Finite Group Databasebeta

← #6607020

Subgroups — #6607020

Order 512.

2379 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3349C211yesmaximal, characteristic, complemented
2C2×#3311C211yesmaximal, characteristic, complemented
3C2×#3315C211yesmaximal, characteristic, complemented
4C2×#3267C211yesmaximal, characteristic
5#36406C211yesmaximal, characteristic, complemented
6#36386C211yesmaximal, characteristic, complemented
7#33250C211yesmaximal, characteristic, complemented
8#33184C211yesmaximal, characteristic, complemented
9#33176C211yesmaximal, characteristic, complemented
10#28548C211yesmaximal, characteristic, complemented
11#28477C211yesmaximal, characteristic, complemented
12#28433C211yesmaximal, characteristic, complemented
13#28426C211yesmaximal, characteristic, complemented
14#28384C211yesmaximal, characteristic, complemented
15#28379C211yesmaximal, characteristic, complemented
16#28361C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28339C211yesmaximal, characteristic, complemented
19#28338C211yesmaximal, characteristic, complemented
20#28318C211yesmaximal, characteristic, complemented
21#28317C211yesmaximal, characteristic, complemented
22#28317C211yesmaximal, characteristic, complemented
23#28311C211yesmaximal, characteristic, complemented
24#27943C211yesmaximal, characteristic, complemented
25#27925C211yesmaximal, characteristic, complemented
26#25796C211yesmaximal, characteristic, complemented
27#25778C211yesmaximal, characteristic, complemented
28#21693C211yesmaximal, 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×#552C2211yescharacteristic
36C2×#547C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3349—28no—
39#3315—28no—
40#3311—28no—
41#3267—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#497C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#494C2211yescharacteristic, complemented
47C2×#491C2211yescharacteristic, complemented
48C2×#489C2211yescharacteristic
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#485C2211yescharacteristic, complemented
54C2×#485C2211yescharacteristic, complemented
55C2×#485C2211yescharacteristic, complemented
56C2×#482C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#470C2211yescharacteristic
64C2×#470C2211yescharacteristic
65C2×#467C2211yescharacteristic, complemented
66C2×#467C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#462C2211yescharacteristic, complemented
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#452C2211yescharacteristic
77C2×#452C2211yescharacteristic, complemented
78C2×#449C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#450C2211yescharacteristic
81C2×#442C2211yescharacteristic
82C2×#441C2211yescharacteristic, complemented
83C2×#440C2211yescharacteristic
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#2862C2211yescharacteristic, complemented
96#2861C2211yescharacteristic
97#2857C2211yescharacteristic
98#2857C2211yescharacteristic
99#2857C2211yescharacteristic, complemented
100#2850C2211yescharacteristic
101#2566C2211yescharacteristic
102#2559—22no—
103#2558—22no—
104#2553—22no—
105#2553—22no—
106#2546C2211yescharacteristic, complemented
107#2545C2211yescharacteristic
108#2542C2211yescharacteristic, complemented
109#2534—22no—
110#2503C2211yescharacteristic
111#2500C2211yescharacteristic
112#2499C2211yescharacteristic
113#2499C2211yescharacteristic, complemented
114#2435C2211yescharacteristic
115#2432C2211yescharacteristic
116#2432C2211yescharacteristic
117#2432C2211yescharacteristic, complemented
118#2427—22no—
119#2360—22no—
120#2342—22no—
121C4×#124C2211yescharacteristic
122C4×#124C2211yescharacteristic, complemented
123#2297C2211yescharacteristic
124#2297C2211yescharacteristic
125#2297C2211yescharacteristic, complemented
126C2×#390C2211yescharacteristic
127C42×D4C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2095C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic, complemented
146#2013C2211yescharacteristic
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2013C2211yescharacteristic, complemented
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1972C2211yescharacteristic
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic
165#1971C2211yescharacteristic, complemented
166#1971C2211yescharacteristic, complemented
167#1971C2211yescharacteristic, complemented
168#1971C2211yescharacteristic, complemented
169#1971C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1971C2211yescharacteristic, complemented
172#1970C2211yescharacteristic
173#1970C2211yescharacteristic
174#1969C2211yescharacteristic, complemented
175#1969C2211yescharacteristic, complemented
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic
178#1968C2211yescharacteristic
179#1968C2211yescharacteristic
180#1960C2211yescharacteristic, complemented
181#1959C2211yescharacteristic
182#1958C2211yescharacteristic
183#1958C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, 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×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
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#547—24no—
234#547—24no—
235#546—24no—
236#546—24no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×#126—21no—
243C2×#126—21no—
244C2×#126—21no—
245C2×#125—21no—
246C2×#125C2311yescharacteristic
247C2×#124—21no—
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#123—21no—
253C2×#123—21no—
254C2×#123—21no—
