Finite Group Databasebeta

← #6345506

Subgroups — #6345506

Order 512.

1503 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60952C211yesmaximal, characteristic
2#60280C211yesmaximal, characteristic
3#60250C211yesmaximal, characteristic, complemented
4#18083C214yesmaximal, complemented
5#18081C214yesmaximal, complemented
6#18032C214yesmaximal, complemented
7#18030C214yesmaximal, complemented
8#17944C212yesmaximal, complemented
9#17941C212yesmaximal, complemented
10#17916C212yesmaximal, complemented
11#17913C212yesmaximal, complemented
12#17808C211yesmaximal, characteristic, complemented
13#17499C211yesmaximal, characteristic
14#17464C211yesmaximal, characteristic, complemented
15#17324C211yesmaximal, characteristic, complemented
16#3444C2211yescharacteristic
17C2×#533C2211yescharacteristic
18#3255C412yes—
19#3254C412yes—
20#3239C411yescharacteristic
21#3239C411yescharacteristic
22#3237C412yes—
23#3218C411yescharacteristic
24#3218C411yescharacteristic
25#3216C412yes—
26#3196C412yes—
27#3196C412yes—
28#3172C2212yes—
29#3172C2212yes—
30#3107C2212yes—
31#3107C2212yes—
32#3104C2212yes—
33#3103C2212yes—
34#2994—22no—
35#2994C2212yes—
36#2994C2212yes—
37#2986C2214yes—
38#2986C2212yes—
39#2985—21no—
40#2985—21no—
41#2984C2214yes—
42#2983—21no—
43#2982—21no—
44#2979C2212yes—
45#2977—22no—
46#2965—21no—
47#2965C2211yescharacteristic
48#2965C2211yescharacteristic
49C8×#41—21no—
50C8×#41C2211yescharacteristic
51C8×#41C2211yescharacteristic
52#2962—22no—
53#2960C2212yes—
54#2960C2212yes—
55#2924—22no—
56#2922—21no—
57#2922—21no—
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60#2920C2211yescharacteristic
61C2×#431C2211yescharacteristic
62C2×#431C2211yescharacteristic
63#1593C2214yescomplemented
64#1592C2214yescomplemented
65#1591C2214yescomplemented
66#1590C2214yescomplemented
67#1588C2214yescomplemented
68#1587C2214yescomplemented
69#1587C2214yescomplemented
70#1585C2214yescomplemented
71#1584C2214yescomplemented
72#1584C2214yescomplemented
73#1583C2214yescomplemented
74#1582C2214yescomplemented
75#1579C2214yescomplemented
76SD16⋊C8C2214yescomplemented
77C8×Q16C2214yescomplemented
78C8×SD16C2214yescomplemented
79#1574C2212yes—
80#1574C2212yes—
81#1572C2214yes—
82#1565C2214yes—
83#1497C2212yes—
84#1496C2212yes—
85#1489C2212yes—
86#1489C2212yes—
87#1485C2212yes—
88#1485C2212yes—
89#1482C2212yes—
90#1482C2212yes—
91#1481C2214yes—
92#1479C2214yes—
93#1454C2214yes—
94#1453C2214yes—
95#1451C2212yes—
96C8×M16C2212yes—
97#533—21no—
98#533—21no—
99#533—21no—
100#533—21no—
101#533C2×C412yes—
102#533C2×C412yes—
103#533C2×C411yescharacteristic
104#533C2×C411yescharacteristic
105#533C2311yescharacteristic
106#533C2312yes—
107#533C2312yes—
108#532C2×C411yescharacteristic
109#532C2×C411yescharacteristic
110#532C2311yescharacteristic
111C2×C4⋊Q8C2×C411yescharacteristic
112C2×C4⋊Q8C2×C411yescharacteristic
113#529—21no—
114#529—21no—
115#529—21no—
116#529—21no—
117#529C2×C411yescharacteristic
118#529C2×C411yescharacteristic
119#529C2311yescharacteristic
120#529C2311yescharacteristic
121C2×#125—21no—
122#525—21no—
123#525—21no—
124#525C2×C411yescharacteristic
125#525C2×C411yescharacteristic
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8C2×C412yes—
128C4×#41—21no—
129C4×#41—21no—
130C4×#41C2311yescharacteristic
131C4×#41C2311yescharacteristic
132C2×C4×Q8—21no—
133C2×C4×Q8C2312yes—
134C2×#117—21no—
135C22×C42C2311yescharacteristic
136#501C2×C412yes—
137#501C2×C412yes—
138#497C2×C412yes—
139#497C2×C412yes—
140#491C2×C412yes—
141#491C2×C412yes—
142#489C2×C412yes—
