Finite Group Databasebeta

← #6376051

Subgroups — #6376051

Order 512.

1727 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60546C211yesmaximal, characteristic
2#60204C211yesmaximal, characteristic, complemented
3C2×#2922C211yesmaximal, characteristic, complemented
4#22166C212yesmaximal, complemented
5#22165C212yesmaximal, complemented
6#22131C212yesmaximal, complemented
7#22130C212yesmaximal, complemented
8#22096C212yesmaximal, complemented
9#22095C212yesmaximal, complemented
10#22061C212yesmaximal, complemented
11#22060C212yesmaximal, complemented
12#21383C211yesmaximal, characteristic, complemented
13#21371C211yesmaximal, characteristic, complemented
14#21296C214yesmaximal, complemented
15#21138C214yesmaximal, complemented
16#20748C211yesmaximal, characteristic, complemented
17#20476C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20#3117C412yescomplemented
21#3116C412yescomplemented
22#3115C412yescomplemented
23#3114C412yescomplemented
24#3113C411yescharacteristic, complemented
25#3112C411yescharacteristic, complemented
26#3111C414yescomplemented
27#3110C411yescharacteristic, complemented
28#3109C411yescharacteristic, complemented
29#3091C2212yes—
30#3076C2212yes—
31#3035C2212yes—
32#3002C2212yes—
33#2966—21no—
34#2966—21no—
35#2966—21no—
36#2966—21no—
37#2965—21no—
38#2965—21no—
39C8×#41—21no—
40C8×#41—21no—
41#2960C2211yescharacteristic, complemented
42#2960C2211yescharacteristic, complemented
43#2943C2214yes—
44#2931C2211yescharacteristic, complemented
45#2931C2211yescharacteristic, complemented
46#2929C2212yes—
47#2929C2212yes—
48#2922—21no—
49#2922—21no—
50#2922—21no—
51#2922—21no—
52#2922C2212yes—
53#2922C2212yes—
54#2922C2212yes—
55#2922C2212yes—
56#2922C2212yescomplemented
57#2920C2211yescharacteristic
58C2×#433—21no—
59C2×#433—21no—
60C2×#432C2211yescharacteristic
61C2×#431—21no—
62C2×#431—21no—
63C2×#424C2211yescharacteristic
64C2×#424C2211yescharacteristic
65C2×#408C2211yescharacteristic
66C2×#408C2211yescharacteristic
67C4×#131C2212yescomplemented
68C2×C4×M16C2211yescharacteristic
69C22×C4×C8C2211yescharacteristic
70#2283C2211yescharacteristic
71#1986C2212yescomplemented
72#1980C2212yescomplemented
73#1975C2214yes—
74#1974C2214yes—
75#1950C2212yescomplemented
76#1950C2212yescomplemented
77#1946C2214yescomplemented
78#1945C2214yescomplemented
79#1938C2214yes—
80#1938C2214yescomplemented
81#1937C2214yes—
82#1937C2214yescomplemented
83#1929C2214yes—
84#1929C2214yes—
85#1922C2214yescomplemented
86#1922C2214yescomplemented
87#1876C2214yes—
88#1876C2214yes—
89#1871C2212yes—
90#1871C2212yes—
91#1866C2214yescomplemented
92#1866C2214yescomplemented
93#1855C2212yes—
94#1855C2212yes—
95#1826C2212yes—
96#1806C2212yes—
97#1806C2212yes—
98#1789C2212yes—
99#1778C2214yescomplemented
100#1770C2212yescomplemented
101C8×C4⋊C4C2212yescomplemented
102#1759C2214yes—
103#1759C2214yescomplemented
104#1752C2212yes—
105C8×C22⋊C4C2212yes—
106#1746C2212yescomplemented
107#1726C2212yescomplemented
108C22×#41C2311yescharacteristic
109C2×#135C2314yes—
110C2×#131C2312yes—
111C2×#131C2312yes—
112C22×M16C2311yescharacteristic
113C22×M16C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C23×C8C2311yescharacteristic
116#533C2×C411yescharacteristic
117#533C2×C411yescharacteristic
118#533C2311yescharacteristic
