Finite Group Databasebeta

← #6558287

Subgroups — #6558287

Order 512.

2527 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3323C211yesmaximal, characteristic, complemented
2C2×#3312C211yesmaximal, characteristic, complemented
3C2×#3276C211yesmaximal, characteristic, complemented
4C2×#3267C211yesmaximal, characteristic
5#38088C211yesmaximal, characteristic, complemented
6#37676C211yesmaximal, characteristic, complemented
7#30272C211yesmaximal, characteristic, complemented
8#30252C211yesmaximal, characteristic, complemented
9#30250C211yesmaximal, characteristic, complemented
10#28477C211yesmaximal, characteristic, complemented
11#28471C211yesmaximal, characteristic, complemented
12#28453C211yesmaximal, characteristic, complemented
13#28429C211yesmaximal, characteristic, complemented
14#28410C211yesmaximal, characteristic, complemented
15#28390C211yesmaximal, characteristic, complemented
16#28362C211yesmaximal, characteristic, complemented
17#28361C211yesmaximal, characteristic, complemented
18#28355C211yesmaximal, characteristic, complemented
19#28347C211yesmaximal, characteristic, complemented
20#28328C211yesmaximal, characteristic, complemented
21#28317C211yesmaximal, characteristic, complemented
22#25796C211yesmaximal, characteristic, complemented
23#25795C211yesmaximal, characteristic, complemented
24#25792C211yesmaximal, characteristic, complemented
25#25786C211yesmaximal, characteristic, complemented
26#25735C211yesmaximal, characteristic, complemented
27#25730C211yesmaximal, characteristic, complemented
28#23813C211yesmaximal, characteristic, complemented
29#23431C211yesmaximal, characteristic, complemented
30#23427C211yesmaximal, characteristic, complemented
31#20564C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C22×#137C2211yescharacteristic, complemented
34C22×AGL(1,ℤ/8)C2211yescharacteristic
35C22×#135C2211yescharacteristic
36C2×#552C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#547C2211yescharacteristic
39C2×#546C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C22×#124C2211yescharacteristic
42#3323—28no—
43#3312—28no—
44#3276—28no—
45#3267—28no—
46C2×#497C2211yescharacteristic
47C2×#497C2211yescharacteristic
48C2×#497C2211yescharacteristic
49C2×#497C2211yescharacteristic
50C2×#497C2211yescharacteristic, complemented
51C2×#495C2211yescharacteristic
52C2×#494C2211yescharacteristic, complemented
53C2×#494C2211yescharacteristic, complemented
54C2×#491C2211yescharacteristic, complemented
55C2×#488C2211yescharacteristic
56C2×#481C2211yescharacteristic
57C2×#485C2211yescharacteristic
58C2×#485C2211yescharacteristic
59C2×#483C2211yescharacteristic, complemented
60C2×#479C2211yescharacteristic, complemented
61C2×#478C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#470C2211yescharacteristic
64C2×#470C2211yescharacteristic
65C2×#470C2211yescharacteristic
66C2×#470C2211yescharacteristic, complemented
67C2×#468C2211yescharacteristic
68C2×#467C2211yescharacteristic, complemented
69C2×#465C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#462C2211yescharacteristic, complemented
72C2×#462C2211yescharacteristic, complemented
73C2×#463C2211yescharacteristic
74C2×#461C2211yescharacteristic
75C2×#461C2211yescharacteristic, complemented
76C2×#452C2211yescharacteristic
77C2×#452C2211yescharacteristic
78C2×#452C2211yescharacteristic
79C2×#452C2211yescharacteristic
