Finite Group Databasebeta

← #6607056

Subgroups — #6607056

Order 512.

2401 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3349C211yesmaximal, characteristic, complemented
2C2×#3313C211yesmaximal, characteristic, complemented
3C2×#3310C211yesmaximal, characteristic, complemented
4C2×#3265C211yesmaximal, characteristic
5#38957C211yesmaximal, characteristic, complemented
6#38946C211yesmaximal, characteristic, complemented
7#33251C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28545C211yesmaximal, characteristic, complemented
11#28481C211yesmaximal, characteristic, complemented
12#28431C211yesmaximal, characteristic, complemented
13#28426C211yesmaximal, characteristic, complemented
14#28386C211yesmaximal, characteristic, complemented
15#28379C211yesmaximal, characteristic, complemented
16#28367C211yesmaximal, characteristic, complemented
17#28357C211yesmaximal, characteristic, complemented
18#28351C211yesmaximal, characteristic, complemented
19#28342C211yesmaximal, characteristic, complemented
20#28327C211yesmaximal, characteristic, complemented
21#28324C211yesmaximal, characteristic, complemented
22#28321C211yesmaximal, characteristic, complemented
23#28320C211yesmaximal, characteristic, complemented
24#27945C211yesmaximal, characteristic, complemented
25#27935C211yesmaximal, characteristic, complemented
26#25796C211yesmaximal, characteristic, complemented
27#25784C211yesmaximal, characteristic, complemented
28#21702C211yesmaximal, characteristic, complemented
29#21235C211yesmaximal, characteristic, complemented
30#21231C211yesmaximal, characteristic, complemented
31#20488C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#552C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×D42C2211yescharacteristic
38#3349—28no—
39#3313—28no—
40#3310—28no—
41#3265—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#497C2211yescharacteristic, complemented
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic, complemented
47C2×#490C2211yescharacteristic
48C2×#489C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic, complemented
50C2×#485C2211yescharacteristic, complemented
51C2×#485C2211yescharacteristic, complemented
52C2×#485C2211yescharacteristic, complemented
53C2×#485C2211yescharacteristic, complemented
54C2×#482C2211yescharacteristic
55C2×#482C2211yescharacteristic, complemented
56C2×#480C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#477C2211yescharacteristic, complemented
60C2×#478C2211yescharacteristic
61C2×#470C2211yescharacteristic, complemented
62C2×#468C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic, complemented
65C2×#467C2211yescharacteristic, complemented
66C2×#467C2211yescharacteristic, complemented
67C2×#466C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic, complemented
70C2×#460C2211yescharacteristic
71C2×#460C2211yescharacteristic
72C2×#463C2211yescharacteristic
73C2×#452C2211yescharacteristic, complemented
74C2×#449C2211yescharacteristic
75C2×#451C2211yescharacteristic, complemented
76C2×#448C2211yescharacteristic
77C2×#450C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#441C2211yescharacteristic, complemented
82C2×#441C2211yescharacteristic, complemented
83C2×#440C2211yescharacteristic
84C2×#440C2211yescharacteristic
85C2×#435C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic, complemented
88C2×#427C2211yescharacteristic, complemented
89C2×#419C2211yescharacteristic, complemented
90C2×#418C2211yescharacteristic
91C2×#416C2211yescharacteristic, complemented
92C22×#102C2211yescharacteristic
93C2×#405C2211yescharacteristic, complemented
94C2×#405C2211yescharacteristic, complemented
95#2861C2211yescharacteristic, complemented
96#2858C2211yescharacteristic
97#2704—22no—
98#2701—22no—
99#2685—22no—
100#2685—22no—
101#2621C2211yescharacteristic, complemented
102#2620C2211yescharacteristic
103#2620C2211yescharacteristic
104#2620C2211yescharacteristic, complemented
105#2565C2211yescharacteristic, complemented
106#2548C2211yescharacteristic
107#2545C2211yescharacteristic, complemented
108#2542C2211yescharacteristic
109#2502C2211yescharacteristic, complemented
110#2500C2211yescharacteristic
111#2500C2211yescharacteristic
112#2500C2211yescharacteristic, complemented
113#2474—22no—
114#2468—22no—
115#2435—22no—
116#2435C2211yescharacteristic
117#2435C2211yescharacteristic
118#2434C2211yescharacteristic, complemented
119#2432C2211yescharacteristic, complemented
120#2426—22no—
121#2311C2211yescharacteristic, complemented