119#532C2×C411yescharacteristic
120#532C2×C411yescharacteristic
121#532C2311yescharacteristic
122#529—21no—
123#529—21no—
124#529—21no—
125#529—21no—
126#529C2×C412yes—
127#529C2×C412yes—
128#525—21no—
129#525—21no—
130#525C2312yes—
131C4×#41—21no—
132C4×#41—21no—
133C4×#41—21no—
134C4×#41—21no—
135C4×#41—21no—
136C4×#41—21no—
137C4×#41C2×C412yes—
138C4×#41C2×C412yes—
139C4×#41C2312yes—
140C4×#41C2312yes—
141C4×#41C2312yes—
142C2×C4×Q8C2×C411yescharacteristic
143C2×C4×Q8C2×C411yescharacteristic
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4C2×C411yescharacteristic
147C2×C4×D4C2×C411yescharacteristic
148C2×#117—21no—
149C2×#117C2311yescharacteristic
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152#485C2×C414yes—
153#484C2×C412yes—
154#483C2×C412yes—
155#482C2×C414yes—
156#481C2×C412yes—
157#480C2×C412yes—
158#479C2×C414yes—
159#478C2×C414yes—
160#477C2×C412yes—
161#476C2×C412yes—
162#475C2×C412yes—
163#474C2×C412yes—
164#464C2×C414yes—
165#463C2×C414yes—
166#462C2×C412yes—
167#461C2×C412yes—
168#460C2×C412yes—
169#459C2×C412yes—
170#452C2×C414yes—
171#451C2×C412yes—
172#450C2×C412yes—
173#449C2×C414yes—
174#448C2×C412yes—
175#447C2×C412yes—
176#446—21no—
177#446—21no—
178#446—21no—
179#446—21no—
180C8×Q8—21no—
181C8×Q8—21no—
182C8×Q8—21no—
183C8×Q8—21no—
184#442C2×C414yes—
185#442C2×C414yes—
186#441C2×C414yes—
187#441C2×C414yes—
188#440C2×C414yes—
189#440C2×C414yes—
190#440C2×C414yes—
191#440C2×C414yes—
192#436—21no—
193#436—21no—
194#436—21no—
195#436—21no—
196#435—22no—
197#435—22no—
198#435—22no—
199#435—22no—
200C8×D4—22no—
201C8×D4—22no—
202C8×D4—22no—
203C8×D4—22no—
204C8×D4—21no—
205C8×D4—21no—
206C8×D4—21no—
207C8×D4—21no—
208#433—22no—
209#433—22no—
210#433—22no—
211#433—22no—
212#433—22no—
213#433—22no—
214#433—22no—
215#433—22no—
216#433—22no—
217#433—22no—
218#432—21no—
219#432—21no—
220#432C2×C411yescharacteristic
221#432C2×C411yescharacteristic
222#432C2×C412yes—
223#432C2×C412yes—
224#432C2×C412yes—
225#431—21no—
226#431—21no—
227#431—22no—
228#431—22no—
229#431—22no—
230#431—22no—
231#431—22no—
232#431—22no—
233#431—22no—
234#431—22no—
235#431—22no—
236#431—22no—
237C2×#108C2314yes—
238C2×#108C2314yes—
239#427C2314yes—
240#424—21no—
241#424—21no—
242#424—21no—
243#424—21no—
244#424C2312yes—
245#424C2312yes—
246#424C2312yes—
247#424C2312yes—
248#424C2312yes—
249#424C2312yes—
250#423C2311yescharacteristic
251#423C2311yescharacteristic
252C2×C4⋊C8—21no—
253C2×C4⋊C8—21no—
254C2×C4⋊C8—21no—
255C2×C4⋊C8—21no—
256C2×C4⋊C8C2312yes—
257C2×#104C2314yes—
258C2×#104C2314yes—
259C2×#104C2314yes—
260C2×#104C2314yes—
261#416C2314yes—
262#416C2314yes—
263#408—21no—
264#408—21no—
265#408—21no—
266#408—21no—
267#408C2312yes—
268#408C2312yes—
269#408C2312yes—
270#408C2312yes—
271#408C2312yes—
272#408C2312yes—
273#407C2312yes—
274C2×C22⋊C8—21no—
275C2×C22⋊C8—21no—
276C2×C22⋊C8—21no—
277C2×C22⋊C8—21no—
278C2×C22⋊C8C2312yes—
279#405—22no—
280#405—22no—
281#405C2312yes—
282#405C2312yes—
283C4×M16—21no—
284C4×M16—21no—
285C4×M16—22no—
286C4×M16C2312yes—
287C4×M16C2312yes—
288C4×M16C2312yes—
289C2×#97—21no—
290C2×#97C2314yes—
291C2×#97C2312yes—
292C2×C4×C8—21no—
293C2×C4×C8—22no—
294C2×C4×C8D411yescharacteristic
295C2×C4×C8D411yescharacteristic
296C2×C4×C8D411yescharacteristic
297C2×C4×C8D411yescharacteristic
