Finite Group Databasebeta

← #6345464

Subgroups — #6345464

Order 512.

1559 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60952C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic
3C2×#2962C211yesmaximal, characteristic, complemented
4#18079C214yesmaximal, complemented
5#18077C214yesmaximal, complemented
6#18013C214yesmaximal, complemented
7#18009C214yesmaximal, complemented
8#17936C211yesmaximal, characteristic, complemented
9#17934C211yesmaximal, characteristic, complemented
10#17931C211yesmaximal, characteristic, complemented
11#17929C211yesmaximal, characteristic, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17906C211yesmaximal, characteristic, complemented
14#17903C211yesmaximal, characteristic, complemented
15#17901C211yesmaximal, characteristic, complemented
16#17807C211yesmaximal, characteristic, complemented
17#17491C211yesmaximal, characteristic, complemented
18#17466C211yesmaximal, characteristic
19#17334C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#533C2211yescharacteristic
22#3255C412yes—
23#3254C412yes—
24#3239C412yes—
25#3237C412yes—
26#3218C412yes—
27#3216C412yes—
28#3196C412yes—
29#3196C412yes—
30#3172C2214yes—
31#3107C2214yes—
32#3104C2211yescharacteristic
33#3104C2211yescharacteristic
34#3103C2211yescharacteristic
35#3103C2211yescharacteristic
36#2971—21no—
37#2971C2212yes—
38#2970—21no—
39#2970C2212yes—
40#2969—21no—
41#2969—21no—
42#2969C2212yes—
43#2969C2212yes—
44#2962—21no—
45#2962—21no—
46#2962—21no—
47#2962—21no—
48#2962C2212yes—
49#2962C2212yes—
50#2962C2212yes—
51#2962C2212yes—
52#2960C2211yescharacteristic
53#2960C2211yescharacteristic
54C2×#446—21no—
55C2×#446—21no—
56C2×#446C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×C8×Q8C2211yescharacteristic
59C2×C8×Q8C2211yescharacteristic
60#2931C2211yescharacteristic
61#2931C2211yescharacteristic
62#2930—21no—
63#2930—21no—
64#2923—21no—
65#2920C2211yescharacteristic
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68C2×#424—21no—
69C22×C4⋊C8C2211yescharacteristic
70#2875—21no—
71C2×#405—21no—
72C2×C4×M16C2211yescharacteristic
73#1593C2214yescomplemented
74#1592C2214yescomplemented
75#1591C2214yescomplemented
76#1590C2214yescomplemented
77#1588C2214yescomplemented
78#1587C2214yescomplemented
79#1587C2214yescomplemented
80#1585C2214yescomplemented
81#1584C2214yescomplemented
82#1584C2214yescomplemented
83#1583C2214yescomplemented
84#1582C2214yescomplemented
85#1579C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×Q16C2214yescomplemented
88C8×SD16C2214yescomplemented
89#1573C2214yes—
90#1571C2211yescharacteristic
91#1571C2211yescharacteristic
92#1570C2211yescharacteristic
93#1570C2211yescharacteristic
94#1565C2214yes—
95#1497C2214yes—
96#1487C2211yescharacteristic
97#1487C2211yescharacteristic
98#1487C2211yescharacteristic
99#1487C2211yescharacteristic
100#1485C2214yes—
101#1483C2214yes—
102#1481C2211yescharacteristic
103#1481C2211yescharacteristic
104#1480C2211yescharacteristic
105#1480C2211yescharacteristic
106#1477C2214yes—
107#1455C2212yes—
108#1455C2212yes—
109#1453C2212yes—
110#1453C2212yes—
111#1452C2211yescharacteristic
112#1452C2211yescharacteristic
113#1450C2211yescharacteristic
114#1450C2211yescharacteristic
115C2×#131—21no—
116C2×#131—21no—
