Finite Group Databasebeta

← #354207

Subgroups — #354207

Order 512.

2220 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#405C211yesmaximal, characteristic, complemented
2C2×#2324C211yesmaximal, characteristic
3C2×#1895C211yesmaximal, characteristic
4C2×#1893C211yesmaximal, characteristic
5C2×#1762C211yesmaximal, characteristic, complemented
6C2×C4×#102C211yesmaximal, characteristic, complemented
7#13777C211yesmaximal, characteristic, complemented
8#10927C211yesmaximal, characteristic, complemented
9#10925C211yesmaximal, characteristic, complemented
10#10881C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10722C211yesmaximal, characteristic, complemented
13#10721C211yesmaximal, characteristic, complemented
14#10703C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C2×#405—24no—
26C2×#405—24no—
27C2×#405—24no—
28C22×#97C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2324—24no—
33#2324C418yescomplemented
34C2×#390—21no—
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#388—21no—
38C2×#386—21no—
39C2×#385—21no—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46#1895C418yescomplemented
47#1893C418yescomplemented
48#1762—24no—
49C4×#102—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62#1437—21no—
63#1437—21no—
64#1436—21no—
65#1436—21no—
66C4⋊#95C2211yescharacteristic
67C4⋊#95C2211yescharacteristic
68C23×D4—21no—
69C23×D4C2311yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16C2×C414yescomplemented
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—22no—
85C23×C8C2×C414yescomplemented
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C2×#121—22no—
91C2×#121—22no—
92C2×#121—22no—
93C2×#121C2×C414yes—
94C2×#121C2×C414yes—
95C2×#121C2×C414yes—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4C2×C414yes—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117C2×C414yes—
107C2×#117D414yes—
108C22×C4⋊C4—21no—
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4D411yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4D411yescharacteristic
126C22×C22⋊C4D411yescharacteristic
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—22no—
140C2×#102C2×C414yes—
141C2×#102C2×C414yes—
142C2×#102C2×C414yes—
143C2×#102C2×C414yes—
144#405—232no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—22no—
150C2×#97D414yescomplemented
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8D414yescomplemented
157#390—28no—
158#390—22no—
159#390C2×C414yes—
160#389—22no—
161#389C2×C414yes—
162#388—28no—
163#386—28no—
164#385—28no—
165#380—22no—
166#380—22no—
167#380—22no—
168#380C2×C414yes—
169#380C2×C414yescomplemented
170#380C2×C414yescomplemented
171C4×C4⋊C4—22no—
172C4×C4⋊C4—22no—
173C4×C4⋊C4—22no—
174C4×C4⋊C4—22no—
175C4×C4⋊C4—22no—
176C4×C4⋊C4C2×C414yes—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188#340—22no—
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340C2×C414yescomplemented
197#340C2×C414yescomplemented
198#340C2×C414yescomplemented
199#340C2×C414yescomplemented
200C25—21no—
201C25C2×D411yescharacteristic
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—81no—
217C22×D4—81no—
218C22×D4—81no—
219C22×D4—81no—
220C22×D4C22×C412yes—
221C22×D4C22×C412yes—
222C22×D4C22×C412yes—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—24no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C22×C412yes—
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D412yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4C2411yescharacteristic
257C2×M16—28no—
258C2×M16—28no—
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—28no—
263C2×M16—28no—
264C22×C8—28no—
265C22×C8—28no—
266C22×C8—28no—
267C22×C8—28no—
268C22×C8—28no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—28no—
286C22×C8—28no—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C22×C8#4112yes—
296C22×C8#4112yes—
297C22×C8#4112yes—
298C22×C8#4112yes—
299#121—28no—
300#121—28no—
301#121—28no—
302#121C42116yescomplemented
