Finite Group Databasebeta

← #6607064

Subgroups — #6607064

Order 512.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3343C211yesmaximal, characteristic, complemented
2C2×#3315C211yesmaximal, characteristic, complemented
3C2×#3306C211yesmaximal, characteristic, complemented
4C2×#3267C211yesmaximal, characteristic, complemented
5#38951C211yesmaximal, characteristic, complemented
6#38947C211yesmaximal, characteristic, complemented
7#33250C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33181C211yesmaximal, characteristic, complemented
10#28548C211yesmaximal, characteristic, complemented
11#28476C211yesmaximal, characteristic, complemented
12#28429C211yesmaximal, characteristic, complemented
13#28426C211yesmaximal, characteristic, complemented
14#28384C211yesmaximal, characteristic, complemented
15#28378C211yesmaximal, characteristic, complemented
16#28362C211yesmaximal, characteristic, complemented
17#28354C211yesmaximal, characteristic, complemented
18#28352C211yesmaximal, characteristic, complemented
19#28342C211yesmaximal, characteristic, complemented
20#28328C211yesmaximal, characteristic, complemented
21#28327C211yesmaximal, characteristic, complemented
22#28326C211yesmaximal, characteristic, complemented
23#28321C211yesmaximal, characteristic, complemented
24#27940C211yesmaximal, characteristic, complemented
25#27938C211yesmaximal, characteristic, complemented
26#25793C211yesmaximal, characteristic, complemented
27#25787C211yesmaximal, characteristic, complemented
28#21701C211yesmaximal, characteristic, complemented
29#21235C211yesmaximal, characteristic, complemented
30#21230C211yesmaximal, characteristic, complemented
31#20488C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×#547C2211yescharacteristic
36C2×#547C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3343—28no—
39#3315—28no—
40#3306—28no—
41#3267—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#497C2211yescharacteristic, complemented
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#491C2211yescharacteristic, complemented
48C2×#489C2211yescharacteristic
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic, complemented
51C2×#481C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#483C2211yescharacteristic, complemented
56C2×#480C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#478C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic, complemented
63C2×#469C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#467C2211yescharacteristic
66C2×#465C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#462C2211yescharacteristic, complemented
70C2×#463C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#452C2211yescharacteristic, complemented
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic
82C2×#442C2211yescharacteristic
83C2×#440C2211yescharacteristic, complemented
84C2×#440C2211yescharacteristic, complemented
85C2×#435C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C22×#107C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic
90C2×#417C2211yescharacteristic, complemented
91C2×#416C2211yescharacteristic
92C22×#102C2211yescharacteristic
93C2×#405C2211yescharacteristic
94C2×#405C2211yescharacteristic, complemented
95#2862C2211yescharacteristic, complemented
96#2861C2211yescharacteristic
97#2707—22no—
98#2706—22no—
99#2706—22no—
100#2697—22no—
101#2621C2211yescharacteristic
102#2620C2211yescharacteristic
103#2620C2211yescharacteristic
104#2620C2211yescharacteristic, complemented
105#2566C2211yescharacteristic
106#2547C2211yescharacteristic, complemented
107#2545C2211yescharacteristic
108#2542C2211yescharacteristic, complemented
109#2504C2211yescharacteristic
110#2502C2211yescharacteristic
111#2502C2211yescharacteristic, complemented
112#2499C2211yescharacteristic
113#2480—22no—
114#2476—22no—
115#2435C2211yescharacteristic
116#2432C2211yescharacteristic
117#2431C2211yescharacteristic
118#2431C2211yescharacteristic, complemented
119#2417—22no—
120#2407—22no—
121#2311C2211yescharacteristic
122#2311C2211yescharacteristic
123#2311C2211yescharacteristic, complemented
124#2309C2211yescharacteristic
125C4×#127C2211yescharacteristic, complemented
126C4×#124C2211yescharacteristic
127#2293C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2093C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic, complemented
146#2013C2211yescharacteristic, complemented
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1972C2211yescharacteristic
162#1972C2211yescharacteristic
163#1972C2211yescharacteristic
164#1971C2211yescharacteristic, complemented
165#1971C2211yescharacteristic, complemented
166#1971C2211yescharacteristic, complemented
167#1971C2211yescharacteristic, complemented
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic
170#1970C2211yescharacteristic
171#1970C2211yescharacteristic
172#1969C2211yescharacteristic, complemented
173#1969C2211yescharacteristic, complemented
174#1969C2211yescharacteristic, complemented
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1961C2211yescharacteristic, complemented
181#1959C2211yescharacteristic
182#1959C2211yescharacteristic
183#1959C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1767C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic, complemented
194#1752C2211yescharacteristic
195#1752C2211yescharacteristic, complemented
196#1750C2211yescharacteristic
197#1750C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41—21no—
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×#135—24no—
208C2×#135—24no—
209C2×#135—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C23×C8C2311yescharacteristic
229C23×C8C2311yescharacteristic
230#552—24no—
231#552—24no—
232#547—24no—
233#547—24no—
234#547—24no—
235#547—24no—
236#546—24no—