122#2310C2211yescharacteristic, complemented
123#2309C2211yescharacteristic
124#2309C2211yescharacteristic
125C4×C4⋊Q8C2211yescharacteristic, complemented
126C4×#124C2211yescharacteristic
127#2293C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2096C2211yescharacteristic, complemented
130#2095C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2094C2211yescharacteristic, complemented
133#2093C2211yescharacteristic
134#2093C2211yescharacteristic, complemented
135#2093C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2013C2211yescharacteristic
145#2013C2211yescharacteristic, complemented
146#2013C2211yescharacteristic, complemented
147#2013C2211yescharacteristic, complemented
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic, complemented
151#2012C2211yescharacteristic, complemented
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1973C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic, complemented
165#1972C2211yescharacteristic, complemented
166#1972C2211yescharacteristic, complemented
167#1971C2211yescharacteristic, complemented
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic, complemented
170#1970C2211yescharacteristic, complemented
171#1969C2211yescharacteristic, complemented
172#1969C2211yescharacteristic, complemented
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic, complemented
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1960C2211yescharacteristic, complemented
181#1959C2211yescharacteristic
182#1959C2211yescharacteristic, complemented
183#1959C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1767C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1753C2211yescharacteristic, complemented
194#1752C2211yescharacteristic, complemented
195#1752C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197#1750C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4—21no—
202C23×D4C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16—24no—
211C22×SD16—24no—
212C22×SD16—42no—
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C23×C8C2311yescharacteristic
229C23×C8C2311yescharacteristic
230#556—24no—
231#556—24no—
232#552—24no—
233#552—24no—
234#548—24no—
235#548—24no—
236D42—24no—
237D42—24no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#126—21no—
243C2×#126—21no—
244C2×#126—21no—
245C2×#125—21no—
246C2×#125C2311yescharacteristic
247C2×#124—21no—
248C2×#124—21no—
249C2×#124—22no—
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#123—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—22no—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×#121—21no—
264C2×#121—21no—
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×#120—21no—
270C2×C4×Q8—21no—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×D4—21no—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284#501—24no—
285#497—24no—
286#497—42no—
287#496—24no—
288#495—42no—
289#490—24no—
290#489—24no—
291#485—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#484—24no—
296#482—24no—
297#482—24no—
298#480—24no—
299#479—24no—
300#478—24no—
301#477—24no—
302#477—24no—
303#470—24no—
304#468—24no—
305#468—24no—
306#468—24no—
307#467—24no—
308#467—24no—
309#466—24no—
310#465—24no—
311#464—24no—
312#463—24no—
313#460—24no—
314#460—24no—
315#452—24no—
316#451—24no—
317#450—24no—
318#450—24no—
319#450—24no—
320#449—24no—
321#448—24no—
322#447—24no—
323#441—24no—
324#441—24no—
325#440—24no—
326#440—24no—
327#435D418yes—
328#435D418yes—
329#428—24no—
330#427—24no—
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×C4⋊C8C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349#419—24no—
350#418—24no—
351#416—24no—
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#102—24no—
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×C22⋊C8C2311yescharacteristic
386C2×C22⋊C8C2311yescharacteristic
387C2×C22⋊C8C2311yescharacteristic
388C2×C22⋊C8C2311yescharacteristic
389#405—42no—
390#405—42no—
391C2×#97C2311yescharacteristic
392C2×#97C2311yescharacteristic
393C2×#97C2311yescharacteristic
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403#399—22no—
404#398—22no—
405#398—22no—
406#398—22no—
407#397—22no—
408#396—22no—
409#396—22no—
410#396—22no—
411#396—22no—
412#395—22no—
413#394—22no—
414#394—22no—
415#394—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#391—22no—
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#390—22no—
433#390—22no—
434#390—22no—
435#390—22no—
436#390D412yes—
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#389—22no—
450#389D412yes—
451#388—22no—
