Finite Group Databasebeta

← #6606787

Subgroups — #6606787

Order 512.

2502 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3316C211yesmaximal, characteristic, complemented
2C2×#3318C211yesmaximal, characteristic, complemented
3C2×#3301C211yesmaximal, characteristic, complemented
4C2×#3295C211yesmaximal, characteristic, complemented
5#37862C211yesmaximal, characteristic, complemented
6#37677C211yesmaximal, characteristic, complemented
7#33228C211yesmaximal, characteristic, complemented
8#33183C211yesmaximal, characteristic, complemented
9#33181C211yesmaximal, characteristic, complemented
10#28524C211yesmaximal, characteristic, complemented
11#28452C211yesmaximal, characteristic, complemented
12#28431C211yesmaximal, characteristic, complemented
13#28430C211yesmaximal, characteristic, complemented
14#28415C211yesmaximal, characteristic, complemented
15#28412C211yesmaximal, characteristic, complemented
16#28364C211yesmaximal, characteristic, complemented
17#28361C211yesmaximal, characteristic, complemented
18#28352C211yesmaximal, characteristic, complemented
19#28347C211yesmaximal, characteristic, complemented
20#28343C211yesmaximal, characteristic, complemented
21#28341C211yesmaximal, characteristic, complemented
22#28334C211yesmaximal, characteristic, complemented
23#28332C211yesmaximal, characteristic, complemented
24#27920C211yesmaximal, characteristic, complemented
25#27906C211yesmaximal, characteristic, complemented
26#25736C211yesmaximal, characteristic, complemented
27#25724C211yesmaximal, characteristic, complemented
28#21694C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30C2×#1959C211yesmaximal, characteristic, complemented
31#20493C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×D42C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C22×#124C2211yescharacteristic
38#3318—28no—
39#3316—28no—
40#3301—28no—
41#3295—28no—
42C2×#496C2211yescharacteristic, complemented
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic, complemented
45C2×#490C2211yescharacteristic
46C2×#489C2211yescharacteristic, complemented
47C2×#488C2211yescharacteristic, complemented
48C2×#486C2211yescharacteristic
49C2×#481C2211yescharacteristic
50C2×#481C2211yescharacteristic
51C2×#481C2211yescharacteristic
52C2×#481C2211yescharacteristic, complemented
53C2×#481C2211yescharacteristic, complemented
54C2×#485C2211yescharacteristic, complemented
55C2×#482C2211yescharacteristic
56C2×#483C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#475C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic, complemented
62C2×#469C2211yescharacteristic
63C2×#466C2211yescharacteristic
64C2×#466C2211yescharacteristic, complemented
65C2×#465C2211yescharacteristic
66C2×#465C2211yescharacteristic
67C2×#465C2211yescharacteristic, complemented
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic, complemented
70C2×#460C2211yescharacteristic
71C2×#463C2211yescharacteristic, complemented
72C2×#459C2211yescharacteristic
73C2×#452C2211yescharacteristic, complemented
74C2×#449C2211yescharacteristic, complemented
75C2×#451C2211yescharacteristic, complemented
76C2×#448C2211yescharacteristic, complemented
77C2×#450C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#447C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic
82C2×#441C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic, complemented
85C2×#435C2211yescharacteristic
86C2×C8×D4C2211yescharacteristic
87C2×#417C2211yescharacteristic, complemented
88C2×#418C2211yescharacteristic
89C2×#416C2211yescharacteristic, complemented
90C22×#103C2211yescharacteristic, complemented
91C22×#103C2211yescharacteristic, complemented
92C22×#102C2211yescharacteristic
93C22×#102C2211yescharacteristic
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic, complemented
96C22×#97C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2850C2211yescharacteristic, complemented
99#2721—22no—
100#2680—22no—
101#2676—22no—
102#2670—22no—
103#2660C2211yescharacteristic, complemented
104#2657C2211yescharacteristic
105#2620C2211yescharacteristic
106#2620C2211yescharacteristic, complemented
