Finite Group Databasebeta

← C22×#22874 #72304708

Subgroups — C22×#22874 #72304708

Order 1024.

37677 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#450C211yesmaximal, characteristic
2C23×C4×SD16C211yesmaximal, characteristic, complemented
3C24×#102C211yesmaximal, characteristic
4C22×#2360C211yesmaximal, characteristic, complemented
5C22×D4×C22⋊C4C211yesmaximal, characteristic
6C2×#22874C2148yesmaximal, direct product factor
7C22×#1968C211yesmaximal, characteristic, complemented
8C22×#1934C211yesmaximal, characteristic, complemented
9C22×#1926C211yesmaximal, characteristic, complemented
10C22×#1892C211yesmaximal, characteristic, complemented
11C22×#1880C211yesmaximal, characteristic, complemented
12C22×#1877C211yesmaximal, characteristic, complemented
13C22×#1864C211yesmaximal, characteristic, complemented
14C22×#1853C211yesmaximal, characteristic, complemented
15C22×C4×#102C211yesmaximal, characteristic, complemented
16C22×C8×C22⋊C4C211yesmaximal, characteristic, complemented
17C25×D4C2211yescharacteristic
18C24×SD16C2211yescharacteristic
19C24×SD16C2211yescharacteristic
20C25×C8C2211yescharacteristic
21C23×C22⋊Q8C2211yescharacteristic
22C23×C4×Q8C2211yescharacteristic, complemented
23C23×C4×D4C2211yescharacteristic
24C23×C4×D4C2211yescharacteristic
25C24×C4⋊C4C2211yescharacteristic
26C24×C22⋊C4—21no—
27C22×#450C4132yescomplemented
28C22×#450C22124yes—
29C22×C4×SD16—216no—
30C22×C4×SD16C22124yescomplemented
31C23×#106C2211yescharacteristic, complemented
32C23×#106C2211yescharacteristic, complemented
33C23×#103C2211yescharacteristic, complemented
34C23×#103C2211yescharacteristic, complemented
35C23×#102—216no—
36C23×#102C2211yescharacteristic
37C23×#102C22124yes—
38C23×#102C2211yescharacteristic
39C23×#102C2211yescharacteristic
40C23×#102C2211yescharacteristic
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44C23×C4×C8C2211yescharacteristic, complemented
45C23×C4×C8C2211yescharacteristic, complemented
46C2×#2360—212no—
47C2×#2360C22124yescomplemented
48C2×D4×C22⋊C4—212no—
49C2×D4×C22⋊C4C22124yes—
50C22×#391C2211yescharacteristic, complemented
51C22×#390C2211yescharacteristic
52C22×#390C2211yescharacteristic
53C22×#389—21no—
54C22×#389C2211yescharacteristic, complemented
55C22×#387—21no—
56C22×#386—21no—
57C22×#386—21no—
58C22×#385—21no—
59C22×#380C2211yescharacteristic
60C22×#379—21no—
61C22×C4×C4⋊C4C2211yescharacteristic, complemented
62C22×C4×C22⋊C4—21no—
63C22×C4×C22⋊C4C2211yescharacteristic
64#22874C221256yesdirect product factor
65C2×#1968C22124yescomplemented
66C2×#1934C22124yescomplemented
67C2×#1926C22124yescomplemented
68C2×#1892C22124yescomplemented
69C2×#1880C22124yescomplemented
70C2×#1877C22124yescomplemented
71C2×#1864C22124yescomplemented
72C2×#1853C22124yescomplemented
73C2×C4×#102C22124yescomplemented
74C2×C8×C22⋊C4C22124yescomplemented
75C22×#340C2211yescharacteristic, complemented
76C22×#340C2211yescharacteristic, complemented
77C22×#340C2211yescharacteristic, complemented
78C22×#340C2211yescharacteristic, complemented
79C22×#336C2211yescharacteristic, complemented
80C22×#336C2211yescharacteristic, complemented
81C27—21no—
82C24×Q8C2311yescharacteristic
83C24×D4—28no—
84C24×D4—28no—
85C24×D4—26no—
86C24×D4—21no—
87C24×D4—28no—
88C24×D4—44no—
89C24×D4—44no—
90C24×D4C2×C4116yes—
91C24×D4C2311yescharacteristic
92C24×D4C23112yes—
93C24×D4C2311yescharacteristic
94C25×C4—21no—
95C25×C4—21no—
96C25×C4—21no—
97C25×C4C2311yescharacteristic
98C23×SD16—28no—
99C23×SD16—28no—
100C23×SD16—44no—
101C23×SD16—44no—
102C23×SD16C2×C4116yescomplemented
103C23×SD16C2×C4116yescomplemented
104C23×SD16C23112yes—
105C23×SD16C23112yes—
106C24×C8—28no—
107C24×C8—28no—
108C24×C8—44no—
109C24×C8C2311yescharacteristic
110C24×C8C23112yes—
111C24×C8C2311yescharacteristic