80C2×#452C2211yescharacteristic, complemented
81C2×#449C2211yescharacteristic
82C2×#451C2211yescharacteristic
83C2×#451C2211yescharacteristic
84C2×#451C2211yescharacteristic, complemented
85C2×#451C2211yescharacteristic, complemented
86C2×#450C2211yescharacteristic
87C2×#450C2211yescharacteristic
88C2×#442C2211yescharacteristic
89C2×#441C2211yescharacteristic, complemented
90C2×C4×SD16C2211yescharacteristic
91C2×C4×SD16C2211yescharacteristic, complemented
92C2×#436C2211yescharacteristic
93C2×#435C2211yescharacteristic
94C2×#417C2211yescharacteristic
95C2×#419C2211yescharacteristic
96C2×#418C2211yescharacteristic
97C22×#103C2211yescharacteristic, complemented
98#2857C2211yescharacteristic
99#2857C2211yescharacteristic
100#2708—22no—
101#2695—22no—
102#2674—22no—
103#2672—22no—
104#2658C2211yescharacteristic
105#2642C2211yescharacteristic, complemented
106#2621C2211yescharacteristic, complemented
107#2620C2211yescharacteristic
108#2566C2211yescharacteristic, complemented
109#2547C2211yescharacteristic
110#2546C2211yescharacteristic, complemented
111#2545C2211yescharacteristic
112#2502C2211yescharacteristic, complemented
113#2499C2211yescharacteristic
114#2473—22no—
115#2470—22no—
116#2437—22no—
117#2436C2211yescharacteristic
118#2435C2211yescharacteristic
119#2434C2211yescharacteristic
120#2432C2211yescharacteristic
121#2432C2211yescharacteristic
122#2432C2211yescharacteristic, complemented
123#2418—22no—
124#2326C2211yescharacteristic
125#2326C2211yescharacteristic, complemented
126#2311C2211yescharacteristic, complemented
127#2297C2211yescharacteristic
128#2290C2211yescharacteristic
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2096C2211yescharacteristic, complemented
134#2096C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2094C2211yescharacteristic
137#2094C2211yescharacteristic, complemented
138#2092C2211yescharacteristic
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2016C2211yescharacteristic, complemented
145#2016C2211yescharacteristic, complemented
146#2016C2211yescharacteristic, complemented
147#2016C2211yescharacteristic, complemented
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic
150#2015C2211yescharacteristic
151#2015C2211yescharacteristic
152#2015C2211yescharacteristic
153#2015C2211yescharacteristic
154#2015C2211yescharacteristic
155#2015C2211yescharacteristic
156#2015C2211yescharacteristic
157#2015C2211yescharacteristic
158#2015C2211yescharacteristic
159#2015C2211yescharacteristic, complemented
160#2013C2211yescharacteristic
161#2013C2211yescharacteristic, complemented
162#2013C2211yescharacteristic, complemented
163#2012C2211yescharacteristic
164#2012C2211yescharacteristic
165#2012C2211yescharacteristic
166#2012C2211yescharacteristic
167#2012C2211yescharacteristic
168#2012C2211yescharacteristic
169#1973C2211yescharacteristic
170#1973C2211yescharacteristic, complemented
171#1973C2211yescharacteristic, complemented
172#1972C2211yescharacteristic
173#1971C2211yescharacteristic, complemented
174#1971C2211yescharacteristic, complemented
175#1971C2211yescharacteristic, complemented
176#1971C2211yescharacteristic, complemented
177#1969C2211yescharacteristic, complemented
178#1968C2211yescharacteristic
179#1968C2211yescharacteristic
180#1968C2211yescharacteristic, complemented
181#1960C2211yescharacteristic, complemented
182#1959C2211yescharacteristic
183#1959C2211yescharacteristic
