Finite Group Databasebeta

← #221491

Subgroups — #221491

Order 512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34720C211yesmaximal, characteristic
2#22748C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4C2×#1481C211yesmaximal, characteristic, complemented
5C2×#1476C211yesmaximal, characteristic, complemented
6#9675C211yesmaximal, characteristic, complemented
7#9645C211yesmaximal, characteristic, complemented
8#9076C211yesmaximal, characteristic, complemented
9#9071C211yesmaximal, characteristic, complemented
10#8939C211yesmaximal, characteristic, complemented
11#8938C211yesmaximal, characteristic, complemented
12#8570C211yesmaximal, characteristic, complemented
13#8314C211yesmaximal, characteristic, complemented
14#8312C211yesmaximal, characteristic, complemented
15#8182C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22#2477—21no—
23#2475—21no—
24#2463—21no—
25#2460—21no—
26#2452C411yescharacteristic
27#2446C411yescharacteristic
28#2439C411yescharacteristic
29#2432C411yescharacteristic
30#2427C411yescharacteristic
31#2421C411yescharacteristic
32#2415C411yescharacteristic
33#2407C411yescharacteristic
34#2398—21no—
35#2392—21no—
36C4×#124C2211yescharacteristic
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2211yescharacteristic
39C4×#121C2211yescharacteristic
40#2295C2211yescharacteristic
41#2290—21no—
42C42×D4C2211yescharacteristic
43#1923—21no—
44#1923—21no—
45#1916—21no—
46#1916—21no—
47#1869—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59#1481—24no—
60#1476—24no—
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2211yescharacteristic
64C2×Q8⋊C8C2211yescharacteristic
65C2×Q8⋊C8C2211yescharacteristic
66C2×Q8⋊C8C2211yescharacteristic
67C2×Q8⋊C8C2211yescharacteristic
68C2×Q8⋊C8C2211yescharacteristic
69C2×D4⋊C8C2211yescharacteristic
70C2×D4⋊C8C2211yescharacteristic
71C2×D4⋊C8C2211yescharacteristic
72C2×D4⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C23×C8—21no—
79C23×C8—21no—
80#533—22no—
81#533—22no—
82#533—41no—
83#533—41no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×#125—21no—
87C2×#124C2×C411yescharacteristic
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8C2×C411yescharacteristic
91C2×C22⋊Q8C2×C411yescharacteristic
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×#121C2×C411yescharacteristic
94C4×#41—22no—
95C4×#41—22no—
96C4×#41—41no—
97C4×#41—41no—
98C2×C4×Q8—21no—
99C2×C4×Q8C2×C411yescharacteristic
100C2×C4×Q8C2311yescharacteristic
101C2×C4×Q8C2311yescharacteristic
102C2×C4×D4—21no—
103C2×C4×D4—21no—
104C2×C4×D4—21no—
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×C4×D4D411yescharacteristic
109C2×C4×D4C2311yescharacteristic
110C2×#117—21no—
111C2×#117—21no—
112C2×#117C2×C411yescharacteristic
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116#431—22no—
117#431—22no—
118#431—41no—
119#431—41no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—41no—
125C2×C4⋊C8C2311yescharacteristic
126C2×C4⋊C8C2311yescharacteristic
127C2×C4⋊C8C2311yescharacteristic
128C2×C4⋊C8C2311yescharacteristic
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C2×C4×C8—22no—
136C2×C4×C8—21no—
137C2×C4×C8—21no—
138C2×C4×C8—21no—
139C2×C4×C8—41no—
140C2×C4×C8C2311yescharacteristic
141C2×C4×C8C2311yescharacteristic
142C2×C4×C8C2311yescharacteristic
143C2×C4×C8C2311yescharacteristic
144#400—21no—
145#400—21no—
146#398—21no—
147#397—21no—
148#397—21no—
149#397—21no—
150#396—21no—
151#396—21no—
152#394—21no—
153#394—21no—
154#394—21no—
155#394—21no—
156#394—21no—
157#393—21no—
158#393—21no—
159#392—21no—
160#391—21no—
161#391C2×C411yescharacteristic