117C22×M16D411yescharacteristic
118C22×M16D411yescharacteristic
119C23×C8—21no—
120#533—21no—
121#533—21no—
122#533—21no—
123#533—21no—
124#533C2×C412yes—
125#533C2×C412yes—
126#533C2×C411yescharacteristic
127#533C2×C411yescharacteristic
128#533C2311yescharacteristic
129#533C2312yes—
130#533C2312yes—
131#532C2×C411yescharacteristic
132#532C2×C411yescharacteristic
133#532C2311yescharacteristic
134C2×C4⋊Q8C2×C411yescharacteristic
135C2×C4⋊Q8C2×C411yescharacteristic
136#529—21no—
137#529—21no—
138#529—21no—
139#529—21no—
140#529C2×C412yes—
141#529C2312yes—
142C2×#125—21no—
143#525—21no—
144#525—21no—
145#525C2×C412yes—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8C2×C411yescharacteristic
148C2×C22⋊Q8C2×C411yescharacteristic
149C4×#41—21no—
150C4×#41—21no—
151C4×#41C2312yes—
152C2×C4×Q8—21no—
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×#117—21no—
156C22×C42C2311yescharacteristic
157#501C2×C414yes—
158#497C2×C414yes—
159#491C2×C414yes—
160#489C2×C414yes—
161#485C2×C414yes—
162#485C2×C414yes—
163#484C2×C412yes—
164#484C2×C412yes—
165#481C2×C412yes—
166#481C2×C412yes—
167#477C2×C412yes—
168#477C2×C412yes—
169#475C2×C412yes—
170#475C2×C412yes—
171#475C2×C414yes—
172#474C2×C414yes—
173#470C2×C414yes—
174#470C2×C414yes—
175#468C2×C414yes—
176#468C2×C414yes—
177#462C2×C412yes—
178#462C2×C412yes—
179#462C2×C414yes—
180#461C2×C414yes—
181#460C2×C412yes—
182#460C2×C412yes—
183#452C2×C414yes—
184#452C2×C414yes—
185#451C2×C412yes—
186#451C2×C412yes—
187#448C2×C412yes—
188#448C2×C412yes—
189#446—22no—
190#446—22no—
191#446—22no—
192#446—22no—
193#446—22no—
194#446—22no—
195#446—22no—
196#446—22no—
197#446—21no—
198#446—21no—
199#446—21no—
200#446—21no—
201#446—21no—
202#446—21no—
203#446C2312yes—
204#446C2312yes—
205#446C2312yes—
206#446C2312yes—
207#446C2312yes—
208#446C2312yes—
209C8×Q8—21no—
210C8×Q8—21no—
211C8×Q8—21no—
212C8×Q8—21no—
213C8×Q8—21no—
214C8×Q8—21no—
215C8×Q8C2312yes—
216C8×Q8C2312yes—
217C8×Q8C2312yes—
218C8×Q8C2312yes—
219C8×Q8C2312yes—
220C8×Q8C2312yes—
221C4×Q16C2314yes—
222C4×Q16C2314yes—
223C4×SD16C2314yes—
224C4×SD16C2314yes—
225#436—22no—
226#436—22no—
227#436—22no—
228#436—22no—
229#436—21no—
230#436—21no—
231#436C2312yes—
232#436C2312yes—
233#435—22no—
234#435—22no—
235#435—22no—
236#435—22no—
237C8×D4—21no—
238C8×D4—21no—
239C8×D4C2312yes—
240C8×D4C2312yes—
241#433—22no—
242#433—22no—
243#432—21no—
244#432—21no—
245#432—21no—
246#432—22no—
247#432—22no—
248#432C2×C412yes—
249#432C2×C412yes—
250#432C2312yes—
251#431—21no—
252#431C2312yes—
253#431C2311yescharacteristic
254#431C2311yescharacteristic
255#431C2312yes—
256#431C2311yescharacteristic
257#431C2311yescharacteristic
258#431C2312yes—
259#424—22no—
260#424—22no—
261#424—22no—
262#424—22no—
263#424—21no—
264#424—21no—
265#423—21no—
266#423C2×C412yes—
267#423C2311yescharacteristic
268#423C2311yescharacteristic
269C2×C4⋊C8—21no—
270C2×C4⋊C8—21no—
271C2×C4⋊C8—21no—
272C2×C4⋊C8—21no—
273C2×C4⋊C8—21no—
274C2×C4⋊C8—21no—
275C2×C4⋊C8—21no—
276C2×C4⋊C8C2312yes—
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2312yes—
280#408—21no—
281#408—21no—
282#407—21no—
283#407—21no—
284#407C2×C412yes—
285#405—22no—
286#405—22no—
287#405—22no—
288#405—22no—
289#405—21no—
290#405—21no—
291#405—22no—
292#405—22no—
293C4×M16—21no—
