Finite Group Databasebeta

← #6344167

Subgroups — #6344167

Order 512.

2975 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#60263C211yesmaximal, characteristic, complemented
4#17781C214yesmaximal, complemented
5#17775C218yesmaximal, complemented
6#17772C214yesmaximal, complemented
7#17750C211yesmaximal, characteristic, complemented
8#17747C212yesmaximal, complemented
9#17745C212yesmaximal, complemented
10#17742C211yesmaximal, characteristic, complemented
11#17717C212yesmaximal, complemented
12#17714C211yesmaximal, characteristic, complemented
13#17708C212yesmaximal, complemented
14C2×#1549C211yesmaximal, characteristic, complemented
15#3511—21no—
16#3511—21no—
17#3511—22no—
18#3511—21no—
19#3511—21no—
20#3511—22no—
21#3511C412yes—
22#3511C414yes—
23#3511C412yes—
24#3511C2212yes—
25#3511C2214yes—
26#3511C2212yes—
27C2×#556—21no—
28C2×#555—21no—
29C2×#554—21no—
30C2×#553—22no—
31C2×#548—22no—
32C2×#547—21no—
33C2×#542C414yes—
34C2×#537C412yes—
35C2×#533C2212yes—
36C2×#532C2211yescharacteristic
37C2×#532C2212yes—
38C22×C4⋊Q8C2211yescharacteristic
39C2×#520C412yes—
40C2×C4×#41C2211yescharacteristic
41#2991C2212yescomplemented
42#2991C2212yescomplemented
43#2990C2214yescomplemented
44#2990C2212yescomplemented
45#2990C2212yescomplemented
46#2990C2214yescomplemented
47#2989—21no—
48#2989—22no—
49#2988—21no—
50#2984—21no—
51#2974—21no—
52#2974—22no—
53#2965—21no—
54#2965—22no—
55C8×#41—21no—
56Q8×M16—21no—
57D4×M16—22no—
58D4×M16—21no—
59#2920C2211yescharacteristic
60#2920C2212yes—
61#2920C2211yescharacteristic
62#2920C2212yes—
63C2×#431C2211yescharacteristic
64C2×#431C2212yes—
65C2×#423C2211yescharacteristic
66C2×#423C2212yes—
67#1560C2214yescomplemented
68#1559C2218yescomplemented
69#1557C2218yescomplemented
70#1556C2214yescomplemented
71#1554C2218yescomplemented
72#1553C2218yescomplemented
73#1551C2214yescomplemented
74#1551C2214yescomplemented
75#1550C2218yescomplemented
76#1549C2212yes—
77#1549C2212yes—
78#1549C2212yes—
79#1549C2212yes—
80#1549C2214yescomplemented
81#1548C2211yescharacteristic
82#1548C2212yes—
83#1548C2211yescharacteristic
84#1547C2218yescomplemented
85#1546C2214yescomplemented
86#1545C2211yescharacteristic
87#1545C2211yescharacteristic
88#1545C2212yes—
89#1543C2214yescomplemented
90#1542C2218yescomplemented
91#1540C2218yescomplemented
92C2×#332C2214yescomplemented
93C22×#41—22no—
94C22×#41C2×C412yes—
95C22×#41C2×C411yescharacteristic
96C23×Q8—21no—
97C22×M16—21no—
98C22×M16—22no—
99#556—22no—
100#556—22no—
101#556—24no—
102#556—22no—
103#556—22no—
104#556—24no—
105#555—22no—
106#555—22no—
107#555—24no—
108#555—22no—
109#555—24no—
110#555—22no—
111#554—22no—
112#554—22no—
113#554—24no—
114#554—22no—
115#554—24no—
116#554—22no—
117#553—24no—
118#553—24no—
119#553—24no—
