Finite Group Databasebeta

← #6344160

Subgroups — #6344160

Order 512.

3191 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3508C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#60263C211yesmaximal, characteristic, complemented
4#17776C214yesmaximal, complemented
5#17776C214yesmaximal, complemented
6#17771C218yesmaximal, complemented
7#17751C211yesmaximal, characteristic, complemented
8#17745C212yesmaximal, complemented
9#17743C212yesmaximal, complemented
10#17741C211yesmaximal, characteristic, complemented
11#17717C212yesmaximal, complemented
12#17715C211yesmaximal, characteristic, complemented
13#17704C212yesmaximal, complemented
14C2×#1545C211yesmaximal, characteristic, complemented
15#3508—21no—
16#3508—21no—
17#3508—22no—
18#3508—21no—
19#3508—21no—
20#3508—22no—
21#3508C414yes—
22#3508C412yes—
23#3508C412yes—
24#3508C2214yes—
25#3508C2212yes—
26#3508C2212yes—
27C2×#559—21no—
28C2×#559—21no—
29C2×#550—21no—
30C2×#550—21no—
31C2×#546—22no—
32C2×#546—22no—
33C2×#540C414yes—
34C2×#535C412yes—
35C2×#533C2211yescharacteristic
36C2×#532C2212yes—
37C2×#532C2212yes—
38C22×#127C2211yescharacteristic
39C2×#518C412yes—
40C2×C4×#41C2211yescharacteristic
41#2991C2212yescomplemented
42#2991C2212yescomplemented
43#2990C2214yescomplemented
44#2990C2214yescomplemented
45#2990C2212yescomplemented
46#2990C2212yescomplemented
47#2989—21no—
48#2989—22no—
49#2988—21no—
50#2984—21no—
51#2974—22no—
52#2974—21no—
53#2965—21no—
54#2965—22no—
55C8×#41—21no—
56Q8×M16—21no—
57D4×M16—22no—
58D4×M16—21no—
59#2920C2211yescharacteristic
60#2920C2211yescharacteristic
61#2920C2212yescomplemented
62#2920C2212yescomplemented
63C2×#431C2211yescharacteristic
64C2×#431C2212yescomplemented
65C2×#423C2211yescharacteristic
66C2×#423C2212yescomplemented
67#1561C2214yescomplemented
68#1557C2218yescomplemented
69#1557C2218yescomplemented
70#1555C2214yescomplemented
71#1553C2218yescomplemented
72#1553C2218yescomplemented
73#1552C2214yescomplemented
74#1552C2214yescomplemented
75#1549C2211yescharacteristic, complemented
76#1549C2211yescharacteristic, complemented
77#1549C2212yescomplemented
78#1547C2218yescomplemented
79#1547C2218yescomplemented
80#1546C2211yescharacteristic, complemented
81#1546C2212yescomplemented
82#1546C2211yescharacteristic, complemented
83#1545C2212yes—
84#1545C2212yes—
85#1545C2212yes—
86#1545C2212yes—
87#1545C2214yescomplemented
88#1545C2214yescomplemented
89#1544C2214yescomplemented
90#1540C2218yescomplemented
91#1540C2218yescomplemented
92C2×#331C2214yescomplemented
93C22×#41—22no—
94C22×#41—22no—
95C22×#41C2×C411yescharacteristic
96C23×D4—21no—
97C23×D4—21no—
98C23×D4C2×C412yes—
99C22×M16—21no—
100C22×M16—22no—
101#559—22no—
102#559—22no—
103#559—22no—
104#559—22no—
105#559—24no—
106#559—24no—
107#559—22no—
108#559—22no—
109#559—24no—
110#559—24no—
111#559—22no—
112#559—22no—
113#550—22no—
114#550—22no—
115#550—24no—
116#550—22no—
117#550—22no—
