Finite Group Databasebeta

← #6520511

Subgroups — #6520511

Order 512.

2294 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×#3224C211yesmaximal, characteristic
2C2×#3222C211yesmaximal, characteristic, complemented
3C2×#3127C211yesmaximal, characteristic, complemented
4C2×#3121C211yesmaximal, characteristic, complemented
5#37389C211yesmaximal, characteristic, complemented
6#35677C211yesmaximal, characteristic, complemented
7#28481C211yesmaximal, characteristic, complemented
8#28481C211yesmaximal, characteristic, complemented
9#28477C211yesmaximal, characteristic, complemented
10#28476C211yesmaximal, characteristic, complemented
11#28473C211yesmaximal, characteristic, complemented
12#28469C211yesmaximal, characteristic, complemented
13#28466C211yesmaximal, characteristic, complemented
14#28460C211yesmaximal, characteristic, complemented
15#28432C211yesmaximal, characteristic, complemented
16#28431C211yesmaximal, characteristic, complemented
17#28425C211yesmaximal, characteristic, complemented
18#28424C211yesmaximal, characteristic, complemented
19#28418C211yesmaximal, characteristic, complemented
20#28410C211yesmaximal, characteristic, complemented
21#28407C211yesmaximal, characteristic, complemented
22#28402C211yesmaximal, characteristic, complemented
23#28321C211yesmaximal, characteristic, complemented
24#28320C211yesmaximal, characteristic, complemented
25#28318C211yesmaximal, characteristic, complemented
26#28308C211yesmaximal, characteristic, complemented
27#25737C211yesmaximal, characteristic, complemented
28#25735C211yesmaximal, characteristic, complemented
29#25730C211yesmaximal, characteristic, complemented
30#25724C211yesmaximal, characteristic, complemented
31#20541C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#536C2211yescharacteristic
35C2×#535C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#3224—28no—
39#3222—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic
42C2×#497C2211yescharacteristic
43C2×#497C2211yescharacteristic, complemented
44C2×#497C2211yescharacteristic, complemented
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic
48C2×#495C2211yescharacteristic
49C2×#495C2211yescharacteristic, complemented
50C2×#494C2211yescharacteristic, complemented
51C2×#492C2211yescharacteristic
52C2×#490C2211yescharacteristic
53C2×#489C2211yescharacteristic
54C2×#488C2211yescharacteristic
55C2×#486C2211yescharacteristic
56#3127—28no—
57#3121—28no—
58C2×#485C2211yescharacteristic
59C2×#485C2211yescharacteristic
60C2×#485C2211yescharacteristic
61C2×#482C2211yescharacteristic
62C2×#479C2211yescharacteristic, complemented
63C2×#479C2211yescharacteristic, complemented
64C2×#477C2211yescharacteristic, complemented
65C2×#475C2211yescharacteristic, complemented
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic
69C2×#464C2211yescharacteristic, complemented
70C2×#464C2211yescharacteristic, complemented
71C2×#462C2211yescharacteristic, complemented
72C2×#462C2211yescharacteristic, complemented
73C2×#460C2211yescharacteristic
74C2×#460C2211yescharacteristic
75C2×#460C2211yescharacteristic
76C2×#463C2211yescharacteristic
77C2×#459C2211yescharacteristic
78C2×#452C2211yescharacteristic
79C2×#452C2211yescharacteristic
80C2×#452C2211yescharacteristic
81C2×#449C2211yescharacteristic
82C2×#451C2211yescharacteristic
83C2×#451C2211yescharacteristic
84C2×#451C2211yescharacteristic
85C2×#448C2211yescharacteristic
86C2×#450C2211yescharacteristic
87C2×#450C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#441C2211yescharacteristic, complemented
91C2×#441C2211yescharacteristic, complemented
92C2×#441C2211yescharacteristic, complemented
93C2×#440C2211yescharacteristic, complemented
94C2×C4×Q16C2211yescharacteristic, complemented
95C2×C4×Q16C2211yescharacteristic, complemented
96C2×C4×Q16C2211yescharacteristic, complemented