112C24×C8C2311yescharacteristic
113C24×C8C2311yescharacteristic
114C22×C22⋊Q8—26no—
115C22×C22⋊Q8—28no—
116C22×C22⋊Q8C2×C4116yescomplemented
117C22×C22⋊Q8C23112yes—
118C22×C4×Q8—26no—
119C22×C4×Q8—28no—
120C22×C4×Q8—44no—
121C22×C4×Q8C23112yescomplemented
122C22×C4×D4—26no—
123C22×C4×D4—26no—
124C22×C4×D4—28no—
125C22×C4×D4—28no—
126C22×C4×D4—44no—
127C22×C4×D4—44no—
128C22×C4×D4C23112yes—
129C22×C4×D4C23112yes—
130C23×C4⋊C4—21no—
131C23×C4⋊C4—28no—
132C23×C4⋊C4—26no—
133C23×C4⋊C4—21no—
134C23×C4⋊C4—21no—
135C23×C4⋊C4—21no—
136C23×C4⋊C4—44no—
137C23×C4⋊C4C2311yescharacteristic
138C23×C4⋊C4C2311yescharacteristic
139C23×C4⋊C4C2311yescharacteristic
140C23×C4⋊C4C23112yes—
141C23×C4⋊C4C2311yescharacteristic
142C23×C4⋊C4C2311yescharacteristic
143C23×C22⋊C4—21no—
144C23×C22⋊C4—21no—
145C23×C22⋊C4—21no—
146C23×C22⋊C4—21no—
147C23×C22⋊C4—21no—
148C23×C22⋊C4—21no—
149C23×C22⋊C4—21no—
150C23×C22⋊C4—21no—
151C23×C22⋊C4—224no—
152C23×C22⋊C4—416no—
153C23×C22⋊C4D411yescharacteristic
154C23×C22⋊C4D411yescharacteristic
155C23×C42—21no—
156C23×C42—21no—
157C23×C42C2311yescharacteristic
158C23×C42C2311yescharacteristic
159C2×#450C2×C41384yescomplemented
160C2×#450C23164yes—
161C2×C4×SD16—2192no—
162C2×C4×SD16C23164yescomplemented
163C22×#106—28no—
164C22×#106—44no—
165C22×#106C23112yescomplemented
166C22×#106C23112yescomplemented
167C22×#103—28no—
168C22×#103—44no—
169C22×#103C23112yescomplemented
170C22×#103C23112yescomplemented
171C22×#102—2192no—
172C22×#102—28no—
173C22×#102—28no—
174C22×#102—28no—
175C22×#102C2×C4116yescomplemented
176C22×#102C2×C4116yescomplemented
177C22×#102D4116yes—
178C22×#102C23112yes—
179C22×#102C23112yes—
180C22×#102C23164yes—
181C22×#102C23112yes—
182C22×#102C23112yes—
183C22×#102C23112yes—
184C22×#102C23112yes—
185C22×C22⋊C8C2×C4116yescomplemented
186C22×C22⋊C8C23112yes—
187C22×C4×C8—28no—
188C22×C4×C8—44no—
189C22×C4×C8C23112yescomplemented
190C22×C4×C8C23112yescomplemented
191#2360—296no—
192#2360C23164yescomplemented
193D4×C22⋊C4—296no—
194D4×C22⋊C4C23164yes—
195C2×#391—26no—
196C2×#391C23112yescomplemented
197C2×#390—26no—
198C2×#390—26no—
199C2×#390C23112yes—
200C2×#390C23112yes—
201C2×#389—26no—
202C2×#389—224no—
203C2×#389C23112yescomplemented
204C2×#387—224no—
205C2×#386—224no—
206C2×#386—224no—
207C2×#385—224no—
208C2×#380—26no—
209C2×#380C23112yes—
210C2×#379—224no—
211C2×C4×C4⋊C4—26no—
212C2×C4×C4⋊C4C23112yescomplemented
213C2×C4×C22⋊C4—224no—
214C2×C4×C22⋊C4D4112yes—
215C2×C4×C22⋊C4C23112yes—
216C22×#95—21no—
217C22×#95—21no—
218C22×#95—21no—
219C22×#95—21no—
220C22×#95—21no—
221C22×#95D411yescharacteristic
222C22×#95D411yescharacteristic
223#1968C23164yescomplemented
224#1934C23164yescomplemented
225#1926C23164yescomplemented
226#1892C23164yescomplemented
227#1880C23164yescomplemented
228#1877C23164yescomplemented
229#1864C23164yescomplemented
230#1853C23164yescomplemented
231C4×#102C23164yescomplemented
232C8×C22⋊C4C23164yescomplemented
233C2×#340C23112yescomplemented
234C2×#340C23112yescomplemented
235C2×#340C23112yescomplemented
236C2×#340C23112yescomplemented
237C2×#336C23112yescomplemented
238C2×#336C23112yescomplemented
239C26—21no—
240C26—21no—
241C26—216no—
242C26—212no—
243C26—48no—
244C26—48no—
245C26—48no—
246C26—48no—
247C26—84no—
248C26—84no—
249C26C2×D411yescharacteristic
250C23×Q8—23no—
251C23×Q8—24no—
252C23×Q8—24no—
253C23×Q8—24no—
254C23×Q8—24no—
255C23×Q8—24no—
256C23×Q8C22×C418yes—
257C23×Q8C2416yes—
258C23×D4—2128no—
259C23×D4—248no—
260C23×D4—248no—
261C23×D4—216no—
262C23×D4—296no—
263C23×D4—23no—
264C23×D4—24no—
265C23×D4—224no—
266C23×D4—212no—
267C23×D4—23no—
268C23×D4—24no—
269C23×D4—24no—
270C23×D4—248no—
271C23×D4—24no—
272C23×D4—24no—
273C23×D4—24no—
274C23×D4—24no—
275C23×D4—24no—
276C23×D4—464no—
277C23×D4—424no—
278C23×D4—424no—
279C23×D4—448no—