118#550—24no—
119#550—22no—
120#550—22no—
121#550—24no—
122#550—24no—
123#550—22no—
124#550—22no—
125#546—24no—
126#546—24no—
127#546—24no—
128#546—24no—
129#546—24no—
130#546—24no—
131#546—24no—
132#546—24no—
133#546—24no—
134#546—24no—
135#546—24no—
136#546—24no—
137#546—24no—
138#546—24no—
139#546—24no—
140#546—24no—
141#540—24no—
142#540—24no—
143#540—24no—
144#540—24no—
145#540C2×C418yes—
146#540C2×C418yes—
147#540C2×C418yes—
148#540C2×C418yes—
149#535—22no—
150#535—22no—
151#535—24no—
152#535C2×C418yes—
153#535C2×C414yes—
154#535C2×C414yes—
155#533—21no—
156#533—21no—
157#533—21no—
158#533—21no—
159#533C2×C412yes—
160#533C2×C412yes—
161#533C2312yes—
162#533C2312yes—
163#532—22no—
164#532—22no—
165#532—22no—
166#532—22no—
167#532—22no—
168#532—22no—
169#532—22no—
170#532—22no—
171#532C2×C414yes—
172#532C2×C414yes—
173#532C2×C414yes—
174#532C2×C414yes—
175#532C2314yes—
176#532C2314yes—
177#532C2314yes—
178#532C2314yes—
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2311yescharacteristic
181C2×#127—22no—
182C2×#127—21no—
183C2×#127—21no—
184C2×#127—21no—
185C2×#127—21no—
186C2×#127—21no—
187C2×#127—21no—
188C2×#127C2×C412yes—
189C2×#127C2×C412yes—
190C2×#127C2×C412yes—
191C2×#127C2312yes—
192C2×#127C2312yes—
193C2×#127C2312yes—
194C2×#125C2×C412yes—
195C2×#124—22no—
196C2×#124—22no—
197C2×#124—22no—
198C2×#123—24no—
199C2×#123—24no—
200C2×C22⋊Q8—21no—
201C2×C22⋊Q8—21no—
202C2×#121—22no—
203C2×#121—22no—
204C2×#121—24no—
205C2×#121—24no—
206C2×#121C2×C414yes—
207C2×#121C2×C414yes—
208C2×#120—24no—
209#518—24no—
210#518—22no—
211#518—22no—
212#518C2×C418yes—
213#518C2×C414yes—
214#518C2×C414yes—
215C4×#41C2×C412yes—
216C4×#41C2×C411yescharacteristic
217C4×#41C2×C411yescharacteristic
218C4×#41D411yescharacteristic
219C4×#41D411yescharacteristic
220C4×#41D412yes—
221C4×#41D411yescharacteristic
222C4×#41D411yescharacteristic
223C4×#41D412yes—
224C4×#41C2312yes—
225C4×#41C2311yescharacteristic
226C4×#41C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8D411yescharacteristic
230C2×C4×Q8D411yescharacteristic
231C2×C4×D4—22no—
232C2×C4×D4—22no—
233C2×C4×D4—22no—
234C2×C4×D4—22no—
235C2×C4×D4C2×C414yes—
236C2×C4×D4C2×C414yes—
237C2×C4×D4D412yes—
238C2×C4×D4D411yescharacteristic
239C2×C4×D4D412yes—
240C2×C4×D4D411yescharacteristic
241C2×#117C2×C412yes—
242C2×#117C2×C411yescharacteristic
243C2×#117C2×C412yes—
244C22×C22⋊C4—24no—
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247#446—22no—
248#446—24no—
249#446—22no—
250#446—24no—
251C8×Q8—22no—
252C8×Q8—22no—
253#436—22no—
254#436—24no—
255#436—22no—
256#436—24no—
257#435—24no—
258#435—24no—
259#435—24no—
260#435—24no—
261#435—24no—
262#435—24no—
263C8×D4—22no—
264C8×D4—24no—
265C8×D4—22no—
266C8×D4—24no—
267#432—21no—
268#432—21no—
269#432—22no—
270#432—22no—
271#432C2312yes—
272#432C2312yes—
273#432C2314yescomplemented
274#432C2314yescomplemented
275#431—21no—
276#431—21no—