97C2×C4×SD16C2211yescharacteristic, complemented
98C2×#433C2211yescharacteristic
99C2×#433C2211yescharacteristic
100#2857C2211yescharacteristic
101#2850C2211yescharacteristic
102#2725—22no—
103#2715—22no—
104#2704—22no—
105#2695—22no—
106#2621C2211yescharacteristic
107#2620C2211yescharacteristic
108#2568C2211yescharacteristic, complemented
109#2567C2211yescharacteristic, complemented
110#2566C2211yescharacteristic, complemented
111#2565C2211yescharacteristic, complemented
112#2548C2211yescharacteristic
113#2548C2211yescharacteristic
114#2548C2211yescharacteristic
115#2548C2211yescharacteristic
116#2547C2211yescharacteristic, complemented
117#2546C2211yescharacteristic, complemented
118#2545C2211yescharacteristic
119#2545C2211yescharacteristic
120#2545C2211yescharacteristic
121#2545C2211yescharacteristic
122#2545C2211yescharacteristic, complemented
123#2545C2211yescharacteristic, complemented
124#2426—22no—
125#2426—22no—
126#2411—22no—
127#2411—22no—
128#2309C2211yescharacteristic
129#2297C2211yescharacteristic
130#2296C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2094C2211yescharacteristic
134#2093C2211yescharacteristic
135#2093C2211yescharacteristic, complemented
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic, complemented
150#2015C2211yescharacteristic, complemented
151#2015C2211yescharacteristic, complemented
152#2015C2211yescharacteristic, complemented
153#2013C2211yescharacteristic
154#2013C2211yescharacteristic
155#2013C2211yescharacteristic, complemented
156#2013C2211yescharacteristic, complemented
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic
159#2012C2211yescharacteristic
160#2012C2211yescharacteristic
161#2012C2211yescharacteristic, complemented
162#2012C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic
166#1973C2211yescharacteristic, complemented
167#1973C2211yescharacteristic, complemented
168#1972C2211yescharacteristic
169#1972C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1969C2211yescharacteristic, complemented
173#1969C2211yescharacteristic, complemented
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1960C2211yescharacteristic, complemented
180#1959C2211yescharacteristic
181#1959C2211yescharacteristic
182#1959C2211yescharacteristic, complemented
183#1958C2211yescharacteristic
184#1958C2211yescharacteristic
185#1958C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C8×C4⋊C4C2211yescharacteristic, complemented
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198C4×C22⋊C8C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
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
226#542—24no—
227#542—24no—
228#541—24no—
229#541—24no—
230#536—42no—
231#536—42no—
232#535—24no—
233#535—24no—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#126—21no—
243C2×#126—21no—
244C2×#126—21no—
245C2×#125—21no—
246C2×#125—21no—
247C2×#125C2311yescharacteristic
248C2×#124—21no—
249C2×#124—22no—
250C2×#124—42no—
251C2×#124—42no—
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#123—22no—
264C2×#123—21no—
265C2×C22⋊Q8—22no—
266C2×C22⋊Q8—21no—
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2311yescharacteristic
270C2×#121—21no—
271C2×#121—21no—
272C2×#121C2311yescharacteristic
273C2×#120—21no—
274C2×#120—21no—
275#519—24no—
276#519—24no—
277C2×C4×Q8—21no—
278C2×C4×Q8—21no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×#117—21no—
288C2×#117—21no—
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C22×C22⋊C4—22no—
293C22×C42C2311yescharacteristic
294#497—24no—
295#497—42no—
296#497—42no—
297#497—42no—
298#497—42no—
299#496—24no—
300#495—24no—
301#495—42no—
302#495—42no—
303#495—42no—
304#494—42no—
305#492—24no—
306#490—24no—
307#489—24no—
308#488—24no—
309#486—24no—
310#485—24no—
311#485—24no—
312#485—24no—
313#482—24no—
314#479—24no—
315#479—24no—
316#477—24no—
317#475—24no—