452#388—22no—
453#388—22no—
454#388—22no—
455#388—22no—
456#388—22no—
457#388—22no—
458#388D412yes—
459#388D412yes—
460#387—22no—
461#386—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#381—22no—
472#380—22no—
473#379—22no—
474#379—22no—
475#379—22no—
476#379—22no—
477C4×C4⋊C4—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—22no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C43C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—44no—
530C22×D4—84no—
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542AGL(1,ℤ/8)—416no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—416no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16#4114yes—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—41no—
595C2×M16—41no—
596C2×M16C2×D414yes—
597C2×M16C2×D414yes—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8—41no—
602C22×C8C2×D414yes—
603C22×C8C2×D414yes—
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614C4⋊Q8—22no—
615C4⋊Q8—41no—
616C4⋊Q8—41no—
617C4⋊Q8—41no—
618#127—22no—
619#127—22no—
620#126—44no—
621#126—44no—
622#126—44no—
623#125—22no—
624#125—22no—
625#125—44no—
626#124—22no—
627#124—22no—
628#124—22no—
629#124—41no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—44no—
637#124—44no—
638#124—84no—
639#123—44no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—44no—
651C22⋊Q8—84no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—44no—
659#121—44no—
660#120—44no—
661#120—44no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×Q8—44no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—44no—
672C4×D4C2×D414yes—
673C4×D4C2×D414yes—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—22no—
678#117—22no—
679#117—22no—
680#117—41no—
681#117—41no—
682#117—41no—
683#117—41no—
684#117—44no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D412yes—
707C2×C4⋊C4C2×D412yes—
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D412yes—
750C2×C22⋊C4C2×D412yes—
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42C2×D412yes—
760C2×C42C2×D412yes—
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—22no—
775#107—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779#106—22no—
780#106—22no—
781#106—22no—
782C4⋊C8C2×D414yes—
783C4⋊C8C2×D414yes—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820#97—22no—
821#97—22no—
822#97—41no—
823#97—41no—
824#97—41no—
825#97—41no—
826#97C2×D414yes—
827#97C2×D414yes—
828C4×C8—22no—
829C4×C8—22no—
830C4×C8—41no—
831C4×C8—41no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—81no—
854C24—81no—
855C24—82no—
856C24—82no—
857C24—82no—
858C24—82no—
859C24C22×D411yescharacteristic
860C24C22×D411yescharacteristic
861#41—44no—
862#41—44no—
863#41—82no—
864#41—82no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—81no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8C2×#4112yes—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—82no—
939C2×D4—82no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—81no—
949C2×D4—816no—
950C2×D4#12714yes—
951C2×D4C2×#4112yes—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—81no—
980C22×C4—82no—
981C22×C4—81no—
982C22×C4C22×D412yes—
983C22×C4C22×D412yes—
984C22×C4C22×D412yes—
985C22×C4C22×D412yes—
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D412yes—
991C22×C4C22×D412yes—
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C2511yescharacteristic
995Q16—44no—
996Q16—44no—
997Q16—82no—
998SD16—28no—
999SD16—44no—
1000SD16—44no—
1001SD16—44no—
1002SD16—44no—
1003SD16—44no—
1004SD16—82no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008D8—44no—
1009D8—44no—
1010D8—82no—
1011M16—28no—
1012M16—44no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—28no—
1028C2×C8—44no—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C2×#4112yes—
1038C2×C8H(5,𝔽2)12yes—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—82no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4—82no—
1075C4⋊C4—82no—
1076C4⋊C4#12714yes—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—82no—
1098C22⋊C4—82no—
1099C22⋊C4—82no—
1100C22⋊C4—82no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4#12714yes—
1112C22⋊C4#12714yes—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42C22×D412yes—
1130C42C22×D412yes—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—42no—
1141C23—42no—
1142C23—41no—
1143C23—41no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—84no—
1160C23—84no—
1161C23—84no—
1162C23—84no—
1163C23—162no—
1164C23—162no—
1165C23—164no—
1166C23—164no—
1167C23—164no—