184#1959C2211yescharacteristic
185#1958C2211yescharacteristic
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195#1749C2211yescharacteristic
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198#1728C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×#137—24no—
206C2×#137—24no—
207C2×#137—42no—
208C2×#137—42no—
209C2×#137—42no—
210C2×#137—42no—
211C2×AGL(1,ℤ/8)—24no—
212C2×AGL(1,ℤ/8)—42no—
213C2×AGL(1,ℤ/8)—42no—
214C2×#135—24no—
215C2×#135—42no—
216C2×#135—42no—
217C22×Q16C2311yescharacteristic
218C22×Q16C2311yescharacteristic
219C22×Q16C2311yescharacteristic
220C22×Q16C2311yescharacteristic
221C22×Q16C2311yescharacteristic
222C22×Q16C2311yescharacteristic
223C22×Q16C2311yescharacteristic
224C22×Q16C2311yescharacteristic
225C22×Q16C2311yescharacteristic
226C22×Q16C2311yescharacteristic
227C22×Q16C2311yescharacteristic
228C22×Q16C2311yescharacteristic
229C22×SD16C2311yescharacteristic
230C22×SD16C2311yescharacteristic
231C22×SD16C2311yescharacteristic
232C22×SD16C2311yescharacteristic
233C22×SD16C2311yescharacteristic
234C22×SD16C2311yescharacteristic
235C22×SD16C2311yescharacteristic
236C22×SD16C2311yescharacteristic
237C22×SD16C2311yescharacteristic
238C22×SD16C2311yescharacteristic
239C22×D8C2311yescharacteristic
240C22×D8C2311yescharacteristic
241C22×M16C2311yescharacteristic
242C22×M16C2311yescharacteristic
243C22×M16C2311yescharacteristic
244C23×C8C2311yescharacteristic
245#552—24no—
246#552—24no—
247D4×Q8—24no—
248D4×Q8—24no—
249#547—24no—
250#547—24no—
251#546—24no—
252#546—24no—
253#536—42no—
254#536—42no—
255C2×C4⋊Q8—21no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×#126—21no—
264C2×#125—21no—
265C2×#125C2311yescharacteristic
266C2×#124—22no—
267C2×#124—42no—
268C2×#124—42no—
269C2×#124C2311yescharacteristic
270C2×#124C2311yescharacteristic
271C2×#124C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#124C2311yescharacteristic
274C2×#124C2311yescharacteristic
275C2×#124C2311yescharacteristic
276C2×#124C2311yescharacteristic
277C2×#123—21no—
278C2×#123—21no—
279C2×#123—22no—
280C2×#123—21no—
281C2×#123—21no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8—21no—
284C2×C22⋊Q8—21no—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2311yescharacteristic
292C2×#121—21no—
293C2×#121—21no—
294C2×#121C2311yescharacteristic
295C2×#120—21no—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4—21no—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×#117—21no—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C22×C4⋊C4—21no—
306C22×C4⋊C4C2311yescharacteristic
307C22×C22⋊C4—22no—
308C22×C22⋊C4—21no—
309C22×C42C2311yescharacteristic
310#497—24no—
311#497—42no—
312#497—42no—
313#497—42no—
314#497—42no—
315#495—42no—
316#494—24no—
317#494—42no—
318#491—24no—
319#488—24no—
320#485—24no—
321#485—24no—
322#483—24no—
323#481—24no—
324#479—24no—
325#478—24no—
326#470—24no—
327#470—24no—
328#470—24no—
329#470—24no—
330#470—24no—
331#468—24no—
332#467—24no—
333#465—24no—
334#464—24no—
335#463—24no—
336#462—24no—
337#462—24no—
338#461—24no—
339#461—24no—
340#452—24no—
341#452—24no—
342#452—24no—
343#452—24no—
344#452—24no—
345#451—24no—
346#451—24no—
347#451—24no—
348#451—24no—
349#450—24no—
350#450—24no—
351#449—24no—
352#442—24no—
353#441—24no—
354C4×SD16—24no—
355C4×SD16—24no—
356#436D418yes—
357#435D418yes—
358C2×#107C2311yescharacteristic
359C2×#107C2311yescharacteristic
