Finite Group Databasebeta

← #6607222

Subgroups — #6607222

Order 512.

2405 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3349C211yesmaximal, characteristic, complemented
2C2×#3317C211yesmaximal, characteristic, complemented
3C2×#3311C211yesmaximal, characteristic, complemented
4C2×#3268C211yesmaximal, characteristic
5#36419C211yesmaximal, characteristic, complemented
6#36386C211yesmaximal, characteristic, complemented
7#33251C211yesmaximal, characteristic, complemented
8#33186C211yesmaximal, characteristic, complemented
9#33173C211yesmaximal, characteristic, complemented
10#28547C211yesmaximal, characteristic, complemented
11#28481C211yesmaximal, characteristic, complemented
12#28425C211yesmaximal, characteristic, complemented
13#28424C211yesmaximal, characteristic, complemented
14#28377C211yesmaximal, characteristic, complemented
15#28371C211yesmaximal, characteristic, complemented
16#28357C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28351C211yesmaximal, characteristic, complemented
19#28351C211yesmaximal, characteristic, complemented
20#28309C211yesmaximal, characteristic, complemented
21#28309C211yesmaximal, characteristic, complemented
22#28308C211yesmaximal, characteristic, complemented
23#28303C211yesmaximal, characteristic, complemented
24#27946C211yesmaximal, characteristic, complemented
25#27935C211yesmaximal, characteristic, complemented
26#25796C211yesmaximal, characteristic, complemented
27#25786C211yesmaximal, characteristic, complemented
28#21702C211yesmaximal, characteristic, complemented
29#21236C211yesmaximal, characteristic, complemented
30#21224C211yesmaximal, characteristic, complemented
31C4×#435C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#552C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3349—28no—
39#3317—28no—
40#3311—28no—
41#3268—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#497C2211yescharacteristic, complemented
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#490C2211yescharacteristic, complemented
48C2×#489C2211yescharacteristic
49C2×#484C2211yescharacteristic
50C2×#481C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#485C2211yescharacteristic, complemented
54C2×#485C2211yescharacteristic, complemented
55C2×#482C2211yescharacteristic
56C2×#482C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#479C2211yescharacteristic, complemented
59C2×#477C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#467C2211yescharacteristic, complemented
66C2×#466C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#460C2211yescharacteristic, complemented
72C2×#459C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#452C2211yescharacteristic, complemented
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#441C2211yescharacteristic, complemented
82C2×#441C2211yescharacteristic, complemented
83C2×#440C2211yescharacteristic
84C2×#440C2211yescharacteristic
85C2×#435C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C2×#427C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic
90C2×#418C2211yescharacteristic
91C2×#416C2211yescharacteristic
92C2×#416C2211yescharacteristic, complemented
93C2×C4×M16C2211yescharacteristic
94C22×C4×C8C2211yescharacteristic, complemented
95#2861C2211yescharacteristic
96#2858C2211yescharacteristic, complemented
97#2857C2211yescharacteristic
98#2850C2211yescharacteristic
99#2850C2211yescharacteristic
100#2850C2211yescharacteristic, complemented
101#2568C2211yescharacteristic, complemented
102#2566C2211yescharacteristic
103#2559—22no—
104#2559—22no—
105#2559—22no—
106#2558—22no—
107#2548C2211yescharacteristic, complemented
108#2545C2211yescharacteristic
109#2544—22no—
110#2534—22no—
111#2503C2211yescharacteristic
112#2500C2211yescharacteristic
113#2500C2211yescharacteristic
114#2500C2211yescharacteristic, complemented
115#2435C2211yescharacteristic
116#2432C2211yescharacteristic
117#2432C2211yescharacteristic
118#2432C2211yescharacteristic, complemented
119#2367—22no—
120#2342—22no—
121C4×C4⋊Q8C2211yescharacteristic, complemented
122C4×#124C2211yescharacteristic
123#2297C2211yescharacteristic
124#2297C2211yescharacteristic