107#2565C2211yescharacteristic, complemented
108#2548C2211yescharacteristic
109#2544C2211yescharacteristic
110#2542C2211yescharacteristic, complemented
111#2504C2211yescharacteristic, complemented
112#2502C2211yescharacteristic, complemented
113#2501C2211yescharacteristic, complemented
114#2499C2211yescharacteristic, complemented
115#2449—22no—
116#2443—22no—
117#2436C2211yescharacteristic
118#2435C2211yescharacteristic
119#2433C2211yescharacteristic
120#2431C2211yescharacteristic
121#2424—22no—
122#2410—22no—
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2317C2211yescharacteristic, complemented
126#2290C2211yescharacteristic
127C2×#384C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2094C2211yescharacteristic
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2094C2211yescharacteristic, complemented
137#2094C2211yescharacteristic, complemented
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic, complemented
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic, complemented
148#2012C2211yescharacteristic, complemented
149#2012C2211yescharacteristic, complemented
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic, complemented
152#1973C2211yescharacteristic, complemented
153#1973C2211yescharacteristic, complemented
154#1972C2211yescharacteristic
155#1972C2211yescharacteristic, complemented
156#1972C2211yescharacteristic, complemented
157#1972C2211yescharacteristic, complemented
158#1971C2211yescharacteristic, complemented
159#1971C2211yescharacteristic, complemented
160#1968C2211yescharacteristic
161#1968C2211yescharacteristic, complemented
162#1968C2211yescharacteristic, complemented
163#1968C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic, complemented
166#1961C2211yescharacteristic, complemented
167#1959C2211yescharacteristic
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic, complemented
172#1959C2211yescharacteristic, complemented
173#1959C2211yescharacteristic, complemented
174#1959C2211yescharacteristic, complemented
175#1959C2211yescharacteristic, complemented
176#1959C2211yescharacteristic, complemented
177#1959C2211yescharacteristic, complemented
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic, complemented
180#1958C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic, complemented
184#1957C2211yescharacteristic, complemented
185#1957C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1844C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic, complemented
194#1752C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4—21no—
202C23×D4C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220#554—24no—
221#554—24no—
222#553—24no—
223#553—24no—
224#548—24no—
225#548—24no—
226D42—24no—
227D42—24no—
228#535—24no—
229#535—42no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#126—21no—
236C2×#125—21no—
237C2×#125C2311yescharacteristic
238C2×#124—21no—
239C2×#124—24no—
240C2×#124—22no—
241C2×#124—42no—
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#123—21no—
251C2×#123—22no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×#121—21no—
260C2×#121—21no—
261C2×#121—22no—
262C2×#121—21no—
263C2×#121—22no—
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#120—22no—
270C2×#120—21no—
271C2×#120—21no—
272C2×#120—22no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4—21no—
277C2×C4×D4—21no—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4—22no—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C22⋊C4—22no—
288C22×C42C2311yescharacteristic
289#496—42no—
290#495—24no—
291#495—42no—
292#490—24no—
293#489—24no—
294#488—24no—
295#486—24no—
296#485—24no—
297#483—24no—
298#482—24no—
299#481—24no—
300#481—24no—
301#481—24no—
302#481—24no—
303#481—24no—
304#479—24no—
305#478—24no—
306#476—24no—
307#475—24no—
308#470—24no—
309#469—24no—
310#466—24no—
311#466—24no—
312#465—24no—
313#465—24no—
314#465—24no—
315#465—24no—
316#464—24no—
317#463—24no—
318#460—24no—
319#459—24no—
320#452—24no—
321#451—24no—
322#450—24no—
323#450—24no—
324#449—24no—
325#448—24no—
326#447—24no—
327#447—24no—
328#442—24no—