294C4×M16—22no—
295C4×M16D411yescharacteristic
296C4×M16D411yescharacteristic
297C4×M16D411yescharacteristic
298C4×M16D411yescharacteristic
299C4×M16C2312yes—
300C4×M16C2312yes—
301C4×M16C2311yescharacteristic
302C4×M16C2311yescharacteristic
303C4×M16C2311yescharacteristic
304C4×M16C2311yescharacteristic
305C2×#97—21no—
306C2×#97—21no—
307C2×#97—22no—
308C2×#97D411yescharacteristic
309C2×#97D411yescharacteristic
310C2×C4×C8—21no—
311C2×C4×C8—21no—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#334C2314yes—
317#334C2314yes—
318Q8⋊C8C2314yes—
319Q8⋊C8C2314yes—
320Q8⋊C8C2314yes—
321Q8⋊C8C2314yes—
322Q8⋊C8C2314yes—
323Q8⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yes—
326#322C2312yes—
327#322C2312yes—
328#322C2312yes—
329#322C2312yes—
330#322C2312yes—
331#322C2312yes—
332C82C2312yes—
333C82C2312yes—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C22×C412yes—
337C22×Q8—21no—
338C22×Q8C22×C411yescharacteristic
339C22×Q8C22×C411yescharacteristic
340C23×C4C22×C411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4#4111yescharacteristic
343C2×Q16C22×C414yes—
344C2×Q16C22×C414yes—
345C2×SD16C22×C414yes—
346C2×SD16C22×C414yes—
347#131—44no—
348#131—44no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—22no—
352C2×M16—24no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—42no—
356C2×M16C22×C414yes—
357C2×M16C2×D411yescharacteristic
358C2×M16C2×D411yescharacteristic
359C2×M16C2×D411yescharacteristic
360C2×M16C2×D411yescharacteristic
361C2×M16C2×D411yescharacteristic
362C2×M16C2×D411yescharacteristic
363C2×M16C2×D411yescharacteristic
364C2×M16C2×D411yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—44no—
372C22×C8C2×D411yescharacteristic
373C22×C8C2×D411yescharacteristic
374C22×C8C2×D411yescharacteristic
375C22×C8C2×D411yescharacteristic
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8C22×C412yes—
381C4⋊Q8C22×C412yes—
382C4⋊Q8C22×C411yescharacteristic
383C4⋊Q8C22×C412yes—
384C4⋊Q8C22×C412yes—
385C4⋊Q8C22×C411yescharacteristic
386C4⋊Q8C22×C411yescharacteristic
387#127C22×C411yescharacteristic
388#126—22no—
389#126—22no—
390#125—22no—
391#125—22no—
392#125—21no—
393#125—22no—
394#125—22no—
395#125—21no—
396#125C22×C412yes—
397#124—21no—
398#124—21no—
399#124C22×C412yes—
400#123—22no—
401#123—22no—
402#123—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8C22×C412yes—
416C22⋊Q8C22×C412yes—
417C22⋊Q8C22×C412yes—
418C22⋊Q8C22×C412yes—
419C22⋊Q8C22×C412yes—
420C22⋊Q8C22×C412yes—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121C22×C412yes—
426#121C22×C412yes—
427#120—22no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8C22×C412yes—
441C4×Q8C22×C412yes—
442C4×Q8C22×C412yes—
443C4×Q8C2412yes—
444C4×Q8C2412yes—
445C4×Q8C2412yes—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4C22×C412yes—
457C4×D4C2412yes—
458#117—22no—
459#117—22no—
460#117—21no—
461#117—22no—
462#117—22no—
463#117—21no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117C22×C412yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4C22×C411yescharacteristic
476C2×C4⋊C4C22×C411yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—22no—
482C2×C42C22×C411yescharacteristic
483C2×C42C22×C411yescharacteristic
484C2×C42C22×C411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42#4111yescharacteristic