277#431—22no—
278#431—22no—
279#431—21no—
280#431—21no—
281#431—22no—
282#431—22no—
283#431C2312yes—
284#431C2312yes—
285#431C2311yescharacteristic
286#431C2311yescharacteristic
287#431C2312yes—
288#431C2314yescomplemented
289#431C2314yescomplemented
290#423—21no—
291#423—21no—
292#423—22no—
293#423—22no—
294#423C2312yes—
295#423C2311yescharacteristic
296#423C2311yescharacteristic
297#423C2312yes—
298#423C2312yes—
299#423C2314yescomplemented
300#423C2314yescomplemented
301C2×C4⋊C8—21no—
302C2×C4⋊C8—22no—
303C2×C4⋊C8C2312yes—
304C2×C4⋊C8C2312yes—
305C2×C4⋊C8C2314yescomplemented
306C2×C4⋊C8C2314yescomplemented
307#407—21no—
308#407—21no—
309#407—22no—
310#407—22no—
311C2×C22⋊C8—21no—
312C2×C22⋊C8—22no—
313C4×M16—21no—
314C4×M16—21no—
315C4×M16—22no—
316C4×M16—22no—
317C2×C4×C8—21no—
318C2×C4×C8—22no—
319#332C2314yescomplemented
320#332C2314yescomplemented
321#332C2318yescomplemented
322#332C2318yescomplemented
323#332C2314yescomplemented
324#332C2314yescomplemented
325#331C2318yes—
326#331C2318yes—
327#331C2318yes—
328#331C2318yes—
329C25—22no—
330C2×#41—24no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—24no—
338C2×#41—44no—
339C2×#41—84no—
340C2×#41—84no—
341C2×#41—88no—
342C2×#41C22⋊C411yescharacteristic
343C2×#41C22⋊C411yescharacteristic
344C2×#41C22⋊C412yes—
345C2×#41C22×C412yes—
346C2×#41C22×C411yescharacteristic
347C2×#41C22×C411yescharacteristic
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8C22⋊C411yescharacteristic
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—48no—
369C22×D4—82no—
370C22×D4—82no—
371C22×D4—84no—
372C22×D4C22⋊C412yes—
373C22×D4C22⋊C411yescharacteristic
374C22×D4C22×C414yes—
375C22×D4C22×C414yes—
376C22×D4C22×C414yes—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4C22×C411yescharacteristic
380C23×C4C22×C412yes—
381C23×C4C2×D412yes—
382C23×C4C2×D411yescharacteristic
383C23×C4C2×D412yes—
384C23×C4C2×D411yescharacteristic
385C2×M16—22no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—22no—
389C2×M16—24no—
390C2×M16—22no—
391C2×M16—24no—
392C2×M16—82no—
393C2×M16—84no—
394C22×C8—22no—
395C22×C8—24no—
396C22×C8—22no—
397C22×C8—24no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8C22×C412yes—
403C4⋊Q8C22×C412yes—
404C4⋊Q8C2412yes—
405C4⋊Q8C2412yes—
406#127—24no—
407#127—24no—
408#127—28no—
409#127—22no—
410#127—22no—
411#127—22no—
412#127—22no—
413#127—22no—
414#127—22no—
415#127—22no—
416#127—22no—
417#127—22no—
418#127—22no—
419#127—22no—
420#127—22no—
421#127C22×C414yes—
422#127C22×C414yes—
423#127C22×C414yes—
424#127C2414yes—
425#125—22no—
426#125—22no—
427#125C22×C414yes—
428#125C22×C414yes—
429#124—24no—
430#124—24no—
431#124—28no—
432#124—24no—
433#124—24no—
434#124—24no—
435#124—24no—
436#124—24no—
437#124—24no—
438#124—24no—
439#124—24no—
440#123—28no—
441#123—28no—
442#123—28no—
443#123—28no—
444#123—28no—
445#123—28no—
446#123—28no—
447#123—28no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456#121—24no—