329#441—24no—
330C4×SD16—24no—
331C4×SD16—24no—
332#435D418yescomplemented
333C8×D4D418yescomplemented
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×C4⋊C8C2311yescharacteristic
347C2×C4⋊C8C2311yescharacteristic
348#418—24no—
349#417—24no—
350#416—24no—
351C2×#103—24no—
352C2×#103—24no—
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×#102—24no—
368C2×#102—24no—
369C2×#102—24no—
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×#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
400#405—42no—
401C2×#97—42no—
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×#97C2311yescharacteristic
408C2×#97C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412C2×C4×C8C2311yescharacteristic
413C2×C4×C8C2311yescharacteristic
414#399—22no—
415#399—22no—
416#398—22no—
417#398—22no—
418#398—22no—
419#397—22no—
420#397—22no—
421#396—22no—
422#396—22no—
423#395—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#394—22no—
429#393—22no—
430#392—22no—
431#392—22no—
432#392—22no—
433#392—22no—
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#390—22no—
440#390—22no—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#389—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388D412yes—
453#387—22no—
454#387—22no—
455#387D412yes—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386D412yes—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385D412yes—
467#384—22no—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#382C2311yescharacteristic
478#379—22no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—44no—
534C22×D4—84no—
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C2×D412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×D8—41no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C2×M16—41no—
588C2×M16—41no—
589C2×M16C2×D414yes—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8—41no—
593C22×C8—41no—
594C22×C8—41no—
595C22×C8—41no—
596C22×C8C2×D414yes—
597C22×C8C2×D414yes—
598C22×C8C2×D414yes—
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609#127—22no—
610#127—22no—
611#127—22no—
612#127—22no—
613#127—22no—
614#127—41no—
615#127—41no—
616#127—41no—
617#126—44no—
618#125—22no—
619#125—22no—
620#125—44no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—22no—
631#124—48no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—41no—
637#124—44no—
638#124#4114yes—
639#123—44no—
640#123—84no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—44no—
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—22no—
660#121—22no—
661#121—48no—
662#121—44no—
663#121—44no—
664#121—44no—
665#121—84no—
666#120—48no—
667#120—44no—
668#120—44no—
669#120—84no—
670C4×Q8—22no—
671C4×Q8—22no—
672C4×Q8—22no—
673C4×Q8—22no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—44no—
679C4×D4—44no—
680C4×D4—44no—
681C4×D4C2×D414yes—
682C4×D4C2×D414yes—
683#117—22no—
684#117—22no—
685#117—22no—
686#117—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
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—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—84no—
712C2×C4⋊C4C2×D412yes—
713C2×C4⋊C4C2×D412yes—
714C2×C4⋊C4C2×D411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C22⋊C4—22no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
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—21no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
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—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—48no—
751C2×C22⋊C4C2×D412yes—
752C2×C22⋊C4C2×D412yes—
753C2×C22⋊C4C2×D412yes—
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42C2×D412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767#107—22no—
768#107—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779C4⋊C8C2×D414yes—
780C4⋊C8C2×D414yes—
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#102—22no—
796#102—22no—
797#102—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—
818#102—22no—
819#102—22no—
820#102—22no—
821C22⋊C8C2×D414yes—
822C22⋊C8C2×D414yes—
823C22⋊C8C2×D414yes—
824C22⋊C8C2×D414yes—
825#97—22no—
826#97—22no—
827#97—41no—
