Finite Group Databasebeta

← C4⋊C4×#121 #519310

Subgroups — C4⋊C4×#121 #519310

Order 512.

4846 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×D4×C4⋊C4C212yesmaximal, complemented
3C2×C4×#121C212yesmaximal
4C2×C4×#121C211yesmaximal, characteristic
5C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
6#14697C212yesmaximal, complemented
7#14686C211yesmaximal, characteristic, complemented
8#14112C214yesmaximal, complemented
9#14046C212yesmaximal, complemented
10#14018C212yesmaximal, complemented
11#13975C214yesmaximal, complemented
12#13910C211yesmaximal, characteristic, complemented
13#13906C211yesmaximal, characteristic, complemented
14#13876C212yesmaximal, complemented
15#13872C212yesmaximal, complemented
16C4⋊C42C211yesmaximal, characteristic, complemented
17C22⋊C4×C4⋊C4C212yesmaximal, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2214yes—
20C22×C4×D4C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2212yes—
27C23×C42C2211yescharacteristic
28D4×C4⋊C4—28no—
29D4×C4⋊C4—216no—
30C4×#121—216no—
31C4×#121C4116yescomplemented
32C2×#390C2212yes—
33C2×#390C2211yescharacteristic
34C2×#389C2214yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#388C2214yes—
40C2×#388C2212yes—
41C2×#386C2214yes—
42C2×#386C2212yes—
43C2×#385C2214yes—
44C2×#385C2214yes—
45C2×#385C2214yes—
46C2×#384C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—28no—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2214yes—
67C2×C4×C22⋊C4C2212yes—
68C22×#95C2212yes—
69#1444C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78#1436C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2214yes—
87C22⋊#95C2214yes—
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2314yes—
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C2×#121C2×C418yes—
98C2×#121D418yes—
99C2×#121Q818yes—
100C2×C4×D4—28no—
101C2×C4×D4—28no—
102C2×C4×D4—28no—
103C2×C4×D4—216no—
104C2×C4×D4—216no—
105C2×C4×D4—24no—
106C2×C4×D4—28no—
107C2×C4×D4—24no—
108C2×C4×D4—44no—
109C2×C4×D4—48no—
110C2×C4×D4C2×C4116yescomplemented
111C2×C4×D4C2×C418yescomplemented
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—28no—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4D418yescomplemented
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—28no—
152C22×C42—28no—
153C22×C42—44no—
154C22×C42C2×C418yescomplemented
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2314yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165#390—28no—
166#390C2×C418yescomplemented
167#389—216no—
168#389—28no—
169#389—28no—
170#389—44no—
171#389C2×C418yescomplemented
172#388—216no—
173#388C2×C4116yescomplemented
174#386—216no—
175#386C2×C4116yescomplemented
176#385—216no—
177#385—216no—
178#385—216no—
179#384—28no—
180#384—24no—
181#384—24no—
182#380—28no—
183#380—28no—
184#380—28no—
185#380—28no—
186#380—28no—
187#380—44no—
188#380C2×C418yescomplemented
189C4×C4⋊C4—28no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—28no—
193C4×C4⋊C4—28no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—28no—
196C4×C4⋊C4C2×C418yescomplemented
197C4×C4⋊C4D418yescomplemented
198C4×C22⋊C4—216no—
199C4×C22⋊C4C2×C4116yescomplemented
200C2×#95—28no—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4C22×C418yes—
230C22×D4C22×C414yes—
231C22×D4C2×D418yes—
232C22×D4C2×D414yes—
233C22×D4C2×Q818yes—
234C22×D4C2×Q814yes—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—28no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—28no—
264C23×C4—28no—
265C23×C4—28no—
266C23×C4—41no—
267C23×C4—41no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4C22×C418yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C2×D418yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×Q814yes—
283C23×C4#4114yes—