298C2×C4×C8D411yescharacteristic
299C2×C4×C8D411yescharacteristic
300C2×C4×C8D411yescharacteristic
301C2×C4×C8D411yescharacteristic
302C2×C4×C8C2314yes—
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307#383—21no—
308#382—21no—
309#381—21no—
310#380—21no—
311C4×C4⋊C4C2312yes—
312C4×C22⋊C4C2312yes—
313#376C2312yes—
314#341C2314yes—
315#341C2314yes—
316#339C2314yes—
317#339C2314yes—
318#339C2314yes—
319#339C2314yes—
320#336C2314yes—
321#336C2314yes—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—42no—
327C2×#41—42no—
328C2×#41C22×C412yes—
329C2×#41C2412yes—
330C2×#41C2412yes—
331C22×Q8C22×C411yescharacteristic
332C22×D4—21no—
333C22×D4C22×C411yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4#4111yescharacteristic
338C23×C4#4111yescharacteristic
339C23×C4C2411yescharacteristic
340#135—44no—
341#135—44no—
342C2×Q16C22×C414yes—
343C2×SD16C22×C414yes—
344C2×SD16C22×C414yes—
345C2×D8C22×C414yes—
346#131—44no—
347#131—44no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16C2412yes—
355C2×M16C2412yes—
356C2×M16C2412yes—
357C2×M16C2412yes—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—42no—
363C22×C8—42no—
364C22×C8C2×D411yescharacteristic
365C22×C8C2×D411yescharacteristic
366C22×C8C2×D411yescharacteristic
367C22×C8C2×D411yescharacteristic
368C22×C8C2×D411yescharacteristic
369C22×C8C2×D411yescharacteristic
370C22×C8C2×D411yescharacteristic
371C22×C8C2×D411yescharacteristic
372C22×C8C2414yes—
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C4⋊Q8C22×C411yescharacteristic
378C4⋊Q8C22×C411yescharacteristic
379C4⋊Q8C22×C411yescharacteristic
380#127C22×C411yescharacteristic
381#126—22no—
382#126—22no—
383#125—21no—
384#125—21no—
385#125C22×C412yes—
386#124—21no—
387#124—21no—
388#124C22×C412yes—
389#123—22no—
390#123—22no—
391#123—22no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8C22×C412yes—
397C22⋊Q8C22×C412yes—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121C22×C412yes—
403#121C22×C412yes—
404#120—22no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C22×C412yes—
414C4×Q8C22×C412yes—
415C4×Q8C22×C412yes—
416C4×Q8C22×C412yes—
417C4×Q8C22×C412yes—
418C4×Q8C22×C412yes—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4C22×C412yes—
442C4×D4C22×C412yes—
443C4×D4C22×C412yes—
444C4×D4C22×C412yes—
445C4×D4C22×C412yes—
446C4×D4C22×C412yes—
447#117—21no—
448#117—21no—
449#117—21no—
450#117—21no—
451#117—22no—
452#117—22no—
453#117—22no—
454#117—22no—
455#117—22no—
456#117—22no—
457#117—22no—
458#117C22×C412yes—
459#117C2412yes—
460#117C2412yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4C22×C411yescharacteristic
465C2×C4⋊C4C22×C411yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42C22×C411yescharacteristic
479C2×C42C22×C411yescharacteristic
480C2×C42C22×C411yescharacteristic
481C2×C42C22×C411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42#4111yescharacteristic
487C2×C42#4111yescharacteristic
488C2×C42C2414yes—
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491#108—44no—
492#108—44no—
493#107C22×C414yes—
494#107C22×C414yes—
495#106C22×C414yes—
496#106C22×C414yes—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513C4⋊C8C22×C412yes—
514C4⋊C8C22×C412yes—
515C4⋊C8C22×C414yes—
516#104—44no—
517#104—44no—
518#104—44no—
519#104—44no—
520#103C22×C414yes—
