Finite Group Databasebeta

← #221586

Subgroups — #221586

Order 512.

1176 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34691C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic
3C4×C8×D4C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic, complemented
5C22×Q8⋊C8C211yesmaximal, characteristic, complemented
6#9677C211yesmaximal, characteristic, complemented
7#9637C211yesmaximal, characteristic, complemented
8#9071C211yesmaximal, characteristic, complemented
9#9071C211yesmaximal, characteristic, complemented
10#8942C211yesmaximal, characteristic, complemented
11#8937C211yesmaximal, characteristic, complemented
12#8568C211yesmaximal, characteristic, complemented
13#8314C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8176C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#435—21no—
19C2×C8×D4—21no—
20C2×#423C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24#2473—21no—
25#2465—21no—
26#2462—21no—
27#2451C411yescharacteristic
28#2449—21no—
29#2446C411yescharacteristic
30#2440C411yescharacteristic
31#2434C411yescharacteristic
32#2429C411yescharacteristic
33#2423C411yescharacteristic
34#2417C411yescharacteristic
35#2409C411yescharacteristic
36#2399—21no—
37#2396—21no—
38C4×C4⋊Q8C2211yescharacteristic
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8C2211yescharacteristic
41C4×C22⋊Q8C2211yescharacteristic
42#2295C2211yescharacteristic
43#2290—21no—
44C42×D4C2211yescharacteristic
45#1940—21no—
46#1851—21no—
47#1850—21no—
48#1842C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51C8×C4⋊C4—21no—
52#1767C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C8×C22⋊C4—21no—
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C42×C8C2211yescharacteristic
59#1493—24no—
60C2×Q8⋊C8—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×Q8⋊C8C2211yescharacteristic
70C2×Q8⋊C8C2211yescharacteristic
71C2×Q8⋊C8C2211yescharacteristic
72C2×Q8⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C22×M16—21no—
79C23×C8—21no—
80C23×C8—21no—
81C23×C8—21no—
82#533—22no—
83#533—22no—
84#533—41no—
85#533—41no—
86C2×C4⋊Q8C2×C411yescharacteristic
87C2×C4⋊Q8C2×C411yescharacteristic
88C2×C4⋊Q8C2×C411yescharacteristic
89C2×#125—21no—
90C2×C22⋊Q8—21no—
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×C22⋊Q8C2×C411yescharacteristic
95C2×C22⋊Q8C2×C411yescharacteristic
96C2×C4×Q8—21no—
97C2×C4×Q8—21no—
98C2×C4×Q8—21no—
99C2×C4×Q8—22no—
100C2×C4×Q8—22no—
101C2×C4×Q8—41no—
102C2×C4×Q8—41no—
103C2×C4×Q8C2×C411yescharacteristic
104C2×C4×Q8C2×C411yescharacteristic
105C2×C4×Q8C2311yescharacteristic
106C2×C4×Q8C2311yescharacteristic
107C2×C4×Q8C2311yescharacteristic
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4D411yescharacteristic
110C2×C4×D4D411yescharacteristic
111C2×#117—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4C2×C411yescharacteristic
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117#435—44no—
118C8×D4—28no—
119#423—22no—
120#423—41no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8C2311yescharacteristic
129C2×C4⋊C8C2311yescharacteristic
130C2×C4⋊C8C2311yescharacteristic
131C2×C4⋊C8C2311yescharacteristic
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×#97—21no—
137C2×C4×C8—21no—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—21no—
141C2×C4×C8—21no—
142C2×C4×C8—21no—
143C2×C4×C8—41no—
144C2×C4×C8—41no—
145C2×C4×C8C2311yescharacteristic
146C2×C4×C8C2311yescharacteristic
147C2×C4×C8C2311yescharacteristic
148C2×C4×C8C2311yescharacteristic
149#400—21no—
150#399—21no—
151#398—21no—
152#398—21no—
153#398—21no—
154#398—21no—
155#398—21no—
156#398—21no—
157#396—21no—
158#396—21no—
159#395—21no—
160#395—21no—
161#395—21no—
162#395—21no—
163#395—21no—
164#393—21no—
165#391—21no—
166#391C2×C411yescharacteristic
167#391C2×C411yescharacteristic
168#391C2×C411yescharacteristic
169#391C2×C411yescharacteristic
170#391C2×C411yescharacteristic