360C2×#106C2311yescharacteristic
361C2×#106C2311yescharacteristic
362C2×#106C2311yescharacteristic
363C2×#106C2311yescharacteristic
364C2×#106C2311yescharacteristic
365C2×#106C2311yescharacteristic
366C2×C4⋊C8C2311yescharacteristic
367C2×C4⋊C8C2311yescharacteristic
368#419—24no—
369#418—24no—
370#417—24no—
371C2×#103—24no—
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#103C2311yescharacteristic
380C2×#103C2311yescharacteristic
381C2×#103C2311yescharacteristic
382C2×#103C2311yescharacteristic
383C2×#103C2311yescharacteristic
384C2×#103C2311yescharacteristic
385C2×#103C2311yescharacteristic
386C2×#103C2311yescharacteristic
387C2×#103C2311yescharacteristic
388C2×#103C2311yescharacteristic
389C2×#103C2311yescharacteristic
390C2×#103C2311yescharacteristic
391C2×#103C2311yescharacteristic
392C2×#103C2311yescharacteristic
393C2×#103C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×#102C2311yescharacteristic
397C2×#102C2311yescharacteristic
398C2×#102C2311yescharacteristic
399C2×#102C2311yescharacteristic
400C2×#102C2311yescharacteristic
401C2×#102C2311yescharacteristic
402C2×#102C2311yescharacteristic
403C2×#102C2311yescharacteristic
404C2×C22⋊C8C2311yescharacteristic
405C2×C22⋊C8C2311yescharacteristic
406C2×C22⋊C8C2311yescharacteristic
407C2×C22⋊C8C2311yescharacteristic
408C2×#97C2311yescharacteristic
409C2×#97C2311yescharacteristic
410C2×#97C2311yescharacteristic
411C2×#97C2311yescharacteristic
412C2×#97C2311yescharacteristic
413C2×C4×C8C2311yescharacteristic
414C2×C4×C8C2311yescharacteristic
415C2×C4×C8C2311yescharacteristic
416#400—22no—
417#400—22no—
418#399—22no—
419#399—22no—
420#398—22no—
421#398—22no—
422#398—22no—
423#397—22no—
424#397—22no—
425#397—22no—
426#396—22no—
427#396—22no—
428#396—22no—
429#395—22no—
430#394—22no—
431#394—22no—
432#394—22no—
433#394—22no—
434#394—22no—
435#393—22no—
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#389—22no—
453#389—22no—
454#389—22no—
455#388—22no—
456#388—22no—
457#388—22no—
458#388D412yes—
459#387—22no—
460#387D412yes—
461#386—22no—
462#386—22no—
463#386—22no—
464#386D412yes—
465#385—22no—
466#385—22no—
467#385—22no—
468#385—22no—
469#385—22no—
470#385—22no—
471#385—22no—
472#385—22no—
473#385D412yes—
474#384C2311yescharacteristic
475#384C2311yescharacteristic
476#384C2311yescharacteristic
477#382C2311yescharacteristic
478#380—22no—
479#380—22no—
480#380—22no—
481#380—22no—
482#379—22no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4—22no—
485C4×C22⋊C4C2311yescharacteristic
486C4×C22⋊C4C2311yescharacteristic
487#376C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498C25—21no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—22no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—22no—
524C22×Q8—22no—
525C22×Q8—41no—
526C22×Q8—41no—
527C22×Q8—41no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×D4—22no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—41no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C2×D411yescharacteristic
550C22×D4C2411yescharacteristic
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C2×D412yes—
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564#137—416no—
565#137—416no—
566AGL(1,ℤ/8)—416no—
567#135—416no—
568C2×Q16—22no—
569C2×Q16—22no—
570C2×Q16—22no—
571C2×Q16—22no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16—22no—
580C2×Q16—22no—
581C2×Q16—22no—
582C2×Q16—22no—
