Finite Group Databasebeta

← #6344161

Subgroups — #6344161

Order 512.

2975 conjugacy classes of subgroups.

The subgroup lattice has 1038 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#17749C212yesmaximal, complemented
9#17743C212yesmaximal, complemented
10#17742C211yesmaximal, characteristic, complemented
11#17718C212yesmaximal, complemented
12#17714C211yesmaximal, characteristic, complemented
13#17704C212yesmaximal, complemented
14C2×#1546C211yesmaximal, 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#2990C2212yescomplemented
44#2990C2214yescomplemented
45#2990C2214yescomplemented
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—21no—
58D4×M16—22no—
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#1549C2214yescomplemented
77#1548C2211yescharacteristic
78#1548C2211yescharacteristic
79#1548C2212yes—
80#1547C2218yescomplemented
81#1546C2212yes—
82#1546C2212yes—
83#1546C2212yes—
84#1546C2212yes—
85#1546C2214yescomplemented
86#1545C2211yescharacteristic
87#1545C2212yes—
88#1545C2211yescharacteristic
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×D4D411yescharacteristic
235C2×C4×D4D412yes—
236C2×C4×D4D412yes—
237C2×C4×D4D411yescharacteristic
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—22no—
248#446—24no—
249#446—24no—
250#446—22no—
251C8×Q8—22no—
252C8×Q8—22no—
253#436—22no—
254#436—24no—
255#436—24no—
256#436—22no—
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—24no—
266C8×D4—22no—
267#432—22no—
268#432—21no—
269#432—21no—
270#432—22no—
271#432C2312yes—
272#432C2312yes—
273#432C2314yes—
274#432C2314yes—
275#431—21no—
276#431—22no—
277#431—22no—
278#431—21no—
279#431—21no—
280#431—22no—
281#431—21no—
282#431—22no—
283#431C2314yes—
284#431C2314yes—
285#431C2312yes—
286#431C2312yes—
287#431C2311yescharacteristic
288#431C2312yes—
289#431C2311yescharacteristic
290#423—21no—
291#423—22no—
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—21no—
314C4×M16—22no—
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—84no—
338C2×#41—84no—
339C2×#41C22⋊C411yescharacteristic
340C2×#41C22⋊C411yescharacteristic
341C2×#41C22⋊C412yes—
342C2×#41C22×C414yes—
343C2×#41C22×C414yes—
344C2×#41C22×C412yes—
345C2×#41C22×C411yescharacteristic
346C2×#41C22×C411yescharacteristic
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—82no—
354C22×Q8—82no—
355C22×Q8C22⋊C411yescharacteristic
356C22×Q8C22×C412yes—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4C22⋊C411yescharacteristic
362C22×D4C22⋊C412yes—
363C22×D4C22×C412yes—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4C22×C411yescharacteristic
368C23×C4C22×C412yes—
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D412yes—
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D412yes—
373C2×M16—22no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—22no—
377C2×M16—24no—