1168C23—164no—
1169C23C2×#12712yes—
1170C23C2×#12712yes—
1171C23C23×D411yescharacteristic
1172Q8—22no—
1173Q8—22no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—84no—
1189Q8—84no—
1190D4—22no—
1191D4—22no—
1192D4—44no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—84no—
1212D4—84no—
1213D4—84no—
1214D4—162no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4C2×#12712yes—
1274C2×C4C2×#12712yes—
1275C2×C4C2×#12712yes—
1276C2×C4C2×#12712yes—
1277C2×C4C23×D411yescharacteristic
1278C2×C4C23×D411yescharacteristic
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—22no—
1284C8—22no—
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—22no—
1290C8#54614yes—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—42no—
1303C22—82no—
1304C22—81no—
1305C22—81no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22—168no—
1323C22C22×#12711yescharacteristic
1324C22D4×#4111yescharacteristic
1325C22#349611yescharacteristic
1326C22#358512yes—
1327C22#358612yes—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4C2×#54611yescharacteristic
1349C4D4×#4111yescharacteristic
1350C4#349611yescharacteristic
1351C4#350011yescharacteristic
1352C2—42no—
1353C2—42no—
1354C2—82no—
1355C2—161no—
1356C2—161no—
1357C2—161no—
1358C2#3626011yescharacteristic
1359C2#6064411yescharacteristic
1360C2#6065111yescharacteristic
1361C2#6151312yes—
1362C2#6233312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3265C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3349C2semidirect
2. C2×#3313C2semidirect
3. C2×#3310C2semidirect
5. #38957C2semidirect
6. #38946C2semidirect
7. #33251C2semidirect
8. #33188C2semidirect
9. #33182C2semidirect
10. #28545C2semidirect
11. #28481C2semidirect
12. #28431C2semidirect
13. #28426C2semidirect
14. #28386C2semidirect
15. #28379C2semidirect
16. #28367C2semidirect
17. #28357C2semidirect
18. #28351C2semidirect
19. #28342C2semidirect
20. #28327C2semidirect
21. #28324C2semidirect
22. #28321C2semidirect
23. #28320C2semidirect
24. #27945C2semidirect
25. #27935C2semidirect
26. #25796C2semidirect
27. #25784C2semidirect
28. #21702C2semidirect
29. #21235C2semidirect
30. #21231C2semidirect
31. #20488C2semidirect
42. C2×#501C22semidirect
44. C2×#497C22semidirect
46. C2×#495C22semidirect
48. C2×#489C22semidirect
49. C2×#484C22semidirect
50. C2×#485C22semidirect
51. C2×#485C22semidirect
52. C2×#485C22semidirect
53. C2×#485C22semidirect
55. C2×#482C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
59. C2×#477C22semidirect
61. C2×#470C22semidirect
64. C2×#468C22semidirect
65. C2×#467C22semidirect
66. C2×#467C22semidirect
69. C2×#464C22semidirect
73. C2×#452C22semidirect
75. C2×#451C22semidirect
81. C2×#441C22semidirect
82. C2×#441C22semidirect
87. C2×#428C22semidirect
88. C2×#427C22semidirect
89. C2×#419C22semidirect
91. C2×#416C22semidirect
93. C2×#405C22semidirect
94. C2×#405C22semidirect
95. #2861C22semidirect
101. #2621C22semidirect
104. #2620C22semidirect
105. #2565C22semidirect
107. #2545C22semidirect
109. #2502C22semidirect
112. #2500C22semidirect
118. #2434C22semidirect
119. #2432C22semidirect
121. #2311C22semidirect
122. #2310C22semidirect
125. C4×C4⋊Q8C22semidirect
128. #2097C22semidirect
129. #2096C22semidirect
130. #2095C22semidirect
131. #2095C22semidirect
132. #2094C22semidirect
134. #2093C22semidirect
135. #2093C22semidirect
136. #2093C22semidirect
138. #2092C22semidirect
139. #2092C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
145. #2013C22semidirect
146. #2013C22semidirect
147. #2013C22semidirect
150. #2012C22semidirect
151. #2012C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
162. #1973C22semidirect
164. #1972C22semidirect
165. #1972C22semidirect
166. #1972C22semidirect
167. #1971C22semidirect
169. #1970C22semidirect
170. #1970C22semidirect
171. #1969C22semidirect
172. #1969C22semidirect
176. #1968C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
180. #1960C22semidirect
182. #1959C22semidirect
183. #1959C22semidirect
184. #1958C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1767C22semidirect
192. #1753C22semidirect
193. #1753C22semidirect
194. #1752C22semidirect
195. #1752C22semidirect
196. #1750C22semidirect
197. #1750C22semidirect
198. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33492
C2×#33132
C2×#33102
C2×#32652
#389572
#389462
#332512
#331882
#331822
#285452
#284812
#284312
#284262
#283862
#283792
#283672
#283572
#283512
#283422
#283272
#283242
#283212
#283202
#279452
#279352
#257962
#257842
#217022
#212352
#212312
#204882