255C2×#123—21no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×#121—21no—
265C2×#121—21no—
266C2×#121C2311yescharacteristic
267C2×#120—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4D412yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—21no—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C22×C4⋊C4—21no—
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#495—24no—
289#494—42no—
290#491—24no—
291#489—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#485—24no—
296#485—24no—
297#484—24no—
298#484—24no—
299#482—24no—
300#479—24no—
301#478—24no—
302#477—24no—
303#476—24no—
304#470—24no—
305#470—24no—
306#470—24no—
307#470—24no—
308#467—24no—
309#467—24no—
310#465—24no—
311#465—24no—
312#464—24no—
313#463—24no—
314#462—24no—
315#461—24no—
316#452—24no—
317#452—24no—
318#452—24no—
319#452—24no—
320#452—24no—
321#450—24no—
322#450—24no—
323#449—24no—
324#442—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×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
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×#97—42no—
392C2×#97C2311yescharacteristic
393C2×#97C2311yescharacteristic
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404#400—22no—
405#399—22no—
406#398—22no—
407#397—22no—
408#397—22no—
409#396—22no—
410#396—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#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#390—22no—
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#389—22no—
439#389—22no—
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#387—22no—
450#387—22no—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#385—22no—
456#385—22no—
457#385—22no—
458#385—22no—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#382—22no—
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#382C2311yescharacteristic
466#381—22no—
467#380—22no—
468#380—22no—
469#380—22no—
470#379—22no—
471C4×C4⋊C4D412yes—
472C4×C4⋊C4C2311yescharacteristic
473C4×C22⋊C4—22no—
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×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2×D412yes—
536C23×C4C2×D412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539AGL(1,ℤ/8)—416no—
540#135—416no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×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—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—41no—
588C2×D8#4114yes—
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—41no—
592C2×M16—41no—
593C2×M16C2×D414yes—
594C2×M16C2×D414yes—
595C22×C8—22no—
596C22×C8—22no—
597C22×C8—41no—
598C22×C8—41no—
599C22×C8C2×D414yes—
600C22×C8C2×D414yes—
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C4⋊Q8—22no—
610C4⋊Q8—22no—
611C4⋊Q8—22no—
612C4⋊Q8—22no—
613C4⋊Q8—41no—
614C4⋊Q8—41no—
615C4⋊Q8—41no—
616C4⋊Q8—41no—
617C4⋊Q8—41no—
618C4⋊Q8—41no—
619#126—44no—
620#126—44no—
621#126—44no—
622#125—22no—
623#125—22no—
624#125—44no—
625#124—22no—
626#124—22no—
627#124—22no—
628#124—22no—
629#124—41no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—44no—
634#123—44no—
635#123—44no—
636#123—44no—
637#123—44no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—48no—
653#121—22no—
654#121—22no—
655#121—44no—
656#121—44no—
657#120—44no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—44no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—22no—
667C4×D4—44no—
668C4×D4C2×D414yes—
669C4×D4C2×D414yes—
670#117—22no—
671#117—22no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—44no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
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—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—44no—
701C2×C4⋊C4C2×D412yes—
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
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—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
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—48no—
739C2×C22⋊C4—44no—
740C2×C22⋊C4C2×D412yes—
741C2×C22⋊C4C2×D412yes—
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—41no—
750C2×C42—41no—
751C2×C42—41no—
752C2×C42—41no—
753C2×C42C2×D412yes—
754C2×C42C2×D412yes—
755C2×C42C2×D412yes—
756C2×C42C2×D412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778C4⋊C8C2×D414yes—
779C4⋊C8C2×D414yes—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—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—
812C22⋊C8C2×D414yes—
813C22⋊C8C2×D414yes—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816#97—22no—
817#97—22no—
818#97—41no—
819#97—41no—
820#97—41no—
821#97—41no—
822#97C2×D414yes—
823#97C2×D414yes—
824C4×C8—22no—
825C4×C8—22no—
826C4×C8—41no—
827C4×C8—41no—
828#95—22no—
829#95—22no—
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—42no—
849C24—44no—
850C24—42no—
851C24—81no—
852C24—82no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855#41—44no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—44no—
861#41—82no—
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—44no—
898C2×Q8—42no—
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—44no—
916C2×D4—44no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—82no—
928C2×D4—82no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—82no—
934C2×D4#12714yes—
935C2×D4C2×#4112yes—
936C2×D4C2×#4112yes—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—24no—
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—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—82no—
979C22×C4C22×D412yes—
