—248no—
847C22×C4—248no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—248no—
851C22×C4—28no—
852C22×C4—216no—
853C22×C4—216no—
854C22×C4—212no—
855C22×C4—212no—
856C22×C4—224no—
857C22×C4—248no—
858C22×C4—248no—
859C22×C4—2128no—
860C22×C4—2192no—
861C22×C4—224no—
862C22×C4—248no—
863C22×C4—224no—
864C22×C4—248no—
865C22×C4—264no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—248no—
869C22×C4—296no—
870C22×C4—2384no—
871C22×C4—248no—
872C22×C4—296no—
873C22×C4—264no—
874C22×C4—212no—
875C22×C4—216no—
876C22×C4—216no—
877C22×C4—212no—
878C22×C4—212no—
879C22×C4—216no—
880C22×C4—216no—
881C22×C4—212no—
882C22×C4—232no—
883C22×C4—232no—
884C22×C4—232no—
885C22×C4—232no—
886C22×C4—448no—
887C22×C4—4192no—
888C22×C4—496no—
889C22×C4—4192no—
890C22×C4—496no—
891C22×C4—448no—
892C22×C4—424no—
893C22×C4—432no—
894C22×C4—432no—
895C22×C4—424no—
896C22×C4—448no—
897C22×C4—464no—
898C22×C4—464no—
899C22×C4—448no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—424no—
903C22×C4—448no—
904C22×C4—4192no—
905C22×C4—424no—
906C22×C4—448no—
907C22×C4—448no—
908C22×C4—424no—
909C22×C4—412no—
910C22×C4—424no—
911C22×C4—46no—
912C22×C4—412no—
913C22×C4—424no—
914C22×C4—424no—
915C22×C4—412no—
916C22×C4—424no—
917C22×C4—464no—
918C22×C4—448no—
919C22×C4—46no—
920C22×C4—48no—
921C22×C4—4256no—
922C22×C4—496no—
923C22×C4—496no—
924C22×C4—4192no—
925C22×C4—4256no—
926C22×C4—4192no—
927C22×C4—4256no—
928C22×C4—464no—
929C22×C4—464no—
930C22×C4—496no—
931C22×C4—424no—
932C22×C4—448no—
933C22×C4—496no—
934C22×C4—424no—
935C22×C4—448no—
936C22×C4—448no—
937C22×C4—48no—
938C22×C4—448no—
939C22×C4—48no—
940C22×C4—4256no—
941C22×C4—496no—
942C22×C4—496no—
943C22×C4—432no—
944C22×C4—424no—
945C22×C4—432no—
946C22×C4—424no—
947C22×C4C2×#99196yes—
948C22×C4C2×#9918yes—
949C22×C4C2×#9918yes—
950C22×C4C22×C22⋊C4116yes—
951C22×C4C22×C22⋊C416yes—
952C22×C4C22×C22⋊C416yes—
953C22×C4C22×C22⋊C4112yes—
954C22×C4C22×C22⋊C4112yes—
955C22×C4C22×C22⋊C4116yes—
956C22×C4C22×C22⋊C4116yes—
957C22×C4C22×C22⋊C4124yes—
958C22×C4C22×C22⋊C416yes—
959C22×C4C22×C22⋊C4112yes—
960C22×C4C22×C22⋊C4132yes—
961C22×C4C22×C22⋊C4124yes—
962C22×C4C22×C22⋊C4124yes—
963C22×C4C22×C22⋊C4132yes—
964C22×C4C22×C22⋊C416yes—
965C22×C4C22×C22⋊C4112yes—
966C22×C4C22×C22⋊C4124yes—
967C22×C4C22×C22⋊C4124yes—
968C22×C4C22×C22⋊C4132yes—
969C22×C4C22×C22⋊C4124yes—
970C22×C4C22×C22⋊C4132yes—
971C22×C4C22×C22⋊C4116yes—
972C22×C4C22×C22⋊C416yes—
973C22×C4C22×C22⋊C416yes—
974C22×C4C22×M16148yescomplemented
975C22×C4C24×C414yes—
976C22×C4C24×C414yes—
977C22×C4C24×C418yes—
978C22×C4C24×C418yes—
979C22×C4C24×C418yes—
980C22×C4C24×C413yes—
981C22×C4C24×C414yes—
982C22×C4C23×D416yes—
983C22×C4C23×D418yes—
984C22×C4C23×D418yes—
985C22×C4C23×D418yes—
986C22×C4C23×D416yes—
987C22×C4C23×D418yes—
988C22×C4C23×D418yes—
989C22×C4C23×D418yes—
990C22×C4C2611yescharacteristic