521#103C22×C414yes—
522#103C22×C414yes—
523#103C22×C414yes—
524#102C22×C414yes—
525#102C22×C414yes—
526#102C22×C414yes—
527#102C22×C414yes—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8C22×C412yes—
543C22⋊C8C22×C412yes—
544C22⋊C8C22×C414yes—
545#97—22no—
546#97—22no—
547#97—22no—
548#97—22no—
549#97—22no—
550#97—44no—
551#97C22×C412yes—
552#97C22×C414yes—
553#97C22×C412yes—
554C4×C8—22no—
555C4×C8—22no—
556C4×C8—22no—
557C4×C8—22no—
558C4×C8—22no—
559C4×C8—44no—
560C4×C8C2×D411yescharacteristic
561C4×C8C2×D411yescharacteristic
562C4×C8C2×D411yescharacteristic
563C4×C8C2×D411yescharacteristic
564C4×C8C2×D411yescharacteristic
565C4×C8C2×D411yescharacteristic
566C4×C8C2×D411yescharacteristic
567C4×C8C2×D411yescharacteristic
568C4×C8C2×D411yescharacteristic
569C4×C8C2×D411yescharacteristic
570C4×C8C2×D411yescharacteristic
571C4×C8C2×D411yescharacteristic
572C4×C8C2×D411yescharacteristic
573C4×C8C2×D411yescharacteristic
574C4×C8C2×D411yescharacteristic
575C4×C8C2×D411yescharacteristic
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580C24—21no—
581C24C2×#4111yescharacteristic
582#41—22no—
583#41—22no—
584#41—24no—
585#41—24no—
586#41—22no—
587#41—22no—
588#41—42no—
589#41—42no—
590#41—44no—
591#41—44no—
592#41—44no—
593#41—42no—
594#41—42no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—42no—
599C2×Q8C23×C412yes—
600C2×Q8C23×C412yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—42no—
610C2×D4—44no—
611C2×D4C23×C412yes—
612C2×D4C23×C412yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—24no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4C4×D411yescharacteristic
635C22×C4C4×D411yescharacteristic
636C22×C4C4×D411yescharacteristic
637C22×C4C4×D411yescharacteristic
638C22×C4C4×D411yescharacteristic
639C22×C4C4×D411yescharacteristic
640C22×C4C4×D411yescharacteristic
641C22×C4C4×D411yescharacteristic
642C22×C4C23×C411yescharacteristic
643C22×C4C23×C411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C2×#4111yescharacteristic
647C22×C4C2×#4111yescharacteristic
648C22×C4C2×#4111yescharacteristic
649C22×C4C2×#4111yescharacteristic
650C22×C4C2×#4111yescharacteristic
651C22×C4C2511yescharacteristic
652Q16—44no—
653SD16—44no—
654SD16—44no—
655D8—44no—
656M16—22no—
657M16—22no—
658M16—24no—
659M16—24no—
660M16—22no—
661M16—22no—
662M16—44no—
663M16—44no—
664M16—42no—
665M16—42no—
666C2×C8—22no—
667C2×C8—24no—
668C2×C8—22no—
669C2×C8—24no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—41no—
684C2×C8—44no—
685C2×C8—44no—
686C2×C8—42no—
687C2×C8—42no—
688C2×C8C23×C414yes—
689C2×C8C23×C414yes—
690C2×C8C22×D411yescharacteristic
691C2×C8C22×D411yescharacteristic
692C2×C8C22×D411yescharacteristic
693C2×C8C22×D411yescharacteristic
694C2×C8C22×D411yescharacteristic
695C2×C8C22×D411yescharacteristic
696C2×C8C22×D411yescharacteristic
697C2×C8C22×D411yescharacteristic
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—44no—
715C4⋊C4C23×C412yes—
716C4⋊C4C23×C412yes—
717C4⋊C4C23×C412yes—
718C4⋊C4C23×C412yes—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—44no—
735C42—22no—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—22no—
741C42—22no—
742C42—22no—
743C42—22no—
744C42—24no—
745C42—24no—
746C42C4×D411yescharacteristic
747C42C4×D411yescharacteristic
748C42C4×D411yescharacteristic