828#97—41no—
829#97—41no—
830#97—41no—
831#97C2×D414yes—
832C4×C8—22no—
833C4×C8—22no—
834C4×C8—41no—
835C4×C8—41no—
836C4×C8C2×D414yes—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95—22no—
843#95—22no—
844#95—22no—
845#95C2×D412yes—
846#95C2×D412yes—
847#95C2×D412yes—
848#95C2×D412yes—
849#95C2×D412yes—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—42no—
856C24—42no—
857C24—42no—
858C24—42no—
859C24—44no—
860C24—81no—
861C24—81no—
862C24—82no—
863C24—82no—
864C24—82no—
865C24C22×D411yescharacteristic
866C24C22×D411yescharacteristic
867#41—44no—
868#41—44no—
869#41—82no—
870#41—82no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—81no—
894C2×Q8—82no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8C2×#4112yes—
898C2×D4—24no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—82no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4—82no—
954C2×D4—81no—
955C2×D4—81no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C2×D4—82no—
965C2×D4—82no—
966C2×D4—81no—
967C2×D4—82no—
968C2×D4—816no—
969C2×D4#12714yes—
970C2×D4C2×#4112yes—
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—24no—
980C22×C4—21no—
981C22×C4—24no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—82no—
1003C22×C4—81no—
1004C22×C4—82no—
1005C22×C4—81no—
1006C22×C4—82no—
1007C22×C4—82no—
1008C22×C4—82no—
1009C22×C4C22×D412yes—
1010C22×C4C22×D412yes—
1011C22×C4C22×D412yes—
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D412yes—
1017C22×C4C22×D412yes—
1018C22×C4C22×D412yes—
1019C22×C4C22×D412yes—
1020C22×C4C22×D412yes—
1021C22×C4C2511yescharacteristic
1022Q16—44no—
1023Q16—82no—
1024SD16—44no—
1025SD16—44no—
1026SD16—82no—
1027SD16—82no—
1028SD16—82no—
1029SD16—82no—
1030D8—44no—
1031D8—82no—
1032D8—82no—
1033D8—82no—
1034M16—44no—
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×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—44no—
1052C2×C8—44no—
1053C2×C8—44no—
1054C2×C8C22×D412yes—
1055C2×C8C22×D412yes—
1056C2×C8C22×D412yes—
1057C2×C8C22×D412yes—
1058C2×C8C22×D412yes—
1059C2×C8C22×D412yes—
1060C2×C8C22×D412yes—
1061C2×C8C22×D412yes—
1062C4⋊C4—24no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—82no—
1094C4⋊C4—82no—
1095C4⋊C4—82no—
1096C4⋊C4—82no—
1097C4⋊C4—82no—
1098C4⋊C4#12714yes—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—82no—
1123C22⋊C4—82no—
1124C22⋊C4—82no—
1125C22⋊C4—82no—
1126C22⋊C4—82no—
1127C22⋊C4—82no—
1128C22⋊C4—82no—
1129C22⋊C4#12714yes—
1130C22⋊C4#12714yes—
1131C42—24no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42C22×D412yes—
1142C42C22×D412yes—
1143C42C2×#4112yes—
1144C42H(5,𝔽2)12yes—
1145C23—22no—
1146C23—21no—
1147C23—21no—
1148C23—22no—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—22no—
1153C23—42no—
1154C23—41no—
1155C23—41no—
1156C23—42no—
1157C23—42no—
1158C23—42no—
1159C23—42no—
1160C23—42no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—42no—
1174C23—42no—
1175C23—42no—
1176C23—42no—
1177C23—84no—
1178C23—84no—
1179C23—88no—
1180C23—84no—
1181C23—84no—
1182C23—164no—
1183C23—162no—
1184C23—162no—
1185C23—164no—
1186C23—164no—
1187C23C2×#12712yes—
1188C23C2×#12712yes—
1189C23#57714yes—
1190C23C23×D411yescharacteristic
1191Q8—22no—
1192Q8—22no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—84no—
1204Q8—162no—
1205D4—28no—
1206D4—22no—
1207D4—22no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—84no—
1232D4—84no—
1233D4—84no—
1234D4—164no—
1235D4—162no—
1236D4—164no—
1237D4—164no—
1238D4—162no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—48no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4C2×#12712yes—
1298C2×C4C2×#12712yes—
1299C2×C4C2×#12712yes—
1300C2×C4C2×#12712yes—
1301C2×C4#54614yes—
1302C2×C4C23×D411yescharacteristic
1303C2×C4C23×D411yescharacteristic
1304C2×C4C22×#4111yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4#58511yescharacteristic
1307C2×C4#58511yescharacteristic
1308C8—22no—
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C8—22no—
1314C8—22no—
1315C8—22no—
1316C22—24no—
1317C22—24no—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—42no—
1324C22—42no—