583C2×Q16—41no—
584C2×Q16—41no—
585C2×Q16—41no—
586C2×Q16—41no—
587C2×Q16—41no—
588C2×Q16—41no—
589C2×Q16—41no—
590C2×Q16—41no—
591C2×Q16—41no—
592C2×Q16—41no—
593C2×Q16—41no—
594C2×Q16—41no—
595C2×Q16—41no—
596C2×Q16—41no—
597C2×Q16—41no—
598C2×Q16—41no—
599C2×Q16—41no—
600C2×Q16—41no—
601C2×Q16—41no—
602C2×Q16—41no—
603C2×Q16—41no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—22no—
608C2×SD16—22no—
609C2×SD16—22no—
610C2×SD16—22no—
611C2×SD16—22no—
612C2×SD16—22no—
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—41no—
623C2×SD16—41no—
624C2×SD16—41no—
625C2×SD16—41no—
626C2×SD16—41no—
627C2×SD16—41no—
628C2×SD16—41no—
629C2×SD16—41no—
630C2×SD16—41no—
631C2×SD16—41no—
632C2×SD16—41no—
633C2×SD16—41no—
634C2×D8—22no—
635C2×D8—22no—
636C2×D8—22no—
637C2×D8—22no—
638C2×D8—22no—
639C2×D8—41no—
640C2×M16—41no—
641C2×M16—41no—
642C2×M16—41no—
643C2×M16—41no—
644C2×M16—41no—
645C2×M16—41no—
646C2×M16C2×D414yes—
647C2×M16C2×D414yes—
648C2×M16C2×D414yes—
649C22×C8—41no—
650C22×C8—41no—
651C22×C8C2×D414yes—
652C22×C8C2411yescharacteristic
653C22×C8C2411yescharacteristic
654C22×C8C2411yescharacteristic
655C22×C8C2411yescharacteristic
656C22×C8C2411yescharacteristic
657C22×C8C2411yescharacteristic
658C22×C8C2411yescharacteristic
659C22×C8C2411yescharacteristic
660C4⋊Q8—22no—
661C4⋊Q8—22no—
662C4⋊Q8—22no—
663C4⋊Q8—22no—
664C4⋊Q8—22no—
665C4⋊Q8—41no—
666C4⋊Q8—41no—
667C4⋊Q8—41no—
668C4⋊Q8—41no—
669C4⋊Q8—41no—
670C4⋊Q8—41no—
671C4⋊Q8—41no—
672C4⋊Q8—41no—
673C4⋊Q8—41no—
674C4⋊Q8—44no—
675#126—44no—
676#125—22no—
677#125—22no—
678#125—44no—
679#124—22no—
680#124—22no—
681#124—22no—
682#124—22no—
683#124—22no—
684#124—22no—
685#124—22no—
686#124—22no—
687#124—41no—
688#124—41no—
689#124—41no—
690#124—41no—
691#124—41no—
692#124—41no—
693#124—41no—
694#124—41no—
695#124—48no—
696#123—48no—
697#123—44no—
698#123—44no—
699#123—44no—
700#123—44no—
701C22⋊Q8—22no—
702C22⋊Q8—22no—
703C22⋊Q8—22no—
704C22⋊Q8—22no—
705C22⋊Q8—22no—
706C22⋊Q8—22no—
707C22⋊Q8—22no—
708C22⋊Q8—22no—
709C22⋊Q8—22no—
710C22⋊Q8—22no—
711C22⋊Q8—22no—
712C22⋊Q8—22no—
713C22⋊Q8—22no—
714C22⋊Q8—22no—
715C22⋊Q8—48no—
716C22⋊Q8—44no—
717C22⋊Q8—44no—
718#121—22no—
719#121—22no—
720#121—44no—
721#121—44no—
722#120—44no—
723C4×Q8—22no—
724C4×Q8—22no—
725C4×Q8—22no—
726C4×Q8—22no—
727C4×D4—22no—
728C4×D4—22no—
729C4×D4—22no—
730C4×D4—22no—
731C4×D4—44no—
732C4×D4C2×D414yes—
733C4×D4C2×D414yes—
734#117—22no—
735#117—22no—
736#117—41no—
737#117—41no—
738#117—44no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—21no—
742C2×C4⋊C4—21no—
743C2×C4⋊C4—21no—
744C2×C4⋊C4—21no—
745C2×C4⋊C4—21no—
746C2×C4⋊C4—21no—
747C2×C4⋊C4—21no—
748C2×C4⋊C4—21no—
749C2×C4⋊C4—21no—
750C2×C4⋊C4—21no—
751C2×C4⋊C4—21no—
752C2×C4⋊C4—21no—
753C2×C4⋊C4—21no—
754C2×C4⋊C4—22no—
755C2×C4⋊C4—22no—
756C2×C4⋊C4—21no—
757C2×C4⋊C4—21no—
758C2×C4⋊C4—21no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—44no—
766C2×C4⋊C4C2×D412yes—
767C2×C4⋊C4C2×D412yes—
768C2×C4⋊C4C2×D411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C22⋊C4—22no—
776C2×C22⋊C4—21no—
777C2×C22⋊C4—21no—
778C2×C22⋊C4—21no—
779C2×C22⋊C4—21no—
780C2×C22⋊C4—21no—
781C2×C22⋊C4—21no—
782C2×C22⋊C4—21no—
783C2×C22⋊C4—21no—
784C2×C22⋊C4—21no—
785C2×C22⋊C4—21no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—21no—
791C2×C22⋊C4—21no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—48no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4C2×D412yes—