237#546—24no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#126—21no—
243C2×#125—21no—
244C2×#125C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#123—21no—
251C2×#123—21no—
252C2×#123—21no—
253C2×#123—21no—
254C2×#123—21no—
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×C4×Q8C2311yescharacteristic
270C2×C4×D4—22no—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—21no—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C22⋊C4—21no—
284#501—24no—
285#497—24no—
286#497—42no—
287#496—24no—
288#495—42no—
289#491—24no—
290#489—24no—
291#485—24no—
292#484—24no—
293#484—24no—
294#483—24no—
295#483—24no—
296#482—24no—
297#481—24no—
298#480—24no—
299#478—24no—
300#478—24no—
301#477—24no—
302#476—24no—
303#470—24no—
304#470—24no—
305#469—24no—
306#468—24no—
307#467—24no—
308#465—24no—
309#465—24no—
310#465—24no—
311#463—24no—
312#463—24no—
313#462—24no—
314#461—24no—
315#452—24no—
316#452—24no—
317#452—24no—
318#452—24no—
319#450—24no—
320#449—24no—
321#449—24no—
322#447—24no—
323#442—24no—
324#442—24no—
325#440—24no—
326#440—24no—
327#435D418yescomplemented
328#435D418yescomplemented
329#428—24no—
330C2×#107—24no—
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×C4⋊C8C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349#417—24no—
350#417—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#397—22no—
409#397—22no—
410#397—22no—
411#396—22no—
412#396—22no—
413#396—22no—
414#396—22no—
415#396—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#392—22no—
422#392—22no—
423#391—22no—
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
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#389D412yes—
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388D412yes—
453#388D412yes—
454#387—22no—
455#386—22no—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#382—22no—
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#380—22no—
473#380—22no—
474#380—22no—
475#380—22no—
476#379—22no—
477#379—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—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—84no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545AGL(1,ℤ/8)—416no—
546#135—416no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
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—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—22no—
590C2×D8—41no—
591C2×D8—41no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8#4114yescomplemented
595C2×M16—22no—
596C2×M16—22no—
597C2×M16—41no—
598C2×M16—41no—
599C2×M16C2×D414yes—
600C2×M16C2×D414yes—
601C22×C8—22no—
602C22×C8—22no—
603C22×C8—41no—
604C22×C8—41no—
605C22×C8C2×D414yes—
606C22×C8C2×D414yes—
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C4⋊Q8—22no—
616C4⋊Q8—22no—
617C4⋊Q8—22no—
618C4⋊Q8—22no—
619C4⋊Q8—41no—
620C4⋊Q8—41no—
621#127—22no—
622#127—41no—
623#126—44no—
624#125—22no—
625#125—22no—
626#125—44no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—41no—
637#123—44no—
638#123—44no—
639#123—44no—
640#123—44no—
641#123—44no—
642#123—44no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—44no—
654C22⋊Q8—84no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—22no—
660#121—22no—
661#121—44no—
662#121—44no—
663#120—44no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×D4—22no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—84no—
673C4×D4C2×D414yes—
674C4×D4C2×D414yes—
675#117—22no—
676#117—22no—
677#117—41no—
678#117—41no—
679#117—41no—
680#117—41no—
681#117—44no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
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—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—44no—
708C2×C4⋊C4C2×D412yes—
709C2×C4⋊C4C2×D412yes—
710C2×C4⋊C4C2×D412yes—
711C2×C4⋊C4C2×D411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
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—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
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⋊C4—22no—
748C2×C22⋊C4—44no—
749C2×C22⋊C4C2×D412yes—
750C2×C22⋊C4C2×D412yes—
751C2×C22⋊C4C2×D412yes—
752C2×C22⋊C4C2×D412yes—
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C42—21no—
756C2×C42—21no—
757C2×C42C2×D412yes—
758C2×C42C2×D412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779#106—22no—
780C4⋊C8C2×D414yes—
781C4⋊C8C2×D414yes—
782#103—22no—
783#103—22no—
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#102—22no—
799#102—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—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818#97—22no—
819#97—22no—
820#97—41no—
821#97—41no—
822#97—41no—
823#97—41no—
824#97C2×D414yes—
825#97C2×D414yes—
826C4×C8—22no—
827C4×C8—22no—
828C4×C8—41no—
829C4×C8—41no—
830#95—22no—
831#95—22no—
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—81no—
852C24—82no—
853C24—82no—
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—44no—
861#41—44no—
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867#41—82no—
868#41—816no—
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—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—44no—
894C2×Q8—42no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
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—44no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—82no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4#12714yes—
944C2×D4C2×#4112yes—
945C2×D4C2×#4112yes—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
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—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—82no—
984C22×C4—82no—
985C22×C4—82no—
986C22×C4—82no—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D412yes—
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C22×D412yes—
998C22×C4C22×D412yes—
