Finite Group Databasebeta

← #6607024

Subgroups — #6607024

Order 512.

2466 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3350C211yesmaximal, characteristic, complemented
2C2×#3309C211yesmaximal, characteristic, complemented
3C2×#3311C211yesmaximal, characteristic, complemented
4C2×#3268C211yesmaximal, characteristic, complemented
5#36419C211yesmaximal, characteristic, complemented
6#36362C211yesmaximal, characteristic, complemented
7#33251C211yesmaximal, characteristic, complemented
8#33183C211yesmaximal, characteristic, complemented
9#33177C211yesmaximal, characteristic, complemented
10#28547C211yesmaximal, characteristic, complemented
11#28474C211yesmaximal, characteristic, complemented
12#28436C211yesmaximal, characteristic, complemented
13#28425C211yesmaximal, characteristic, complemented
14#28381C211yesmaximal, characteristic, complemented
15#28380C211yesmaximal, characteristic, complemented
16#28362C211yesmaximal, characteristic, complemented
17#28353C211yesmaximal, characteristic, complemented
18#28339C211yesmaximal, characteristic, complemented
19#28337C211yesmaximal, characteristic, complemented
20#28318C211yesmaximal, characteristic, complemented
21#28318C211yesmaximal, characteristic, complemented
22#28316C211yesmaximal, characteristic, complemented
23#28312C211yesmaximal, characteristic, complemented
24#27945C211yesmaximal, characteristic, complemented
25#27928C211yesmaximal, characteristic, complemented
26#25791C211yesmaximal, characteristic, complemented
27#25775C211yesmaximal, characteristic, complemented
28#21692C211yesmaximal, characteristic, complemented
29#21236C211yesmaximal, characteristic, complemented
30#21228C211yesmaximal, characteristic, complemented
31#20491C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#553C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3350—28no—
39#3311—28no—
40#3309—28no—
41#3268—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic
45C2×#495C2211yescharacteristic, complemented
46C2×#492C2211yescharacteristic
47C2×#490C2211yescharacteristic, complemented
48C2×#489C2211yescharacteristic
49C2×#485C2211yescharacteristic
50C2×#485C2211yescharacteristic, complemented
51C2×#482C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic, complemented
54C2×#482C2211yescharacteristic, complemented
55C2×#483C2211yescharacteristic
56C2×#480C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#479C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic
60C2×#476C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#466C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#459C2211yescharacteristic
72C2×#459C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#449C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic
83C2×#440C2211yescharacteristic, complemented
84C2×#440C2211yescharacteristic, complemented
85C2×#435C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C2×#427C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic
90C2×#418C2211yescharacteristic
91C2×#416C2211yescharacteristic
92C2×#416C2211yescharacteristic, complemented
93C2×C4×M16C2211yescharacteristic
94C22×#97C2211yescharacteristic, complemented
95#2861C2211yescharacteristic
96#2858C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2850C2211yescharacteristic
99#2850C2211yescharacteristic
100#2850C2211yescharacteristic, complemented
101#2568C2211yescharacteristic, complemented
102#2566C2211yescharacteristic
103#2559—22no—
104#2559—22no—
105#2554—22no—
106#2548C2211yescharacteristic, complemented
107#2544—22no—
108#2544C2211yescharacteristic
109#2502C2211yescharacteristic
110#2500C2211yescharacteristic
111#2500C2211yescharacteristic
112#2500C2211yescharacteristic, complemented
113#2464—22no—
114#2433C2211yescharacteristic
115#2432C2211yescharacteristic
116#2432C2211yescharacteristic, complemented
117#2431C2211yescharacteristic
118#2424—22no—
119#2367—22no—
120#2358—22no—
121C4×C4⋊Q8C2211yescharacteristic, complemented
122C4×#127C2211yescharacteristic
123#2297C2211yescharacteristic
124#2297C2211yescharacteristic
125#2297C2211yescharacteristic, complemented
126C2×#390C2211yescharacteristic
127C42×D4C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2094C2211yescharacteristic
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2093C2211yescharacteristic, complemented
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2014C2211yescharacteristic
144#2013C2211yescharacteristic
145#2012C2211yescharacteristic
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic, complemented
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1972C2211yescharacteristic
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic
167#1972C2211yescharacteristic, complemented
168#1972C2211yescharacteristic, complemented
169#1971C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1971C2211yescharacteristic, complemented
172#1970C2211yescharacteristic
173#1970C2211yescharacteristic
174#1970C2211yescharacteristic
175#1970C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1961C2211yescharacteristic
181#1959C2211yescharacteristic, complemented
182#1958C2211yescharacteristic, complemented
183#1958C2211yescharacteristic, complemented
184#1957C2211yescharacteristic
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1767C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1749C2211yescharacteristic
197#1749C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C2×AGL(1,ℤ/8)—24no—
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—42no—
206C2×#135—24no—
207C2×#135—24no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×M16C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C23×C8C2311yescharacteristic
228C23×C8C2311yescharacteristic
229#556—24no—
230#556—24no—
231#553—24no—
232#553—24no—
233#550—24no—
234#550—24no—
235#546—24no—
236#546—24no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×#127—21no—
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#126—21no—
244C2×#126—21no—
245C2×#126—21no—
246C2×#125C2311yescharacteristic
247C2×#124—21no—
248C2×#124—22no—
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#123—21no—
254C2×#123—21no—
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×#121—21no—
259C2×#121—22no—
260C2×#121—21no—
261C2×#121—21no—
262C2×#121—21no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×#120—22no—
270C2×C4×Q8—21no—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4—21no—
275C2×C4×D4—22no—
276C2×C4×D4D412yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4—22no—
285C22×C22⋊C4—21no—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288#501—24no—
289#496—24no—
290#496—42no—
291#495—42no—
292#492—24no—
293#490—24no—
294#489—24no—
295#485—24no—
296#485—24no—
297#483—24no—
298#482—24no—
299#482—24no—
300#482—24no—
301#482—24no—
302#480—24no—
303#479—24no—
304#479—24no—
305#476—24no—
306#476—24no—
307#470—24no—
308#469—24no—
309#468—24no—
310#468—24no—
311#466—24no—
312#466—24no—
313#465—24no—
314#465—24no—
315#464—24no—
316#464—24no—
317#459—24no—
318#459—24no—
319#452—24no—
320#452—24no—
321#450—24no—
322#449—24no—
323#449—24no—
324#449—24no—
325#449—24no—
326#447—24no—
327#440—24no—
328#440—24no—
329#440—24no—
330#440—24no—
331#435D418yescomplemented
332#435D418yescomplemented
333#428—24no—
334#427—24no—
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
342C2×#107C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×#106C2311yescharacteristic
349C2×#106C2311yescharacteristic
350C2×#106C2311yescharacteristic
351C2×C4⋊C8C2311yescharacteristic
352C2×C4⋊C8C2311yescharacteristic
353#418—24no—
354#417—24no—
355#416—24no—
356#416—24no—
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×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×C22⋊C8C2311yescharacteristic
390C2×C22⋊C8C2311yescharacteristic
391C2×C22⋊C8C2311yescharacteristic
392C2×C22⋊C8C2311yescharacteristic
393C4×M16—42no—
394C2×#97—42no—
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407#400—22no—
408#398—22no—
409#396—22no—
410#394—22no—
411#394—22no—
412#394—22no—
413#394—22no—
414#394—22no—
415#394—22no—
416#394—22no—
417#392—22no—
418#392—22no—
419#391—22no—
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#390—22no—
428#390—22no—
429#390—22no—
430#390—22no—
431#390—22no—
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#389—22no—
446#388—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#386—22no—
455#386—22no—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472C4×C4⋊C4—22no—
473C4×C4⋊C4D412yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4—22no—
476C4×C22⋊C4—22no—
477C4×C22⋊C4—22no—
478C4×C22⋊C4D412yes—
479C4×C22⋊C4D412yes—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C43C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C22×Q8—21no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
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×C4C2×D412yes—
544C23×C4C2×D412yes—
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547AGL(1,ℤ/8)—416no—
548#135—416no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
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—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16#4114yes—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8—41no—
595C2×D8—41no—
596C2×D8—41no—
597C2×M16—22no—
598C2×M16—22no—
599C2×M16—41no—
600C2×M16—41no—
601C2×M16C2×D414yes—