803C2×C22⋊C4C2×D412yes—
804C2×C22⋊C4C2×D412yes—
805C2×C22⋊C4C2×D411yescharacteristic
806C2×C22⋊C4C2×D411yescharacteristic
807C2×C42—21no—
808C2×C42—21no—
809C2×C42—21no—
810C2×C42—41no—
811C2×C42—41no—
812C2×C42C2×D412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818#107—22no—
819#107—22no—
820#106—22no—
821#106—22no—
822#106—22no—
823#106—22no—
824#106—22no—
825#106—22no—
826C4⋊C8C2×D414yes—
827C4⋊C8C2×D414yes—
828#103—22no—
829#103—22no—
830#103—22no—
831#103—22no—
832#103—22no—
833#103—22no—
834#103—22no—
835#103—22no—
836#103—22no—
837#103—22no—
838#103—22no—
839#103—22no—
840#103—22no—
841#103—22no—
842#103—22no—
843#103—22no—
844#103—22no—
845#103—22no—
846#103—22no—
847#103—22no—
848#103—22no—
849#103—22no—
850#102—22no—
851#102—22no—
852#102—22no—
853#102—22no—
854#102—22no—
855#102—22no—
856#102—22no—
857#102—22no—
858#102—22no—
859#102—22no—
860C22⋊C8C2×D414yes—
861C22⋊C8C2×D414yes—
862C22⋊C8C2×D414yes—
863C22⋊C8C2×D414yes—
864#97—41no—
865#97—41no—
866#97—41no—
867#97—41no—
868#97C2×D414yes—
869C4×C8—41no—
870C4×C8—41no—
871C4×C8C2×D414yes—
872#95—22no—
873#95—22no—
874#95—22no—
875#95—22no—
876#95—22no—
877#95—22no—
878#95—22no—
879#95—22no—
880#95—22no—
881#95—22no—
882#95—22no—
883#95—22no—
884#95C2×D412yes—
885#95C2×D412yes—
886#95C2×D412yes—
887#95C2×D412yes—
888#95C2×D412yes—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—42no—
893C24—44no—
894C24—42no—
895C24—81no—
896C24—82no—
897C24C22×D411yescharacteristic
898C24C22×D411yescharacteristic
899#41—44no—
900#41—44no—
901#41—44no—
902#41—44no—
903#41—44no—
904#41—44no—
905#41—82no—
906#41—82no—
907#41—82no—
908#41—82no—
909#41—82no—
910#41—82no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—21no—
917C2×Q8—21no—
918C2×Q8—21no—
919C2×Q8—21no—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—21no—
923C2×Q8—21no—
924C2×Q8—21no—
925C2×Q8—21no—
926C2×Q8—21no—
927C2×Q8—21no—
928C2×Q8—21no—
929C2×Q8—21no—
930C2×Q8—21no—
931C2×Q8—21no—
932C2×Q8—21no—
933C2×Q8—21no—
934C2×Q8—21no—
935C2×Q8—21no—
936C2×Q8—21no—
937C2×Q8—21no—
938C2×Q8—21no—
939C2×Q8—21no—
940C2×Q8—21no—
941C2×Q8—21no—
942C2×Q8—21no—
943C2×Q8—21no—
944C2×Q8—21no—
945C2×Q8—21no—
946C2×Q8—21no—
947C2×Q8—21no—
948C2×Q8—21no—
949C2×Q8—21no—
950C2×Q8—21no—
951C2×Q8—21no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—81no—
961C2×Q8—81no—
962C2×Q8—82no—
963C2×Q8—82no—
964C2×Q8—82no—
965C2×Q8—82no—
966C2×Q8H(5,𝔽2)12yes—
967C2×D4—21no—
968C2×D4—21no—
969C2×D4—21no—
970C2×D4—21no—
971C2×D4—21no—
972C2×D4—21no—
973C2×D4—21no—
974C2×D4—21no—
975C2×D4—21no—
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—21no—
979C2×D4—21no—
980C2×D4—21no—
981C2×D4—21no—
982C2×D4—21no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—82no—
996C2×D4—82no—
997C2×D4—81no—
998C2×D4—81no—
999C2×D4—81no—
1000C2×D4—81no—
1001C2×D4—82no—
1002C2×D4#12714yes—
1003C2×D4H(5,𝔽2)12yes—
1004C2×D4H(5,𝔽2)12yes—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—21no—
1025C22×C4—21no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—82no—
1043C22×C4—81no—
1044C22×C4—81no—
1045C22×C4—81no—
1046C22×C4—82no—
1047C22×C4—82no—
1048C22×C4—81no—
1049C22×C4—81no—
1050C22×C4C22×D412yes—
1051C22×C4C22×D412yes—
1052C22×C4C22×D412yes—
1053C22×C4C22×D412yes—
1054C22×C4C22×D411yescharacteristic
1055C22×C4C22×D411yescharacteristic
1056C22×C4C22×D411yescharacteristic