749C42C4×D411yescharacteristic
750C42C4×D411yescharacteristic
751C42C4×D411yescharacteristic
752C42C4×D411yescharacteristic
753C42C4×D411yescharacteristic
754C42C23×C411yescharacteristic
755C42C23×C411yescharacteristic
756C42C23×C411yescharacteristic
757C42C23×C411yescharacteristic
758C42C22×D411yescharacteristic
759C42C22×D411yescharacteristic
760C42C22×D411yescharacteristic
761C42C22×D411yescharacteristic
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23C2×C4×D411yescharacteristic
771C23C2×C4×D411yescharacteristic
772C23C22×#4111yescharacteristic
773Q8—22no—
774Q8—24no—
775Q8—22no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779D4—22no—
780D4—24no—
781D4—22no—
782D4—42no—
783D4—42no—
784D4—44no—
785D4—44no—
786D4—42no—
787D4—42no—
788D4—44no—
789D4—44no—
790D4—42no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4C2×C4×D411yescharacteristic
834C2×C4C2×C4×D411yescharacteristic
835C2×C4C2×C4×D411yescharacteristic
836C2×C4C2×C4×D411yescharacteristic
837C2×C4C2×C4×D411yescharacteristic
838C2×C4C2×C4×D411yescharacteristic
839C2×C4C2×C4×D411yescharacteristic
840C2×C4C2×C4×D411yescharacteristic
841C2×C4C2×C4×D411yescharacteristic
842C2×C4C2×C4×D411yescharacteristic
843C2×C4C24×C411yescharacteristic
844C2×C4C23×D411yescharacteristic
845C2×C4#58512yes—
846C2×C4#58512yes—
847C8—24no—
848C8—24no—
849C8—21no—
850C8—21no—
851C8—21no—
852C8—21no—
853C8—21no—
854C8—21no—
855C8—21no—
856C8—21no—
857C8—42no—
858C8—42no—
859C8—42no—
860C8—42no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—84no—
876C22#295512yes—
877C22C22×C4×D411yescharacteristic
878C22#345512yes—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—84no—
895C4#295512yes—
896C4#342812yes—
897C4#344911yescharacteristic
898C4#344911yescharacteristic
899C2—22no—
900C2—22no—
901C2—41no—
902C2—82no—
903C2—82no—
904C2#3406511yescharacteristic
905C2C2×#295511yescharacteristic
906C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#60546C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60204C2semidirect
3. C2×#2922C2semidirect
4. #22166C2semidirect
5. #22165C2semidirect
6. #22131C2semidirect
7. #22130C2semidirect
8. #22096C2semidirect
9. #22095C2semidirect
10. #22061C2semidirect
11. #22060C2semidirect
12. #21383C2semidirect
13. #21371C2semidirect
14. #21296C2semidirect
15. #21138C2semidirect
16. #20748C2semidirect
17. #20476C2semidirect
20. #3117C4semidirect
21. #3116C4semidirect
22. #3115C4semidirect
23. #3114C4semidirect
24. #3113C4semidirect
25. #3112C4semidirect
26. #3111C4semidirect
27. #3110C4semidirect
28. #3109C4semidirect
41. #2960C22semidirect
42. #2960C22semidirect
44. #2931C22semidirect
45. #2931C22semidirect
56. #2922C22semidirect
67. C4×#131C22semidirect
71. #1986C22semidirect
72. #1980C22semidirect
75. #1950C22semidirect
76. #1950C22semidirect
77. #1946C22semidirect
78. #1945C22semidirect
80. #1938C22semidirect
82. #1937C22semidirect
85. #1922C22semidirect
86. #1922C22semidirect
91. #1866C22semidirect
92. #1866C22semidirect
99. #1778C22semidirect
100. #1770C22semidirect
101. C8×C4⋊C4C22semidirect
103. #1759C22semidirect
106. #1746C22semidirect
107. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#605462
#602042
C2×#29222
#221662
#221652
#221312
#221302
#220962
#220952
#220612
#220602
#213832
#213712
#212962
#211382
#207482
#204762