280C23×D4—464no—
281C23×D4—448no—
282C23×D4—464no—
283C23×D4—48no—
284C23×D4—48no—
285C23×D4C22×C418yes—
286C23×D4C22×C4196yes—
287C23×D4C22×C418yes—
288C23×D4C2×D418yes—
289C23×D4#4118yes—
290C23×D4C2416yes—
291C23×D4C24116yes—
292C23×D4C2416yes—
293C24×C4—24no—
294C24×C4—24no—
295C24×C4—24no—
296C24×C4—24no—
297C24×C4—21no—
298C24×C4—21no—
299C24×C4—21no—
300C24×C4—21no—
301C24×C4—21no—
302C24×C4—21no—
303C24×C4—212no—
304C24×C4—212no—
305C24×C4—212no—
306C24×C4—48no—
307C24×C4—48no—
308C24×C4—48no—
309C24×C4—48no—
310C24×C4—48no—
311C24×C4—48no—
312C24×C4—84no—
313C24×C4—84no—
314C24×C4—84no—
315C24×C4C22×C418yes—
316C24×C4C2×D411yescharacteristic
317C24×C4C2×D411yescharacteristic
318C24×C4C2×D416yes—
319C24×C4C2×D411yescharacteristic
320C24×C4C2×D411yescharacteristic
321C24×C4C2×D411yescharacteristic
322C24×C4#4118yes—
323C24×C4C2416yes—
324C24×C4C2411yescharacteristic
325C22×SD16—2128no—
326C22×SD16—248no—
327C22×SD16—248no—
328C22×SD16—464no—
329C22×SD16—424no—
330C22×SD16—424no—
331C22×SD16C22×C4196yescomplemented
332C22×SD16C22×C4196yescomplemented
333C22×SD16C24116yes—
334C22×SD16C24116yes—
335C23×C8—24no—
336C23×C8—24no—
337C23×C8—24no—
338C23×C8—24no—
339C23×C8—24no—
340C23×C8—24no—
341C23×C8—24no—
342C23×C8—248no—
343C23×C8—24no—
344C23×C8—24no—
345C23×C8—248no—
346C23×C8—424no—
347C23×C8—464no—
348C23×C8C22×C418yes—
349C23×C8C22×C418yes—
350C23×C8C2×D418yes—
351C23×C8C2416yes—
352C23×C8C24116yes—
353C23×C8C2416yes—
354C23×C8C2416yes—
355C23×C8C2416yes—
356C2×C22⋊Q8—296no—
357C2×C22⋊Q8—224no—
358C2×C22⋊Q8—248no—
359C2×C22⋊Q8C22×C4196yescomplemented
360C2×C22⋊Q8C24116yes—
361C2×C4×Q8—224no—
362C2×C4×Q8—248no—
363C2×C4×Q8—424no—
364C2×C4×Q8—448no—
365C2×C4×Q8C24116yescomplemented
366C2×C4×D4—248no—
367C2×C4×D4—248no—
368C2×C4×D4—224no—
369C2×C4×D4—224no—
370C2×C4×D4—424no—
371C2×C4×D4—424no—
372C2×C4×D4—448no—
373C2×C4×D4—448no—
374C2×C4×D4C24116yes—
375C2×C4×D4C24116yes—
376C22×C4⋊C4—216no—
377C22×C4⋊C4—23no—
378C22×C4⋊C4—212no—
379C22×C4⋊C4—23no—
380C22×C4⋊C4—24no—
381C22×C4⋊C4—24no—
382C22×C4⋊C4—24no—
383C22×C4⋊C4—24no—
384C22×C4⋊C4—24no—
385C22×C4⋊C4—24no—
386C22×C4⋊C4—24no—
387C22×C4⋊C4—24no—
388C22×C4⋊C4—248no—
389C22×C4⋊C4—224no—
390C22×C4⋊C4—212no—
391C22×C4⋊C4—23no—
392C22×C4⋊C4—212no—
393C22×C4⋊C4—23no—
394C22×C4⋊C4—23no—
395C22×C4⋊C4—212no—
396C22×C4⋊C4—424no—
397C22×C4⋊C4—448no—
398C22×C4⋊C4—48no—
399C22×C4⋊C4—48no—
400C22×C4⋊C4—84no—
401C22×C4⋊C4C22×C418yes—
402C22×C4⋊C4C2×D418yes—
403C22×C4⋊C4C2416yes—
404C22×C4⋊C4C2416yes—
405C22×C4⋊C4C2416yes—
406C22×C4⋊C4C24116yes—
407C22×C4⋊C4C2416yes—
408C22×C4⋊C4C2416yes—
409C22×C22⋊C4—216no—
410C22×C22⋊C4—28no—
411C22×C22⋊C4—212no—
412C22×C22⋊C4—212no—
413C22×C22⋊C4—212no—
414C22×C22⋊C4—212no—
415C22×C22⋊C4—212no—
416C22×C22⋊C4—212no—
417C22×C22⋊C4—212no—
418C22×C22⋊C4—212no—
419C22×C22⋊C4—264no—
420C22×C22⋊C4—48no—
421C22×C22⋊C4—48no—
422C22×C22⋊C4—48no—
423C22×C22⋊C4—48no—
424C22×C22⋊C4—48no—
425C22×C22⋊C4—4192no—
426C22×C22⋊C4—84no—
427C22×C22⋊C4—84no—
428C22×C22⋊C4SD16116yescomplemented
429C22×C22⋊C4C2×D4112yes—
430C22×C22⋊C4C2×D4112yes—
431C22×C42—24no—
432C22×C42—24no—
433C22×C42—24no—
434C22×C42—24no—
435C22×C42—212no—
436C22×C42—212no—
437C22×C42—48no—
438C22×C42—84no—
439C22×C42C2×D416yes—
440C22×C42C2×D416yes—
441C22×C42C2416yes—
442C22×C42C2416yes—
443#450C22×C41512yescomplemented
444C4×SD16—2256no—
445C2×#106—248no—
446C2×#106—424no—
447C2×#106C24116yescomplemented
448C2×#106C24116yescomplemented
449C2×#103—248no—
450C2×#103—424no—
451C2×#103C24116yescomplemented
452C2×#103C24116yescomplemented
453C2×#102—248no—
454C2×#102—248no—
455C2×#102—248no—
456C2×#102—2256no—
457C2×#102C22×C4196yescomplemented
458C2×#102C22×C4196yescomplemented
459C2×#102C2×D4196yes—
460C2×#102C24116yes—
461C2×#102C24116yes—