489C2×C42#4111yescharacteristic
490C2×C42#4111yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494#107C22×C414yes—
495#107C22×C414yes—
496#106C22×C414yes—
497#106C22×C414yes—
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—22no—
510C4⋊C8—21no—
511C4⋊C8—22no—
512C4⋊C8—21no—
513C4⋊C8—22no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—22no—
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8C22×C412yes—
520C4⋊C8C22×C412yes—
521C4⋊C8C22×C414yes—
522C4⋊C8C2412yes—
523C4⋊C8C2412yes—
524C4⋊C8C2412yes—
525C4⋊C8C2412yes—
526#103C22×C414yes—
527#103C22×C414yes—
528#103C22×C414yes—
529#103C22×C414yes—
530#103C22×C414yes—
531#103C22×C414yes—
532#102C22×C414yes—
533#102C22×C414yes—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8C22×C412yes—
544C22⋊C8C22×C412yes—
545C22⋊C8C22×C414yes—
546#97—22no—
547#97—22no—
548#97—22no—
549#97—22no—
550#97—22no—
551#97—22no—
552#97—22no—
553#97—22no—
554#97C22×C414yes—
555#97C2×D411yescharacteristic
556#97C2×D411yescharacteristic
557#97C2×D411yescharacteristic
558#97C2×D411yescharacteristic
559#97C2×D411yescharacteristic
560#97C2×D411yescharacteristic
561#97C2×D411yescharacteristic
562#97C2×D411yescharacteristic
563C4×C8—22no—
564C4×C8—22no—
565C4×C8—22no—
566C4×C8—22no—
567C4×C8—22no—
568C4×C8—22no—
569C4×C8—22no—
570C4×C8C2×D411yescharacteristic
571C4×C8C2×D411yescharacteristic
572C4×C8C2×D411yescharacteristic
573C4×C8C2×D411yescharacteristic
574C4×C8C2412yes—
575C4×C8C2412yes—
576C4×C8C2412yes—
577C4×C8C2412yes—
578C4×C8C2411yescharacteristic
579C4×C8C2411yescharacteristic
580C4×C8C2411yescharacteristic
581C4×C8C2411yescharacteristic
582C24C4×D411yescharacteristic
583#41—44no—
584#41—42no—
585#41—42no—
586#41—82no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—42no—
594C2×Q8—42no—
595C2×Q8—82no—
596C2×Q8C23×C412yes—
597C2×Q8C23×C412yes—
598C2×Q8C23×C412yes—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4C23×C412yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4C4×D411yescharacteristic
617C22×C4C4×D411yescharacteristic
618C22×C4C4×D411yescharacteristic
619C22×C4C4×D411yescharacteristic
620C22×C4C4×D411yescharacteristic
621C22×C4C4×D411yescharacteristic
622C22×C4C4×D411yescharacteristic
623C22×C4C4×D411yescharacteristic
624C22×C4C4×D411yescharacteristic
625C22×C4C23×C411yescharacteristic
626C22×C4C23×C411yescharacteristic
627C22×C4C23×C411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C2×#4111yescharacteristic
632C22×C4C2×#4111yescharacteristic
633C22×C4C2×#4111yescharacteristic
634Q16—44no—
635Q16—44no—
636SD16—44no—
637SD16—44no—
638M16—22no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—41no—
643M16—41no—
644M16—41no—
645M16—41no—
646M16—44no—
647M16—44no—
648M16—42no—
649M16—42no—
650M16—44no—
651M16—82no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—44no—
662C2×C8—44no—
663C2×C8—44no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—44no—
667C2×C8#13714yes—
668C2×C8C23×C414yes—
669C2×C8C23×C414yes—
670C2×C8C22×D411yescharacteristic
671C2×C8C22×D411yescharacteristic
672C2×C8C22×D411yescharacteristic
673C2×C8C22×D411yescharacteristic
674C2×C8C22×D411yescharacteristic
675C2×C8C22×D411yescharacteristic
676C2×C8C22×D411yescharacteristic
677C2×C8C22×D411yescharacteristic