980C22×C4C22×D412yes—
981C22×C4C22×D412yes—
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D412yes—
991C22×C4C2511yescharacteristic
992Q16—44no—
993Q16—44no—
994Q16—82no—
995Q16—82no—
996Q16—82no—
997Q16—82no—
998SD16—44no—
999SD16—44no—
1000SD16—44no—
1001SD16—44no—
1002SD16—44no—
1003SD16—44no—
1004SD16—82no—
1005SD16—82no—
1006D8—28no—
1007D8—44no—
1008M16—28no—
1009M16—44no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
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—28no—
1025C2×C8—44no—
1026C2×C8C22×D412yes—
1027C2×C8C22×D412yes—
1028C2×C8C22×D412yes—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C2×#4112yes—
1035C2×C8H(5,𝔽2)12yes—
1036C4⋊C4—24no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
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—44no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
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—44no—
1070C4⋊C4—82no—
1071C4⋊C4—82no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4#12714yes—
1075C22⋊C4—24no—
1076C22⋊C4—42no—
1077C22⋊C4—44no—
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—42no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4#12714yes—
1105C22⋊C4#12714yes—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42C22×D412yes—
1124C42C22×D412yes—
1125C23—22no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—42no—
1136C23—42no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—42no—
1148C23—84no—
1149C23—84no—
1150C23—88no—
1151C23—162no—
1152C23—164no—
1153C23C2×#12712yes—
1154C23C2×#12712yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—84no—
1177D4—22no—
1178D4—22no—
1179D4—22no—
1180D4—22no—
1181D4—44no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—162no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—84no—
1258C2×C4—162no—
1259C2×C4C2×#12712yes—
1260C2×C4C2×#12712yes—
1261C2×C4C2×#12712yes—
1262C2×C4C2×#12712yes—
1263C2×C4#57514yes—
1264C2×C4C23×D411yescharacteristic
1265C2×C4C23×D411yescharacteristic
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4#58511yescharacteristic
1269C2×C4#58511yescharacteristic
1270C8—22no—
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8#54614yes—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—44no—
1289C22—44no—
1290C22—42no—
1291C22—42no—
1292C22—82no—
1293C22—82no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—82no—
1299C22—82no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—168no—
1304C22C22×#12711yescharacteristic
1305C22D4×#4111yescharacteristic
1306C22#349611yescharacteristic
1307C22C2×#57512yes—
1308C22#358612yes—
1309C4—24no—
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4C2×#54611yescharacteristic
1331C4D4×#4111yescharacteristic
1332C4#349611yescharacteristic
1333C4#350011yescharacteristic
1334C2—42no—
1335C2—42no—
1336C2—82no—
1337C2—82no—
1338C2—161no—
1339C2#3626011yescharacteristic
1340C2#6063911yescharacteristic
1341C2#6065111yescharacteristic
1342C2#6146112yes—
1343C2#6230212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3267C2
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×#3311C2semidirect
3. C2×#3315C2semidirect
5. #36406C2semidirect
6. #36386C2semidirect
7. #33250C2semidirect
8. #33184C2semidirect
9. #33176C2semidirect
10. #28548C2semidirect
11. #28477C2semidirect
12. #28433C2semidirect
13. #28426C2semidirect
14. #28384C2semidirect
15. #28379C2semidirect
16. #28361C2semidirect
17. #28356C2semidirect
18. #28339C2semidirect
19. #28338C2semidirect
20. #28318C2semidirect
21. #28317C2semidirect
22. #28317C2semidirect
23. #28311C2semidirect
24. #27943C2semidirect
25. #27925C2semidirect
26. #25796C2semidirect
27. #25778C2semidirect
28. #21693C2semidirect
29. #21236C2semidirect
30. #21228C2semidirect
31. #20491C2semidirect
42. C2×#501C22semidirect
46. C2×#494C22semidirect
47. C2×#491C22semidirect
53. C2×#485C22semidirect
54. C2×#485C22semidirect
55. C2×#485C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
59. C2×#478C22semidirect
65. C2×#467C22semidirect
66. C2×#467C22semidirect
70. C2×#462C22semidirect
77. C2×#452C22semidirect
82. C2×#441C22semidirect
84. C2×#440C22semidirect
88. C2×#427C22semidirect
92. C2×#416C22semidirect
94. C22×#97C22semidirect
95. #2862C22semidirect
99. #2857C22semidirect
106. #2546C22semidirect
108. #2542C22semidirect
113. #2499C22semidirect
117. #2432C22semidirect
122. C4×#124C22semidirect
125. #2297C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2095C22semidirect
133. #2095C22semidirect
135. #2094C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
145. #2015C22semidirect
149. #2013C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
165. #1971C22semidirect
166. #1971C22semidirect
167. #1971C22semidirect
168. #1971C22semidirect
169. #1971C22semidirect
170. #1971C22semidirect
171. #1971C22semidirect
174. #1969C22semidirect
175. #1969C22semidirect
180. #1960C22semidirect
183. #1958C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1844C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1767C22semidirect
194. C8×C22⋊C4C22semidirect
195. C8×C22⋊C4C22semidirect
197. #1749C22semidirect
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×#33112
C2×#33152
C2×#32672
#364062
#363862
#332502
#331842
#331762
#285482
#284772
#284332
#284262
#283842
#283792
#283612
#283562
#283392
#283382
#283182
#283172
#283112
#279432
#279252
#257962
#257782
#216932
#212362
#212282
#204912