318#464—24no—
319#464—24no—
320#464—24no—
321#464—24no—
322#464—24no—
323#463—24no—
324#462—24no—
325#462—24no—
326#460—24no—
327#460—24no—
328#460—24no—
329#459—24no—
330#452—24no—
331#452—24no—
332#452—24no—
333#451—24no—
334#451—24no—
335#451—24no—
336#450—24no—
337#450—24no—
338#450—24no—
339#449—24no—
340#448—24no—
341#447—24no—
342#441—24no—
343#441—24no—
344#441—24no—
345#440—24no—
346C4×Q16—24no—
347C4×Q16—24no—
348C4×Q16—24no—
349C4×SD16—24no—
350#433D418yes—
351#433D418yes—
352C2×#107C2311yescharacteristic
353C2×#107C2311yescharacteristic
354C2×#107C2311yescharacteristic
355C2×#107C2311yescharacteristic
356C2×#106C2311yescharacteristic
357C2×#106C2311yescharacteristic
358C2×#106C2311yescharacteristic
359C2×#106C2311yescharacteristic
360C2×C4⋊C8C2311yescharacteristic
361C2×C4⋊C8C2311yescharacteristic
362C2×C4⋊C8C2311yescharacteristic
363C2×C4⋊C8C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#103C2311yescharacteristic
380C2×#103C2311yescharacteristic
381C2×#103C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398C2×C22⋊C8C2311yescharacteristic
399C2×C22⋊C8C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412#400—22no—
413#398—22no—
414#398—22no—
415#398—22no—
416#397—22no—
417#397—22no—
418#396—22no—
419#396—22no—
420#396—22no—
421#396—22no—
422#396—22no—
423#396—22no—
424#396—22no—
425#396—22no—
426#395—22no—
427#394—22no—
428#394—22no—
429#394—22no—
430#394—22no—
431#394—22no—
432#391—22no—
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#390—22no—
442#390—22no—
443#390—22no—
444#390—22no—
445#390—22no—
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2311yescharacteristic
454#389—22no—
455#389—22no—
456#389—22no—
457#389D412yes—
458#389D412yes—
459#388—22no—
460#388—22no—
461#388—22no—
462#388—22no—
463#388—22no—
464#388—22no—
465#388—22no—
466#387—22no—
467#386—22no—
468#386—22no—
469#385—22no—
470#385D412yes—
471#385D412yes—
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#380—22no—
477#380—22no—
478#379—22no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C22⋊C4—22no—
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492C25—21no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2×D412yes—
534C23×C4C2411yescharacteristic
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
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×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
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—22no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16—41no—
594C2×SD16—41no—
595C2×SD16—41no—
596C2×SD16—41no—
597C2×SD16—41no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—41no—
602C2×D8—41no—
603C2×D8—41no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
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—22no—
620C4⋊Q8—22no—
621C4⋊Q8—41no—
622C4⋊Q8—41no—
623C4⋊Q8—41no—
624C4⋊Q8—41no—
625C4⋊Q8—41no—
626C4⋊Q8—41no—
627#127—22no—
628#127—22no—
629#127—22no—
630#127—22no—
631#126—44no—
632#126—44no—
633#126—44no—
634#125—22no—
635#125—22no—
636#125—44no—
637#125—44no—
638#124—22no—
639#124—22no—
640#124—22no—
641#124—22no—
642#124—22no—
643#124—22no—
644#124—22no—
645#124—22no—
646#124—22no—
647#124—22no—
648#124—22no—
649#124—22no—
650#124—41no—
651#124—41no—
652#124—41no—
653#124—41no—
654#124—41no—
655#124—41no—
656#124—41no—
657#124—41no—
658#124—41no—
659#124—41no—
660#124—48no—
661#124—44no—
662#123—48no—
663#123—44no—
664C22⋊Q8—22no—
665C22⋊Q8—22no—
666C22⋊Q8—22no—
667C22⋊Q8—22no—
668C22⋊Q8—22no—
669C22⋊Q8—22no—
670C22⋊Q8—48no—
671C22⋊Q8—44no—
672#121—22no—
673#121—22no—
674#121—44no—
675#121—44no—
676#120—44no—
677#120—44no—
678C4×Q8—22no—
679C4×Q8—22no—
680C4×Q8—22no—
681C4×Q8—22no—
682C4×Q8—22no—
683C4×Q8—22no—
684C4×Q8—22no—
685C4×Q8—22no—
686C4×Q8—22no—
687C4×Q8—22no—
688C4×Q8—22no—
689C4×Q8—22no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—44no—