991M16—4128no—
992M16—4128no—
993C2×C8—232no—
994C2×C8—496no—
995C2×C8—4128no—
996C4⋊C4—216no—
997C4⋊C4—248no—
998C4⋊C4—264no—
999C22⋊C4—264no—
1000C22⋊C4—264no—
1001C22⋊C4—216no—
1002C22⋊C4—248no—
1003C22⋊C4—264no—
1004C42—232no—
1005C42—232no—
1006C42—232no—
1007C42—232no—
1008C23—2192no—
1009C23—2192no—
1010C23—28no—
1011C23—224no—
1012C23—212no—
1013C23—212no—
1014C23—224no—
1015C23—26no—
1016C23—212no—
1017C23—28no—
1018C23—26no—
1019C23—224no—
1020C23—224no—
1021C23—26no—
1022C23—212no—
1023C23—28no—
1024C23—26no—
1025C23—224no—
1026C23—232no—
1027C23—232no—
1028C23—232no—
1029C23—264no—
1030C23—264no—
1031C23—264no—
1032C23—28no—
1033C23—28no—
1034C23—264no—
1035C23—264no—
1036C23—224no—
1037C23—224no—
1038C23—248no—
1039C23—248no—
1040C23—264no—
1041C23—224no—
1042C23—264no—
1043C23—224no—
1044C23—28no—
1045C23—412no—
1046C23—432no—
1047C23—412no—
1048C23—44no—
1049C23—44no—
1050C23—412no—
1051C23—432no—
1052C23—412no—
1053C23—496no—
1054C23—44no—
1055C23—44no—
1056C23—496no—
1057C23—4384no—
1058C23—4384no—
1059C23—48no—
1060C23—496no—
1061C23—48no—
1062C23—424no—
1063C23—432no—
1064C23—4768no—
1065C23—4256no—
1066C23—4256no—
1067C23—4768no—
1068C23—496no—
1069C23—4192no—
1070C23—4384no—
1071C23—4384no—
1072C23—496no—
1073C23—496no—
1074C23—424no—
1075C23—432no—
1076C23—432no—
1077C23—424no—
1078C23—432no—
1079C23—424no—
1080C23—432no—
1081C23—464no—
1082C23C2×#407112yes—
1083C23C2×#407148yes—
1084C23C2×#407148yes—
1085C23C2×#40714yes—
1086C23C22×#99124yes—
1087C23C22×#9914yes—
1088C23C2×#413124yes—
1089C23C2×#41314yes—
1090C23C23×C22⋊C418yes—
1091C23C23×C22⋊C418yes—
1092C23C23×C22⋊C413yes—
1093C23C23×C22⋊C414yes—
1094C23C23×C22⋊C414yes—
1095C23C23×C22⋊C413yes—
1096C23C23×M16112yes—
1097C23C23×M16116yes—
1098C23C23×M16116yescomplemented
1099C23C25×C411yescharacteristic
1100D4—2256no—
1101D4—2256no—
1102C2×C4—264no—
1103C2×C4—264no—
1104C2×C4—28no—
1105C2×C4—248no—
1106C2×C4—248no—
1107C2×C4—212no—
1108C2×C4—216no—
1109C2×C4—232no—
1110C2×C4—212no—
1111C2×C4—212no—
1112C2×C4—248no—
1113C2×C4—212no—
1114C2×C4—224no—
1115C2×C4—28no—
1116C2×C4—216no—
1117C2×C4—216no—
1118C2×C4—224no—
1119C2×C4—232no—
1120C2×C4—224no—
1121C2×C4—232no—
1122C2×C4—28no—
1123C2×C4—28no—
1124C2×C4—248no—
1125C2×C4—264no—
1126C2×C4—248no—
1127C2×C4—264no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—424no—
1131C2×C4—432no—
1132C2×C4—424no—
1133C2×C4—432no—
1134C2×C4—46no—
1135C2×C4—424no—
1136C2×C4—412no—
1137C2×C4—43no—
1138C2×C4—44no—
1139C2×C4—48no—
1140C2×C4—48no—
1141C2×C4—46no—
1142C2×C4—48no—
1143C2×C4—41no—
1144C2×C4—464no—
1145C2×C4—464no—
1146C2×C4—424no—
1147C2×C4—432no—
1148C2×C4—424no—
1149C2×C4—432no—
1150C2×C4—432no—
1151C2×C4—424no—
1152C2×C4—432no—
1153C2×C4—424no—
1154C2×C4—464no—
1155C2×C4—464no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4C22×#99164yes—
