Finite Group Databasebeta

← #370497

Subgroups — #370497

Order 512.

1620 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2441C211yesmaximal, characteristic
2C2×#1992C211yesmaximal, characteristic, complemented
3C2×#1753C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5#13880C211yesmaximal, characteristic
6#11385C211yesmaximal, characteristic, complemented
7#11357C211yesmaximal, characteristic, complemented
8#11207C211yesmaximal, characteristic, complemented
9#11207C211yesmaximal, characteristic, complemented
10#10881C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10841C211yesmaximal, characteristic, complemented
13#10731C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10722C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×#125C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×#97C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2441—24no—
24#2441C418yescomplemented
25C2×#399—21no—
26C2×#396—21no—
27C2×#389—21no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#387—21no—
31C2×#385—21no—
32C2×#385—21no—
33C2×#384C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1992—24no—
40#1753—24no—
41#1736—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1444—21no—
61#1444—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16Q814yes—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×#125—22no—
78C2×#125—22no—
79C2×#125—22no—
80C2×#125—41no—
81C2×#125—41no—
82C2×#125C2×C414yescomplemented
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—41no—
87C2×#117—41no—
88C2×#117C2×C414yes—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—41no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4D411yescharacteristic
118C22×C22⋊C4D411yescharacteristic
119C22×C42—21no—
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8Q814yes—
125C2×#97—22no—
126C2×#97—22no—
127C2×#97—41no—
128C2×C4×C8—22no—
129C2×C4×C8—22no—
130C2×C4×C8—41no—
131#399—28no—
132#396—28no—
133#389—22no—
134#389—22no—
135#389—28no—
136#389C2×C414yescomplemented
137#389C2×C414yescomplemented
138#387—28no—
139#385—44no—
140#385—44no—
141#384—22no—
142#384—22no—
143#384—22no—
144#384—41no—
145#384—41no—
146#384C2×C414yescomplemented
147#380—22no—
148#380—22no—
149#380—22no—
150#380C2×C414yes—
151C4×C22⋊C4C2×C414yes—
152C4×C22⋊C4D414yes—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95D411yescharacteristic
162C2×#95D411yescharacteristic
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#340—41no—
177#340—41no—
178#340D414yes—
179#336—22no—
180#336—22no—
181C25C2×D411yescharacteristic
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—81no—
204C23×C4—81no—
205C23×C4C22×C412yes—
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D412yes—
212C23×C4C2×Q812yes—
213C23×C4C2×Q812yes—
214C23×C4#4112yes—
215C23×C4#4112yes—
216C23×C4C2411yescharacteristic
217C2×M16—28no—
218C2×M16—28no—
219C2×M16—44no—
220C2×M16—44no—
221C2×M16—44no—
222C2×M16—44no—
223C2×M16—44no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8C2×D412yes—
247C22×C8C2×Q812yes—
248C22×C8C2×Q812yes—
249C22×C8C2×Q812yes—
250C22×C8C2×Q812yes—
251C22×C8#4112yes—
252#125—28no—
253#125—44no—
254#125—44no—
255#125—44no—
256#117—28no—
257#117—44no—
258#117—44no—
259#117—44no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—81no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4—81no—
332C2×C4⋊C4—81no—
333C2×C4⋊C4—81no—
334C2×C4⋊C4—81no—
335C2×C4⋊C4—81no—
336C2×C4⋊C4—81no—
337C2×C4⋊C4C22×C412yes—
338C2×C4⋊C4C22×C412yes—
339C2×C4⋊C4C22×C412yes—
340C2×C4⋊C4C22×C412yes—
341C2×C4⋊C4C2×D412yes—
342C2×C4⋊C4C2×D412yes—
343C2×C4⋊C4#4112yes—
344C2×C4⋊C4#4112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—81no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4C22⋊C414yes—
359C2×C22⋊C4C22⋊C414yes—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—24no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42C22×C412yes—
372C2×C42C22×C412yes—
373C2×C42C2×D412yes—
374C2×C42C2×D412yes—
375C22⋊C8—28no—
376#97—44no—
377C4×C8—44no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95C22⋊C414yes—
387#95C22⋊C414yes—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24C2×C22⋊C412yes—
401C24#12412yes—
402C24C4⋊Q812yes—
403C24C22×D411yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—48no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—84no—
512C22×C4—84no—
513C22×C4—84no—
514C22×C4—84no—
515C22×C4C2×C22⋊C412yes—
516C22×C4C2×C22⋊C412yes—
517C22×C4C2×C22⋊C412yes—
518C22×C4C2×C22⋊C412yes—
519C22×C4C2×C22⋊C412yes—
520C22×C4C4×Q814yes—
521C22×C4C4×Q814yes—
522C22×C4C22⋊Q814yes—
523C22×C4C22⋊Q814yes—
524C22×C4#12412yes—
525C22×C4C4⋊Q812yes—
526C22×C4AGL(1,ℤ/8)12yes—
527C22×C4AGL(1,ℤ/8)12yes—
528C22×C4#13712yes—
529C22×C4#13712yes—