462C2×#102C24116yes—
463C2×#102C24116yes—
464C2×#102C24116yes—
465C2×#102C24116yes—
466C2×C22⋊C8C22×C4196yescomplemented
467C2×C22⋊C8C24116yes—
468C2×C4×C8—248no—
469C2×C4×C8—424no—
470C2×C4×C8C24116yescomplemented
471C2×C4×C8C24116yescomplemented
472#391—224no—
473#391C24116yescomplemented
474#390—224no—
475#390—224no—
476#390C24116yes—
477#390C24116yes—
478#389—224no—
479#389—264no—
480#389C24116yescomplemented
481#387—264no—
482#386—264no—
483#386—264no—
484#385—264no—
485#380—224no—
486#380C24116yes—
487#379—264no—
488C4×C4⋊C4—224no—
489C4×C4⋊C4C24116yescomplemented
490C4×C22⋊C4—264no—
491C4×C22⋊C4C2×D4148yes—
492C4×C22⋊C4C24116yes—
493C2×#95—212no—
494C2×#95—212no—
495C2×#95—212no—
496C2×#95—212no—
497C2×#95—212no—
498C2×#95C2×D4112yes—
499C2×#95C2×D4112yes—
500#340C24116yescomplemented
501#340C24116yescomplemented
502#340C24116yescomplemented
503#340C24116yescomplemented
504#336C24116yescomplemented
505#336C24116yescomplemented
506C25—24no—
507C25—24no—
508C25—24no—
509C25—24no—
510C25—28no—
511C25—28no—
512C25—28no—
513C25—26no—
514C25—28no—
515C25—26no—
516C25—296no—
517C25—216no—
518C25—4128no—
519C25—448no—
520C25—448no—
521C25—44no—
522C25—44no—
523C25—44no—
524C25—44no—
525C25—44no—
526C25—44no—
527C25—448no—
528C25—44no—
529C25—448no—
530C25—44no—
531C25—44no—
532C25—44no—
533C25—4128no—
534C25—864no—
535C25—824no—
536C25—824no—
537C25—864no—
538C25—864no—
539C25—864no—
540C25—864no—
541C25C4×D418yes—
542C25C2×SD1618yes—
543C25#13518yes—
544C25C22×D416yes—
545C25C22×D411yescharacteristic
546C22×Q8—224no—
547C22×Q8—26no—
548C22×Q8—212no—
549C22×Q8—232no—
550C22×Q8—232no—
551C22×Q8—212no—
552C22×Q8—212no—
553C22×Q8—212no—
554C22×Q8—212no—
555C22×Q8—412no—
556C22×Q8—416no—
557C22×Q8—412no—
558C22×Q8—416no—
559C22×Q8C23×C4124yes—
560C22×Q8C2514yes—
561C22×D4—2384no—
562C22×D4—232no—
563C22×D4—232no—
564C22×D4—224no—
565C22×D4—232no—
566C22×D4—296no—
567C22×D4—2192no—
568C22×D4—224no—
569C22×D4—232no—
570C22×D4—232no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—232no—
574C22×D4—232no—
575C22×D4—26no—
576C22×D4—212no—
577C22×D4—216no—
578C22×D4—26no—
579C22×D4—212no—
580C22×D4—212no—
581C22×D4—232no—
582C22×D4—212no—
583C22×D4—212no—
584C22×D4—212no—
585C22×D4—212no—
586C22×D4—212no—
587C22×D4—4192no—
588C22×D4—416no—
589C22×D4—416no—
590C22×D4—4768no—
591C22×D4—496no—
592C22×D4—4192no—
593C22×D4—496no—
594C22×D4—4192no—
595C22×D4—4128no—
596C22×D4—448no—
597C22×D4—448no—
598C22×D4—412no—
599C22×D4—412no—
600C22×D4—416no—
601C22×D4—416no—
602C22×D4C4×D4164yes—
603C22×D4C23×C4124yes—
604C22×D4C23×C4164yes—
605C22×D4C23×C4124yes—
606C22×D4C22×D4124yes—
607C22×D4C2×#41124yes—
608C22×D4C2514yes—
609C22×D4C2514yes—
610C23×C4—24no—
611C23×C4—24no—
612C23×C4—24no—
613C23×C4—24no—
614C23×C4—24no—
615C23×C4—24no—
616C23×C4—232no—
617C23×C4—232no—
618C23×C4—224no—
619C23×C4—232no—
620C23×C4—224no—
621C23×C4—232no—
622C23×C4—212no—
623C23×C4—212no—
624C23×C4—212no—
625C23×C4—212no—
626C23×C4—28no—
627C23×C4—28no—
628C23×C4—24no—
629C23×C4—28no—
630C23×C4—24no—
631C23×C4—24no—
632C23×C4—24no—
633C23×C4—24no—
634C23×C4—24no—
635C23×C4—26no—
636C23×C4—26no—
637C23×C4—26no—
638C23×C4—26no—
639C23×C4—26no—
640C23×C4—26no—
641C23×C4—216no—
642C23×C4—216no—
643C23×C4—216no—
644C23×C4—448no—
645C23×C4—448no—
646C23×C4—448no—
647C23×C4—44no—
648C23×C4—44no—
649C23×C4—44no—
650C23×C4—44no—
651C23×C4—44no—
652C23×C4—44no—
653C23×C4—44no—
654C23×C4—44no—
655C23×C4—44no—
656C23×C4—44no—
657C23×C4—44no—
658C23×C4—448no—
659C23×C4—44no—
660C23×C4—44no—
661C23×C4—44no—
662C23×C4—44no—
663C23×C4—448no—
664C23×C4—448no—
665C23×C4—824no—
666C23×C4—824no—
667C23×C4—864no—
668C23×C4—864no—
669C23×C4—824no—
670C23×C4—864no—
671C23×C4C4×D418yes—
672C23×C4C4×D4148yes—
673C23×C4C2×SD1618yes—
674C23×C4C2×SD1618yes—