125#2297C2211yescharacteristic, complemented
126C2×#390C2211yescharacteristic
127C42×D4C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2093C2211yescharacteristic
133#2093C2211yescharacteristic, complemented
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic, complemented
144#2013C2211yescharacteristic
145#2013C2211yescharacteristic, complemented
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1972C2211yescharacteristic
157#1972C2211yescharacteristic
158#1972C2211yescharacteristic
159#1972C2211yescharacteristic
160#1970C2211yescharacteristic
161#1970C2211yescharacteristic
162#1970C2211yescharacteristic
163#1970C2211yescharacteristic
164#1970C2211yescharacteristic
165#1969C2211yescharacteristic, complemented
166#1969C2211yescharacteristic, complemented
167#1969C2211yescharacteristic, complemented
168#1969C2211yescharacteristic, complemented
169#1969C2211yescharacteristic, complemented
170#1968C2211yescharacteristic
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic, complemented
176#1968C2211yescharacteristic, complemented
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1960C2211yescharacteristic, complemented
181#1960C2211yescharacteristic, complemented
182#1959C2211yescharacteristic
183#1959C2211yescharacteristic, complemented
184#1958C2211yescharacteristic
185#1958C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191C4×C4⋊C8C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195#1752C2211yescharacteristic, complemented
196C4×C22⋊C8C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic, 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×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×M16C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C23×C8C2311yescharacteristic
228C23×C8C2311yescharacteristic
229#556—24no—
230#556—24no—
231#552—24no—
232#552—24no—
233#550—24no—
234#550—24no—
235#546—24no—
236#546—24no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127—21no—
241C2×#127C2311yescharacteristic
242C2×#126—21no—
243C2×#126—21no—
244C2×#126—21no—
245C2×#125—21no—
246C2×#125C2311yescharacteristic
247C2×#124—21no—
248C2×#124—22no—
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#123—21no—
255C2×#123—21no—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×#121—21no—
262C2×#121—21no—
263C2×#121—21no—
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#120—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4D412yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×#117—21no—
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C22⋊C4—22no—
282C22×C22⋊C4—21no—
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285#501—24no—
286#497—24no—
287#497—42no—
288#496—24no—
289#495—42no—
290#490—24no—
291#489—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#485—24no—
296#484—24no—
297#482—24no—
298#482—24no—
299#481—24no—
300#479—24no—
301#479—24no—
302#477—24no—
303#476—24no—
304#470—24no—
305#470—24no—
306#468—24no—
307#468—24no—
308#467—24no—
309#466—24no—
310#465—24no—
311#465—24no—
312#464—24no—
313#464—24no—
314#460—24no—
315#459—24no—
316#452—24no—
317#452—24no—
318#452—24no—
319#452—24no—
320#450—24no—
321#449—24no—
322#449—24no—
323#447—24no—
324#441—24no—
325#441—24no—
326#440—24no—
327#440—24no—
328#435D418yes—
329#435D418yes—
330#428—24no—
331#427—24no—
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349C2×C4⋊C8C2311yescharacteristic
350#418—24no—
351#417—24no—
352#416—24no—
353#416—24no—
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#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×C22⋊C8C2311yescharacteristic
387C2×C22⋊C8C2311yescharacteristic
388C2×C22⋊C8C2311yescharacteristic
389C2×C22⋊C8C2311yescharacteristic
390C4×M16—42no—
391C2×#97C2311yescharacteristic
392C2×#97C2311yescharacteristic
393C2×#97C2311yescharacteristic
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×C4×C8—42no—
398C2×C4×C8C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404#400—22no—
405#400—22no—
406#396—22no—
407#396—22no—
408#394—22no—
409#394—22no—
410#394—22no—
411#394—22no—
412#394—22no—
413#394—22no—
414#394—22no—
415#394—22no—
416#391—22no—