303C4×D4—28no—
304C4×D4—28no—
305C4×D4—44no—
306C4×D4—44no—
307#117—28no—
308#117—28no—
309#117—28no—
310#117—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
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⋊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—24no—
349C2×C4⋊C4—81no—
350C2×C4⋊C4—81no—
351C2×C4⋊C4C22⋊C414yes—
352C2×C4⋊C4C22⋊C414yes—
353C2×C4⋊C4C22×C412yes—
354C2×C4⋊C4C22×C412yes—
355C2×C4⋊C4C22×C412yes—
356C2×C4⋊C4C22×C412yes—
357C2×C4⋊C4C22×C412yes—
358C2×C4⋊C4C22×C412yes—
359C2×C4⋊C4C22×C412yes—
360C2×C4⋊C4C22×C412yes—
361C2×C4⋊C4C22×C412yes—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—81no—
378C2×C22⋊C4—81no—
379C2×C22⋊C4—81no—
380C2×C22⋊C4—81no—
381C2×C22⋊C4—81no—
382C2×C22⋊C4—81no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4C22⋊C414yes—
388C2×C22⋊C4C22⋊C414yes—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—24no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—81no—
397C2×C42—81no—
398C2×C42—81no—
399C2×C42—81no—
400C2×C42—81no—
401C2×C42—81no—
402C2×C42C22×C412yes—
403C2×C42C22×C412yes—
404C2×C42C2×D412yes—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D412yes—
408C2×C42#4112yes—
409C2×C42#4112yes—
410#102—28no—
411#102—28no—
412#102—28no—
413#102—28no—
414#97—28no—
415#97—28no—
416C4×C8—28no—
417C4×C8—28no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—42no—
424#95—42no—
425#95—81no—
426#95—81no—
427#95—81no—
428#95—81no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24—41no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24C2×C22⋊C412yes—
457C24C4×D412yes—
458C24C4×D412yes—
459C24C22×D411yescharacteristic
460C2×D4—216no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4—84no—
493C2×D4—84no—
494C2×D4C2×C4214yes—
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—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—48no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C2×C4214yes—
600C22×C4C2×C22⋊C412yes—
601C22×C4C2×C22⋊C412yes—
602C22×C4C2×C22⋊C412yes—
603C22×C4C2×C22⋊C412yes—
604C22×C4C2×C22⋊C412yes—
605C22×C4#11714yes—
606C22×C4C4×D414yes—
607C22×C4C4×D414yes—
608C22×C4C4×D412yes—
609C22×C4C4×D412yes—
610C22×C4#12112yes—
611C22×C4#12112yes—
612C22×C4#12112yes—
613C22×C4#12112yes—
614C22×C4C23×C411yescharacteristic
615C22×C4C23×C411yescharacteristic
616C22×C4C23×C411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4C2×#4111yescharacteristic
628M16—232no—
629C2×C8—232no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8C4×D414yes—
655C2×C8C4×D414yes—
656C2×C8C4×D414yes—
657C2×C8C4×D414yes—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—41no—
687C4⋊C4—84no—
688C4⋊C4C2×C4214yes—
689C22⋊C4—216no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—48no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—84no—
703C42—84no—
704C42—84no—
705C42C4×D414yes—
706C42C4×D414yes—
707C42#12014yes—
708C42#12314yes—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—81no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23C4×C22⋊C414yes—
779C23C22×C22⋊C411yescharacteristic
780C23C2×C4×D411yescharacteristic
781C23C2×C4×D411yescharacteristic
782C23C2×#12111yescharacteristic
783C23C2×#12111yescharacteristic
784C23#53211yescharacteristic
785C23#53211yescharacteristic
786C23#57611yescharacteristic
787C23#57611yescharacteristic
788C23#57611yescharacteristic
789C23#57711yescharacteristic
790C23#57711yescharacteristic
791C23#57711yescharacteristic
792C23#57711yescharacteristic
793C23#57811yescharacteristic
794D4—24no—
795D4—24no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—816no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—816no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4C4×C22⋊C414yes—
894C2×C4#38614yes—
895C2×C4#38614yes—
896C2×C4C22×C4211yescharacteristic
897C2×C4C2×#11711yescharacteristic
898C2×C4C2×C4×D411yescharacteristic
899C2×C4C2×C4×D411yescharacteristic
900C2×C4C2×C4×D411yescharacteristic