143#489C2×C412yes—
144#485C2×C414yes—
145#485C2×C414yes—
146#484C2×C412yes—
147#484C2×C412yes—
148#481C2×C412yes—
149#481C2×C412yes—
150#477C2×C414yes—
151#475C2×C414yes—
152#475C2×C412yes—
153#475C2×C412yes—
154#474C2×C412yes—
155#474C2×C412yes—
156#470C2×C414yes—
157#470C2×C414yes—
158#468C2×C414yes—
159#468C2×C414yes—
160#462C2×C414yes—
161#462C2×C412yes—
162#462C2×C412yes—
163#461C2×C412yes—
164#461C2×C412yes—
165#460C2×C414yes—
166#452C2×C414yes—
167#452C2×C414yes—
168#451C2×C412yes—
169#451C2×C412yes—
170#448C2×C412yes—
171#448C2×C412yes—
172#446—24no—
173#446—24no—
174#446—24no—
175#446—22no—
176#446—22no—
177#446—22no—
178#446C2314yes—
179#446C2312yes—
180#446C2314yes—
181#446C2312yes—
182C8×Q8—24no—
183C8×Q8—22no—
184C8×Q8—22no—
185C8×Q8—22no—
186C8×Q8C2314yes—
187C8×Q8C2312yes—
188C8×Q8C2314yes—
189C8×Q8C2312yes—
190C4×Q16C2314yes—
191C4×Q16C2314yes—
192C4×SD16C2314yes—
193C4×SD16C2314yes—
194#436—22no—
195#436C2312yes—
196#436C2312yes—
197#435—22no—
198#435—22no—
199#435—22no—
200#435—22no—
201C8×D4—22no—
202C8×D4—22no—
203C8×D4—22no—
204C8×D4—22no—
205C8×D4—22no—
206C8×D4C2312yes—
207C8×D4C2312yes—
208#433—22no—
209#433—22no—
210#433—22no—
211#433—22no—
212#433—24no—
213#433—24no—
214#432—21no—
215#432—21no—
216#432—21no—
217#432—24no—
218#432C2×C412yes—
219#432C2×C411yescharacteristic
220#432C2×C411yescharacteristic
221#432C2312yes—
222#431—21no—
223#431—21no—
224#431—21no—
225#431—24no—
226#431—21no—
227#431—21no—
228#431—21no—
229#431—21no—
230#431D411yescharacteristic
231#431D411yescharacteristic
232#431D411yescharacteristic
233#431D411yescharacteristic
234#431C2312yes—
235#431C2312yes—
236#431C2311yescharacteristic
237#431C2311yescharacteristic
238#431C2312yes—
239#431C2312yes—
240#431C2312yes—
241#431C2312yes—
242#431C2312yes—
243#431C2312yes—
244#424—22no—
245#424—22no—
246#424—22no—
247#424—22no—
248#423—21no—
249#423C2×C412yes—
250#423C2312yes—
251C2×C4⋊C8D412yes—
252C2×C4⋊C8C2312yes—
253#408—22no—
254#408—22no—
255#407—21no—
256#407—21no—
257#407C2×C412yes—
258C2×C22⋊C8—21no—
259C2×C22⋊C8D412yes—
260#405—22no—
261#405—22no—
262C4×M16—21no—
263C4×M16—21no—
264C4×M16—21no—
265C4×M16C2312yes—
266C4×M16C2312yes—
267C2×C4×C8—21no—
268C2×C4×C8—21no—
269C2×C4×C8—21no—
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#335C2314yes—
273#335C2314yes—
274#334C2314yes—
275#334C2314yes—
276Q8⋊C8C2314yes—
277Q8⋊C8C2314yes—
278Q8⋊C8C2314yes—
279Q8⋊C8C2314yes—
280Q8⋊C8C2314yes—
281Q8⋊C8C2314yes—
282D4⋊C8C2314yes—
283D4⋊C8C2314yes—
284#322C2314yes—
285#322C2314yes—
286#322C2314yes—
287C82C2314yes—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41C22×C411yescharacteristic
291C2×#41C22×C411yescharacteristic
292C22×Q8—21no—
293C22×Q8C22×C412yes—
294C23×C4C22×C411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4#4111yescharacteristic
297C2×Q16C22×C414yes—
298C2×Q16C22×C414yes—
299C2×SD16C22×C414yes—
300C2×SD16C22×C414yes—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16C22×C414yes—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8C2×D412yes—
310C22×C8C2×D412yes—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8C22×C412yes—
316C4⋊Q8C22×C412yes—
317C4⋊Q8C22×C411yescharacteristic
318C4⋊Q8C22×C412yes—
319C4⋊Q8C22×C412yes—
320C4⋊Q8C22×C411yescharacteristic
321C4⋊Q8C22×C411yescharacteristic
322#127C22×C411yescharacteristic
323#126—21no—
324#126—21no—
325#126—21no—
326#126—21no—
327#125—22no—
328#125—22no—
329#125—21no—
330#125—22no—
331#125—22no—
332#125—21no—
333#125C22×C411yescharacteristic
334#125C22×C411yescharacteristic