457#121—24no—
458#121—24no—
459#121—24no—
460#121—24no—
461#121—24no—
462#121—24no—
463#121—24no—
464#121—24no—
465#121—24no—
466#121—24no—
467#121—24no—
468#121—28no—
469#121—28no—
470#121—28no—
471#121—28no—
472#121—28no—
473#121—28no—
474#121—28no—
475#121—28no—
476#121C22×C418yes—
477#121C22×C418yes—
478#121C22×C418yes—
479#121C22×C418yes—
480#120—28no—
481#120—28no—
482#120—28no—
483#120—28no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8C22⋊C411yescharacteristic
493C4×Q8C22⋊C411yescharacteristic
494C4×Q8C22⋊C411yescharacteristic
495C4×Q8C22⋊C411yescharacteristic
496C4×Q8C22⋊C412yes—
497C4×Q8C22⋊C412yes—
498C4×Q8C2×D411yescharacteristic
499C4×Q8C2×D411yescharacteristic
500C4×Q8C2×D412yes—
501C4×Q8C2×D412yes—
502C4×Q8C2×D411yescharacteristic
503C4×Q8C2×D411yescharacteristic
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—24no—
514C4×D4—24no—
515C4×D4—24no—
516C4×D4—24no—
517C4×D4—24no—
518C4×D4—24no—
519C4×D4—24no—
520C4×D4—24no—
521C4×D4—24no—
522C4×D4C22⋊C412yes—
523C4×D4C22⋊C412yes—
524C4×D4C22⋊C412yes—
525C4×D4C22⋊C412yes—
526C4×D4C22⋊C412yes—
527C4×D4C22⋊C412yes—
528C4×D4C22⋊C412yes—
529C4×D4C22⋊C412yes—
530C4×D4C22⋊C411yescharacteristic
531C4×D4C22⋊C411yescharacteristic
532C4×D4C22⋊C412yes—
533C4×D4C22⋊C411yescharacteristic
534C4×D4C22⋊C411yescharacteristic
535C4×D4C22⋊C412yes—
536C4×D4C22×C418yes—
537C4×D4C22×C418yes—
538C4×D4C22×C418yes—
539C4×D4C22×C418yes—
540C4×D4C2×D412yes—
541C4×D4C2×D412yes—
542C4×D4C2×D412yes—
543C4×D4C2×D412yes—
544C4×D4C2×D412yes—
545C4×D4C2×D412yes—
546C4×D4C2×D412yes—
547C4×D4C2×D412yes—
548C4×D4C2×D411yescharacteristic
549C4×D4C2×D411yescharacteristic
550C4×D4C2×D412yes—
551C4×D4C2×D412yes—
552C4×D4C2×D411yescharacteristic
553C4×D4C2×D411yescharacteristic
554#117—22no—
555#117—22no—
556#117C22⋊C412yes—
557#117C22⋊C411yescharacteristic
558#117C22⋊C411yescharacteristic
559#117C22⋊C412yes—
560#117C22⋊C412yes—
561#117C22⋊C412yes—
562#117C22⋊C412yes—
563#117C22×C414yes—
564#117C22×C414yes—
565#117C22×C412yes—
566#117C22×C411yescharacteristic
567#117C22×C411yescharacteristic
568#117C22×C412yes—
569#117C22×C412yes—
570#117C22×C412yes—
571#117C22×C412yes—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4C22⋊C411yescharacteristic
577C2×C4⋊C4C22⋊C411yescharacteristic
578C2×C4⋊C4C22⋊C412yes—
579C2×C4⋊C4C22⋊C412yes—
580C2×C4⋊C4C22×C412yes—
581C2×C4⋊C4C22×C412yes—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—28no—
588C2×C22⋊C4—28no—
589C2×C22⋊C4—28no—
590C2×C22⋊C4—28no—
591C2×C22⋊C4C22⋊C412yes—
592C2×C22⋊C4C22⋊C412yes—
593C2×C22⋊C4C22⋊C412yes—
594C2×C42—22no—
595C2×C42C22×C412yes—
596C2×C42C22×C411yescharacteristic
597C2×C42C22×C411yescharacteristic
598C2×C42C22×C411yescharacteristic
599C2×C42C22×C412yes—
600C2×C42C22×C412yes—
601C2×C42C2×D412yes—
602C2×C42C2×D412yes—
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2×D411yescharacteristic
609C2×C42C2×D412yes—