901C2×C4C2×C4×D411yescharacteristic
902C2×C4C2×C4×D411yescharacteristic
903C2×C4C2×C4×D411yescharacteristic
904C2×C4C2×C4×D411yescharacteristic
905C2×C4C2×C4×D411yescharacteristic
906C2×C4C4×#4111yescharacteristic
907C2×C4C4×#4111yescharacteristic
908C2×C4C4×#4111yescharacteristic
909C2×C4C4×#4111yescharacteristic
910C2×C4C4×#4111yescharacteristic
911C2×C4C4×#4111yescharacteristic
912C2×C4C2×#12011yescharacteristic
913C2×C4C2×#12311yescharacteristic
914C2×C4#52511yescharacteristic
915C2×C4#52511yescharacteristic
916C2×C4#52511yescharacteristic
917C2×C4#52511yescharacteristic
918C2×C4#52511yescharacteristic
919C2×C4#52511yescharacteristic
920C2×C4#52911yescharacteristic
921C2×C4#52911yescharacteristic
922C2×C4#52911yescharacteristic
923C2×C4#52911yescharacteristic
924C8—24no—
925C8—24no—
926C8—24no—
927C8—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—82no—
947C22—82no—
948C22—82no—
949C22—82no—
950C22—82no—
951C22—82no—
952C22—82no—
953C22—82no—
954C22—82no—
955C22—82no—
956C22—82no—
957C22—82no—
958C22C2×C4×C22⋊C411yescharacteristic
959C22C2×#38611yescharacteristic
960C22#229711yescharacteristic
961C22C4×#12111yescharacteristic
962C22C4×#12111yescharacteristic
963C22C4×#12111yescharacteristic
964C22C4×#12111yescharacteristic
965C22#289711yescharacteristic
966C22#289711yescharacteristic
967C22#289711yescharacteristic
968C22#289811yescharacteristic
969C22#294611yescharacteristic
970C22#294611yescharacteristic
971C22#294611yescharacteristic
972C22#294711yescharacteristic
973C22#294811yescharacteristic
974C22#294911yescharacteristic
975C22#295111yescharacteristic
976C22#295211yescharacteristic
977C22#305711yescharacteristic
978C22#305811yescharacteristic
979C22#306011yescharacteristic
980C22#306111yescharacteristic
981C22#306211yescharacteristic
982C22#306211yescharacteristic
983C22#306211yescharacteristic
984C22#306311yescharacteristic
985C22#317311yescharacteristic
986C22#317411yescharacteristic
987C22#317511yescharacteristic
988C22#317611yescharacteristic
989C22#317811yescharacteristic
990C22#317911yescharacteristic
991C22#317911yescharacteristic
992C22#317911yescharacteristic
993C4—24no—
994C4—24no—
995C4—24no—
996C4—44no—
997C4—42no—
998C4—42no—
999C4—82no—
1000C4—82no—
1001C4—82no—
1002C4—82no—
1003C4—82no—
1004C4—82no—
1005C4C42×D411yescharacteristic
1006C4C42×D411yescharacteristic
1007C4#229011yescharacteristic
1008C4#229011yescharacteristic
1009C4C4×#12011yescharacteristic
1010C4C4×#12011yescharacteristic
1011C4C4×#12311yescharacteristic
1012C4C4×#12311yescharacteristic
1013C2—44no—
1014C2—84no—
1015C2C4×#38611yescharacteristic
1016C2#2041511yescharacteristic
1017C2#2041611yescharacteristic
1018C2#2097511yescharacteristic
1019C2#2097611yescharacteristic
1020C2#2141211yescharacteristic
1021C2#2141411yescharacteristic
1022C2#2152311yescharacteristic
1023C2#2152411yescharacteristic
1024C2#2152911yescharacteristic
1025C2#2153111yescharacteristic
1026C2#2153511yescharacteristic
1027C2#2153611yescharacteristic
1028C2#2154111yescharacteristic
1029C2#2154311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#405C2semidirect
5. C2×#1762C2semidirect
6. C2×C4×#102C2semidirect
7. #13777C2semidirect
8. #10927C2semidirect
9. #10925C2semidirect
10. #10881C2semidirect
11. #10880C2semidirect
12. #10722C2semidirect
13. #10721C2semidirect
14. #10703C2semidirect
15. C4×#340C2semidirect
33. #2324C4semidirect
46. #1895C4semidirect
47. #1893C4semidirect
78. C22×M16C2×C4semidirect
85. C23×C8C2×C4semidirect
150. C2×#97D4semidirect
156. C2×C4×C8D4semidirect
169. #380C2×C4semidirect
170. #380C2×C4semidirect
196. #340C2×C4semidirect
197. #340C2×C4semidirect
198. #340C2×C4semidirect
199. #340C2×C4semidirect
302. #121C42semidirect

Maximal subgroups

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

subgroupindex
C22×#4052
C2×#23242
C2×#18952
C2×#18932
C2×#17622
C2×C4×#1022
#137772
#109272
#109252
#108812
#108802
#107222
#107212
#107032
C4×#3402