120#553—24no—
121#553—24no—
122#553—24no—
123#553—24no—
124#553—24no—
125#548—24no—
126#548—24no—
127#548—24no—
128#548—24no—
129#548—24no—
130#548—24no—
131#548—24no—
132#548—24no—
133#547—22no—
134#547—22no—
135#547—24no—
136#547—22no—
137#547—24no—
138#547—22no—
139#542—24no—
140#542—24no—
141#542—24no—
142#542—24no—
143#542C2×C418yes—
144#542C2×C418yes—
145#542C2×C418yes—
146#542C2×C418yes—
147#537—22no—
148#537—22no—
149#537—24no—
150#537C2×C414yes—
151#537C2×C418yes—
152#537C2×C414yes—
153#533—22no—
154#533—22no—
155#533—22no—
156#533—22no—
157#533C2×C414yes—
158#533C2×C414yes—
159#533C2314yes—
160#533C2314yes—
161#532—21no—
162#532—21no—
163#532—21no—
164#532—21no—
165#532—22no—
166#532—22no—
167#532—22no—
168#532—22no—
169#532C2×C412yes—
170#532C2×C412yes—
171#532C2×C414yes—
172#532C2×C414yes—
173#532C2312yes—
174#532C2312yes—
175#532C2314yes—
176#532C2314yes—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8—21no—
179C2×C4⋊Q8—21no—
180C2×C4⋊Q8—21no—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8—21no—
183C2×C4⋊Q8C2×C412yes—
184C2×C4⋊Q8C2×C412yes—
185C2×C4⋊Q8C2×C412yes—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×#127C2311yescharacteristic
191C2×#126—24no—
192C2×#125—22no—
193C2×#124—24no—
194C2×#124—22no—
195C2×#124C2×C412yes—
196C2×#123—24no—
197C2×C22⋊Q8—22no—
198C2×C22⋊Q8—22no—
199C2×C22⋊Q8—24no—
200C2×C22⋊Q8C2×C414yes—
201C2×#121—22no—
202C2×#121—24no—
203C2×#121—21no—
204C2×#121—21no—
205C2×#121—22no—
206C2×#121C2×C414yes—
207#520—24no—
208#520—22no—
209#520—22no—
210#520C2×C414yes—
211#520C2×C418yes—
212#520C2×C414yes—
213C4×#41C2×C412yes—
214C4×#41C2×C411yescharacteristic
215C4×#41C2×C411yescharacteristic
216C4×#41D411yescharacteristic
217C4×#41D411yescharacteristic
218C4×#41D412yes—
219C4×#41D411yescharacteristic
220C4×#41D411yescharacteristic
221C4×#41D412yes—
222C4×#41C2312yes—
223C4×#41C2311yescharacteristic
224C4×#41C2311yescharacteristic
225C2×C4×Q8—22no—
226C2×C4×Q8C2×C414yes—
227C2×C4×Q8D411yescharacteristic
228C2×C4×Q8D411yescharacteristic
229C2×C4×D4—24no—
230C2×C4×D4—21no—
231C2×C4×D4—22no—
232C2×C4×D4—21no—
233C2×C4×D4C2×C414yes—
234C2×C4×D4D412yes—
235C2×C4×D4D411yescharacteristic
236C2×C4×D4D411yescharacteristic
237C2×C4×D4D412yes—
238C2×#117—22no—
239C2×#117—22no—
240C2×#117C2×C411yescharacteristic
241C2×#117C2×C412yes—
242C22×C4⋊C4—21no—
243C22×C4⋊C4—22no—
244C22×C4⋊C4C2×C412yes—
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247#446—24no—
248#446—22no—
249#446—22no—
250#446—24no—
251C8×Q8—22no—
252C8×Q8—22no—
253#436—24no—
254#436—22no—
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—24no—
264C8×D4—22no—
265C8×D4—22no—
266C8×D4—24no—
267#432—21no—
268#432—22no—
269#432—21no—
270#432—22no—
271#432C2312yes—
272#432C2312yes—