693C4×Q8—44no—
694C4×D4—22no—
695C4×D4—22no—
696#117—22no—
697#117—22no—
698#117—41no—
699#117—41no—
700#117—44no—
701#117—44no—
702#117C2×D414yes—
703#117C2×D414yes—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C2×D412yes—
726C2×C4⋊C4C2×D412yes—
727C2×C4⋊C4C2×D412yes—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D412yes—
730C2×C4⋊C4C2×D411yescharacteristic
731C2×C4⋊C4C2×D411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—48no—
767C2×C22⋊C4C2×D412yes—
768C2×C22⋊C4C2×D411yescharacteristic
769C2×C22⋊C4C2×D411yescharacteristic
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—41no—
779C2×C42—41no—
780C2×C42C2×D412yes—
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787#107—22no—
788#107—22no—
789#107—22no—
790#107—22no—
791#106—22no—
792#106—22no—
793#106—22no—
794#106—22no—
795C4⋊C8C2×D414yes—
796C4⋊C8C2×D414yes—
797C4⋊C8C2×D414yes—
798C4⋊C8C2×D414yes—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831C22⋊C8C2×D414yes—
832C22⋊C8C2×D414yes—
833C22⋊C8C2×D414yes—
834C22⋊C8C2×D414yes—
835#97—41no—
836#97—41no—
837#97—41no—
838#97—41no—
839#97C2×D414yes—
840#97C2×D414yes—
841C4×C8—41no—
842C4×C8—41no—
843C4×C8—41no—
844C4×C8—41no—
845C4×C8C2×D414yes—
846C4×C8C2×D414yes—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95C2×D412yes—
858#95C2×D412yes—
859#95C2×D412yes—
860#95C2×D412yes—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—42no—
866C24—42no—
867C24—42no—
868C24—82no—
869C24—82no—
870C24C22×D411yescharacteristic
871#41—82no—
872#41—82no—
873#41—82no—
874#41—82no—
875C2×Q8—24no—
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—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—44no—
911C2×Q8—44no—
912C2×Q8—44no—
913C2×Q8—44no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—82no—
918C2×Q8H(5,𝔽2)12yes—
919C2×Q8H(5,𝔽2)12yes—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—82no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—24no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—82no—
991C22×C4C22×D412yes—
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C2511yescharacteristic
1003Q16—44no—
1004Q16—44no—
1005Q16—44no—
1006Q16—44no—
1007Q16—44no—
1008Q16—44no—
1009Q16—82no—
1010Q16—82no—
1011Q16—82no—
1012SD16—44no—
1013SD16—44no—
1014SD16—82no—
1015SD16—82no—
1016SD16—82no—
1017SD16—82no—
1018SD16—82no—
1019SD16—82no—
1020SD16—82no—
1021SD16—82no—
1022SD16—82no—
1023SD16—82no—
1024D8—82no—
1025D8—82no—
1026D8—82no—
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—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8C22×D412yes—
1044C2×C8C22×D412yes—
1045C2×C8C22×D412yes—
1046C2×C8C22×D412yes—
1047C2×C8C22×D412yes—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C2×C8C22×D412yes—
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—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—82no—
1086C4⋊C4—82no—
1087C4⋊C4—82no—
1088C4⋊C4—82no—
1089C4⋊C4#12714yes—
1090C4⋊C4#12714yes—
1091C22⋊C4—42no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
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—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—82no—
1112C22⋊C4—82no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C22⋊C4—82no—
1120C22⋊C4#12714yes—
1121C22⋊C4#12714yes—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42C22×D412yes—
1140C42C22×D412yes—
1141C42C22×D412yes—
1142C42C22×D412yes—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—21no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—42no—
1154C23—42no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—84no—
1168C23—88no—
1169C23—162no—
1170C23—162no—
1171C23—164no—
1172C23C2×#12712yes—
1173C23C23×D411yescharacteristic
1174Q8—22no—
1175Q8—22no—
1176Q8—22no—
1177Q8—22no—
1178Q8—48no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—162no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