675C23×C4C23×C4124yes—
676C23×C4C23×C414yes—
677C23×C4C22×D416yes—
678C23×C4C22×D416yes—
679C23×C4C22×D416yes—
680C23×C4C22×D4112yes—
681C23×C4C22×D416yes—
682C23×C4C22×D416yes—
683C23×C4C22×D413yes—
684C23×C4C22×D414yes—
685C23×C4C2×#41124yes—
686C23×C4C2×#4114yes—
687C23×C4C2×#4114yes—
688C23×C4H(5,𝔽2)14yes—
689C23×C4H(5,𝔽2)14yes—
690C23×C4C2514yes—
691C23×C4C2513yes—
692C2×SD16—2384no—
693C2×SD16—232no—
694C2×SD16—232no—
695C2×SD16—4192no—
696C2×SD16—416no—
697C2×SD16—416no—
698C2×SD16C23×C4164yescomplemented
699C2×SD16C23×C4164yescomplemented
700C22×C8—232no—
701C22×C8—232no—
702C22×C8—232no—
703C22×C8—212no—
704C22×C8—212no—
705C22×C8—212no—
706C22×C8—212no—
707C22×C8—212no—
708C22×C8—212no—
709C22×C8—212no—
710C22×C8—232no—
711C22×C8—212no—
712C22×C8—212no—
713C22×C8—232no—
714C22×C8—416no—
715C22×C8—4192no—
716C22×C8—416no—
717C22×C8C23×C4124yes—
718C22×C8C23×C4124yes—
719C22×C8C22×D4124yes—
720C22×C8C2514yes—
721C22×C8C2514yes—
722C22×C8C2514yes—
723C22×C8C2514yes—
724C22⋊Q8—2192no—
725C22⋊Q8—232no—
726C22⋊Q8C23×C4164yescomplemented
727C4×Q8—232no—
728C4×Q8—416no—
729C4×Q8—496no—
730C4×D4—232no—
731C4×D4—232no—
732C4×D4—416no—
733C4×D4—416no—
734C4×D4—496no—
735C4×D4—496no—
736C2×C4⋊C4—296no—
737C2×C4⋊C4—224no—
738C2×C4⋊C4—224no—
739C2×C4⋊C4—26no—
740C2×C4⋊C4—216no—
741C2×C4⋊C4—26no—
742C2×C4⋊C4—212no—
743C2×C4⋊C4—212no—
744C2×C4⋊C4—212no—
745C2×C4⋊C4—212no—
746C2×C4⋊C4—212no—
747C2×C4⋊C4—212no—
748C2×C4⋊C4—212no—
749C2×C4⋊C4—212no—
750C2×C4⋊C4—232no—
751C2×C4⋊C4—216no—
752C2×C4⋊C4—26no—
753C2×C4⋊C4—216no—
754C2×C4⋊C4—26no—
755C2×C4⋊C4—26no—
756C2×C4⋊C4—216no—
757C2×C4⋊C4—416no—
758C2×C4⋊C4—496no—
759C2×C4⋊C4—448no—
760C2×C4⋊C4—448no—
761C2×C4⋊C4—412no—
762C2×C4⋊C4—412no—
763C2×C4⋊C4—412no—
764C2×C4⋊C4—824no—
765C2×C4⋊C4C23×C4124yes—
766C2×C4⋊C4C22×D4124yes—
767C2×C4⋊C4C2514yes—
768C2×C4⋊C4C2514yes—
769C2×C4⋊C4C2514yes—
770C2×C4⋊C4C2514yes—
771C2×C4⋊C4C2514yes—
772C2×C22⋊C4—296no—
773C2×C22⋊C4—248no—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—216no—
776C2×C22⋊C4—216no—
777C2×C22⋊C4—216no—
778C2×C22⋊C4—216no—
779C2×C22⋊C4—216no—
780C2×C22⋊C4—216no—
781C2×C22⋊C4—216no—
782C2×C22⋊C4—448no—
783C2×C22⋊C4—448no—
784C2×C22⋊C4—448no—
785C2×C22⋊C4—448no—
786C2×C22⋊C4—448no—
787C2×C22⋊C4—4256no—
788C2×C22⋊C4—824no—
789C2×C22⋊C4—824no—
790C2×C22⋊C4C2×SD16196yescomplemented
791C2×C22⋊C4C22×D4116yes—
792C2×C22⋊C4C22×D4116yes—
793C2×C42—224no—
794C2×C42—224no—
795C2×C42—212no—
796C2×C42—212no—
797C2×C42—212no—
798C2×C42—212no—
799C2×C42—216no—
800C2×C42—216no—
801C2×C42—448no—
802C2×C42—824no—
803C2×C42C22×D4112yes—
804C2×C42C22×D4112yes—
805C2×C42C2514yes—
806C2×C42C2514yes—
807#106—232no—
808#106—416no—
809#103—232no—
810#103—416no—
811#102—232no—
812#102—232no—
813#102—232no—
814#102C23×C4164yescomplemented
815#102C23×C4164yescomplemented
816#102C22×D4164yes—
817C22⋊C8C23×C4164yescomplemented
818C4×C8—232no—
819C4×C8—416no—
820#95—216no—
821#95—216no—
822#95—216no—
823#95—216no—
824#95—216no—
825#95C22×D4116yes—
826#95C22×D4116yes—
827C24—232no—
828C24—232no—
829C24—212no—
830C24—212no—
831C24—232no—
832C24—232no—
833C24—232no—
834C24—232no—
835C24—212no—
836C24—212no—
837C24—24no—
838C24—264no—
839C24—224no—
840C24—224no—
841C24—224no—
842C24—24no—
843C24—224no—
844C24—264no—
845C24—4384no—
846C24—432no—
847C24—432no—
848C24—432no—
849C24—432no—
850C24—432no—
851C24—432no—
852C24—432no—
853C24—432no—
854C24—412no—
855C24—412no—
856C24—412no—
857C24—412no—
858C24—432no—
859C24—432no—
860C24—4384no—
861C24—432no—
862C24—412no—
863C24—412no—
864C24—432no—
865C24—412no—
866C24—432no—
867C24—412no—
868C24—412no—
869C24—412no—
870C24—816no—
871C24—816no—
872C24—8192no—
873C24—81024no—
874C24—8192no—
875C24—8192no—
876C24—8192no—
877C24—8192no—
878C24—816no—
879C24—816no—
880C24—816no—
