Finite Group Databasebeta

← #6606906

Subgroups — #6606906

Order 512.

2395 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3313C211yesmaximal, characteristic, complemented
2C2×#3311C211yesmaximal, characteristic, complemented
3C2×#3308C211yesmaximal, characteristic, complemented
4C2×#3306C211yesmaximal, characteristic, complemented
5#39488C211yesmaximal, characteristic, complemented
6#39357C211yesmaximal, characteristic, complemented
7#33230C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33187C211yesmaximal, characteristic, complemented
10#28519C211yesmaximal, characteristic, complemented
11#28446C211yesmaximal, characteristic, complemented
12#28436C211yesmaximal, characteristic, complemented
13#28430C211yesmaximal, characteristic, complemented
14#28426C211yesmaximal, characteristic, complemented
15#28424C211yesmaximal, characteristic, complemented
16#28363C211yesmaximal, characteristic, complemented
17#28362C211yesmaximal, characteristic, complemented
18#28360C211yesmaximal, characteristic, complemented
19#28357C211yesmaximal, characteristic, complemented
20#28351C211yesmaximal, characteristic, complemented
21#28349C211yesmaximal, characteristic, complemented
22#28347C211yesmaximal, characteristic, complemented
23#28342C211yesmaximal, characteristic, complemented
24#27923C211yesmaximal, characteristic, complemented
25#27922C211yesmaximal, characteristic, complemented
26#25737C211yesmaximal, characteristic, complemented
27#25736C211yesmaximal, characteristic, complemented
28#21693C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30#21205C211yesmaximal, characteristic, complemented
31#20488C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#535C2211yescharacteristic
38#3313—28no—
39#3311—28no—
40#3308—28no—
41#3306—28no—
42C2×#497C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#489C2211yescharacteristic
46C2×#489C2211yescharacteristic
47C2×#489C2211yescharacteristic, complemented
48C2×#489C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#481C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#482C2211yescharacteristic, complemented
55C2×#483C2211yescharacteristic
56C2×#480C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic, complemented
65C2×#467C2211yescharacteristic
66C2×#466C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic, complemented
71C2×#463C2211yescharacteristic
72C2×#463C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#449C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#451C2211yescharacteristic, complemented
78C2×#448C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic
82C2×#441C2211yescharacteristic, complemented
83C2×#440C2211yescharacteristic
84C2×#440C2211yescharacteristic, complemented
85C2×#435C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#417C2211yescharacteristic
89C2×#419C2211yescharacteristic, complemented
90C2×#418C2211yescharacteristic
91C2×#416C2211yescharacteristic
92C2×#416C2211yescharacteristic
93C22×#103C2211yescharacteristic, complemented
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic
96C2×#405C2211yescharacteristic, complemented
97#2868C2211yescharacteristic, complemented
98#2858C2211yescharacteristic
99#2718—22no—
100#2718—22no—
101#2681—22no—
102#2678—22no—
103#2621C2211yescharacteristic
104#2620C2211yescharacteristic
105#2620C2211yescharacteristic, complemented
106#2619C2211yescharacteristic
107#2568C2211yescharacteristic, complemented
108#2545C2211yescharacteristic
109#2544C2211yescharacteristic
110#2542C2211yescharacteristic, complemented
111#2502C2211yescharacteristic
112#2502C2211yescharacteristic, complemented
113#2500C2211yescharacteristic
114#2500C2211yescharacteristic, complemented
115#2472—22no—
116#2464—22no—
117#2436C2211yescharacteristic
118#2435C2211yescharacteristic
119#2432—22no—
120#2432C2211yescharacteristic
121#2431C2211yescharacteristic
122#2429—22no—
123#2317C2211yescharacteristic
124#2317C2211yescharacteristic, complemented
125C4×#124C2211yescharacteristic
126C4×#124C2211yescharacteristic, complemented
127#2293C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2093C2211yescharacteristic
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic
146#2013C2211yescharacteristic, complemented
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic, complemented
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1972C2211yescharacteristic