1159C2×C4C22×#99124yes—
1160C2×C4C22×#99124yes—
1161C2×C4C23×C22⋊C414yes—
1162C2×C4C23×C22⋊C414yes—
1163C2×C4C23×C22⋊C416yes—
1164C2×C4C23×C22⋊C418yes—
1165C2×C4C23×C22⋊C414yes—
1166C2×C4C23×C22⋊C414yes—
1167C2×C4C23×M16116yescomplemented
1168C2×C4C24×D412yes—
1169C8—432no—
1170C22—232no—
1171C22—296no—
1172C22—224no—
1173C22—248no—
1174C22—248no—
1175C22—224no—
1176C22—296no—
1177C22—21no—
1178C22—23no—
1179C22—24no—
1180C22—28no—
1181C22—21no—
1182C22—23no—
1183C22—24no—
1184C22—28no—
1185C22—24no—
1186C22—24no—
1187C22—28no—
1188C22—28no—
1189C22—28no—
1190C22—216no—
1191C22—448no—
1192C22—416no—
1193C22—4128no—
1194C22—4128no—
1195C22—416no—
1196C22—416no—
1197C22—416no—
1198C22—448no—
1199C22—496no—
1200C22—4128no—
1201C22—4128no—
1202C22—448no—
1203C22—496no—
1204C22—48no—
1205C22—48no—
1206C22#17362116yesdirect product factor
1207C22C22×#40716yes—
1208C22C22×#407116yes—
1209C22C22×#40716yes—
1210C22C23×#9918yes—
1211C22C23×#9916yes—
1212C22C22×#41318yes—
1213C22C22×#41316yes—
1214C22C24×C22⋊C411yescharacteristic
1215C22C24×M1612yes—
1216C4—22no—
1217C4—24no—
1218C4—24no—
1219C4—26no—
1220C4—28no—
1221C4—216no—
1222C4—48no—
1223C4—48no—
1224C4C23×#9918yes—
1225C4C23×#9918yes—
1226C2—22no—
1227C2—26no—
1228C2—28no—
1229C2—28no—
1230C2—216no—
1231C2—48no—
1232C2—416no—
1233C2C2×#17362112yesdirect product factor
1234C2C24×#9911yescharacteristic
1235C2C23×#41311yescharacteristic
1236C2C23×#40711yescharacteristic
subgroupG/H
centerC23×C4C2×C22⋊C4
commutatorC23C25×C4
Frattini, cosocleC22×C4C26
socleC24C22×C22⋊C4
prime radicalC25×D4C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C26×C4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C23×#407C2semidirect
3. C2×#17362C2direct (N × H)
4. C22×#1465C2semidirect
5. C22×#1463C2semidirect
6. C22×#1462C2semidirect
7. C22×#1459C2semidirect
31. C22×#407C22semidirect
32. C22×#407C22semidirect
34. C23×C22⋊C8C22semidirect
35. #17362C22direct (N × H)
36. C2×#1465C22semidirect
37. C2×#1463C22semidirect
38. C2×#1462C22semidirect
39. C2×#1459C22semidirect
40. C22×#324C22semidirect
41. C22×#323C22semidirect
146. C2×#407C23semidirect
147. C2×#407C23semidirect
154. C22×C22⋊C8C23semidirect
155. #1465C23semidirect
156. #1463C23semidirect
157. #1462C23semidirect
158. #1459C23semidirect
159. C2×#324C23semidirect
160. C2×#323C23semidirect
193. C23×D4M16semidirect
395. #407C24semidirect
403. C2×C22⋊C8C24semidirect
404. #324C24semidirect
405. #323C24semidirect
459. C25C2×M16semidirect
484. C22×D4C2×M16semidirect
618. C23×C4C2×M16semidirect
822. C24C22×M16semidirect
839. C2×D4C22×M16semidirect
974. C22×C4C22×M16semidirect
1098. C23C23×M16semidirect
1167. C2×C4C23×M16semidirect
1206. C22#17362direct (N × H)
1233. C2C2×#17362direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D42
C23×#4072
C2×#173622
C22×#14652
C22×#14632
C22×#14622
C22×#14592