273#432C2314yes—
274#432C2314yes—
275#431—21no—
276#431—22no—
277#431—21no—
278#431—22no—
279#431—21no—
280#431—22no—
281#431—21no—
282#431—22no—
283#431C2314yes—
284#431C2314yes—
285#431C2312yes—
286#431C2312yes—
287#431C2311yescharacteristic
288#431C2311yescharacteristic
289#431C2312yes—
290#423—22no—
291#423—21no—
292#423—21no—
293#423—22no—
294#423C2311yescharacteristic
295#423C2312yes—
296#423C2311yescharacteristic
297#423C2312yes—
298#423C2314yes—
299#423C2312yes—
300#423C2314yes—
301C2×C4⋊C8—21no—
302C2×C4⋊C8—22no—
303C2×C4⋊C8C2312yes—
304C2×C4⋊C8C2312yes—
305C2×C4⋊C8C2314yes—
306C2×C4⋊C8C2314yes—
307#407—21no—
308#407—22no—
309#407—21no—
310#407—22no—
311C2×C22⋊C8—21no—
312C2×C22⋊C8—22no—
313C4×M16—22no—
314C4×M16—21no—
315C4×M16—21no—
316C4×M16—22no—
317C2×C4×C8—21no—
318C2×C4×C8—22no—
319#333C2314yes—
320#333C2318yes—
321#333C2314yes—
322#332C2318yes—
323#332C2318yes—
324#332C2318yes—
325#332C2318yes—
326#331C2314yes—
327#331C2318yes—
328#331C2314yes—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—44no—
336C2×#41—48no—
337C2×#41—88no—
338C2×#41C22⋊C411yescharacteristic
339C2×#41C22⋊C411yescharacteristic
340C2×#41C22⋊C412yes—
341C2×#41C22×C414yes—
342C2×#41C22×C414yes—
343C2×#41C22×C412yes—
344C2×#41C22×C411yescharacteristic
345C2×#41C22×C411yescharacteristic
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—84no—
353C22×Q8C22⋊C411yescharacteristic
354C22×Q8C22×C412yes—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C22⋊C411yescharacteristic
360C22×D4C22⋊C412yes—
361C22×D4C22×C412yes—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4C22×C411yescharacteristic
366C23×C4C22×C412yes—
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D412yes—
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D412yes—
371C2×M16—22no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—22no—
375C2×M16—24no—
376C2×M16—22no—
377C2×M16—24no—
378C2×M16—82no—
379C2×M16—84no—
380C22×C8—22no—
381C22×C8—24no—
382C22×C8—22no—
383C22×C8—24no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8C22×C412yes—
399C4⋊Q8C22×C414yes—
400C4⋊Q8C22×C414yes—
401C4⋊Q8C22×C414yes—
402C4⋊Q8C2412yes—
403C4⋊Q8C2414yes—
404#127—21no—
405#127—21no—
406#127C22×C412yes—
407#127C2412yes—
408#126—28no—
409#126—28no—
410#126—28no—
411#126—28no—
412#125—24no—
413#125—24no—
414#125—24no—
415#125—24no—
416#124—28no—
417#124—28no—
418#124—28no—
419#124—28no—
420#124—24no—
421#124—24no—
422#124—22no—
423#124—22no—
424#124—24no—
425#124—24no—
426#124C22×C414yes—
427#124C22×C414yes—
428#123—28no—
429#123—28no—
430#123—28no—
431#123—28no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—28no—
435C22⋊Q8—24no—
436C22⋊Q8—24no—
437C22⋊Q8—24no—
438C22⋊Q8—24no—
439C22⋊Q8—24no—
440C22⋊Q8—24no—