157#1972C2211yescharacteristic, complemented
158#1971C2211yescharacteristic, complemented
159#1971C2211yescharacteristic, complemented
160#1970C2211yescharacteristic
161#1969C2211yescharacteristic, complemented
162#1968C2211yescharacteristic, complemented
163#1968C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic
166#1960C2211yescharacteristic, complemented
167#1960C2211yescharacteristic, complemented
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1959C2211yescharacteristic
173#1959C2211yescharacteristic
174#1959C2211yescharacteristic, complemented
175#1959C2211yescharacteristic, complemented
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic, complemented
180#1957C2211yescharacteristic
181#1957C2211yescharacteristic
182#1957C2211yescharacteristic
183#1956C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, 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
202C23×Q8C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220#556—24no—
221#556—24no—
222#548—24no—
223#548—24no—
224#547—24no—
225#547—24no—
226#546—24no—
227#546—24no—
228#536—24no—
229#536—42no—
230#535—24no—
231#535—42no—
232C2×C4⋊Q8—22no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#127C2311yescharacteristic
239C2×#126—21no—
240C2×#126—21no—
241C2×#124—21no—
242C2×#124—21no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#123—21no—
252C2×#123—22no—
253C2×#123—21no—
254C2×#123—21no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—22no—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×#121—21no—
264C2×#121—22no—
265C2×#121—21no—
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#121C2311yescharacteristic
270C2×#120—21no—
271C2×#120—22no—
272C2×C4×Q8—21no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4—21no—
286#497—42no—
287#496—42no—
288#495—24no—
289#489—24no—
290#489—24no—
291#489—24no—
292#489—24no—
293#485—24no—
294#485—24no—
295#484—24no—
296#483—24no—
297#482—24no—
298#482—24no—
299#481—24no—
300#480—24no—
301#477—24no—
302#477—24no—
303#476—24no—
304#476—24no—
305#470—24no—
306#469—24no—
307#468—24no—
308#468—24no—
309#467—24no—
310#466—24no—
311#465—24no—
312#465—24no—
313#464—24no—
314#464—24no—
315#463—24no—
316#463—24no—
317#452—24no—
318#452—24no—
319#451—24no—
320#450—24no—
321#449—24no—
322#449—24no—
323#448—24no—
324#447—24no—
325#442—24no—
326#441—24no—
327#440—24no—
328#440—24no—
329#435D418yescomplemented
330#435D418yescomplemented
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×C4⋊C8C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345#419—24no—
346#418—24no—
347#417—24no—
348#417—24no—
349#416—24no—
350#416—24no—
351C2×#103—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×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#102—24no—
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×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×C22⋊C8C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397#405—42no—
398#405—42no—
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411#400—22no—
412#399—22no—
413#398—22no—
414#398—22no—
415#398—22no—
416#397—22no—
417#396—22no—
418#396—22no—
419#396—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#393—22no—
429#392—22no—
430#392—22no—
431#391—22no—
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390—22no—
440#390D412yes—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#389—22no—
448#389—22no—
449#389D412yes—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#388—22no—
455#388D412yes—
456#388D412yes—
457#386—22no—
458#386—22no—
459#386—22no—
460#385—22no—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#384—22no—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#379—22no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C22⋊C4—22no—
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—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—44no—
503C2×#41—84no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
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—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×D8—41no—
582C2×M16—41no—
583C2×M16—41no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16C2×D414yes—
587C2×M16C2×D414yes—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8C2×D414yes—
593C22×C8C2×D414yes—
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—22no—
605C4⋊Q8—22no—
606C4⋊Q8—22no—
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609C4⋊Q8—41no—