171#391C2×C411yescharacteristic
172#389—21no—
173#389—21no—
174#389—21no—
175#389C2×C411yescharacteristic
176#389C2×C411yescharacteristic
177#389C2×C411yescharacteristic
178#389C2×C411yescharacteristic
179#388—21no—
180#388—21no—
181#387—21no—
182#387—21no—
183#387—21no—
184#387—21no—
185#387—21no—
186#387—21no—
187#387—21no—
188#387—21no—
189#386—21no—
190#386—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#385—21no—
195#385—21no—
196#385—21no—
197#384C2×C411yescharacteristic
198#380—21no—
199#380C2×C411yescharacteristic
200#380C2×C411yescharacteristic
201C4×C4⋊C4—21no—
202C4×C4⋊C4—21no—
203C4×C4⋊C4—21no—
204C4×C4⋊C4—21no—
205C4×C4⋊C4—21no—
206C4×C4⋊C4C2×C411yescharacteristic
207C4×C4⋊C4D411yescharacteristic
208C4×C4⋊C4D411yescharacteristic
209C4×C4⋊C4C2311yescharacteristic
210C4×C22⋊C4—21no—
211C4×C22⋊C4—21no—
212C4×C22⋊C4C2×C411yescharacteristic
213C4×C22⋊C4C2×C411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217C4×C22⋊C4D411yescharacteristic
218#376—21no—
219C43C2311yescharacteristic
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—22no—
230Q8⋊C8—22no—
231Q8⋊C8—22no—
232Q8⋊C8—22no—
233Q8⋊C8—41no—
234Q8⋊C8—41no—
235Q8⋊C8—41no—
236Q8⋊C8—41no—
237Q8⋊C8D414yescomplemented
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—41no—
245C22×Q8—41no—
246C22×Q8C22×C411yescharacteristic
247C22×Q8C22×C411yescharacteristic
248C22×Q8C22×C411yescharacteristic
249C22×D4C22⋊C411yescharacteristic
250C23×C4—21no—
251C23×C4—21no—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C2×M16—42no—
259C2×M16—42no—
260C2×M16—81no—
261C22×C8—21no—
262C22×C8—24no—
263C22×C8—24no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—42no—
272C22×C8—42no—
273C22×C8—42no—
274C22×C8—42no—
275C22×C8—42no—
276C22×C8—42no—
277C22×C8—81no—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—41no—
282C4⋊Q8—41no—
283C4⋊Q8—41no—
284#125—42no—
285#125—42no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—41no—
292C22⋊Q8—41no—
293C22⋊Q8—41no—
294C22⋊Q8—42no—
295C22⋊Q8—42no—
296C22⋊Q8—44no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—42no—
310C4×Q8—42no—
311C4×Q8—42no—
312C4×Q8—42no—
313C4×Q8—41no—
314C4×Q8—41no—
315C4×Q8—42no—
316C4×Q8—42no—
317C4×Q8C2×D412yes—
318C4×Q8#4112yes—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—24no—
322C4×D4SD1614yes—
323C4×D4Q1614yes—
324#117—42no—
325#117—42no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
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⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C22⋊C411yescharacteristic
352C2×C4⋊C4C22⋊C411yescharacteristic
353C2×C4⋊C4C22⋊C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22⋊C411yescharacteristic
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—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C22×C411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2411yescharacteristic
400C4⋊C8—24no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—42no—
409C4⋊C8—42no—
410C4⋊C8—42no—
411C4⋊C8—81no—
412C4⋊C8C2×D412yes—
413C22⋊C8—24no—
414C22⋊C8—24no—
415C22⋊C8—42no—
416C22⋊C8—42no—
417#97—42no—
418C4×C8—24no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—42no—
427C4×C8—42no—
428C4×C8—42no—
429C4×C8C2×D412yes—
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#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95C22⋊C411yescharacteristic
450#95C22⋊C411yescharacteristic
451#95C22⋊C411yescharacteristic
452#95C22⋊C411yescharacteristic
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455C24C2×C22⋊C411yescharacteristic
456C24C2×C22⋊C411yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—28no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—81no—
483C2×Q8C4×D412yes—
484C2×Q8#13112yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4#10314yes—
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—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