881C24—816no—
882C24C4×SD16164yescomplemented
883C24C2×C4×D4124yes—
884C24C2×C4×D414yes—
885C24D4214yes—
886C24#54614yes—
887C24C22×SD16124yes—
888C24C22×SD1614yes—
889C24C2×#135124yes—
890C24C2×#13514yes—
891C24#57614yes—
892C24#57714yes—
893C24C23×D414yes—
894C24C23×D413yes—
895C2×Q8—24no—
896C2×Q8—224no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—248no—
902C2×Q8—248no—
903C2×Q8—496no—
904C2×Q8—412no—
905C2×Q8—424no—
906C2×Q8—412no—
907C2×Q8—424no—
908C2×Q8C24×C418yes—
909C2×D4—2128no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—2192no—
919C2×D4—224no—
920C2×D4—248no—
921C2×D4—264no—
922C2×D4—224no—
923C2×D4—248no—
924C2×D4—248no—
925C2×D4—224no—
926C2×D4—224no—
927C2×D4—248no—
928C2×D4—248no—
929C2×D4—464no—
930C2×D4—4768no—
931C2×D4—464no—
932C2×D4—464no—
933C2×D4—4384no—
934C2×D4—432no—
935C2×D4—432no—
936C2×D4—496no—
937C2×D4—412no—
938C2×D4—412no—
939C2×D4—424no—
940C2×D4—424no—
941C2×D4C2×C4×D4196yes—
942C2×D4C24×C418yes—
943C2×D4C24×C418yes—
944C2×D4C23×D418yes—
945C2×D4C22×#4118yes—
946C22×C4—232no—
947C22×C4—212no—
948C22×C4—212no—
949C22×C4—212no—
950C22×C4—212no—
951C22×C4—232no—
952C22×C4—232no—
953C22×C4—212no—
954C22×C4—212no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—2192no—
960C22×C4—248no—
961C22×C4—248no—
962C22×C4—224no—
963C22×C4—248no—
964C22×C4—224no—
965C22×C4—248no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—224no—
970C22×C4—224no—
971C22×C4—212no—
972C22×C4—224no—
973C22×C4—212no—
974C22×C4—212no—
975C22×C4—212no—
976C22×C4—212no—
977C22×C4—212no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—432no—
982C22×C4—432no—
983C22×C4—432no—
984C22×C4—432no—
985C22×C4—432no—
986C22×C4—412no—
987C22×C4—412no—
988C22×C4—416no—
989C22×C4—432no—
990C22×C4—416no—
991C22×C4—412no—
992C22×C4—412no—
993C22×C4—412no—
994C22×C4—412no—
995C22×C4—412no—
996C22×C4—412no—
997C22×C4—412no—
998C22×C4—412no—
999C22×C4—412no—
1000C22×C4—432no—
1001C22×C4—412no—
1002C22×C4—412no—
1003C22×C4—412no—
1004C22×C4—412no—
1005C22×C4—432no—
1006C22×C4—432no—
1007C22×C4—816no—
1008C22×C4—816no—
1009C22×C4—8192no—
1010C22×C4—8192no—
1011C22×C4—816no—
1012C22×C4—8192no—
1013C22×C4—816no—
1014C22×C4—816no—
1015C22×C4—816no—
1016C22×C4C2×C4×D4124yes—
1017C22×C4C2×C4×D4148yes—
1018C22×C4C2×C4×D4112yes—
1019C22×C4C2×C4×D4116yes—
1020C22×C4#518116yes—
1021C22×C4D42112yes—
1022C22×C4#546112yes—
1023C22×C4#546116yes—
1024C22×C4#551116yes—
1025C22×C4C22×SD16124yes—
1026C22×C4C22×SD16124yes—
1027C22×C4C24×C418yes—
1028C22×C4C24×C416yes—
1029C22×C4C23×D414yes—
1030C22×C4C23×D414yes—
1031C22×C4C23×D414yes—
1032C22×C4C23×D414yes—
1033C22×C4C23×D414yes—
1034C22×C4C23×D416yes—
1035C22×C4C23×D413yes—
1036C22×C4C22×#4118yes—
1037C22×C4C22×#4116yes—
1038C22×C4C22×#4116yes—
1039C22×C4C2×H(5,𝔽2)16yes—
1040C22×C4C2×H(5,𝔽2)16yes—
1041C22×C4C2611yescharacteristic
1042SD16—2128no—
1043SD16—464no—
1044C2×C8—24no—
1045C2×C8—24no—
1046C2×C8—24no—
1047C2×C8—24no—
1048C2×C8—24no—
1049C2×C8—24no—
1050C2×C8—248no—
1051C2×C8—248no—
1052C2×C8—248no—
1053C2×C8—24no—
1054C2×C8—24no—
1055C2×C8—24no—
1056C2×C8—464no—
1057C2×C8—424no—
1058C2×C8C24×C418yes—
1059C2×C8C24×C418yes—
1060C2×C8C23×D418yes—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—264no—
1064C4⋊C4—224no—
1065C4⋊C4—224no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—432no—
1073C4⋊C4—432no—
1074C4⋊C4—412no—
1075C4⋊C4—412no—
1076C4⋊C4—412no—
1077C4⋊C4—816no—
1078C4⋊C4C24×C418yes—
1079C4⋊C4C23×D418yes—
1080C22⋊C4—264no—
1081C22⋊C4—232no—
1082C22⋊C4—432no—
1083C22⋊C4—432no—
1084C22⋊C4—432no—
1085C22⋊C4—432no—
1086C22⋊C4—432no—
1087C22⋊C4—816no—
1088C22⋊C4—816no—
1089C22⋊C4C22×SD16164yescomplemented
1090C42—24no—
1091C42—24no—
1092C42—24no—
1093C42—24no—
1094C42—224no—
1095C42—224no—
1096C42—432no—
1097C42—816no—