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#390—22no—
426#390—22no—
427#390—22no—
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#389—22no—
441#389—22no—
442#388—22no—
443#388—22no—
444#388—22no—
445#388—22no—
446#388—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#386—22no—
456#386—22no—
457#386—22no—
458#385—22no—
459#385—22no—
460#385—22no—
461#385—22no—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381—22no—
469#380—22no—
470#379—22no—
471C4×C4⋊C4—22no—
472C4×C4⋊C4D412yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4—22no—
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×Q8C2411yescharacteristic
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D412yes—
539C23×C4C2×D412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542AGL(1,ℤ/8)—416no—
543#135—416no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
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—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16#4114yes—
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—41no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—41no—
595C2×M16—41no—
596C2×M16C2×D414yes—
597C2×M16C2×D414yes—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8—41no—
602C22×C8C2×D414yes—
603C22×C8C2×D414yes—
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614C4⋊Q8—22no—
615C4⋊Q8—41no—
616C4⋊Q8—41no—
617C4⋊Q8—41no—
618#127—22no—
619#127—22no—
620#127—44no—
621#126—44no—
622#126—44no—
623#126—44no—
624#125—22no—
625#125—22no—
626#125—44no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—41no—
631#124—48no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—41no—
637#124—41no—
638#124—44no—
639#123—44no—
640#123—44no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
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—44no—
658#121—44no—
659#121—44no—
660#120—44no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—22no—
667C4×Q8—44no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—44no—
671C4×D4—44no—
672C4×D4C2×D414yes—
673C4×D4C2×D414yes—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—22no—
678#117—22no—
679#117—22no—
680#117—44no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—48no—
740C2×C22⋊C4—44no—
741C2×C22⋊C4C2×D412yes—
742C2×C22⋊C4C2×D412yes—
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—41no—
752C2×C42—41no—
753C2×C42—41no—
754C2×C42—41no—
755C2×C42C2×D412yes—
756C2×C42C2×D412yes—
757C2×C42C2×D412yes—
758C2×C42C2×D412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779#106—22no—
780C4⋊C8C2×D414yes—
781C4⋊C8C2×D414yes—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818#97—22no—
819#97—22no—
820#97—41no—
821#97—41no—
822#97C2×D414yes—
823#97C2×D414yes—
824C4×C8—22no—
825C4×C8—22no—
826C4×C8—41no—
827C4×C8—41no—
828C4×C8—41no—
829C4×C8—41no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—42no—
850C24—44no—
851C24—42no—
852C24—81no—
853C24—82no—
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—44no—
861#41—44no—
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867#41—82no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8C2×#4112yes—
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—44no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—82no—
935C2×D4—82no—
936C2×D4—81no—
937C2×D4—82no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4—82no—
944C2×D4#12714yes—
945C2×D4C2×#4112yes—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—82no—
985C22×C4C22×D412yes—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C2511yescharacteristic
998Q16—44no—
999Q16—44no—
1000Q16—44no—
1001Q16—82no—
1002SD16—28no—
1003SD16—44no—
1004SD16—44no—
1005SD16—44no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009SD16—82no—
1010D8—44no—
1011D8—44no—
1012D8—44no—
1013D8—82no—
1014M16—28no—
1015M16—44no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—28no—
1031C2×C8—44no—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C2×C8C22×D412yes—
1040C2×C8C2×#4112yes—
1041C2×C8H(5,𝔽2)12yes—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4—82no—
1075C4⋊C4#12714yes—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4#12714yes—