530C22×C4C23×C411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×Q811yescharacteristic
534C22×C4C22×Q811yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4H(5,𝔽2)11yescharacteristic
541C22×C4H(5,𝔽2)11yescharacteristic
542C22×C4H(5,𝔽2)11yescharacteristic
543C22×C42−1+411yescharacteristic
544M16—416no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
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×C8C22⋊Q814yes—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—84no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4C4×D414yes—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—48no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23#39114yes—
665C23C22×C22⋊C411yescharacteristic
666C23C2×#12411yescharacteristic
667C23C2×C4⋊Q811yescharacteristic
668C23D4211yescharacteristic
669C23#54611yescharacteristic
670C23#54611yescharacteristic
671C23#54711yescharacteristic
672C23C2×AGL(1,ℤ/8)11yescharacteristic
673C23C2×AGL(1,ℤ/8)11yescharacteristic
674C23C2×#13711yescharacteristic
675C23C2×#13711yescharacteristic
676C23#57611yescharacteristic
677C23#57711yescharacteristic
678C23#57711yescharacteristic
679C23#57811yescharacteristic
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—816no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4#39114yes—
778C2×C4#41714yes—
779C2×C4#41714yes—
780C2×C4C2×C4×D411yescharacteristic
781C2×C4C2×C4×Q811yescharacteristic
782C2×C4C2×C4×Q811yescharacteristic
783C2×C4C4×#4111yescharacteristic
784C2×C4#51811yescharacteristic
785C2×C4#52011yescharacteristic
786C2×C4C2×C22⋊Q811yescharacteristic
787C2×C4C2×C22⋊Q811yescharacteristic
788C2×C4C2×C22⋊Q811yescharacteristic
789C2×C4#52511yescharacteristic
790C2×C4#52911yescharacteristic
791C2×C4#53311yescharacteristic
792C2×C4#53811yescharacteristic
793C2×C4#53911yescharacteristic
794C2×C4#54311yescharacteristic
795C2×C4#54411yescharacteristic
796C2×C4D4211yescharacteristic
797C2×C4#54611yescharacteristic
798C2×C4#54611yescharacteristic
799C2×C4#54611yescharacteristic
800C2×C4#54711yescharacteristic
801C2×C4D4×Q811yescharacteristic
802C2×C4#55111yescharacteristic
803C2×C4#55111yescharacteristic
804C2×C4#55211yescharacteristic
805C2×C4#55411yescharacteristic
806C2×C4#55411yescharacteristic
807C2×C4#55411yescharacteristic
808C8—24no—
809C8—42no—
810C8—42no—
811C8—42no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22C2×#39111yescharacteristic
828C22D4×C22⋊C411yescharacteristic
829C22#233911yescharacteristic
830C22#244011yescharacteristic
831C22#247211yescharacteristic
832C22#248811yescharacteristic
833C22#254911yescharacteristic
834C22C2×#41711yescharacteristic
835C22C2×#41711yescharacteristic
836C22#289711yescharacteristic
837C22#289811yescharacteristic
838C22#313611yescharacteristic
839C22#313711yescharacteristic
840C22#313811yescharacteristic
841C22#313911yescharacteristic
842C22#316311yescharacteristic
843C22#316411yescharacteristic
844C22#316511yescharacteristic
845C22#316511yescharacteristic
846C22#327211yescharacteristic
847C22#327411yescharacteristic
848C22#327611yescharacteristic
849C22#327811yescharacteristic
850C22#331011yescharacteristic
851C22#331211yescharacteristic
852C22#331811yescharacteristic
853C22#332011yescharacteristic
854C22#333011yescharacteristic
855C22#333111yescharacteristic
856C22#333211yescharacteristic
857C22#333311yescharacteristic
858C22#334311yescharacteristic
859C22#334411yescharacteristic
860C22#334511yescharacteristic
861C22#334611yescharacteristic
862C4—24no—
863C4—24no—
864C4—24no—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—161no—
874C4—161no—
875C4C4×C22⋊Q811yescharacteristic
876C4#232911yescharacteristic
877C4#236011yescharacteristic
878C4#236811yescharacteristic
879C4#243711yescharacteristic
880C4#243811yescharacteristic
881C4#244911yescharacteristic
882C4#245011yescharacteristic
883C2—44no—
884C2#1405211yescharacteristic
885C2#2132211yescharacteristic
886C2#2132611yescharacteristic
887C2#2243111yescharacteristic
888C2#2243211yescharacteristic
889C2#2249111yescharacteristic
890C2#2249311yescharacteristic
891C2#2607711yescharacteristic
892C2#2607811yescharacteristic
893C2#2727911yescharacteristic
894C2#2728311yescharacteristic
895C2#2770711yescharacteristic
896C2#2770911yescharacteristic
897C2#2878111yescharacteristic
898C2#2878311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1992C2semidirect
6. #11385C2semidirect
7. #11357C2semidirect
8. #11207C2semidirect
9. #11207C2semidirect
10. #10881C2semidirect
11. #10880C2semidirect
12. #10841C2semidirect
24. #2441C4semidirect
82. C2×#125C2×C4semidirect
136. #389C2×C4semidirect
137. #389C2×C4semidirect
146. #384C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24412
C2×#19922
C2×#17532
C2×#17362
#138802
#113852
#113572
#112072
#108812
#108802
#108412
#107312
#107302
#107222