602C2×M16C2×D414yes—
603C22×C8—22no—
604C22×C8—22no—
605C22×C8—41no—
606C22×C8—41no—
607C22×C8C2×D414yes—
608C22×C8C2×D414yes—
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C4⋊Q8—22no—
618C4⋊Q8—22no—
619C4⋊Q8—22no—
620C4⋊Q8—41no—
621#127—22no—
622#127—22no—
623#127—22no—
624#127—41no—
625#127—41no—
626#127—41no—
627#127—44no—
628#126—44no—
629#126—44no—
630#126—44no—
631#125—22no—
632#125—22no—
633#124—22no—
634#124—22no—
635#124—48no—
636#124—41no—
637#124—41no—
638#124—41no—
639#124—41no—
640#124—41no—
641#124—41no—
642#124—44no—
643#123—44no—
644#123—44no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
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—44no—
662#121—44no—
663#121—44no—
664#121—44no—
665#121—84no—
666#120—48no—
667#120—44no—
668C4×Q8—22no—
669C4×Q8—22no—
670C4×Q8—22no—
671C4×Q8—22no—
672C4×Q8—44no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—44no—
678C4×D4—44no—
679C4×D4—44no—
680C4×D4—84no—
681C4×D4C2×D414yes—
682C4×D4C2×D414yes—
683#117—22no—
684#117—22no—
685#117—22no—
686#117—22no—
687#117—22no—
688#117—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4—84no—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—41no—
757C2×C42—41no—
758C2×C42—41no—
759C2×C42—41no—
760C2×C42C2×D412yes—
761C2×C42C2×D412yes—
762C2×C42C2×D412yes—
763C2×C42C2×D412yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—22no—
775#107—22no—
776#107—22no—
777#106—22no—
778#106—22no—
779#106—22no—
780#106—22no—
781#106—22no—
782#106—22no—
783#106—22no—
784#106—22no—
785C4⋊C8C2×D414yes—
786C4⋊C8C2×D414yes—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#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—
819C22⋊C8C2×D414yes—
820C22⋊C8C2×D414yes—
821C22⋊C8C2×D414yes—
822C22⋊C8C2×D414yes—
823#97—22no—
824#97—22no—
825#97—41no—
826#97—41no—
827#97—41no—
828#97—41no—
829#97C2×D414yes—
830#97C2×D414yes—
831C4×C8—22no—
832C4×C8—22no—
833C4×C8—41no—
834C4×C8—41no—
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#95—22no—
845#95C2×D412yes—
846#95C2×D412yes—
847#95C2×D412yes—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—44no—
855C24—42no—
856C24—82no—
857C24—81no—
858C24C22×D411yescharacteristic
859C24C22×D411yescharacteristic
860#41—44no—
861#41—44no—
862#41—44no—
863#41—44no—
864#41—44no—
865#41—44no—
866#41—82no—
867#41—82no—
868#41—82no—
869#41—82no—
870#41—82no—
871#41—82no—
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—44no—
890C2×Q8—42no—
891C2×Q8C2×#4112yes—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—44no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—81no—
948C2×D4—82no—
949C2×D4—82no—
950C2×D4—82no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4—82no—
955C2×D4—82no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4#12714yes—
959C2×D4C2×#4112yes—
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—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—42no—
980C22×C4—42no—
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—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—82no—
998C22×C4—82no—
999C22×C4—82no—
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D412yes—
1008C22×C4C22×D412yes—
1009C22×C4C22×D412yes—
1010C22×C4C22×D412yes—
1011C22×C4C22×D412yes—
1012C22×C4C2511yescharacteristic
1013Q16—44no—
1014Q16—82no—
1015SD16—28no—
1016SD16—44no—
1017SD16—44no—
1018SD16—44no—
1019SD16—44no—
1020SD16—44no—
1021SD16—82no—
1022SD16—82no—
1023D8—44no—
1024D8—44no—
1025D8—44no—
1026D8—82no—
1027D8—82no—
1028D8—82no—
1029M16—28no—
1030M16—44no—
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×C8—21no—
1044C2×C8—21no—
1045C2×C8—28no—
1046C2×C8—44no—
1047C2×C8C22×D412yes—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C2×C8C22×D412yes—
1051C2×C8C22×D412yes—
1052C2×C8C22×D412yes—
1053C2×C8C22×D412yes—
1054C2×C8C22×D412yes—
1055C2×C8C2×#4112yes—
1056C2×C8H(5,𝔽2)12yes—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
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—42no—
1074C4⋊C4—44no—
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—82no—
1085C4⋊C4—82no—
1086C4⋊C4—82no—
1087C4⋊C4#12714yes—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
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—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C22⋊C4—82no—
1120C22⋊C4—82no—
1121C22⋊C4#12714yes—
1122C22⋊C4#12714yes—
1123C42—24no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42C22×D412yes—
1141C42C22×D412yes—
1142C23—22no—
1143C23—22no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—42no—
1152C23—41no—
1153C23—41no—
1154C23—42no—
1155C23—42no—
1156C23—42no—
1157C23—42no—
1158C23—42no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—42no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—84no—