378C2×M16—22no—
379C2×M16—24no—
380C2×M16—82no—
381C2×M16—84no—
382C22×C8—22no—
383C22×C8—24no—
384C22×C8—22no—
385C22×C8—24no—
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—22no—
397C4⋊Q8—22no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8C22×C412yes—
401C4⋊Q8C22×C414yes—
402C4⋊Q8C22×C414yes—
403C4⋊Q8C22×C414yes—
404C4⋊Q8C2412yes—
405C4⋊Q8C2414yes—
406#127—21no—
407#127—21no—
408#127C22×C412yes—
409#127C2412yes—
410#126—28no—
411#126—28no—
412#126—28no—
413#126—28no—
414#125—24no—
415#125—24no—
416#125—24no—
417#125—24no—
418#124—28no—
419#124—28no—
420#124—28no—
421#124—28no—
422#124—24no—
423#124—24no—
424#124—22no—
425#124—22no—
426#124—24no—
427#124—24no—
428#124C22×C414yes—
429#124C22×C414yes—
430#123—28no—
431#123—28no—
432#123—28no—
433#123—28no—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436C22⋊Q8—28no—
437C22⋊Q8—24no—
438C22⋊Q8—24no—
439C22⋊Q8—24no—
440C22⋊Q8—24no—
441C22⋊Q8—24no—
442C22⋊Q8—24no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—28no—
447C22⋊Q8C22×C418yes—
448C22⋊Q8C22×C418yes—
449#121—24no—
450#121—24no—
451#121—28no—
452#121—28no—
453#121—28no—
454#121—28no—
455#121—28no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—24no—
461#121—24no—
462#121—24no—
463#121—24no—
464#121—22no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—24no—
469#121—24no—
470#121C22×C418yes—
471#121C22×C418yes—
472C4×Q8—24no—
473C4×Q8—24no—
474C4×Q8—24no—
475C4×Q8—24no—
476C4×Q8—24no—
477C4×Q8—24no—
478C4×Q8C22⋊C411yescharacteristic
479C4×Q8C22⋊C411yescharacteristic
480C4×Q8C22⋊C412yes—
481C4×Q8C22⋊C411yescharacteristic
482C4×Q8C22⋊C411yescharacteristic
483C4×Q8C22⋊C412yes—
484C4×Q8C22×C418yes—
485C4×Q8C22×C418yes—
486C4×Q8C2×D411yescharacteristic
487C4×Q8C2×D412yes—
488C4×Q8C2×D411yescharacteristic
489C4×Q8C2×D411yescharacteristic
490C4×Q8C2×D411yescharacteristic
491C4×Q8C2×D412yes—
492C4×D4—28no—
493C4×D4—28no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—24no—
503C4×D4—24no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4C22⋊C411yescharacteristic
511C4×D4C22⋊C411yescharacteristic
512C4×D4C22⋊C412yes—
513C4×D4C22⋊C412yes—
514C4×D4C22⋊C412yes—
515C4×D4C22⋊C412yes—
516C4×D4C22⋊C412yes—
517C4×D4C22⋊C412yes—
518C4×D4C22⋊C412yes—
519C4×D4C22⋊C412yes—
520C4×D4C22⋊C412yes—
521C4×D4C22⋊C411yescharacteristic
522C4×D4C22⋊C411yescharacteristic
523C4×D4C22⋊C412yes—
524C4×D4C22×C418yes—
525C4×D4C22×C418yes—
526C4×D4C2×D411yescharacteristic
527C4×D4C2×D412yes—
528C4×D4C2×D411yescharacteristic
529C4×D4C2×D412yes—
530C4×D4C2×D412yes—
531C4×D4C2×D412yes—
532C4×D4C2×D412yes—
533C4×D4C2×D412yes—
534C4×D4C2×D412yes—
535C4×D4C2×D412yes—
536C4×D4C2×D412yes—
537C4×D4C2×D411yescharacteristic
538C4×D4C2×D412yes—
539C4×D4C2×D411yescharacteristic
540#117—24no—
541#117—24no—
542#117—24no—
543#117—24no—
544#117—28no—
545#117—24no—
546#117—24no—