1098C23—248no—
1099C23—2256no—
1100C23—24no—
1101C23—24no—
1102C23—248no—
1103C23—248no—
1104C23—248no—
1105C23—248no—
1106C23—24no—
1107C23—24no—
1108C23—248no—
1109C23—296no—
1110C23—28no—
1111C23—28no—
1112C23—28no—
1113C23—28no—
1114C23—4128no—
1115C23—4256no—
1116C23—44no—
1117C23—44no—
1118C23—44no—
1119C23—44no—
1120C23—448no—
1121C23—448no—
1122C23—448no—
1123C23—448no—
1124C23—448no—
1125C23—448no—
1126C23—448no—
1127C23—44no—
1128C23—44no—
1129C23—44no—
1130C23—44no—
1131C23—44no—
1132C23—44no—
1133C23—448no—
1134C23—4128no—
1135C23—448no—
1136C23—864no—
1137C23—81536no—
1138C23—864no—
1139C23—864no—
1140C23—864no—
1141C23—864no—
1142C23—8128no—
1143C23—824no—
1144C23—824no—
1145C23—824no—
1146C23—824no—
1147C23#2358116yes—
1148C23C2×C4×SD16116yes—
1149C23C2×C4×SD16196yescomplemented
1150C23#2946116yes—
1151C23#3280116yes—
1152C23D4×SD16116yes—
1153C23#3295116yes—
1154C23#3296116yes—
1155C23C22×C4×D418yes—
1156C23C22×C4×D416yes—
1157C23C2×D4216yes—
1158C23C2×#54616yes—
1159C23C23×SD1618yes—
1160C23C23×SD1616yes—
1161C23C22×#13518yes—
1162C23C22×#13516yes—
1163C23C2×#57616yes—
1164C23C2×#57716yes—
1165C23C24×D411yescharacteristic
1166Q8—28no—
1167Q8—28no—
1168Q8—448no—
1169Q8—44no—
1170Q8—44no—
1171D4—296no—
1172D4—28no—
1173D4—28no—
1174D4—28no—
1175D4—28no—
1176D4—28no—
1177D4—4128no—
1178D4—448no—
1179D4—44no—
1180D4—44no—
1181D4C22×C4×D4116yes—
1182C2×C4—248no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—248no—
1186C2×C4—248no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—296no—
1192C2×C4—28no—
1193C2×C4—28no—
1194C2×C4—28no—
1195C2×C4—28no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—28no—
1201C2×C4—28no—
1202C2×C4—24no—
1203C2×C4—28no—
1204C2×C4—24no—
1205C2×C4—448no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—424no—
1211C2×C4—448no—
1212C2×C4—424no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—448no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—864no—
1226C2×C4—864no—
1227C2×C4—864no—
1228C2×C4—824no—
1229C2×C4—824no—
1230C2×C4—824no—
1231C2×C4#2358148yes—
1232C2×C4C22×C4×D418yes—
1233C2×C4C22×C4×D416yes—
1234C2×C4C22×C4×D4112yes—
1235C2×C4C2×#518112yes—
1236C2×C4C2×D4216yes—
1237C2×C4C2×#54616yes—
1238C2×C4C2×#546112yes—
1239C2×C4C2×#551112yes—
1240C2×C4C23×SD1618yes—
1241C2×C4C23×SD1618yes—
1242C2×C4C25×C411yescharacteristic
1243C2×C4C24×D411yescharacteristic
1244C2×C4C23×#4111yescharacteristic
1245C2×C4C23×#4111yescharacteristic
1246C2×C4C22×H(5,𝔽2)11yescharacteristic
1247C2×C4C22×H(5,𝔽2)11yescharacteristic
1248C8—28no—
1249C8—28no—
1250C8—28no—
1251C8—44no—
1252C22—28no—
1253C22—2192no—
1254C22—28no—
1255C22—28no—
1256C22—28no—
1257C22—28no—
1258C22—28no—
1259C22—216no—
1260C22—48no—
1261C22—48no—
1262C22—4192no—
1263C22—48no—
1264C22—48no—
1265C22—48no—
1266C22—48no—
1267C22—48no—
1268C22—48no—
1269C22—48no—
1270C22—8256no—
1271C22—896no—
1272C22—84no—
1273C22—84no—
1274C22—84no—
1275C22—84no—
1276C22#22874164yesdirect product factor
1277C22C2×#2358112yes—
1278C22C22×C4×SD16112yes—
1279C22C22×C4×SD16116yescomplemented
1280C22C2×#2946112yes—
1281C22C2×#3280112yes—
1282C22C2×D4×SD16112yes—
1283C22C2×#3295112yes—
1284C22C2×#3296112yes—
1285C22C23×C4×D411yescharacteristic
1286C22C22×D4211yescharacteristic
1287C22C22×#54611yescharacteristic
1288C22C24×SD1611yescharacteristic
1289C22C23×#13511yescharacteristic
1290C22C22×#57611yescharacteristic
1291C22C22×#57711yescharacteristic
1292C4—28no—
1293C4—28no—
1294C4—28no—
1295C4—48no—
1296C4—48no—
1297C4—44no—
1298C4—44no—
1299C4—48no—
1300C4—84no—
1301C4—84no—
1302C4—84no—
1303C4C2×#2358112yes—
1304C4C23×C4×D411yescharacteristic
1305C4C22×#51811yescharacteristic
1306C4C22×#54611yescharacteristic
1307C4C22×#55111yescharacteristic
1308C2—216no—
1309C2—416no—
1310C2—88no—