441C22⋊Q8—28no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C22⋊Q8C22×C418yes—
446C22⋊Q8C22×C418yes—
447#121—24no—
448#121—24no—
449#121—28no—
450#121—28no—
451#121—28no—
452#121—28no—
453#121—28no—
454#121—22no—
455#121—22no—
456#121—22no—
457#121—22no—
458#121—24no—
459#121—24no—
460#121—24no—
461#121—24no—
462#121—22no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—24no—
467#121—24no—
468#121C22×C418yes—
469#121C22×C418yes—
470C4×Q8—24no—
471C4×Q8—24no—
472C4×Q8—24no—
473C4×Q8—24no—
474C4×Q8—24no—
475C4×Q8—24no—
476C4×Q8C22⋊C411yescharacteristic
477C4×Q8C22⋊C411yescharacteristic
478C4×Q8C22⋊C412yes—
479C4×Q8C22⋊C411yescharacteristic
480C4×Q8C22⋊C411yescharacteristic
481C4×Q8C22⋊C412yes—
482C4×Q8C22×C418yes—
483C4×Q8C22×C418yes—
484C4×Q8C2×D411yescharacteristic
485C4×Q8C2×D412yes—
486C4×Q8C2×D411yescharacteristic
487C4×Q8C2×D411yescharacteristic
488C4×Q8C2×D411yescharacteristic
489C4×Q8C2×D412yes—
490C4×D4—28no—
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—28no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—24no—
501C4×D4—24no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—24no—
505C4×D4—24no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4C22⋊C411yescharacteristic
509C4×D4C22⋊C411yescharacteristic
510C4×D4C22⋊C412yes—
511C4×D4C22⋊C412yes—
512C4×D4C22⋊C412yes—
513C4×D4C22⋊C412yes—
514C4×D4C22⋊C412yes—
515C4×D4C22⋊C412yes—
516C4×D4C22⋊C412yes—
517C4×D4C22⋊C412yes—
518C4×D4C22⋊C412yes—
519C4×D4C22⋊C411yescharacteristic
520C4×D4C22⋊C411yescharacteristic
521C4×D4C22⋊C412yes—
522C4×D4C22×C418yes—
523C4×D4C22×C418yes—
524C4×D4C2×D411yescharacteristic
525C4×D4C2×D412yes—
526C4×D4C2×D411yescharacteristic
527C4×D4C2×D412yes—
528C4×D4C2×D412yes—
529C4×D4C2×D412yes—
530C4×D4C2×D412yes—
531C4×D4C2×D412yes—
532C4×D4C2×D412yes—
533C4×D4C2×D412yes—
534C4×D4C2×D412yes—
535C4×D4C2×D411yescharacteristic
536C4×D4C2×D412yes—
537C4×D4C2×D411yescharacteristic
538#117—24no—
539#117—24no—
540#117—24no—
541#117—24no—
542#117—28no—
543#117—24no—
544#117—24no—
545#117C22⋊C412yes—
546#117C22⋊C411yescharacteristic
547#117C22⋊C411yescharacteristic
548#117C22⋊C412yes—
549#117C22⋊C412yes—
550#117C22⋊C412yes—
551#117C22⋊C412yes—
552#117C22×C412yes—
553#117C22×C411yescharacteristic
554#117C22×C411yescharacteristic
555#117C22×C412yes—
556#117C22×C412yes—
557#117C22×C412yes—
558#117C22×C412yes—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4C22⋊C411yescharacteristic
576C2×C4⋊C4C22⋊C411yescharacteristic
577C2×C4⋊C4C22⋊C412yes—
578C2×C4⋊C4C22⋊C412yes—
579C2×C4⋊C4C22×C414yes—
580C2×C4⋊C4C22×C414yes—
581C2×C4⋊C4C22×C414yes—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4C22⋊C412yes—
588C2×C22⋊C4C22⋊C412yes—
589C2×C22⋊C4C22⋊C412yes—
590C2×C42—24no—
591C2×C42C22×C412yes—
592C2×C42C22×C411yescharacteristic