610C4⋊Q8—84no—
611#127—22no—
612#127—22no—
613#127—22no—
614#127—41no—
615#126—44no—
616#126—44no—
617#124—22no—
618#124—22no—
619#124—22no—
620#124—22no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—41no—
627#124—41no—
628#124—41no—
629#124—41no—
630#124—41no—
631#124—41no—
632#124—44no—
633#124—44no—
634#124#4114yescomplemented
635#123—48no—
636#123—44no—
637#123—44no—
638#123—44no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—48no—
648C22⋊Q8—44no—
649C22⋊Q8—44no—
650C22⋊Q8—84no—
651#121—22no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—48no—
660#121—44no—
661#121—44no—
662#120—48no—
663#120—44no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×Q8—44no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—22no—
673C4×D4—44no—
674C4×D4C2×D414yes—
675C4×D4C2×D414yes—
676#117—22no—
677#117—22no—
678#117—22no—
679#117—22no—
680#117—22no—
681#117—22no—
682#117—22no—
683#117—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—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4C2×D412yes—
707C2×C4⋊C4C2×D412yes—
708C2×C4⋊C4C2×D412yes—
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C22⋊C4—22no—
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—22no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
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—44no—
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×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#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776C4⋊C8C2×D414yes—
777C4⋊C8C2×D414yes—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
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—
814#102—22no—
815#102—22no—
816#102—22no—
817#102—22no—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820C22⋊C8C2×D414yes—
821C22⋊C8C2×D414yes—
822#97—22no—
823#97—22no—
824#97—41no—
825#97—41no—
826#97—41no—
827#97—41no—
828#97C2×D414yes—
829#97C2×D414yes—
830C4×C8—22no—
831C4×C8—22no—
832C4×C8—41no—
833C4×C8—41no—
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#95—22no—
843#95—22no—
844#95C2×D412yes—
845#95C2×D412yes—
846#95C2×D412yes—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—42no—
852C24—42no—
853C24—81no—
854C24—82no—
855C24—82no—
856C24C22×D411yescharacteristic
857C24C22×D411yescharacteristic
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—816no—
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—21no—
889C2×Q8—21no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—81no—
899C2×Q8—82no—
900C2×Q8—82no—
901C2×Q8C2×#4112yes—
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—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—81no—
943C2×D4—82no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—82no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4#12714yes—
954C2×D4C2×#4112yes—
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—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—82no—
989C22×C4—81no—
990C22×C4—82no—
991C22×C4—82no—
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D412yes—
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D412yes—
1004C22×C4C2511yescharacteristic
1005Q16—44no—
1006Q16—82no—
1007Q16—82no—
1008SD16—44no—
1009SD16—44no—
1010SD16—82no—
1011SD16—82no—
1012SD16—82no—
1013SD16—82no—
1014D8—44no—
1015D8—82no—
1016D8—82no—
1017M16—44no—
1018M16—44no—
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—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—44no—
1036C2×C8—44no—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C2×C8C22×D412yes—
1040C2×C8C22×D412yes—
1041C2×C8C22×D412yes—
1042C2×C8C22×D412yes—
1043C2×C8C22×D412yes—
1044C2×C8C22×D412yes—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
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—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
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—44no—
1076C4⋊C4—82no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4#12714yes—
1083C22⋊C4—28no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
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—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—44no—
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—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42C22×D412yes—
1130C42C22×D412yes—
1131C42C2×#4112yes—
1132C42H(5,𝔽2)12yes—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—22no—
1142C23—42no—
1143C23—42no—