1311C2C2×#22874124yesdirect product factor
1312C2C22×#235811yescharacteristic
1313C2C23×C4×SD1611yescharacteristic
1314C2C22×#294611yescharacteristic
1315C2C22×D4×SD1611yescharacteristic
1316C2C22×#328011yescharacteristic
1317C2C22×#329611yescharacteristic
1318C2C22×#329511yescharacteristic
subgroupG/H
center, socleC25C22×D4
commutatorC2×C4C25×C4
Frattini, cosocleC22×C4C26
prime radicalC25×D4C22
LCSG ▷ C2×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×C4×SD16C2semidirect
4. C22×#2360C2semidirect
6. C2×#22874C2direct (N × H)
7. C22×#1968C2semidirect
8. C22×#1934C2semidirect
9. C22×#1926C2semidirect
10. C22×#1892C2semidirect
11. C22×#1880C2semidirect
12. C22×#1877C2semidirect
13. C22×#1864C2semidirect
14. C22×#1853C2semidirect
15. C22×C4×#102C2semidirect
16. C22×C8×C22⋊C4C2semidirect
22. C23×C4×Q8C22semidirect
27. C22×#450C4semidirect
30. C22×C4×SD16C22semidirect
31. C23×#106C22semidirect
32. C23×#106C22semidirect
33. C23×#103C22semidirect
34. C23×#103C22semidirect
44. C23×C4×C8C22semidirect
45. C23×C4×C8C22semidirect
47. C2×#2360C22semidirect
50. C22×#391C22semidirect
54. C22×#389C22semidirect
61. C22×C4×C4⋊C4C22semidirect
64. #22874C22direct (N × H)
65. C2×#1968C22semidirect
66. C2×#1934C22semidirect
67. C2×#1926C22semidirect
68. C2×#1892C22semidirect
69. C2×#1880C22semidirect
70. C2×#1877C22semidirect
71. C2×#1864C22semidirect
72. C2×#1853C22semidirect
73. C2×C4×#102C22semidirect
74. C2×C8×C22⋊C4C22semidirect
75. C22×#340C22semidirect
76. C22×#340C22semidirect
77. C22×#340C22semidirect
78. C22×#340C22semidirect
79. C22×#336C22semidirect
80. C22×#336C22semidirect
102. C23×SD16C2×C4semidirect
103. C23×SD16C2×C4semidirect
116. C22×C22⋊Q8C2×C4semidirect
121. C22×C4×Q8C23semidirect
159. C2×#450C2×C4semidirect
162. C2×C4×SD16C23semidirect
165. C22×#106C23semidirect
166. C22×#106C23semidirect
169. C22×#103C23semidirect
170. C22×#103C23semidirect
175. C22×#102C2×C4semidirect
176. C22×#102C2×C4semidirect
185. C22×C22⋊C8C2×C4semidirect
189. C22×C4×C8C23semidirect
190. C22×C4×C8C23semidirect
192. #2360C23semidirect
196. C2×#391C23semidirect
203. C2×#389C23semidirect
212. C2×C4×C4⋊C4C23semidirect
223. #1968C23semidirect
224. #1934C23semidirect
225. #1926C23semidirect
226. #1892C23semidirect
227. #1880C23semidirect
228. #1877C23semidirect
229. #1864C23semidirect
230. #1853C23semidirect
231. C4×#102C23semidirect
232. C8×C22⋊C4C23semidirect
233. C2×#340C23semidirect
234. C2×#340C23semidirect
235. C2×#340C23semidirect
236. C2×#340C23semidirect
237. C2×#336C23semidirect
238. C2×#336C23semidirect
331. C22×SD16C22×C4semidirect
332. C22×SD16C22×C4semidirect
359. C2×C22⋊Q8C22×C4semidirect
365. C2×C4×Q8C24semidirect
428. C22×C22⋊C4SD16semidirect
443. #450C22×C4semidirect
447. C2×#106C24semidirect
448. C2×#106C24semidirect
451. C2×#103C24semidirect
452. C2×#103C24semidirect
457. C2×#102C22×C4semidirect
458. C2×#102C22×C4semidirect
466. C2×C22⋊C8C22×C4semidirect
470. C2×C4×C8C24semidirect
471. C2×C4×C8C24semidirect
473. #391C24semidirect
480. #389C24semidirect
489. C4×C4⋊C4C24semidirect
500. #340C24semidirect
501. #340C24semidirect
502. #340C24semidirect
503. #340C24semidirect
504. #336C24semidirect
505. #336C24semidirect
698. C2×SD16C23×C4semidirect
699. C2×SD16C23×C4semidirect
726. C22⋊Q8C23×C4semidirect
790. C2×C22⋊C4C2×SD16semidirect
814. #102C23×C4semidirect
815. #102C23×C4semidirect
817. C22⋊C8C23×C4semidirect
882. C24C4×SD16semidirect
1089. C22⋊C4C22×SD16semidirect
1149. C23C2×C4×SD16semidirect
1276. C22#22874direct (N × H)
1279. C22C22×C4×SD16semidirect
1311. C2C2×#22874direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#4502
C23×C4×SD162
C24×#1022
C22×#23602
C22×D4×C22⋊C42
C2×#228742
C22×#19682
C22×#19342
C22×#19262
C22×#18922
C22×#18802
C22×#18772
C22×#18642
C22×#18532
C22×C4×#1022
C22×C8×C22⋊C42