1176C23—84no—
1177C23—88no—
1178C23—162no—
1179C23—164no—
1180C23C2×#12712yes—
1181C23C2×#12712yes—
1182C23C23×D411yescharacteristic
1183Q8—22no—
1184Q8—22no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—84no—
1196D4—22no—
1197D4—22no—
1198D4—44no—
1199D4—41no—
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—41no—
1217D4—84no—
1218D4—88no—
1219D4—84no—
1220D4—84no—
1221D4—84no—
1222D4—84no—
1223D4—84no—
1224D4—162no—
1225D4—164no—
1226D4—162no—
1227D4—162no—
1228D4—162no—
1229D4—162no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
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—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—41no—
1257C2×C4—41no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
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—41no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—84no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4C2×#12712yes—
1289C2×C4C2×#12712yes—
1290C2×C4C2×#12712yes—
1291C2×C4C2×#12712yes—
1292C2×C4#57514yes—
1293C2×C4C23×D411yescharacteristic
1294C2×C4C23×D411yescharacteristic
1295C2×C4C22×#4111yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4#58511yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—22no—
1300C8—22no—
1301C8—22no—
1302C8—22no—
1303C8—22no—
1304C8—22no—
1305C8—22no—
1306C8#54614yes—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—42no—
1319C22—82no—
1320C22—81no—
1321C22—81no—
1322C22—82no—
1323C22—82no—
1324C22—82no—
1325C22—82no—
1326C22—82no—
1327C22—82no—
1328C22—82no—
1329C22—82no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—168no—
1343C22C22×#12711yescharacteristic
1344C22D4×#4111yescharacteristic
1345C22#349611yescharacteristic
1346C22C2×#57512yes—
1347C22#358512yes—
1348C4—24no—
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—22no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4C2×#54611yescharacteristic
1368C4D4×#4111yescharacteristic
1369C4#349611yescharacteristic
1370C4#350011yescharacteristic
1371C2—42no—
1372C2—42no—
1373C2—82no—
1374C2—161no—
1375C2—161no—
1376C2—161no—
1377C2—161no—
1378C2#3626011yescharacteristic
1379C2#6063911yescharacteristic
1380C2#6065011yescharacteristic
1381C2#6145612yes—
1382C2#6230412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3350C2semidirect
2. C2×#3309C2semidirect
3. C2×#3311C2semidirect
4. C2×#3268C2semidirect
5. #36419C2semidirect
6. #36362C2semidirect
7. #33251C2semidirect
8. #33183C2semidirect
9. #33177C2semidirect
10. #28547C2semidirect
11. #28474C2semidirect
12. #28436C2semidirect
13. #28425C2semidirect
14. #28381C2semidirect
15. #28380C2semidirect
16. #28362C2semidirect
17. #28353C2semidirect
18. #28339C2semidirect
19. #28337C2semidirect
20. #28318C2semidirect
21. #28318C2semidirect
22. #28316C2semidirect
23. #28312C2semidirect
24. #27945C2semidirect
25. #27928C2semidirect
26. #25791C2semidirect
27. #25775C2semidirect
28. #21692C2semidirect
29. #21236C2semidirect
30. #21228C2semidirect
31. #20491C2semidirect
42. C2×#501C22semidirect
45. C2×#495C22semidirect
47. C2×#490C22semidirect
50. C2×#485C22semidirect
53. C2×#482C22semidirect
54. C2×#482C22semidirect
57. C2×#479C22semidirect
58. C2×#479C22semidirect
60. C2×#476C22semidirect
66. C2×#466C22semidirect
68. C2×#465C22semidirect
72. C2×#459C22semidirect
78. C2×#449C22semidirect
83. C2×#440C22semidirect
84. C2×#440C22semidirect
88. C2×#427C22semidirect
92. C2×#416C22semidirect
94. C22×#97C22semidirect
96. #2858C22semidirect
100. #2850C22semidirect
101. #2568C22semidirect
106. #2548C22semidirect
112. #2500C22semidirect
116. #2432C22semidirect
121. C4×C4⋊Q8C22semidirect
125. #2297C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2095C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2093C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
148. #2012C22semidirect
157. #1973C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
167. #1972C22semidirect
168. #1972C22semidirect
169. #1971C22semidirect
170. #1971C22semidirect
171. #1971C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
181. #1959C22semidirect
182. #1958C22semidirect
183. #1958C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1767C22semidirect
194. C8×C22⋊C4C22semidirect
195. C8×C22⋊C4C22semidirect
197. #1749C22semidirect
198. C4×#97C22semidirect
331. #435D4semidirect
332. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33502
C2×#33092
C2×#33112
C2×#32682
#364192
#363622
#332512
#331832
#331772
#285472
#284742
#284362
#284252
#283812
#283802
#283622
#283532
#283392
#283372
#283182
#283162
#283122
#279452
#279282
#257912
#257752
#216922
#212362
#212282
#204912