610C2×C42C2×D412yes—
611C2×C42C2×D412yes—
612C2×C42C2×D412yes—
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618C4⋊C8—22no—
619C4⋊C8—21no—
620C4⋊C8—22no—
621C4⋊C8—24no—
622C4⋊C8—22no—
623C4⋊C8—22no—
624C4⋊C8—24no—
625C4⋊C8—24no—
626C4⋊C8—21no—
627C4⋊C8—22no—
628C4⋊C8—24no—
629C4⋊C8C2412yes—
630C4⋊C8C2414yes—
631C4⋊C8C2412yes—
632C4⋊C8C2412yes—
633C4⋊C8C2414yes—
634C4⋊C8C2412yes—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—24no—
640C22⋊C8—22no—
641C22⋊C8—22no—
642C22⋊C8—24no—
643C22⋊C8—24no—
644C22⋊C8—22no—
645C22⋊C8—24no—
646#97—22no—
647#97—22no—
648#97—24no—
649#97—24no—
650C4×C8—21no—
651C4×C8—21no—
652C4×C8—22no—
653C4×C8—22no—
654C4×C8—24no—
655C4×C8—22no—
656C4×C8—24no—
657C24—24no—
658C24—24no—
659C24—24no—
660C24—48no—
661C24—84no—
662C24—84no—
663C24C2×C22⋊C411yescharacteristic
664C24C2×C22⋊C412yes—
665#41—24no—
666#41—24no—
667#41—44no—
668#41—44no—
669#41—42no—
670#41—42no—
671#41—88no—
672#41—88no—
673#41—88no—
674#41—88no—
675#41—84no—
676#41—84no—
677#41—84no—
678#41—84no—
679#41—88no—
680#41—88no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—22no—
685C2×Q8—42no—
686C2×Q8—44no—
687C2×Q8—42no—
688C2×Q8—42no—
689C2×Q8C2×C22⋊C411yescharacteristic
690C2×Q8C2×C22⋊C411yescharacteristic
691C2×Q8C2×C22⋊C412yes—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—42no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—82no—
723C2×D4—82no—
724C2×D4—82no—
725C2×D4—82no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—88no—
730C2×D4—84no—
731C2×D4—88no—
732C2×D4C2×C22⋊C412yes—
733C2×D4C2×C22⋊C412yes—
734C2×D4C2×C22⋊C411yescharacteristic
735C2×D4C2×C22⋊C411yescharacteristic
736C2×D4C2×C22⋊C412yes—
737C2×D4C2×C22⋊C412yes—
738C2×D4C2×C22⋊C412yes—
739C2×D4C23×C418yes—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—22no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—44no—
754C22×C4—88no—
755C22×C4—88no—
756C22×C4C2×C22⋊C411yescharacteristic
757C22×C4C2×C22⋊C412yes—
758C22×C4C2×C22⋊C411yescharacteristic
759C22×C4C2×C22⋊C412yes—
760C22×C4C2×C22⋊C412yes—
761C22×C4C2×C22⋊C411yescharacteristic
762C22×C4C2×C22⋊C411yescharacteristic
763C22×C4C2×C22⋊C411yescharacteristic
764C22×C4C2×C22⋊C412yes—
765C22×C4C2×C22⋊C412yes—
766C22×C4C2×C22⋊C412yes—
767C22×C4C2×C22⋊C411yescharacteristic
768C22×C4C2×C22⋊C412yes—
769C22×C4C2×C22⋊C412yes—
770C22×C4C2×C22⋊C411yescharacteristic
771C22×C4C2×C22⋊C411yescharacteristic
772C22×C4C2×C22⋊C412yes—
773C22×C4C2×C22⋊C411yescharacteristic
774C22×C4C23×C411yescharacteristic
775C22×C4C23×C411yescharacteristic
776C22×C4C23×C411yescharacteristic
777C22×C4C23×C412yes—
778C22×C4C23×C412yes—
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D412yes—
781C22×C4C22×D412yes—
782C22×C4C22×D412yes—
783C22×C4C22×D412yes—
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789M16—44no—
790M16—42no—
791M16—42no—
792M16—82no—
793M16—84no—
794M16—82no—
795M16—84no—