1057C22×C4C22×D411yescharacteristic
1058C22×C4C22×D412yes—
1059C22×C4C22×D412yes—
1060C22×C4C22×D412yes—
1061C22×C4C22×D412yes—
1062C22×C4C2511yescharacteristic
1063Q16—44no—
1064Q16—44no—
1065Q16—44no—
1066Q16—44no—
1067Q16—44no—
1068Q16—44no—
1069Q16—82no—
1070Q16—82no—
1071Q16—82no—
1072Q16—82no—
1073Q16—82no—
1074Q16—82no—
1075SD16—28no—
1076SD16—44no—
1077SD16—44no—
1078SD16—44no—
1079SD16—44no—
1080SD16—44no—
1081SD16—44no—
1082SD16—44no—
1083SD16—82no—
1084SD16—82no—
1085D8—28no—
1086D8—44no—
1087M16—44no—
1088M16—44no—
1089M16—44no—
1090C2×C8—21no—
1091C2×C8—21no—
1092C2×C8—21no—
1093C2×C8—21no—
1094C2×C8—21no—
1095C2×C8—21no—
1096C2×C8—21no—
1097C2×C8—21no—
1098C2×C8—21no—
1099C2×C8—21no—
1100C2×C8—21no—
1101C2×C8—21no—
1102C2×C8—21no—
1103C2×C8—21no—
1104C2×C8—21no—
1105C2×C8—21no—
1106C2×C8—44no—
1107C2×C8C22×D412yes—
1108C2×C8C22×D412yes—
1109C2×C8C22×D412yes—
1110C2×C8C22×D412yes—
1111C2×C8C22×D412yes—
1112C2×C8C22×D412yes—
1113C2×C8C22×D412yes—
1114C2×C8C22×D412yes—
1115C4⋊C4—21no—
1116C4⋊C4—21no—
1117C4⋊C4—21no—
1118C4⋊C4—21no—
1119C4⋊C4—21no—
1120C4⋊C4—21no—
1121C4⋊C4—21no—
1122C4⋊C4—21no—
1123C4⋊C4—21no—
1124C4⋊C4—21no—
1125C4⋊C4—21no—
1126C4⋊C4—21no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—82no—
1148C4⋊C4—82no—
1149C4⋊C4—82no—
1150C4⋊C4—82no—
1151C4⋊C4—82no—
1152C4⋊C4—82no—
1153C4⋊C4#12714yes—
1154C22⋊C4—28no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—82no—
1178C22⋊C4—82no—
1179C22⋊C4—82no—
1180C22⋊C4—82no—
1181C22⋊C4—82no—
1182C22⋊C4#12714yes—
1183C22⋊C4#12714yes—
1184C42—21no—
1185C42—21no—
1186C42—21no—
1187C42—21no—
1188C42—21no—
1189C42—21no—
1190C42—21no—
1191C42—21no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—42no—
1196C42C22×D412yes—
1197C42C22×D412yes—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—22no—
1207C23—22no—
1208C23—42no—
1209C23—42no—
1210C23—42no—
1211C23—42no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—42no—
1217C23—42no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—84no—
1222C23—84no—
1223C23—88no—
1224C23—162no—
1225C23—164no—
1226C23C2×#12712yes—
1227C23C2×#12712yes—
1228C23C23×D411yescharacteristic
1229Q8—22no—
1230Q8—22no—
1231Q8—41no—
1232Q8—41no—
1233Q8—41no—
1234Q8—41no—
1235Q8—41no—
1236Q8—41no—
1237Q8—41no—
1238Q8—41no—
1239Q8—41no—
1240Q8—41no—
1241Q8—41no—
1242Q8—41no—
1243Q8—41no—
1244Q8—41no—
1245Q8—41no—
1246Q8—41no—
1247Q8—41no—
1248Q8—41no—
1249Q8—41no—
1250Q8—41no—
1251Q8—41no—
1252Q8—41no—
1253Q8—41no—
1254Q8—41no—
1255Q8—41no—
1256Q8—41no—
1257Q8—84no—
1258Q8—84no—
1259D4—22no—
1260D4—22no—
1261D4—22no—
1262D4—22no—
1263D4—44no—
1264D4—41no—
1265D4—41no—
1266D4—41no—
1267D4—41no—
1268D4—41no—
1269D4—41no—
1270D4—41no—
1271D4—41no—
1272D4—84no—
1273D4—84no—
1274D4—84no—
1275D4—84no—
1276D4—162no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—42no—
1307C2×C4—42no—
1308C2×C4—42no—
1309C2×C4—42no—
1310C2×C4—42no—
1311C2×C4—42no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—84no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—84no—
1342C2×C4—84no—
1343C2×C4—84no—
1344C2×C4—162no—
1345C2×C4C2×#12712yes—
1346C2×C4C2×#12712yes—
1347C2×C4C2×#12712yes—
1348C2×C4C2×#12712yes—
1349C2×C4C23×D411yescharacteristic
1350C2×C4C23×D411yescharacteristic
1351C2×C4C2×H(5,𝔽2)11yescharacteristic
1352C2×C4C2×H(5,𝔽2)11yescharacteristic
1353C2×C4C2×H(5,𝔽2)11yescharacteristic