547#117C22⋊C412yes—
548#117C22⋊C411yescharacteristic
549#117C22⋊C411yescharacteristic
550#117C22⋊C412yes—
551#117C22⋊C412yes—
552#117C22⋊C412yes—
553#117C22⋊C412yes—
554#117C22×C412yes—
555#117C22×C411yescharacteristic
556#117C22×C411yescharacteristic
557#117C22×C412yes—
558#117C22×C412yes—
559#117C22×C412yes—
560#117C22×C412yes—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4C22⋊C411yescharacteristic
578C2×C4⋊C4C22⋊C411yescharacteristic
579C2×C4⋊C4C22⋊C412yes—
580C2×C4⋊C4C22⋊C412yes—
581C2×C4⋊C4C22×C414yes—
582C2×C4⋊C4C22×C414yes—
583C2×C4⋊C4C22×C414yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4C22⋊C412yes—
590C2×C22⋊C4C22⋊C412yes—
591C2×C22⋊C4C22⋊C412yes—
592C2×C42—24no—
593C2×C42C22×C412yes—
594C2×C42C22×C411yescharacteristic
595C2×C42C22×C411yescharacteristic
596C2×C42C22×C411yescharacteristic
597C2×C42C22×C412yes—
598C2×C42C22×C412yes—
599C2×C42C2×D412yes—
600C2×C42C2×D411yescharacteristic
601C2×C42C2×D411yescharacteristic
602C2×C42C2×D412yes—
603C2×C42C2×D411yescharacteristic
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D412yes—
608C2×C42C2×D412yes—
609C2×C42C2×D412yes—
610C2×C42C2×D412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C4⋊C8—22no—
617C4⋊C8—21no—
618C4⋊C8—22no—
619C4⋊C8—24no—
620C4⋊C8—22no—
621C4⋊C8—24no—
622C4⋊C8—24no—
623C4⋊C8—22no—
624C4⋊C8—21no—
625C4⋊C8—24no—
626C4⋊C8—22no—
627C4⋊C8C2412yes—
628C4⋊C8C2412yes—
629C4⋊C8C2414yes—
630C4⋊C8C2414yes—
631C4⋊C8C2412yes—
632C4⋊C8C2412yes—
633C22⋊C8—21no—
634C22⋊C8—21no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637C22⋊C8—24no—
638C22⋊C8—22no—
639C22⋊C8—24no—
640C22⋊C8—22no—
641C22⋊C8—24no—
642C22⋊C8—22no—
643C22⋊C8—24no—
644#97—24no—
645#97—22no—
646#97—22no—
647#97—24no—
648C4×C8—21no—
649C4×C8—21no—
650C4×C8—22no—
651C4×C8—24no—
652C4×C8—22no—
653C4×C8—22no—
654C4×C8—24no—
655C24—22no—
656C24C2×C22⋊C411yescharacteristic
657C24C2×C22⋊C412yes—
658#41—24no—
659#41—24no—
660#41—44no—
661#41—44no—
662#41—42no—
663#41—42no—
664#41—48no—
665#41—48no—
666#41—48no—
667#41—48no—
668#41—88no—
669#41—88no—
670#41—84no—
671#41—84no—
672#41—84no—
673#41—84no—
674C2×Q8—22no—
675C2×Q8—24no—
676C2×Q8—24no—
677C2×Q8—24no—
678C2×Q8—24no—
679C2×Q8—42no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—84no—
684C2×Q8—84no—
685C2×Q8—84no—
686C2×Q8—82no—
687C2×Q8—82no—
688C2×Q8—82no—
689C2×Q8—82no—
690C2×Q8C2×C22⋊C411yescharacteristic
691C2×Q8C2×C22⋊C411yescharacteristic
692C2×Q8C2×C22⋊C412yes—
693C2×Q8C23×C414yes—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—42no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—88no—
711C2×D4C2×C22⋊C412yes—
712C2×D4C2×C22⋊C412yes—
713C2×D4C2×C22⋊C411yescharacteristic
714C2×D4C2×C22⋊C411yescharacteristic
715C2×D4C2×C22⋊C412yes—
716C2×D4C2×C22⋊C412yes—
717C2×D4C2×C22⋊C412yes—