1325C22—44no—
1326C22—42no—
1327C22—82no—
1328C22—81no—
1329C22—81no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22—82no—
1336C22—82no—
1337C22—82no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—168no—
1351C22—168no—
1352C22#315414yes—
1353C22C22×#12711yescharacteristic
1354C22C2×#54611yescharacteristic
1355C22#350011yescharacteristic
1356C22C2×#57712yes—
1357C22#358512yes—
1358C4—24no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4D4×#4111yescharacteristic
1378C4D4×#4111yescharacteristic
1379C4#349611yescharacteristic
1380C4#349611yescharacteristic
1381C2—24no—
1382C2—42no—
1383C2—82no—
1384C2—161no—
1385C2—161no—
1386C2—161no—
1387C2—161no—
1388C2#3626011yescharacteristic
1389C2C2×#315411yescharacteristic
1390C2#6065011yescharacteristic
1391C2#6119212yes—
1392C2#6260212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3316C2semidirect
2. C2×#3318C2semidirect
3. C2×#3301C2semidirect
4. C2×#3295C2semidirect
5. #37862C2semidirect
6. #37677C2semidirect
7. #33228C2semidirect
8. #33183C2semidirect
9. #33181C2semidirect
10. #28524C2semidirect
11. #28452C2semidirect
12. #28431C2semidirect
13. #28430C2semidirect
14. #28415C2semidirect
15. #28412C2semidirect
16. #28364C2semidirect
17. #28361C2semidirect
18. #28352C2semidirect
19. #28347C2semidirect
20. #28343C2semidirect
21. #28341C2semidirect
22. #28334C2semidirect
23. #28332C2semidirect
24. #27920C2semidirect
25. #27906C2semidirect
26. #25736C2semidirect
27. #25724C2semidirect
28. #21694C2semidirect
29. #21206C2semidirect
30. C2×#1959C2semidirect
31. #20493C2semidirect
42. C2×#496C22semidirect
44. C2×#495C22semidirect
46. C2×#489C22semidirect
47. C2×#488C22semidirect
52. C2×#481C22semidirect
53. C2×#481C22semidirect
54. C2×#485C22semidirect
56. C2×#483C22semidirect
57. C2×#479C22semidirect
58. C2×#475C22semidirect
61. C2×#470C22semidirect
64. C2×#466C22semidirect
67. C2×#465C22semidirect
68. C2×#465C22semidirect
69. C2×#464C22semidirect
71. C2×#463C22semidirect
73. C2×#452C22semidirect
74. C2×#449C22semidirect
75. C2×#451C22semidirect
76. C2×#448C22semidirect
82. C2×#441C22semidirect
84. C2×C4×SD16C22semidirect
87. C2×#417C22semidirect
89. C2×#416C22semidirect
90. C22×#103C22semidirect
91. C22×#103C22semidirect
95. C2×#405C22semidirect
96. C22×#97C22semidirect
98. #2850C22semidirect
103. #2660C22semidirect
106. #2620C22semidirect
107. #2565C22semidirect
110. #2542C22semidirect
111. #2504C22semidirect
112. #2502C22semidirect
113. #2501C22semidirect
114. #2499C22semidirect
124. #2326C22semidirect
125. #2317C22semidirect
127. C2×#384C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2094C22semidirect
136. #2094C22semidirect
137. #2094C22semidirect
139. #2092C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
145. #2014C22semidirect
147. #2012C22semidirect
148. #2012C22semidirect
149. #2012C22semidirect
151. #2011C22semidirect
152. #1973C22semidirect
153. #1973C22semidirect
155. #1972C22semidirect
156. #1972C22semidirect
157. #1972C22semidirect
158. #1971C22semidirect
159. #1971C22semidirect
161. #1968C22semidirect
162. #1968C22semidirect
163. #1968C22semidirect
165. #1961C22semidirect
166. #1961C22semidirect
171. #1959C22semidirect
172. #1959C22semidirect
173. #1959C22semidirect
174. #1959C22semidirect
175. #1959C22semidirect
176. #1959C22semidirect
177. #1959C22semidirect
179. #1958C22semidirect
180. #1958C22semidirect
181. #1958C22semidirect
183. #1957C22semidirect
184. #1957C22semidirect
185. #1957C22semidirect
186. #1847C22semidirect
187. #1844C22semidirect
188. #1844C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
192. #1753C22semidirect
193. #1752C22semidirect
194. #1752C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
197. C4×C22⋊C8C22semidirect
198. #1726C22semidirect
332. #435D4semidirect
333. C8×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33162
C2×#33182
C2×#33012
C2×#32952
#378622
#376772
#332282
#331832
#331812
#285242
#284522
#284312
#284302
#284152
#284122
#283642
#283612
#283522
#283472
#283432
#283412
#283342
#283322
#279202
#279062
#257362
#257242
#216942
#212062
C2×#19592
#204932