999C22×C4C2511yescharacteristic
1000Q16—44no—
1001Q16—82no—
1002Q16—82no—
1003Q16—82no—
1004SD16—44no—
1005SD16—44no—
1006SD16—44no—
1007SD16—44no—
1008SD16—44no—
1009SD16—44no—
1010SD16—82no—
1011SD16—82no—
1012D8—28no—
1013D8—44no—
1014D8—44no—
1015D8—82no—
1016M16—28no—
1017M16—44no—
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—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—28no—
1033C2×C8—44no—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C2×C8C22×D412yes—
1040C2×C8C22×D412yes—
1041C2×C8C22×D412yes—
1042C2×C8C2×#4112yes—
1043C2×C8H(5,𝔽2)12yes—
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—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
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—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4#12714yes—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
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—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
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—82no—
1112C22⋊C4—82no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4#12714yes—
1116C22⋊C4#12714yes—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
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—22no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—84no—
1160C23—84no—
1161C23—162no—
1162C23—164no—
1163C23—164no—
1164C23C2×#12712yes—
1165C23C2×#12712yes—
1166C23C23×D411yescharacteristic
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—84no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—44no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—84no—
1202D4—88no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—162no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
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—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
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—84no—
1264C2×C4—84no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—162no—
1272C2×C4C2×#12712yes—
1273C2×C4C2×#12712yes—
1274C2×C4C2×#12712yes—
1275C2×C4C2×#12712yes—
1276C2×C4C23×D411yescharacteristic
1277C2×C4C23×D411yescharacteristic
1278C2×C4C22×#4111yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C8—22no—
1283C8—22no—
1284C8—22no—
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8#54614yes—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—44no—
1301C22—44no—
1302C22—42no—
1303C22—42no—
1304C22—82no—
1305C22—82no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—82no—
1311C22—82no—
1312C22—82no—
1313C22—82no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—168no—
1321C22C22×#12711yescharacteristic
1322C22D4×#4111yescharacteristic
1323C22#349611yescharacteristic
1324C22#358512yes—
1325C22#358612yes—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4C2×#54611yescharacteristic
1347C4D4×#4111yescharacteristic
1348C4#349611yescharacteristic
1349C4#350011yescharacteristic
1350C2—42no—
1351C2—42no—
1352C2—82no—
1353C2—82no—
1354C2—161no—
1355C2—161no—
1356C2#3626011yescharacteristic
1357C2#6064411yescharacteristic
1358C2#6065111yescharacteristic
1359C2#6151012yes—
1360C2#6233812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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×#3343C2semidirect
2. C2×#3315C2semidirect
3. C2×#3306C2semidirect
4. C2×#3267C2semidirect
5. #38951C2semidirect
6. #38947C2semidirect
7. #33250C2semidirect
8. #33188C2semidirect
9. #33181C2semidirect
10. #28548C2semidirect
11. #28476C2semidirect
12. #28429C2semidirect
13. #28426C2semidirect
14. #28384C2semidirect
15. #28378C2semidirect
16. #28362C2semidirect
17. #28354C2semidirect
18. #28352C2semidirect
19. #28342C2semidirect
20. #28328C2semidirect
21. #28327C2semidirect
22. #28326C2semidirect
23. #28321C2semidirect
24. #27940C2semidirect
25. #27938C2semidirect
26. #25793C2semidirect
27. #25787C2semidirect
28. #21701C2semidirect
29. #21235C2semidirect
30. #21230C2semidirect
31. #20488C2semidirect
42. C2×#501C22semidirect
44. C2×#497C22semidirect
47. C2×#491C22semidirect
50. C2×#484C22semidirect
55. C2×#483C22semidirect
56. C2×#480C22semidirect
57. C2×#477C22semidirect
58. C2×#478C22semidirect
59. C2×#478C22semidirect
62. C2×#470C22semidirect
68. C2×#465C22semidirect
69. C2×#462C22semidirect
76. C2×#452C22semidirect
83. C2×#440C22semidirect
84. C2×#440C22semidirect
88. C22×#107C22semidirect
90. C2×#417C22semidirect
94. C2×#405C22semidirect
95. #2862C22semidirect
104. #2620C22semidirect
106. #2547C22semidirect
108. #2542C22semidirect
111. #2502C22semidirect
118. #2431C22semidirect
123. #2311C22semidirect
125. C4×#127C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2096C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
135. #2094C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
144. #2015C22semidirect
145. #2014C22semidirect
146. #2013C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
164. #1971C22semidirect
165. #1971C22semidirect
166. #1971C22semidirect
167. #1971C22semidirect
172. #1969C22semidirect
173. #1969C22semidirect
174. #1969C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
180. #1961C22semidirect
183. #1959C22semidirect
184. #1958C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1844C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1767C22semidirect
193. #1753C22semidirect
195. #1752C22semidirect
197. #1750C22semidirect
198. C4×#97C22semidirect
327. #435D4semidirect
328. #435D4semidirect
594. C2×D8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33432
C2×#33152
C2×#33062
C2×#32672
#389512
#389472
#332502
#331882
#331812
#285482
#284762
#284292
#284262
#283842
#283782
#283622
#283542
#283522
#283422
#283282
#283272
#283262
#283212
#279402
#279382
#257932
#257872
#217012
#212352
#212302
#204882