718C2×D4C23×C414yes—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—22no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—44no—
733C22×C4—42no—
734C22×C4—44no—
735C22×C4—48no—
736C22×C4—88no—
737C22×C4—84no—
738C22×C4C2×C22⋊C411yescharacteristic
739C22×C4C2×C22⋊C412yes—
740C22×C4C2×C22⋊C411yescharacteristic
741C22×C4C2×C22⋊C411yescharacteristic
742C22×C4C2×C22⋊C412yes—
743C22×C4C2×C22⋊C412yes—
744C22×C4C2×C22⋊C411yescharacteristic
745C22×C4C2×C22⋊C411yescharacteristic
746C22×C4C2×C22⋊C412yes—
747C22×C4C2×C22⋊C412yes—
748C22×C4C2×C22⋊C412yes—
749C22×C4C2×C22⋊C411yescharacteristic
750C22×C4C2×C22⋊C411yescharacteristic
751C22×C4C2×C22⋊C411yescharacteristic
752C22×C4C2×C22⋊C412yes—
753C22×C4C2×C22⋊C412yes—
754C22×C4C2×C22⋊C412yes—
755C22×C4C2×C22⋊C411yescharacteristic
756C22×C4C23×C411yescharacteristic
757C22×C4C23×C411yescharacteristic
758C22×C4C23×C411yescharacteristic
759C22×C4C23×C412yes—
760C22×C4C23×C412yes—
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D412yes—
765C22×C4C22×D412yes—
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D412yes—
769C22×C4C22×D412yes—
770C22×C4C22×D411yescharacteristic
771M16—44no—
772M16—42no—
773M16—42no—
774M16—82no—
775M16—84no—
776M16—82no—
777M16—84no—
778C2×C8—22no—
779C2×C8—22no—
780C2×C8—24no—
781C2×C8—22no—
782C2×C8—22no—
783C2×C8—24no—
784C2×C8—82no—
785C2×C8—84no—
786C2×C8—82no—
787C2×C8—84no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4C2×C22⋊C412yes—
804C4⋊C4C2×C22⋊C411yescharacteristic
805C4⋊C4C2×C22⋊C411yescharacteristic
806C4⋊C4C2×C22⋊C412yes—
807C4⋊C4C2×C22⋊C411yescharacteristic
808C4⋊C4C2×C22⋊C411yescharacteristic
809C4⋊C4C2×C22⋊C412yes—
810C4⋊C4C2×C22⋊C412yes—
811C4⋊C4C2×C22⋊C412yes—
812C4⋊C4C2×C22⋊C412yes—
813C4⋊C4C2×C22⋊C412yes—
814C4⋊C4C2×C22⋊C412yes—
815C4⋊C4C2×C22⋊C412yes—
816C4⋊C4C2×C22⋊C412yes—
817C4⋊C4C23×C418yes—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4C2×C22⋊C412yes—
829C22⋊C4C2×C22⋊C412yes—
830C22⋊C4C2×C22⋊C412yes—
831C22⋊C4C2×C22⋊C412yes—
832C22⋊C4C2×C22⋊C412yes—
833C22⋊C4C2×C22⋊C412yes—
834C22⋊C4C2×C22⋊C412yes—
835C22⋊C4C2×C22⋊C412yes—
836C22⋊C4C2×C22⋊C412yes—
837C22⋊C4C2×C22⋊C412yes—
838C22⋊C4C2×C22⋊C412yes—
839C22⋊C4C2×C22⋊C412yes—
840C42—28no—
841C42—28no—
842C42C2×C22⋊C412yes—
843C42C2×C22⋊C412yes—
844C42C2×C22⋊C411yescharacteristic
845C42C2×C22⋊C411yescharacteristic
846C42C2×C22⋊C412yes—
847C42C2×C22⋊C412yes—
848C42C2×C22⋊C411yescharacteristic
849C42C2×C22⋊C411yescharacteristic
850C42C2×C22⋊C411yescharacteristic
851C42C2×C22⋊C411yescharacteristic
852C42C2×C22⋊C412yes—
853C42C2×C22⋊C412yes—
854C42C23×C411yescharacteristic
855C42C23×C412yes—
856C42C23×C412yes—
857C42C23×C411yescharacteristic
858C42C23×C411yescharacteristic
859C42C22×D411yescharacteristic
860C42C22×D412yes—
861C42C22×D411yescharacteristic
862C42C22×D411yescharacteristic
863C42C22×D412yes—
864C42C22×D412yes—
865C42C22×D411yescharacteristic