284C23×C4C2414yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#121C4⋊C4164yesdirect product factor
300C4×D4—264no—
301C4×D4—232no—
302C4×D4—432no—
303C4×D4—464no—
304C2×C4⋊C4—232no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—232no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C22×C418yes—
353C2×C4⋊C4C22×C414yes—
354C2×C4⋊C4C22×C414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D418yes—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×Q814yes—
362C2×C4⋊C4#4114yes—
363C2×C4⋊C4#4114yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C22×C418yes—
385C2×C22⋊C4C22×C418yes—
386C2×C22⋊C4C22×C418yes—
387C2×C22⋊C4C22×C418yes—
388C2×C22⋊C4C22×C418yes—
389C2×C22⋊C4C2×D418yes—
390C2×C22⋊C4C2×Q818yes—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—232no—
402C2×C42—28no—
403C2×C42—28no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—432no—
412C2×C42—44no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42C22×C418yes—
416C2×C42C22×C414yes—
417C2×C42C22×C414yes—
418C2×C42C22×C414yes—
419C2×C42C22×C414yes—
420C2×C42C2×D418yes—
421C2×C42C2×D414yes—
422C2×C42#4114yes—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95C22×C418yes—
438#95C22×C418yes—
439#95C22×C418yes—
440#95C2×D418yes—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C23×C414yes—
462C24C23×C412yes—
463C24C22×D414yes—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C22×Q814yes—
467C24C22×Q812yes—
468C24C2×#4112yes—
469C24H(5,𝔽2)12yes—
470C242−1+412yes—
471C24C2511yescharacteristic
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4C2×C4⋊C4132yescomplemented
485C2×D4C2×C4⋊C4116yescomplemented
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—216no—
559C22×C4—216no—
560C22×C4—216no—
561C22×C4—216no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—416no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—416no—
600C22×C4—88no—
601C22×C4—88no—
602C22×C4—88no—
603C22×C4C2×C4⋊C4116yescomplemented
604C22×C4C4×D4116yescomplemented
605C22×C4C23×C412yes—
606C22×C4C23×C414yes—
607C22×C4C23×C414yes—
608C22×C4C23×C412yes—
609C22×C4C23×C414yes—
610C22×C4C23×C412yes—
611C22×C4C23×C412yes—
612C22×C4C23×C412yes—
613C22×C4C23×C412yes—
614C22×C4C22×D414yes—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×Q812yes—
627C22×C4C22×Q814yes—
628C22×C4C22×Q812yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C42−1+412yes—
640C4⋊C4—216no—
641C4⋊C4—216no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—84no—
655C4⋊C4—84no—
656C4⋊C4—88no—
657C4⋊C4C2×C4⋊C4116yescomplemented
658C4⋊C4#121116yesdirect product factor
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—48no—
663C22⋊C4—416no—
664C22⋊C4—416no—
665C22⋊C4—416no—
666C22⋊C4—416no—
667C22⋊C4C2×C4⋊C4132yescomplemented
668C42—28no—
669C42—28no—
670C42—28no—
671C42—216no—
672C42—216no—
673C42—48no—
674C42—48no—
675C42—416no—
676C42—48no—
677C42C4×D4116yescomplemented
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23C22×C4⋊C418yes—
741C23C22×C4⋊C414yes—
742C23C2×C4×D414yes—
743C23#52014yes—
744C23D4214yes—
745C23#54714yes—
746C23D4×Q814yes—
747C23#55414yes—
748C23C24×C411yescharacteristic
749C23C23×D411yescharacteristic
750C23C23×D411yescharacteristic
751C23C23×D411yescharacteristic
752C23C23×Q811yescharacteristic
753C23C22×#4111yescharacteristic
754C23C22×#4111yescharacteristic
755C23C22×#4111yescharacteristic
756C23C22×#4111yescharacteristic
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×H(5,𝔽2)11yescharacteristic
759C23C2×2−1+411yescharacteristic
760C23C2×2−1+411yescharacteristic
761C23#58511yescharacteristic
762C23#58511yescharacteristic
763D4—264no—
764D4—232no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—232no—
796C2×C4—232no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—416no—
816C2×C4—432no—