335#124—21no—
336#124—21no—
337#124C22×C411yescharacteristic
338#124C22×C411yescharacteristic
339#123—21no—
340#123—21no—
341#123—21no—
342#123—21no—
343#123—21no—
344#123—21no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8C22×C414yes—
356C22⋊Q8C22×C414yes—
357C22⋊Q8C22×C411yescharacteristic
358C22⋊Q8C22×C411yescharacteristic
359C22⋊Q8C22×C411yescharacteristic
360C22⋊Q8C22×C411yescharacteristic
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121C22×C411yescharacteristic
366#121C22×C411yescharacteristic
367#121C22×C411yescharacteristic
368#121C22×C411yescharacteristic
369#120—21no—
370#120—21no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—21no—
380C4×Q8—22no—
381C4×Q8C22×C414yes—
382C4×Q8C22×C411yescharacteristic
383C4×Q8C22×C411yescharacteristic
384C4×Q8C2414yes—
385C4×Q8C2411yescharacteristic
386C4×Q8C2411yescharacteristic
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4C22×C411yescharacteristic
404C4×D4C22×C411yescharacteristic
405C4×D4C2411yescharacteristic
406C4×D4C2411yescharacteristic
407#117—22no—
408#117—22no—
409#117—21no—
410#117—22no—
411#117—22no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117—21no—
419#117C22×C411yescharacteristic
420#117C22×C411yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4C22×C412yes—
427C2×C22⋊C4—22no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42C22×C411yescharacteristic
432C2×C42C22×C411yescharacteristic
433C2×C42C22×C411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42#4111yescharacteristic
438C2×C42#4111yescharacteristic
439C2×C42#4111yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107C22×C414yes—
444#107C22×C414yes—
445#106C22×C414yes—
446#106C22×C414yes—
447C4⋊C8—22no—
448C4⋊C8—22no—
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—24no—
452C4⋊C8—24no—
453C4⋊C8—24no—
454C4⋊C8—24no—
455C4⋊C8—22no—
456C4⋊C8—22no—
457C4⋊C8—22no—
458C4⋊C8—22no—
459C4⋊C8C22×C414yes—
460C4⋊C8C22×C412yes—
461C4⋊C8C22×C412yes—
462C4⋊C8C2×D412yes—
463C4⋊C8C2×D412yes—
464C4⋊C8C2×D412yes—
465C4⋊C8C2×D412yes—
466C4⋊C8C2414yes—
467C4⋊C8C2412yes—
468C4⋊C8C2412yes—
469#103C22×C414yes—
470#103C22×C414yes—
471#103C22×C414yes—
472#103C22×C414yes—
473#103C22×C414yes—
474#103C22×C414yes—
475#102C22×C414yes—
476#102C22×C414yes—
477C22⋊C8—22no—
478C22⋊C8—21no—
479C22⋊C8—21no—
480C22⋊C8—22no—
481C22⋊C8—22no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8C22×C412yes—
489C22⋊C8C22×C412yes—
490C22⋊C8C22×C414yes—
491C22⋊C8C2×D412yes—
492C22⋊C8C2×D412yes—
493C22⋊C8C2×D412yes—
494C22⋊C8C2×D412yes—
495#97—22no—
496#97—22no—
497#97—24no—
498#97—24no—
499#97—22no—
500#97—22no—
501#97C22×C412yes—
502#97C22×C412yes—
503C4×C8—22no—
504C4×C8—22no—
505C4×C8—24no—
506C4×C8—24no—
507C4×C8—21no—
508C4×C8—21no—
509C4×C8—22no—
510C4×C8—22no—
511C4×C8C2×D411yescharacteristic
512C4×C8C2×D411yescharacteristic
513C4×C8C2×D411yescharacteristic
514C4×C8C2×D411yescharacteristic
515C4×C8C2414yes—
516C4×C8C2414yes—
517C4×C8C2412yes—
518C4×C8C2412yes—
519C24C4×D411yescharacteristic
520#41—42no—
521#41—42no—
522#41—44no—
523#41—82no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8C23×C411yescharacteristic
532C2×Q8C23×C411yescharacteristic
533C2×Q8C23×C414yes—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4C23×C411yescharacteristic
543C2×D4C23×C411yescharacteristic
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4C4×D411yescharacteristic
556C22×C4C4×D411yescharacteristic
557C22×C4C4×D411yescharacteristic
558C22×C4C4×D411yescharacteristic
559C22×C4C4×D411yescharacteristic