866C42C22×D411yescharacteristic
867C42C22×D412yes—
868C42C22×D411yescharacteristic
869C42C2511yescharacteristic
870C23—22no—
871C23—22no—
872C23—24no—
873C23—24no—
874C23—41no—
875C23—42no—
876C23—42no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23C22×C22⋊C412yes—
881C23C22×C22⋊C412yes—
882C23C22×C22⋊C411yescharacteristic
883C23C22×C22⋊C411yescharacteristic
884C23C22×C22⋊C411yescharacteristic
885Q8—22no—
886Q8—22no—
887Q8—42no—
888Q8—44no—
889Q8—44no—
890Q8—48no—
891Q8—44no—
892Q8—44no—
893Q8—84no—
894Q8—84no—
895D4—24no—
896D4—24no—
897D4—22no—
898D4—22no—
899D4—42no—
900D4—42no—
901D4—42no—
902D4—44no—
903D4—44no—
904D4—48no—
905D4—48no—
906D4—44no—
907D4—44no—
908D4—44no—
909D4—42no—
910D4—42no—
911D4—88no—
912D4—88no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—48no—
951C2×C4—44no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4—84no—
957C2×C4—84no—
958C2×C4#41314yes—
959C2×C4C22×C22⋊C412yes—
960C2×C4C22×C22⋊C412yes—
961C2×C4C22×C22⋊C411yescharacteristic
962C2×C4C22×C22⋊C411yescharacteristic
963C2×C4C22×C22⋊C411yescharacteristic
964C2×C4C22×C22⋊C411yescharacteristic
965C2×C4C22×C22⋊C411yescharacteristic
966C2×C4C22×C22⋊C412yes—
967C2×C4C22×C22⋊C412yes—
968C2×C4C22×C22⋊C412yes—
969C2×C4C22×C22⋊C412yes—
970C2×C4C22×C22⋊C411yescharacteristic
971C2×C4C22×C22⋊C411yescharacteristic
972C2×C4C22×C22⋊C411yescharacteristic
973C2×C4C22×C22⋊C411yescharacteristic
974C2×C4#57612yes—
975C2×C4#57712yes—
976C2×C4C24×C411yescharacteristic
977C2×C4C23×D411yescharacteristic
978C2×C4C23×D411yescharacteristic
979C8—42no—
980C8—44no—
981C8—42no—
982C8—44no—
983C8—42no—
984C8—42no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—22no—
992C22—21no—
993C22—22no—
994C22—22no—
995C22—21no—
996C22—22no—
997C22—22no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—84no—
1003C22—88no—
1004C22C2×#41312yes—
1005C22#289712yes—
1006C22C23×C22⋊C411yescharacteristic
1007C4—21no—
1008C4—21no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—22no—
1013C4—21no—
1014C4—21no—
1015C4—21no—
1016C4—22no—
1017C4—21no—
1018C4—22no—
1019C4—21no—
1020C4—44no—
1021C4—48no—
1022C4C2×#41312yes—
1023C4C2×#41312yes—
1024C4#289712yes—
1025C4C2×#57611yescharacteristic
1026C4C2×#57711yescharacteristic
1027C4#358612yes—
1028C2—22no—
1029C2—22no—
1030C2—41no—
1031C2—42no—
1032C2—42no—
1033C2—84no—
1034C2C22×#41311yescharacteristic
1035C2C2×#289711yescharacteristic
1036C2#6008811yescharacteristic
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. #17749C2semidirect
9. #17743C2semidirect
10. #17742C2semidirect
11. #17718C2semidirect
12. #17714C2semidirect
13. #17704C2semidirect
14. C2×#1546C2semidirect
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
76. #1549C22semidirect
80. #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
#177492
#177432
#177422
#177182
#177142
#177042
C2×#15462