1144C23—41no—
1145C23—41no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—84no—
1162C23—84no—
1163C23—162no—
1164C23—164no—
1165C23—164no—
1166C23C2×#12712yes—
1167C23C2×#12712yes—
1168C23C23×D411yescharacteristic
1169Q8—22no—
1170Q8—22no—
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—41no—
1184Q8—41no—
1185Q8—84no—
1186Q8—84no—
1187Q8—84no—
1188D4—22no—
1189D4—22no—
1190D4—44no—
1191D4—41no—
1192D4—41no—
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—84no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—84no—
1211D4—164no—
1212D4—164no—
1213D4—162no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
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—41no—
1241C2×C4—41no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
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—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—162no—
1274C2×C4C2×#12712yes—
1275C2×C4C2×#12712yes—
1276C2×C4C2×#12712yes—
1277C2×C4C2×#12712yes—
1278C2×C4#54614yes—
1279C2×C4C23×D411yescharacteristic
1280C2×C4C23×D411yescharacteristic
1281C2×C4C22×#4111yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—44no—
1304C22—42no—
1305C22—82no—
1306C22—81no—
1307C22—81no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—82no—
1313C22—82no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—168no—
1324C22C22×#12711yescharacteristic
1325C22C2×#54611yescharacteristic
1326C22#350011yescharacteristic
1327C22#358512yes—
1328C22#358612yes—
1329C4—24no—
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4D4×#4111yescharacteristic
1350C4D4×#4111yescharacteristic
1351C4#349611yescharacteristic
1352C4#349611yescharacteristic
1353C2—42no—
1354C2—42no—
1355C2—82no—
1356C2—161no—
1357C2—161no—
1358C2—161no—
1359C2#3626011yescharacteristic
1360C2#6064411yescharacteristic
1361C2#6065111yescharacteristic
1362C2#6122212yes—
1363C2#6256612yes—
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×#3313C2semidirect
2. C2×#3311C2semidirect
3. C2×#3308C2semidirect
4. C2×#3306C2semidirect
5. #39488C2semidirect
6. #39357C2semidirect
7. #33230C2semidirect
8. #33188C2semidirect
9. #33187C2semidirect
10. #28519C2semidirect
11. #28446C2semidirect
12. #28436C2semidirect
13. #28430C2semidirect
14. #28426C2semidirect
15. #28424C2semidirect
16. #28363C2semidirect
17. #28362C2semidirect
18. #28360C2semidirect
19. #28357C2semidirect
20. #28351C2semidirect
21. #28349C2semidirect
22. #28347C2semidirect
23. #28342C2semidirect
24. #27923C2semidirect
25. #27922C2semidirect
26. #25737C2semidirect
27. #25736C2semidirect
28. #21693C2semidirect
29. #21206C2semidirect
30. #21205C2semidirect
31. #20488C2semidirect
42. C2×#497C22semidirect
47. C2×#489C22semidirect
48. C2×#489C22semidirect
54. C2×#482C22semidirect
56. C2×#480C22semidirect
57. C2×#477C22semidirect
58. C2×#477C22semidirect
64. C2×#468C22semidirect
66. C2×#466C22semidirect
70. C2×#464C22semidirect
72. C2×#463C22semidirect
77. C2×#451C22semidirect
78. C2×#448C22semidirect
82. C2×#441C22semidirect
84. C2×#440C22semidirect
89. C2×#419C22semidirect
93. C22×#103C22semidirect
96. C2×#405C22semidirect
97. #2868C22semidirect
105. #2620C22semidirect
107. #2568C22semidirect
110. #2542C22semidirect
112. #2502C22semidirect
114. #2500C22semidirect
124. #2317C22semidirect
126. C4×#124C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
134. #2094C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
144. #2015C22semidirect
146. #2013C22semidirect
150. #2012C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
157. #1972C22semidirect
158. #1971C22semidirect
159. #1971C22semidirect
161. #1969C22semidirect
162. #1968C22semidirect
163. #1968C22semidirect
166. #1960C22semidirect
167. #1960C22semidirect
174. #1959C22semidirect
175. #1959C22semidirect
179. #1958C22semidirect
183. #1956C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1846C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1767C22semidirect
193. #1753C22semidirect
195. #1752C22semidirect
197. #1750C22semidirect
198. C4×#97C22semidirect
329. #435D4semidirect
330. #435D4semidirect
634. #124#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33132
C2×#33112
C2×#33082
C2×#33062
#394882
#393572
#332302
#331882
#331872
#285192
#284462
#284362
#284302
#284262
#284242
#283632
#283622
#283602
#283572
#283512
#283492
#283472
#283422
#279232
#279222
#257372
#257362
#216932
#212062
#212052
#204882