593C2×C42C22×C411yescharacteristic
594C2×C42C22×C411yescharacteristic
595C2×C42C22×C412yes—
596C2×C42C22×C412yes—
597C2×C42C2×D412yes—
598C2×C42C2×D411yescharacteristic
599C2×C42C2×D411yescharacteristic
600C2×C42C2×D412yes—
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D412yes—
606C2×C42C2×D412yes—
607C2×C42C2×D412yes—
608C2×C42C2×D412yes—
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614C4⋊C8—22no—
615C4⋊C8—21no—
616C4⋊C8—24no—
617C4⋊C8—22no—
618C4⋊C8—24no—
619C4⋊C8—22no—
620C4⋊C8—22no—
621C4⋊C8—24no—
622C4⋊C8—21no—
623C4⋊C8—22no—
624C4⋊C8—24no—
625C4⋊C8C2412yes—
626C4⋊C8C2414yes—
627C4⋊C8C2412yes—
628C4⋊C8C2414yes—
629C4⋊C8C2412yes—
630C4⋊C8C2412yes—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—22no—
634C22⋊C8—22no—
635C22⋊C8—24no—
636C22⋊C8—22no—
637C22⋊C8—24no—
638C22⋊C8—22no—
639C22⋊C8—24no—
640C22⋊C8—22no—
641C22⋊C8—24no—
642#97—24no—
643#97—22no—
644#97—22no—
645#97—24no—
646C4×C8—21no—
647C4×C8—21no—
648C4×C8—22no—
649C4×C8—22no—
650C4×C8—24no—
651C4×C8—24no—
652C4×C8—22no—
653C24—22no—
654C24C2×C22⋊C411yescharacteristic
655C24C2×C22⋊C412yes—
656#41—24no—
657#41—24no—
658#41—44no—
659#41—44no—
660#41—42no—
661#41—42no—
662#41—48no—
663#41—48no—
664#41—48no—
665#41—48no—
666#41—88no—
667#41—88no—
668#41—88no—
669#41—88no—
670C2×Q8—22no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—42no—
676C2×Q8—44no—
677C2×Q8—48no—
678C2×Q8—84no—
679C2×Q8—84no—
680C2×Q8—84no—
681C2×Q8—84no—
682C2×Q8—84no—
683C2×Q8C2×C22⋊C411yescharacteristic
684C2×Q8C2×C22⋊C411yescharacteristic
685C2×Q8C2×C22⋊C412yes—
686C2×Q8C23×C414yes—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—42no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—48no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—88no—
704C2×D4C2×C22⋊C412yes—
705C2×D4C2×C22⋊C412yes—
706C2×D4C2×C22⋊C411yescharacteristic
707C2×D4C2×C22⋊C411yescharacteristic
708C2×D4C2×C22⋊C412yes—
709C2×D4C2×C22⋊C412yes—
710C2×D4C2×C22⋊C412yes—
711C2×D4C23×C414yes—
712C22×C4—22no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—44no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—84no—
730C22×C4—88no—
731C22×C4C2×C22⋊C412yes—
732C22×C4C2×C22⋊C411yescharacteristic
733C22×C4C2×C22⋊C411yescharacteristic
734C22×C4C2×C22⋊C411yescharacteristic
735C22×C4C2×C22⋊C412yes—
736C22×C4C2×C22⋊C412yes—
737C22×C4C2×C22⋊C411yescharacteristic
738C22×C4C2×C22⋊C411yescharacteristic
739C22×C4C2×C22⋊C412yes—
740C22×C4C2×C22⋊C412yes—
741C22×C4C2×C22⋊C411yescharacteristic
742C22×C4C2×C22⋊C412yes—
743C22×C4C2×C22⋊C411yescharacteristic
744C22×C4C2×C22⋊C411yescharacteristic
745C22×C4C2×C22⋊C412yes—
746C22×C4C2×C22⋊C412yes—
747C22×C4C2×C22⋊C412yes—
748C22×C4C2×C22⋊C411yescharacteristic
749C22×C4C23×C411yescharacteristic