1109C22⋊C4#12714yes—
1110C42—24no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42C22×D412yes—
1129C42C22×D412yes—
1130C23—22no—
1131C23—22no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—42no—
1156C23—42no—
1157C23—42no—
1158C23—84no—
1159C23—84no—
1160C23—88no—
1161C23—162no—
1162C23—164no—
1163C23C2×#12712yes—
1164C23C2×#12712yes—
1165C23C23×D411yescharacteristic
1166Q8—22no—
1167Q8—22no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—84no—
1183D4—22no—
1184D4—22no—
1185D4—44no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—48no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—162no—
1269C2×C4C2×#12712yes—
1270C2×C4C2×#12712yes—
1271C2×C4C2×#12712yes—
1272C2×C4C2×#12712yes—
1273C2×C4#57514yes—
1274C2×C4C23×D411yescharacteristic
1275C2×C4C23×D411yescharacteristic
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—22no—
1282C8—22no—
1283C8—22no—
1284C8—22no—
1285C8—22no—
1286C8—22no—
1287C8#54614yes—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—44no—
1299C22—42no—
1300C22—82no—
1301C22—81no—
1302C22—81no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—168no—
1319C22C22×#12711yescharacteristic
1320C22D4×#4111yescharacteristic
1321C22#349611yescharacteristic
1322C22C2×#57512yes—
1323C22#358412yes—
1324C4—24no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4C2×#54611yescharacteristic
1345C4D4×#4111yescharacteristic
1346C4#349611yescharacteristic
1347C4#350011yescharacteristic
1348C2—42no—
1349C2—42no—
1350C2—82no—
1351C2—161no—
1352C2—161no—
1353C2—161no—
1354C2#3626011yescharacteristic
1355C2#6063911yescharacteristic
1356C2#6064911yescharacteristic
1357C2#6144112yes—
1358C2#6225512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3268C2
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×#3349C2semidirect
2. C2×#3317C2semidirect
3. C2×#3311C2semidirect
5. #36419C2semidirect
6. #36386C2semidirect
7. #33251C2semidirect
8. #33186C2semidirect
9. #33173C2semidirect
10. #28547C2semidirect
11. #28481C2semidirect
12. #28425C2semidirect
13. #28424C2semidirect
14. #28377C2semidirect
15. #28371C2semidirect
16. #28357C2semidirect
17. #28356C2semidirect
18. #28351C2semidirect
19. #28351C2semidirect
20. #28309C2semidirect
21. #28309C2semidirect
22. #28308C2semidirect
23. #28303C2semidirect
24. #27946C2semidirect
25. #27935C2semidirect
26. #25796C2semidirect
27. #25786C2semidirect
28. #21702C2semidirect
29. #21236C2semidirect
30. #21224C2semidirect
31. C4×#435C2semidirect
42. C2×#501C22semidirect
44. C2×#497C22semidirect
47. C2×#490C22semidirect
53. C2×#485C22semidirect
54. C2×#485C22semidirect
56. C2×#482C22semidirect
57. C2×#479C22semidirect
58. C2×#479C22semidirect
59. C2×#477C22semidirect
65. C2×#467C22semidirect
68. C2×#465C22semidirect
71. C2×#460C22semidirect
76. C2×#452C22semidirect
81. C2×#441C22semidirect
82. C2×#441C22semidirect
88. C2×#427C22semidirect
92. C2×#416C22semidirect
94. C22×C4×C8C22semidirect
96. #2858C22semidirect
100. #2850C22semidirect
101. #2568C22semidirect
107. #2548C22semidirect
114. #2500C22semidirect
118. #2432C22semidirect
121. C4×C4⋊Q8C22semidirect
125. #2297C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
133. #2093C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
143. #2015C22semidirect
145. #2013C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
165. #1969C22semidirect
166. #1969C22semidirect
167. #1969C22semidirect
168. #1969C22semidirect
169. #1969C22semidirect
175. #1968C22semidirect
176. #1968C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
180. #1960C22semidirect
181. #1960C22semidirect
183. #1959C22semidirect
185. #1958C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1846C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. C4×C4⋊C8C22semidirect
194. #1752C22semidirect
195. #1752C22semidirect
197. C4×C22⋊C8C22semidirect
198. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33492
C2×#33172
C2×#33112
C2×#32682
#364192
#363862
#332512
#331862
#331732
#285472
#284812
#284252
#284242
#283772
#283712
#283572
#283562
#283512
#283092
#283082
#283032
#279462
#279352
#257962
#257862
#217022
#212362
#212242
C4×#4352