1354C2×C4#58511yescharacteristic
1355C8—22no—
1356C8—22no—
1357C8—22no—
1358C8—22no—
1359C8—22no—
1360C8—22no—
1361C8—22no—
1362C8—22no—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—44no—
1376C22—44no—
1377C22—82no—
1378C22—82no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—82no—
1385C22—82no—
1386C22—81no—
1387C22—81no—
1388C22—168no—
1389C22C22×#12711yescharacteristic
1390C22#348411yescharacteristic
1391C22#348811yescharacteristic
1392C22#358612yes—
1393C22#358612yes—
1394C4—22no—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4—81no—
1415C4#348411yescharacteristic
1416C4#348411yescharacteristic
1417C4#348811yescharacteristic
1418C4#348811yescharacteristic
1419C2—42no—
1420C2—42no—
1421C2—82no—
1422C2—82no—
1423C2—161no—
1424C2#3592111yescharacteristic
1425C2#6064511yescharacteristic
1426C2#6065111yescharacteristic
1427C2#6165512yes—
1428C2#6209012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3267C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3323C2semidirect
2. C2×#3312C2semidirect
3. C2×#3276C2semidirect
5. #38088C2semidirect
6. #37676C2semidirect
7. #30272C2semidirect
8. #30252C2semidirect
9. #30250C2semidirect
10. #28477C2semidirect
11. #28471C2semidirect
12. #28453C2semidirect
13. #28429C2semidirect
14. #28410C2semidirect
15. #28390C2semidirect
16. #28362C2semidirect
17. #28361C2semidirect
18. #28355C2semidirect
19. #28347C2semidirect
20. #28328C2semidirect
21. #28317C2semidirect
22. #25796C2semidirect
23. #25795C2semidirect
24. #25792C2semidirect
25. #25786C2semidirect
26. #25735C2semidirect
27. #25730C2semidirect
28. #23813C2semidirect
29. #23431C2semidirect
30. #23427C2semidirect
31. #20564C2semidirect
33. C22×#137C22semidirect
50. C2×#497C22semidirect
52. C2×#494C22semidirect
53. C2×#494C22semidirect
54. C2×#491C22semidirect
59. C2×#483C22semidirect
60. C2×#479C22semidirect
66. C2×#470C22semidirect
68. C2×#467C22semidirect
71. C2×#462C22semidirect
72. C2×#462C22semidirect
75. C2×#461C22semidirect
80. C2×#452C22semidirect
84. C2×#451C22semidirect
85. C2×#451C22semidirect
89. C2×#441C22semidirect
91. C2×C4×SD16C22semidirect
97. C22×#103C22semidirect
105. #2642C22semidirect
106. #2621C22semidirect
108. #2566C22semidirect
110. #2546C22semidirect
112. #2502C22semidirect
122. #2432C22semidirect
125. #2326C22semidirect
126. #2311C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
132. #2096C22semidirect
133. #2096C22semidirect
134. #2096C22semidirect
135. #2095C22semidirect
137. #2094C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
143. #2016C22semidirect
144. #2016C22semidirect
145. #2016C22semidirect
146. #2016C22semidirect
147. #2016C22semidirect
159. #2015C22semidirect
161. #2013C22semidirect
162. #2013C22semidirect
170. #1973C22semidirect
171. #1973C22semidirect
173. #1971C22semidirect
174. #1971C22semidirect
175. #1971C22semidirect
176. #1971C22semidirect
177. #1969C22semidirect
180. #1968C22semidirect
181. #1960C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1770C22semidirect
189. #1768C22semidirect
192. #1753C22semidirect
193. #1752C22semidirect
194. #1750C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33232
C2×#33122
C2×#32762
C2×#32672
#380882
#376762
#302722
#302522
#302502
#284772
#284712
#284532
#284292
#284102
#283902
#283622
#283612
#283552
#283472
#283282
#283172
#257962
#257952
#257922
#257862
#257352
#257302
#238132
#234312
#234272
#205642