750C22×C4C23×C411yescharacteristic
751C22×C4C23×C411yescharacteristic
752C22×C4C23×C412yes—
753C22×C4C23×C412yes—
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D412yes—
758C22×C4C22×D412yes—
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D412yes—
762C22×C4C22×D412yes—
763C22×C4C22×D411yescharacteristic
764M16—44no—
765M16—42no—
766M16—42no—
767M16—82no—
768M16—84no—
769M16—82no—
770M16—84no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—24no—
775C2×C8—24no—
776C2×C8—22no—
777C2×C8—82no—
778C2×C8—84no—
779C2×C8—82no—
780C2×C8—84no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4C2×C22⋊C412yes—
797C4⋊C4C2×C22⋊C411yescharacteristic
798C4⋊C4C2×C22⋊C411yescharacteristic
799C4⋊C4C2×C22⋊C412yes—
800C4⋊C4C2×C22⋊C411yescharacteristic
801C4⋊C4C2×C22⋊C411yescharacteristic
802C4⋊C4C2×C22⋊C412yes—
803C4⋊C4C2×C22⋊C412yes—
804C4⋊C4C2×C22⋊C412yes—
805C4⋊C4C2×C22⋊C412yes—
806C4⋊C4C2×C22⋊C412yes—
807C4⋊C4C2×C22⋊C412yes—
808C4⋊C4C2×C22⋊C412yes—
809C4⋊C4C2×C22⋊C412yes—
810C4⋊C4C23×C418yes—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4C2×C22⋊C412yes—
822C22⋊C4C2×C22⋊C412yes—
823C22⋊C4C2×C22⋊C412yes—
824C22⋊C4C2×C22⋊C412yes—
825C22⋊C4C2×C22⋊C412yes—
826C22⋊C4C2×C22⋊C412yes—
827C22⋊C4C2×C22⋊C412yes—
828C22⋊C4C2×C22⋊C412yes—
829C22⋊C4C2×C22⋊C412yes—
830C22⋊C4C2×C22⋊C412yes—
831C22⋊C4C2×C22⋊C412yes—
832C22⋊C4C2×C22⋊C412yes—
833C42—28no—
834C42—28no—
835C42C2×C22⋊C412yes—
836C42C2×C22⋊C412yes—
837C42C2×C22⋊C411yescharacteristic
838C42C2×C22⋊C411yescharacteristic
839C42C2×C22⋊C412yes—
840C42C2×C22⋊C412yes—
841C42C2×C22⋊C411yescharacteristic
842C42C2×C22⋊C411yescharacteristic
843C42C2×C22⋊C411yescharacteristic
844C42C2×C22⋊C411yescharacteristic
845C42C2×C22⋊C412yes—
846C42C2×C22⋊C412yes—
847C42C23×C411yescharacteristic
848C42C23×C412yes—
849C42C23×C412yes—
850C42C23×C411yescharacteristic
851C42C23×C411yescharacteristic
852C42C22×D411yescharacteristic
853C42C22×D412yes—
854C42C22×D411yescharacteristic
855C42C22×D411yescharacteristic
856C42C22×D412yes—
857C42C22×D412yes—
858C42C22×D411yescharacteristic
859C42C22×D411yescharacteristic
860C42C22×D412yes—
861C42C22×D411yescharacteristic
862C42C2511yescharacteristic
863C23—22no—
864C23—22no—
865C23—24no—
866C23—24no—
867C23—41no—
868C23—42no—
869C23—42no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23C22×C22⋊C412yes—
874C23C22×C22⋊C412yes—
875C23C22×C22⋊C411yescharacteristic
876C23C22×C22⋊C411yescharacteristic
877C23C22×C22⋊C411yescharacteristic
878Q8—22no—
879Q8—22no—
880Q8—42no—
881Q8—44no—
882Q8—48no—
883Q8—48no—
884Q8—44no—
885Q8—84no—
886Q8—84no—
887D4—24no—
888D4—24no—
889D4—22no—
890D4—22no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—44no—
895D4—44no—
896D4—48no—
897D4—48no—
898D4—44no—
899D4—44no—
900D4—44no—
901D4—42no—