796C2×C8—22no—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—24no—
800C2×C8—22no—
801C2×C8—24no—
802C2×C8—82no—
803C2×C8—84no—
804C2×C8—82no—
805C2×C8—84no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4C2×C22⋊C412yes—
817C4⋊C4C2×C22⋊C412yes—
818C4⋊C4C2×C22⋊C411yescharacteristic
819C4⋊C4C2×C22⋊C411yescharacteristic
820C4⋊C4C2×C22⋊C411yescharacteristic
821C4⋊C4C2×C22⋊C411yescharacteristic
822C4⋊C4C2×C22⋊C412yes—
823C4⋊C4C2×C22⋊C412yes—
824C4⋊C4C2×C22⋊C412yes—
825C4⋊C4C2×C22⋊C412yes—
826C4⋊C4C2×C22⋊C412yes—
827C4⋊C4C2×C22⋊C412yes—
828C4⋊C4C2×C22⋊C412yes—
829C4⋊C4C2×C22⋊C412yes—
830C4⋊C4C23×C414yes—
831C4⋊C4C23×C414yes—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4C2×C22⋊C412yes—
843C22⋊C4C2×C22⋊C412yes—
844C22⋊C4C2×C22⋊C412yes—
845C22⋊C4C2×C22⋊C412yes—
846C22⋊C4C2×C22⋊C412yes—
847C22⋊C4C2×C22⋊C412yes—
848C22⋊C4C2×C22⋊C412yes—
849C22⋊C4C2×C22⋊C412yes—
850C22⋊C4C2×C22⋊C412yes—
851C22⋊C4C2×C22⋊C412yes—
852C22⋊C4C2×C22⋊C412yes—
853C22⋊C4C2×C22⋊C412yes—
854C42—24no—
855C42—24no—
856C42C2×C22⋊C412yes—
857C42C2×C22⋊C412yes—
858C42C2×C22⋊C411yescharacteristic
859C42C2×C22⋊C411yescharacteristic
860C42C2×C22⋊C412yes—
861C42C2×C22⋊C412yes—
862C42C2×C22⋊C412yes—
863C42C2×C22⋊C412yes—
864C42C2×C22⋊C411yescharacteristic
865C42C2×C22⋊C411yescharacteristic
866C42C2×C22⋊C411yescharacteristic
867C42C2×C22⋊C411yescharacteristic
868C42C23×C411yescharacteristic
869C42C23×C412yes—
870C42C23×C412yes—
871C42C23×C411yescharacteristic
872C42C23×C411yescharacteristic
873C42C22×D411yescharacteristic
874C42C22×D412yes—
875C42C22×D412yes—
876C42C22×D411yescharacteristic
877C42C22×D411yescharacteristic
878C42C22×D412yes—
879C42C22×D412yes—
880C42C22×D411yescharacteristic
881C42C22×D411yescharacteristic
882C42C22×D411yescharacteristic
883C42C2511yescharacteristic
884C23—22no—
885C23—22no—
886C23—24no—
887C23—28no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—48no—
892C23—48no—
893C23—48no—
894C23—48no—
895C23—48no—
896C23—84no—
897C23—84no—
898C23—84no—
899C23—84no—
900C23—1616no—
901C23C22×C22⋊C411yescharacteristic
902C23C22×C22⋊C412yes—
903C23C22×C22⋊C412yes—
904C23C22×C22⋊C411yescharacteristic
905C23C22×C22⋊C411yescharacteristic
906Q8—22no—
907Q8—22no—
908Q8—42no—
909Q8—44no—
910Q8—44no—
911Q8—44no—
912Q8—42no—
913Q8—42no—
914D4—24no—
915D4—24no—
916D4—22no—
917D4—22no—
918D4—42no—
919D4—42no—
920D4—42no—
921D4—48no—
922D4—48no—
923D4—48no—
924D4—48no—
925D4—48no—
926D4—48no—
927D4—48no—
928D4—44no—
929D4—44no—
930D4—84no—
931D4—84no—
932D4—84no—
933D4—84no—
934D4—88no—
935D4—88no—
936D4—88no—
937D4—88no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—88no—
978C2×C4—88no—
979C2×C4—88no—
980C2×C4—88no—
981C2×C4#41314yes—
982C2×C4C22×C22⋊C411yescharacteristic
983C2×C4C22×C22⋊C411yescharacteristic
984C2×C4C22×C22⋊C412yes—
985C2×C4C22×C22⋊C412yes—
986C2×C4C22×C22⋊C412yes—
987C2×C4C22×C22⋊C412yes—
988C2×C4C22×C22⋊C411yescharacteristic
989C2×C4C22×C22⋊C411yescharacteristic