817C2×C4—432no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—432no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—832no—
858C2×C4C22×C4⋊C414yes—
859C2×C4C22×C4⋊C418yes—
860C2×C4C22×C4⋊C414yes—
861C2×C4C2×C4×D414yes—
862C2×C4C2×C4×D414yes—
863C2×C4C2×C4×D414yes—
864C2×C4C2×C4×D414yes—
865C2×C4C2×C4×D414yes—
866C2×C4C4×#4114yes—
867C2×C4#52014yes—
868C2×C4C2×#12118yes—
869C2×C4C2×#12114yes—
870C2×C4#52514yes—
871C2×C4#52914yes—
872C2×C4#53214yes—
873C2×C4D4214yes—
874C2×C4#54714yes—
875C2×C4D4×Q814yes—
876C2×C4#55414yes—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—28no—
892C22—28no—
893C22—28no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22D4×C4⋊C418yescomplemented
907C22C23×C4⋊C411yescharacteristic
908C22C22×C4×D411yescharacteristic
909C22C22×C4×D411yescharacteristic
910C22C2×C4×#4111yescharacteristic
911C22C2×#52011yescharacteristic
912C22C2×#52011yescharacteristic
913C22#342811yescharacteristic
914C22C22×#12111yescharacteristic
915C22C2×#52511yescharacteristic
916C22C2×#52911yescharacteristic
917C22C2×#53211yescharacteristic
918C22C2×D4211yescharacteristic
919C22C2×D4211yescharacteristic
920C22C2×#54711yescharacteristic
921C22C2×#54711yescharacteristic
922C22C2×D4×Q811yescharacteristic
923C22C2×D4×Q811yescharacteristic
924C22D4×#4111yescharacteristic
925C22D4×#4111yescharacteristic
926C22C2×#55411yescharacteristic
927C22C2×#55411yescharacteristic
928C22Q8×#4111yescharacteristic
929C22Q8×#4111yescharacteristic
930C22#348811yescharacteristic
931C22#348911yescharacteristic
932C22#349411yescharacteristic
933C22#349511yescharacteristic
934C22#349611yescharacteristic
935C22#349711yescharacteristic
936C22#350611yescharacteristic
937C22#350711yescharacteristic
938C22#351911yescharacteristic
939C22#352011yescharacteristic
940C22#352211yescharacteristic
941C22#352311yescharacteristic
942C4—24no—
943C4—28no—
944C4—24no—
945C4—24no—
946C4—28no—
947C4—44no—
948C4—44no—
949C4—42no—
950C4—44no—
951C4—44no—
952C4—44no—
953C4—84no—
954C4—84no—
955C4C4×#12118yescomplemented
956C4D4×C4⋊C418yescomplemented
957C2—28no—
958C2—48no—
959C2C2×C4×#12111yescharacteristic
960C2C2×D4×C4⋊C411yescharacteristic
961C2C2×D4×C4⋊C411yescharacteristic
962C2C4⋊C4×#4111yescharacteristic
963C2#3420211yescharacteristic
964C2#3420611yescharacteristic
965C2#3424311yescharacteristic
966C2D4×#12111yescharacteristic
967C2#3610011yescharacteristic
968C2#3611611yescharacteristic
969C2#3612611yescharacteristic
970C2Q8×#12111yescharacteristic
971C2#3654411yescharacteristic
972C2#3655111yescharacteristic
973C2#3656111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×D4×C4⋊C4C2semidirect
2. C2×D4×C4⋊C4C2semidirect
5. C22×C4×C4⋊C4C2semidirect
6. #14697C2semidirect
7. #14686C2semidirect
8. #14112C2semidirect
9. #14046C2semidirect
10. #14018C2semidirect
11. #13975C2semidirect
12. #13910C2semidirect
13. #13906C2semidirect
14. #13876C2semidirect
15. #13872C2semidirect
16. C4⋊C42C2semidirect
17. C22⋊C4×C4⋊C4C2semidirect
31. C4×#121C4semidirect
110. C2×C4×D4C2×C4semidirect
111. C2×C4×D4C2×C4semidirect
120. C22×C4⋊C4D4semidirect
154. C22×C42C2×C4semidirect
166. #390C2×C4semidirect
171. #389C2×C4semidirect
173. #388C2×C4semidirect
175. #386C2×C4semidirect
188. #380C2×C4semidirect
196. C4×C4⋊C4C2×C4semidirect
197. C4×C4⋊C4D4semidirect
199. C4×C22⋊C4C2×C4semidirect
299. #121C4⋊C4direct (N × H)
484. C2×D4C2×C4⋊C4semidirect
485. C2×D4C2×C4⋊C4semidirect
603. C22×C4C2×C4⋊C4semidirect
604. C22×C4C4×D4semidirect
657. C4⋊C4C2×C4⋊C4semidirect
658. C4⋊C4#121direct (N × H)
667. C22⋊C4C2×C4⋊C4semidirect
677. C42C4×D4semidirect
906. C22D4×C4⋊C4semidirect
955. C4C4×#121semidirect
956. C4D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×C4×#1212
C22×C4×C4⋊C42
#146972
#146862
#141122
#140462
#140182
#139752
#139102
#139062
#138762
#138722
C4⋊C422
C22⋊C4×C4⋊C42