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—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—48no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
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—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—162no—
1279C2×C4C2×#12712yes—
1280C2×C4C2×#12712yes—
1281C2×C4C2×#12712yes—
1282C2×C4C2×#12712yes—
1283C2×C4C2×#12712yes—
1284C2×C4C23×D411yescharacteristic
1285C2×C4C23×D411yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4C2×H(5,𝔽2)11yescharacteristic
1288C2×C4#58511yescharacteristic
1289C2×C4#58511yescharacteristic
1290C8—22no—
1291C8—22no—
1292C8—22no—
1293C8—22no—
1294C8—22no—
1295C8—22no—
1296C8—22no—
1297C8—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—42no—
1302C22—42no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—168no—
1324C22C22×#12711yescharacteristic
1325C22#348411yescharacteristic
1326C22#348711yescharacteristic
1327C22#358412yes—
1328C22#358612yes—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4#348811yescharacteristic
1351C4#348811yescharacteristic
1352C4#348811yescharacteristic
1353C4#348811yescharacteristic
1354C2—42no—
1355C2—161no—
1356C2—161no—
1357C2—161no—
1358C2—161no—
1359C2#3556511yescharacteristic
1360C2#6064911yescharacteristic
1361C2#6065111yescharacteristic
1362C2#6161512yes—
1363C2#6192512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3224C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3222C2semidirect
3. C2×#3127C2semidirect
4. C2×#3121C2semidirect
5. #37389C2semidirect
6. #35677C2semidirect
7. #28481C2semidirect
8. #28481C2semidirect
9. #28477C2semidirect
10. #28476C2semidirect
11. #28473C2semidirect
12. #28469C2semidirect
13. #28466C2semidirect
14. #28460C2semidirect
15. #28432C2semidirect
16. #28431C2semidirect
17. #28425C2semidirect
18. #28424C2semidirect
19. #28418C2semidirect
20. #28410C2semidirect
21. #28407C2semidirect
22. #28402C2semidirect
23. #28321C2semidirect
24. #28320C2semidirect
25. #28318C2semidirect
26. #28308C2semidirect
27. #25737C2semidirect
28. #25735C2semidirect
29. #25730C2semidirect
30. #25724C2semidirect
31. #20541C2semidirect
43. C2×#497C22semidirect
44. C2×#497C22semidirect
49. C2×#495C22semidirect
50. C2×#494C22semidirect
62. C2×#479C22semidirect
63. C2×#479C22semidirect
64. C2×#477C22semidirect
65. C2×#475C22semidirect
69. C2×#464C22semidirect
70. C2×#464C22semidirect
71. C2×#462C22semidirect
72. C2×#462C22semidirect
90. C2×#441C22semidirect
91. C2×#441C22semidirect
92. C2×#441C22semidirect
93. C2×#440C22semidirect
94. C2×C4×Q16C22semidirect
95. C2×C4×Q16C22semidirect
96. C2×C4×Q16C22semidirect
97. C2×C4×SD16C22semidirect
108. #2568C22semidirect
109. #2567C22semidirect
110. #2566C22semidirect
111. #2565C22semidirect
116. #2547C22semidirect
117. #2546C22semidirect
122. #2545C22semidirect
123. #2545C22semidirect
131. #2097C22semidirect
132. #2096C22semidirect
135. #2093C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
149. #2015C22semidirect
150. #2015C22semidirect
151. #2015C22semidirect
152. #2015C22semidirect
155. #2013C22semidirect
156. #2013C22semidirect
161. #2012C22semidirect
162. #2012C22semidirect
166. #1973C22semidirect
167. #1973C22semidirect
169. #1972C22semidirect
170. #1971C22semidirect
172. #1969C22semidirect
173. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1960C22semidirect
182. #1959C22semidirect
185. #1958C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. #1770C22semidirect
193. C8×C4⋊C4C22semidirect
194. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32242
C2×#32222
C2×#31272
C2×#31212
#373892
#356772
#284812
#284772
#284762
#284732
#284692
#284662
#284602
#284322
#284312
#284252
#284242
#284182
#284102
#284072
#284022
#283212
#283202
#283182
#283082
#257372
#257352
#257302
#257242
#205412