162#391C2×C411yescharacteristic
163#391C2×C411yescharacteristic
164#391C2×C411yescharacteristic
165#390C2×C411yescharacteristic
166#390C2×C411yescharacteristic
167#389—21no—
168#389C2×C411yescharacteristic
169#389C2×C411yescharacteristic
170#389C2×C411yescharacteristic
171#389C2×C411yescharacteristic
172#388—21no—
173#388—21no—
174#388—21no—
175#388—21no—
176#388—21no—
177#387—21no—
178#387—21no—
179#387—21no—
180#387—21no—
181#387—21no—
182#387—21no—
183#387—21no—
184#386—21no—
185#386—21no—
186#386—21no—
187#385—21no—
188#385—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#382C2×C411yescharacteristic
193#380—21no—
194#380C2×C411yescharacteristic
195#380C2×C411yescharacteristic
196C4×C4⋊C4—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4C2×C411yescharacteristic
199C4×C4⋊C4D411yescharacteristic
200C4×C4⋊C4D411yescharacteristic
201C4×C4⋊C4C2311yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4—21no—
205C4×C22⋊C4—21no—
206C4×C22⋊C4C2×C411yescharacteristic
207C4×C22⋊C4C2×C411yescharacteristic
208C4×C22⋊C4D411yescharacteristic
209C4×C22⋊C4D411yescharacteristic
210C4×C22⋊C4D411yescharacteristic
211C4×C22⋊C4D411yescharacteristic
212#376—21no—
213C43C2311yescharacteristic
214#336—21no—
215#336—21no—
216#336—21no—
217#336—21no—
218#336—21no—
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224Q8⋊C8—22no—
225Q8⋊C8—22no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—41no—
230Q8⋊C8—41no—
231Q8⋊C8D414yescomplemented
232D4⋊C8—22no—
233D4⋊C8—22no—
234D4⋊C8—41no—
235D4⋊C8—41no—
236C2×#41—22no—
237C2×#41—22no—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—41no—
241C2×#41—41no—
242C22×Q8—21no—
243C22×Q8C22×C411yescharacteristic
244C22×Q8C22×C411yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4C22⋊C411yescharacteristic
248C22×D4C22×C411yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—42no—
267C22×C8—42no—
268C22×C8—42no—
269C22×C8—42no—
270C22×C8—42no—
271C22×C8—81no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—41no—
275C4⋊Q8—41no—
276#125—42no—
277#125—42no—
278#124—22no—
279#124—41no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—41no—
285C22⋊Q8—41no—
286C22⋊Q8—42no—
287C22⋊Q8—42no—
288C22⋊Q8—44no—
289#121—22no—
290#121—41no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—22no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—42no—
299C4×Q8—42no—
300C4×Q8—41no—
301C4×Q8C2×D412yes—
302C4×Q8#4112yes—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—41no—
313C4×D4—42no—
314C4×D4—42no—
315C4×D4—42no—
316C4×D4—42no—
317C4×D4—42no—
318C4×D4—42no—
319C4×D4—42no—
320#117—22no—
321#117—42no—
322#117—42no—
323#117—42no—
324#117—42no—
325#117—41no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C22⋊C411yescharacteristic
340C2×C4⋊C4C22⋊C411yescharacteristic
341C2×C4⋊C4C22⋊C411yescharacteristic
342C2×C4⋊C4C22×C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C4⋊C4C22×C411yescharacteristic
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C4⋊C4C22×C411yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42C22×C411yescharacteristic
384C2×C42C22×C411yescharacteristic
385C2×C42C22×C411yescharacteristic
386C2×C42C22×C411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2411yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—42no—
404C4⋊C8—42no—
405C4⋊C8—42no—
406C4⋊C8C2×D412yes—
407C22⋊C8—42no—
408C22⋊C8—42no—
409C22⋊C8—42no—
410C22⋊C8—42no—
411C22⋊C8—42no—
412C22⋊C8—81no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—42no—
421C4×C8—42no—
422C4×C8—81no—
423C4×C8C2×D412yes—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95C22⋊C411yescharacteristic