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×C4#13112yes—
539C22×C4#13112yes—
540C22×C4C2×SD1612yes—
541C22×C4C2×SD1612yes—
542C22×C4C2×Q1612yes—
543C22×C4C2×Q1612yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547M16—84no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—48no—
556C2×C8—48no—
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—41no—
574C2×C8—84no—
575C4⋊C4—21no—
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—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4—81no—
609C4⋊C4—81no—
610C4⋊C4#10314yes—
611C4⋊C4C4×D412yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4#10314yes—
622C22⋊C4#10314yes—
623C22⋊C4#10414yes—
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—22no—
645C42—41no—
646C42—42no—
647C42—42no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42C2×SD1612yes—
655C42C2×Q1612yes—
656C42C22×D411yescharacteristic
657C42C2×#4111yescharacteristic
658C42H(5,𝔽2)11yescharacteristic
659C42H(5,𝔽2)11yescharacteristic
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23#40812yes—
671C23C2×#10312yes—
672C23C2×#10312yes—
673C23C2×#10412yes—
674C23C22×C22⋊C411yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—48no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—84no—
689D4—28no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
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—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—48no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
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—84no—
761C2×C4#40812yes—
762C2×C4C2×#10312yes—
763C2×C4C2×#10312yes—
764C2×C4C2×#10312yes—
765C2×C4C2×#10312yes—
766C2×C4C2×#10412yes—
767C2×C4C2×#10412yes—
768C2×C4C2×C4×D411yescharacteristic
769C2×C4#51811yescharacteristic
770C2×C4D4211yescharacteristic
771C2×C4D4211yescharacteristic
772C2×C4#54611yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4C2×#13111yescharacteristic
775C2×C4C2×#13111yescharacteristic
776C2×C4C2×#13111yescharacteristic
777C2×C4#56811yescharacteristic
778C2×C4C22×SD1611yescharacteristic
779C2×C4C22×Q1611yescharacteristic
780C2×C4#57711yescharacteristic
781C2×C4#57811yescharacteristic
782C8—24no—
783C8—42no—
784C8—42no—
785C8—42no—
786C8—42no—
787C8—81no—
788C8—81no—
789C8—81no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22#149314yescomplemented
804C22D4×C22⋊C411yescharacteristic
805C22C2×#40811yescharacteristic
806C22#288011yescharacteristic
807C22C22×#10311yescharacteristic
808C22#289811yescharacteristic
809C22C22×#10411yescharacteristic
810C22#290111yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—21no—
818C4—21no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—81no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4#292911yescharacteristic
832C4#293311yescharacteristic
833C4#297611yescharacteristic
834C4#297711yescharacteristic
835C4D4×SD1611yescharacteristic
836C4D4×Q1611yescharacteristic
837C4#329811yescharacteristic
838C4#329911yescharacteristic
839C2—24no—
840C2—42no—
841C2C2×#149311yescharacteristic
842C2#1748411yescharacteristic
843C2#1750911yescharacteristic
844C2#1751911yescharacteristic
845C2#2239811yescharacteristic
846C2D4×#10311yescharacteristic
847C2D4×#10411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22⋊C4
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
4. C2×#1493C2semidirect
5. C22×Q8⋊C8C2semidirect
6. #9677C2semidirect
7. #9637C2semidirect
8. #9071C2semidirect
9. #9071C2semidirect
10. #8942C2semidirect
11. #8937C2semidirect
12. #8568C2semidirect
13. #8314C2semidirect
14. #8311C2semidirect
15. #8176C2semidirect
237. Q8⋊C8D4semidirect
803. C22#1493semidirect

Maximal subgroups

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

subgroupindex
#346912
#226482
C4×C8×D42
C2×#14932
C22×Q8⋊C82
#96772
#96372
#90712
#89422
#89372
#85682
#83142
#83112
#81762