Finite Group Databasebeta

← #361459

Subgroups — #361459

Order 512.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C2×#1853C211yesmaximal, characteristic, complemented
3C2×#1852C211yesmaximal, characteristic, complemented
4C2×#1809C211yesmaximal, characteristic, complemented
5C22×#340C211yesmaximal, characteristic, complemented
6#13872C211yesmaximal, characteristic
7#13872C211yesmaximal, characteristic
8#11232C211yesmaximal, characteristic, complemented
9#11231C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10863C211yesmaximal, characteristic, complemented
13#10821C211yesmaximal, characteristic, complemented
14#10722C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C2×#435—24no—
22C2×#435—24no—
23C2×#435C418yescomplemented
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C2×#386—21no—
33C2×#386—21no—
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40#1853—24no—
41#1852—24no—
42#1809—24no—
43C2×#340—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56#1441—21no—
57#1441—21no—
58#1439—21no—
59#1439—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C22⋊#95—21no—
65C22⋊#95—21no—
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—41no—
76C22×M16—41no—
77C22×M16C2×C414yescomplemented
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—41no—
83C23×C8—41no—
84C23×C8C2×C414yes—
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4C2×C414yes—
94C2×C4×D4Q814yes—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—22no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
125C22×C22⋊C4D411yescharacteristic
126C22×C42C2311yescharacteristic
127#435—232no—
128C2×#107—22no—
129C2×#107—22no—
130C2×#107—22no—
131C2×#107—22no—
132C2×#107—41no—
133C2×#107—41no—
134C2×#106—22no—
135C2×#106—22no—
136C2×#106—22no—
137C2×#106—22no—
138C2×#106—41no—
139C2×#106—41no—
140C2×C4⋊C8—22no—
141C2×C4⋊C8—22no—
142C2×C4⋊C8C2×C414yescomplemented
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8C2×C414yes—
146C2×C22⋊C8C2×C414yescomplemented
147C2×C22⋊C8D414yes—
148C2×C22⋊C8D414yes—
149C2×#97—22no—
150C2×#97—22no—
151C2×#97C2×C414yescomplemented
152#386—44no—
153#386—44no—
154#380—22no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—22no—
159#380—22no—
160#380—22no—
161#380—22no—
162#380—41no—
163#380—41no—
164#380—41no—
165#380—41no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95—21no—
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#340—22no—
189#340—41no—
190#340—41no—
191#340D414yescomplemented
192C25C2×D411yescharacteristic
193C25C2×D411yescharacteristic
194C22×D4—22no—
195C22×D4—22no—
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4C4⋊C414yes—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—81no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4C22×C412yes—
244C23×C4C22×C412yes—
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D411yescharacteristic
251C23×C4C2×Q812yes—
252C23×C4C2×Q812yes—
253C23×C4#4112yes—
254C23×C4#4112yes—
255C23×C4C2411yescharacteristic
256C2×M16—28no—
257C2×M16—28no—
258C2×M16—44no—
259C2×M16—44no—
260C2×M16—44no—
261C2×M16—44no—
262C2×M16—44no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—28no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—28no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8#4112yes—
298C4×D4—28no—
299C4×D4—28no—
300C4×D4—28no—
301C4×D4—28no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
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—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4C4⋊C414yes—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2×D412yes—
365C2×C4⋊C4#4112yes—
366C2×C4⋊C4#4112yes—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4—81no—
388C2×C22⋊C4—81no—
389C2×C22⋊C4C4⋊C414yes—
390C2×C22⋊C4C4⋊C414yes—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42C22×C412yes—
396C2×C42C2×Q812yes—
397#107—44no—
398#107—44no—
399#106—44no—
400#106—44no—
401C4⋊C8—28no—
402C22⋊C8—28no—
403C22⋊C8C22⋊C4116yescomplemented
404#97—28no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—81no—
416#95—81no—
417#95—81no—
418#95—81no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24C2×C4⋊C412yes—
442C24C2×C4⋊C412yes—
443C24#12112yes—
444C24#12112yes—
445C24AGL(1,ℤ/8)12yes—
446C24AGL(1,ℤ/8)12yes—
447C24#13712yes—
448C24#13712yes—
449C24C22×D411yescharacteristic
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
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—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
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—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
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—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4C2×C22⋊C414yes—
602C22×C4C2×C4⋊C412yes—
603C22×C4C2×C4⋊C412yes—
604C22×C4C2×C4⋊C412yes—
605C22×C4C2×C4⋊C412yes—
606C22×C4#11714yes—
607C22×C4#12112yes—
608C22×C4#12112yes—
609C22×C4C22⋊Q814yes—
610C22×C4C22⋊Q814yes—
611C22×C4C23×C411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×Q811yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4C2×#4111yescharacteristic
619C22×C4C2×#4111yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4H(5,𝔽2)11yescharacteristic
622C22×C4H(5,𝔽2)11yescharacteristic
623C22×C4H(5,𝔽2)11yescharacteristic