442#95C22⋊C411yescharacteristic
443#95C22⋊C411yescharacteristic
444#95C22⋊C411yescharacteristic
445#95C22⋊C411yescharacteristic
446#95C22⋊C411yescharacteristic
447C24—21no—
448C24C2×C22⋊C411yescharacteristic
449C24C2×C22⋊C411yescharacteristic
450#41—28no—
451#41—44no—
452#41—44no—
453#41—44no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—81no—
468C2×Q8C4×D412yes—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—81no—
483C2×D4#13112yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4#13112yes—
542C22×C4#13112yes—
543C22×C4#13512yes—
544C22×C4#13512yes—
545C22×C4C23×C411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—48no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—84no—
574C4⋊C4—21no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4C4×D412yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—41no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—41no—
647C42—41no—
648C42—42no—
649C42—42no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42C22×D411yescharacteristic
655C42C2×#4111yescharacteristic
656C42H(5,𝔽2)11yescharacteristic
657C42H(5,𝔽2)11yescharacteristic
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23#40812yes—
678C23#41612yes—
679C23C22×C22⋊C411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—84no—
689D4—22no—
690D4—22no—
691D4—44no—
692D4—48no—
693D4—41no—
694D4—41no—
695D4—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—48no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—84no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4#40812yes—
773C2×C4#41612yes—
774C2×C4#42112yes—
775C2×C4C2×C4×D411yescharacteristic
776C2×C4#51811yescharacteristic
777C2×C4D4211yescharacteristic
778C2×C4D4211yescharacteristic
779C2×C4#54611yescharacteristic
780C2×C4#54611yescharacteristic
781C2×C4C2×#13111yescharacteristic
782C2×C4C2×#13111yescharacteristic
783C2×C4C2×#13111yescharacteristic
784C2×C4#56811yescharacteristic
785C2×C4C2×#13511yescharacteristic
786C2×C4C2×#13511yescharacteristic
787C2×C4#57711yescharacteristic
788C2×C4#57811yescharacteristic
789C8—42no—
790C8—42no—
791C8—42no—
792C8—81no—
793C8—81no—
794C8—81no—
795C8—81no—
796C8—81no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22D4×C22⋊C411yescharacteristic
819C22C2×#40811yescharacteristic
820C22#288011yescharacteristic
821C22C2×#41611yescharacteristic
822C22#289811yescharacteristic
823C22C2×#42111yescharacteristic
824C22#290111yescharacteristic
825C4—22no—
826C4—22no—
827C4—21no—
828C4—21no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4#292911yescharacteristic
845C4#293311yescharacteristic
846C4#297611yescharacteristic
847C4#297711yescharacteristic
848C4#328211yescharacteristic
849C4#328511yescharacteristic
850C4#330011yescharacteristic
851C4#330111yescharacteristic
852C2—42no—
853C2—42no—
854C2—82no—
855C2#1745811yescharacteristic
856C2#1746911yescharacteristic
857C2#1750811yescharacteristic
858C2#1752311yescharacteristic
859C2#2239811yescharacteristic
860C2#2241611yescharacteristic
861C2#2243411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2407C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22748C2semidirect
3. #21101C2semidirect
4. C2×#1481C2semidirect
5. C2×#1476C2semidirect
6. #9675C2semidirect
7. #9645C2semidirect
8. #9076C2semidirect
9. #9071C2semidirect
10. #8939C2semidirect
11. #8938C2semidirect
12. #8570C2semidirect
13. #8314C2semidirect
14. #8312C2semidirect
15. #8182C2semidirect
231. Q8⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#347202
#227482
#211012
C2×#14812
C2×#14762
#96752
#96452
#90762
#90712
#89392
#89382
#85702
#83142
#83122
#81822