902D4—42no—
903D4—88no—
904D4—88no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—48no—
943C2×C4—44no—
944C2×C4—48no—
945C2×C4—48no—
946C2×C4—88no—
947C2×C4—88no—
948C2×C4—84no—
949C2×C4—84no—
950C2×C4#41314yes—
951C2×C4C22×C22⋊C412yes—
952C2×C4C22×C22⋊C412yes—
953C2×C4C22×C22⋊C411yescharacteristic
954C2×C4C22×C22⋊C411yescharacteristic
955C2×C4C22×C22⋊C411yescharacteristic
956C2×C4C22×C22⋊C411yescharacteristic
957C2×C4C22×C22⋊C411yescharacteristic
958C2×C4C22×C22⋊C412yes—
959C2×C4C22×C22⋊C412yes—
960C2×C4C22×C22⋊C412yes—
961C2×C4C22×C22⋊C412yes—
962C2×C4C22×C22⋊C411yescharacteristic
963C2×C4C22×C22⋊C411yescharacteristic
964C2×C4C22×C22⋊C411yescharacteristic
965C2×C4C22×C22⋊C411yescharacteristic
966C2×C4#57712yes—
967C2×C4#57812yes—
968C2×C4C24×C411yescharacteristic
969C2×C4C23×D411yescharacteristic
970C2×C4C23×D411yescharacteristic
971C8—42no—
972C8—42no—
973C8—44no—
974C8—44no—
975C8—42no—
976C8—42no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—22no—
983C22—22no—
984C22—21no—
985C22—22no—
986C22—22no—
987C22—21no—
988C22—22no—
989C22—22no—
990C22—44no—
991C22—44no—
992C22—44no—
993C22—44no—
994C22—84no—
995C22—88no—
996C22C2×#41312yes—
997C22#289812yes—
998C22C23×C22⋊C411yescharacteristic
999C4—21no—
1000C4—21no—
1001C4—22no—
1002C4—22no—
1003C4—22no—
1004C4—21no—
1005C4—22no—
1006C4—21no—
1007C4—21no—
1008C4—22no—
1009C4—22no—
1010C4—21no—
1011C4—21no—
1012C4—44no—
1013C4—48no—
1014C4C2×#41312yes—
1015C4C2×#41312yes—
1016C4#289812yes—
1017C4C2×#57711yescharacteristic
1018C4C2×#57811yescharacteristic
1019C4#358512yes—
1020C2—22no—
1021C2—22no—
1022C2—41no—
1023C2—42no—
1024C2—42no—
1025C2—84no—
1026C2C22×#41311yescharacteristic
1027C2C2×#289811yescharacteristic
1028C2#6008711yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radicalC2×#3511C2
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. #17781C2semidirect
5. #17775C2semidirect
6. #17772C2semidirect
7. #17750C2semidirect
8. #17747C2semidirect
9. #17745C2semidirect
10. #17742C2semidirect
11. #17717C2semidirect
12. #17714C2semidirect
13. #17708C2semidirect
14. C2×#1549C2semidirect
41. #2991C22semidirect
42. #2991C22semidirect
43. #2990C22semidirect
44. #2990C22semidirect
45. #2990C22semidirect
46. #2990C22semidirect
67. #1560C22semidirect
68. #1559C22semidirect
69. #1557C22semidirect
70. #1556C22semidirect
71. #1554C22semidirect
72. #1553C22semidirect
73. #1551C22semidirect
74. #1551C22semidirect
75. #1550C22semidirect
80. #1549C22semidirect
84. #1547C22semidirect
85. #1546C22semidirect
89. #1543C22semidirect
90. #1542C22semidirect
91. #1540C22semidirect
92. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#602782
#602632
#177812
#177752
#177722
#177502
#177472
#177452
#177422
#177172
#177142
#177082
C2×#15492