990C2×C4C22×C22⋊C411yescharacteristic
991C2×C4C22×C22⋊C411yescharacteristic
992C2×C4C22×C22⋊C412yes—
993C2×C4C22×C22⋊C412yes—
994C2×C4C22×C22⋊C411yescharacteristic
995C2×C4C22×C22⋊C411yescharacteristic
996C2×C4C22×C22⋊C411yescharacteristic
997C2×C4#57612yes—
998C2×C4#57712yes—
999C2×C4C24×C411yescharacteristic
1000C2×C4C23×D411yescharacteristic
1001C2×C4C23×D411yescharacteristic
1002C8—42no—
1003C8—42no—
1004C8—44no—
1005C8—42no—
1006C8—44no—
1007C8—42no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—21no—
1018C22—22no—
1019C22—22no—
1020C22—21no—
1021C22—44no—
1022C22—48no—
1023C22—48no—
1024C22—48no—
1025C22—84no—
1026C22—816no—
1027C22—168no—
1028C22—168no—
1029C22C2×#41312yes—
1030C22#289712yes—
1031C22C23×C22⋊C411yescharacteristic
1032C4—21no—
1033C4—21no—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—22no—
1042C4—22no—
1043C4—21no—
1044C4—21no—
1045C4—44no—
1046C4—44no—
1047C4C2×#41312yes—
1048C4C2×#41312yes—
1049C4#289712yes—
1050C4C2×#57611yescharacteristic
1051C4C2×#57711yescharacteristic
1052C4#358512yes—
1053C2—22no—
1054C2—22no—
1055C2—41no—
1056C2—42no—
1057C2—42no—
1058C2—88no—
1059C2C22×#41311yescharacteristic
1060C2C2×#289711yescharacteristic
1061C2#6008711yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radicalC2×#3508C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60278C2semidirect
3. #60263C2semidirect
4. #17776C2semidirect
5. #17776C2semidirect
6. #17771C2semidirect
7. #17751C2semidirect
8. #17745C2semidirect
9. #17743C2semidirect
10. #17741C2semidirect
11. #17717C2semidirect
12. #17715C2semidirect
13. #17704C2semidirect
14. C2×#1545C2semidirect
41. #2991C22semidirect
42. #2991C22semidirect
43. #2990C22semidirect
44. #2990C22semidirect
45. #2990C22semidirect
46. #2990C22semidirect
61. #2920C22semidirect
62. #2920C22semidirect
64. C2×#431C22semidirect
66. C2×#423C22semidirect
67. #1561C22semidirect
68. #1557C22semidirect
69. #1557C22semidirect
70. #1555C22semidirect
71. #1553C22semidirect
72. #1553C22semidirect
73. #1552C22semidirect
74. #1552C22semidirect
75. #1549C22semidirect
76. #1549C22semidirect
77. #1549C22semidirect
78. #1547C22semidirect
79. #1547C22semidirect
80. #1546C22semidirect
81. #1546C22semidirect
82. #1546C22semidirect
87. #1545C22semidirect
88. #1545C22semidirect
89. #1544C22semidirect
90. #1540C22semidirect
91. #1540C22semidirect
92. C2×#331C22semidirect
273. #432C23semidirect
274. #432C23semidirect
288. #431C23semidirect
289. #431C23semidirect
299. #423C23semidirect
300. #423C23semidirect
305. C2×C4⋊C8C23semidirect
306. C2×C4⋊C8C23semidirect
319. #332C23semidirect
320. #332C23semidirect
321. #332C23semidirect
322. #332C23semidirect
323. #332C23semidirect
324. #332C23semidirect

Maximal subgroups

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

subgroupindex
C2×#35082
#602782
#602632
#177762
#177712
#177512
#177452
#177432
#177412
#177172
#177152
#177042
C2×#15452