560C22×C4C4×D411yescharacteristic
561C22×C4C4×D411yescharacteristic
562C22×C4C4×D411yescharacteristic
563C22×C4C4×D411yescharacteristic
564C22×C4C23×C411yescharacteristic
565C22×C4C23×C411yescharacteristic
566C22×C4C23×C411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573Q16—44no—
574Q16—44no—
575SD16—44no—
576SD16—44no—
577M16—44no—
578M16—44no—
579M16—44no—
580M16—82no—
581M16—82no—
582C2×C8—22no—
583C2×C8—24no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—42no—
587C2×C8—42no—
588C2×C8—82no—
589C2×C8—82no—
590C2×C8—82no—
591C2×C8C23×C414yes—
592C2×C8C23×C414yes—
593C2×C8C22×D412yes—
594C2×C8C22×D412yes—
595C2×C8C22×D412yes—
596C2×C8C22×D412yes—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C23×C414yes—
625C4⋊C4C23×C411yescharacteristic
626C4⋊C4C23×C411yescharacteristic
627C4⋊C4C23×C411yescharacteristic
628C4⋊C4C23×C411yescharacteristic
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C42—21no—
650C42—21no—
651C42—24no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—24no—
657C42C4×D411yescharacteristic
658C42C4×D411yescharacteristic
659C42C4×D411yescharacteristic
660C42C4×D411yescharacteristic
661C42C4×D411yescharacteristic
662C42C4×D411yescharacteristic
663C42C23×C411yescharacteristic
664C42C23×C411yescharacteristic
665C42C23×C411yescharacteristic
666C42C22×D411yescharacteristic
667C42C22×D411yescharacteristic
668C42C22×D411yescharacteristic
669C42C2×#4111yescharacteristic
670C42C2×#4111yescharacteristic
671C42C2×#4111yescharacteristic
672C42C2511yescharacteristic
673C23—21no—
674C23—21no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23C2×C4×D411yescharacteristic
679C23C2×C4×D411yescharacteristic
680C23C2×C4×D411yescharacteristic
681Q8—24no—
682Q8—24no—
683Q8—22no—
684Q8—22no—
685Q8—44no—
686Q8—42no—
687Q8—44no—
688Q8—82no—
689Q8—81no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—81no—
698D4—81no—
699D4—81no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4C2×C4×D411yescharacteristic
735C2×C4C2×C4×D411yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C24×C411yescharacteristic
744C2×C4C23×D411yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C8—24no—
751C8—24no—
752C8—44no—
753C8—42no—
754C8—42no—
755C8—44no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—82no—
772C22C22×C4×D411yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—44no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4#295512yes—
791C4#357312yes—
792C4#358612yes—
793C2—41no—
794C2—41no—
795C2—41no—
796C2—81no—
797C2—81no—
798C2#6014211yescharacteristic
799C2#6016911yescharacteristic
800C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#3444C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #60250C2semidirect
4. #18083C2semidirect
5. #18081C2semidirect
6. #18032C2semidirect
7. #18030C2semidirect
8. #17944C2semidirect
9. #17941C2semidirect
10. #17916C2semidirect
11. #17913C2semidirect
12. #17808C2semidirect
14. #17464C2semidirect
15. #17324C2semidirect
63. #1593C22semidirect
64. #1592C22semidirect
65. #1591C22semidirect
66. #1590C22semidirect
67. #1588C22semidirect
68. #1587C22semidirect
69. #1587C22semidirect
70. #1585C22semidirect
71. #1584C22semidirect
72. #1584C22semidirect
73. #1583C22semidirect
74. #1582C22semidirect
75. #1579C22semidirect
76. SD16⋊C8C22semidirect
77. C8×Q16C22semidirect
78. C8×SD16C22semidirect

Maximal subgroups

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

subgroupindex
#609522
#602802
#602502
#180832
#180812
#180322
#180302
#179442
#179412
#179162
#179132
#178082
#174992
#174642
#173242