624C22×C42−1+411yescharacteristic
625M16—416no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
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—416no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8C2×C22⋊C414yes—
653C2×C8C2×C22⋊C414yes—
654C2×C8C4×D414yes—
655C4⋊C4—28no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
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—41no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
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—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23#38014yes—
766C23#42814yes—
767C23#42814yes—
768C23#46814yes—
769C23#46814yes—
770C23#46914yes—
771C23#47014yes—
772C23C22×C4⋊C411yescharacteristic
773C23C2×#12111yescharacteristic
774C23C2×#12111yescharacteristic
775C23D4211yescharacteristic
776C23#54611yescharacteristic
777C23#54611yescharacteristic
778C23#54711yescharacteristic
779C23C2×AGL(1,ℤ/8)11yescharacteristic
780C23C2×AGL(1,ℤ/8)11yescharacteristic
781C23C2×#13711yescharacteristic
782C23C2×#13711yescharacteristic
783C23#57611yescharacteristic
784C23#57711yescharacteristic
785C23#57711yescharacteristic
786C23#57811yescharacteristic
787D4—416no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
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—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—816no—
844C2×C4—816no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
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#38014yes—
890C2×C4C22×C22⋊C411yescharacteristic
891C2×C4C2×#11711yescharacteristic
892C2×C4C2×C4×D411yescharacteristic
893C2×C4C4×#4111yescharacteristic
894C2×C4#51811yescharacteristic
895C2×C4#52011yescharacteristic
896C2×C4C2×C22⋊Q811yescharacteristic
897C2×C4C2×C22⋊Q811yescharacteristic
898C2×C4#52511yescharacteristic
899C2×C4#52511yescharacteristic
900C2×C4#52911yescharacteristic
901C2×C4#52911yescharacteristic
902C2×C4#53811yescharacteristic
903C2×C4#53811yescharacteristic
904C2×C4#53911yescharacteristic
905C2×C4#53911yescharacteristic
906C2×C4D4211yescharacteristic
907C2×C4D4211yescharacteristic
908C2×C4#54611yescharacteristic
909C2×C4#54611yescharacteristic
910C2×C4#54611yescharacteristic
911C2×C4#54611yescharacteristic
912C2×C4#54711yescharacteristic
913C2×C4#54711yescharacteristic
914C2×C4D4×Q811yescharacteristic
915C2×C4#55411yescharacteristic
916C2×C4#55411yescharacteristic
917C2×C4#55411yescharacteristic
918C8—24no—
919C8—24no—
920C8—24no—
921C8—42no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22—81no—
951C22#180918yescomplemented
952C22C2×#38011yescharacteristic
953C22D4×C4⋊C411yescharacteristic
954C22#234911yescharacteristic
955C22#242411yescharacteristic
956C22#242411yescharacteristic
957C22#242511yescharacteristic
958C22#242511yescharacteristic
959C22C2×#42811yescharacteristic
960C22C2×#42811yescharacteristic
961C22#291211yescharacteristic
962C22#291311yescharacteristic
963C22C2×#46811yescharacteristic
964C22C2×#46811yescharacteristic
965C22C2×#46911yescharacteristic
966C22C2×#47011yescharacteristic
967C22#306211yescharacteristic
968C22#306211yescharacteristic
969C22#306311yescharacteristic
970C22#306311yescharacteristic
971C22#326411yescharacteristic
972C22#326511yescharacteristic
973C22#326611yescharacteristic
974C22#327011yescharacteristic
975C22#330611yescharacteristic
976C22#330811yescharacteristic
977C22#331011yescharacteristic
978C22#331211yescharacteristic
979C22#331411yescharacteristic
980C22#331611yescharacteristic
981C22#331811yescharacteristic
982C22#332011yescharacteristic
983C22#334311yescharacteristic
984C22#334411yescharacteristic
985C22#334511yescharacteristic
986C22#334611yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—82no—
992C4—82no—
993C4—82no—
994C4—82no—
995C4—161no—
996C4—161no—
997C4—161no—
998C4—161no—
999C4#229011yescharacteristic
1000C4#231811yescharacteristic
1001C4D4×C22⋊C411yescharacteristic
1002C4#233911yescharacteristic
1003C4#244911yescharacteristic
1004C4#244911yescharacteristic
1005C4#245011yescharacteristic
1006C4#245011yescharacteristic
1007C2—28no—
1008C2—82no—
1009C2#1389911yescharacteristic
1010C2C2×#180911yescharacteristic
1011C2#2066411yescharacteristic
1012C2#2265911yescharacteristic
1013C2#2266111yescharacteristic
1014C2#2270911yescharacteristic
1015C2#2271111yescharacteristic
1016C2#2512411yescharacteristic
1017C2#2512611yescharacteristic
1018C2#2512811yescharacteristic
1019C2#2513011yescharacteristic
1020C2#2524811yescharacteristic
1021C2#2525011yescharacteristic
1022C2#2525211yescharacteristic
1023C2#2525411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1853C2semidirect
3. C2×#1852C2semidirect
4. C2×#1809C2semidirect
5. C22×#340C2semidirect
8. #11232C2semidirect
9. #11231C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10863C2semidirect
13. #10821C2semidirect
14. #10722C2semidirect
15. #10721C2semidirect
23. C2×#435C4semidirect
77. C22×M16C2×C4semidirect
142. C2×C4⋊C8C2×C4semidirect
146. C2×C22⋊C8C2×C4semidirect
151. C2×#97C2×C4semidirect
191. #340D4semidirect
403. C22⋊C8C22⋊C4semidirect
951. C22#1809semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×#18532
C2×#18522
C2×#18092
C22×#3402
#138722
#112322
#112312
#110962
#110952
#108632
#108212
#107222
#107212