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4C23×C412yes—
705C4⋊C4C23×C412yes—
706C4⋊C4C23×C412yes—
707C4⋊C4C23×C412yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42C4×D411yescharacteristic
729C42C4×D411yescharacteristic
730C42C4×D411yescharacteristic
731C42C4×D411yescharacteristic
732C42C4×D411yescharacteristic
733C42C4×D411yescharacteristic
734C42C23×C411yescharacteristic
735C42C23×C411yescharacteristic
736C42C23×C411yescharacteristic
737C42C22×D411yescharacteristic
738C42C22×D411yescharacteristic
739C42C22×D411yescharacteristic
740C42C2×#4111yescharacteristic
741C42C2×#4111yescharacteristic
742C42C2×#4111yescharacteristic
743C42C2511yescharacteristic
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23C2×C4×D411yescharacteristic
749C23C2×C4×D411yescharacteristic
750C23C2×C4×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—24no—
756Q8—42no—
757Q8—42no—
758Q8—42no—
759Q8—42no—
760Q8—82no—
761Q8—82no—
762D4—24no—
763D4—42no—
764D4—44no—
765D4—42no—
766D4—82no—
767D4—82no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—82no—
801C2×C4—82no—
802C2×C4C2×C4×D411yescharacteristic
803C2×C4C2×C4×D411yescharacteristic
804C2×C4C2×C4×D411yescharacteristic
805C2×C4C2×C4×D411yescharacteristic
806C2×C4C2×C4×D411yescharacteristic
807C2×C4C2×C4×D411yescharacteristic
808C2×C4C2×C4×D411yescharacteristic
809C2×C4C2×C4×D411yescharacteristic
810C2×C4C2×C4×D411yescharacteristic
811C2×C4C2×#13712yes—
812C2×C4#57512yes—
813C2×C4C24×C411yescharacteristic
814C2×C4C23×D411yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C8—24no—
817C8—24no—
818C8—21no—
819C8—21no—
820C8—21no—
821C8—21no—
822C8—21no—
823C8—21no—
824C8—42no—
825C8—42no—
826C8—42no—
827C8—42no—
828C8—42no—
829C8—42no—
830C8C2×#13712yes—
831C8C2×#13712yes—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22C4×#13712yes—
845C22C22×C4×D411yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4C4×#13712yes—
863C4#357312yes—
864C4C22×#13711yescharacteristic
865C4C2×#57511yescharacteristic
866C2—22no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2#6014211yescharacteristic
871C2C2×C4×#13711yescharacteristic
872C2#6018211yescharacteristic
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×C4×M16 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2962C2semidirect
4. #18079C2semidirect
5. #18077C2semidirect
6. #18013C2semidirect
7. #18009C2semidirect
8. #17936C2semidirect
9. #17934C2semidirect
10. #17931C2semidirect
11. #17929C2semidirect
12. #17908C2semidirect
13. #17906C2semidirect
14. #17903C2semidirect
15. #17901C2semidirect
16. #17807C2semidirect
17. #17491C2semidirect
19. #17334C2semidirect
73. #1593C22semidirect
74. #1592C22semidirect
75. #1591C22semidirect
76. #1590C22semidirect
77. #1588C22semidirect
78. #1587C22semidirect
79. #1587C22semidirect
80. #1585C22semidirect
81. #1584C22semidirect
82. #1584C22semidirect
83. #1583C22semidirect
84. #1582C22semidirect
85. #1579C22semidirect
86. SD16⋊C8C22semidirect
87. C8×Q16C22semidirect
88. C8×SD16C22semidirect

Maximal subgroups

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

subgroupindex
#609522
#602082
C2×#29622
#180792
#180772
#180132
#180092
#179362
#179342
#179312
#179292
#179082
#179062
#179032
#179012
#178072
#174912
#174662
#173342