Finite Group Databasebeta

← #368566

Subgroups — #368566

Order 512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1875C211yesmaximal, characteristic
2C2×#1874C211yesmaximal, characteristic
3C2×#1750C211yesmaximal, characteristic, complemented
4#14257C211yesmaximal, characteristic
5#13795C211yesmaximal, characteristic, complemented
6#11316C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11189C211yesmaximal, characteristic, complemented
9#11189C211yesmaximal, characteristic, complemented
10#10927C211yesmaximal, characteristic, complemented
11#10925C211yesmaximal, characteristic, complemented
12#10821C211yesmaximal, characteristic, complemented
13#10820C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#380C2211yescharacteristic
31#1875—24no—
32#1874C418yescomplemented
33#1750—24no—
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48#1439—21no—
49#1439—21no—
50#1438—21no—
51#1438—21no—
52C4⋊#95—21no—
53C4⋊#95—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×#121—22no—
71C2×#121—22no—
72C2×#121—22no—
73C2×#121—22no—
74C2×#121—22no—
75C2×#121C2×C414yes—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—41no—
85C2×#117—41no—
86C2×#117—41no—
87C2×#117—41no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4—41no—
93C22×C4⋊C4—41no—
94C22×C4⋊C4C2×C414yes—
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4D411yescharacteristic
112C22×C22⋊C4D411yescharacteristic
113C22×C42—21no—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—41no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102C2×C414yes—
127C2×#102C2×C414yes—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8D414yes—
134C2×#97—22no—
135C2×#97—22no—
136C2×#97—41no—
137C2×C4×C8—22no—
138C2×C4×C8—22no—
139C2×C4×C8—41no—
140#390—22no—
141#390—22no—
142#390—41no—
143#390—41no—
144#380—22no—
145#380—22no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—41no—
164#340—41no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340C2×C414yes—
170#340C2×C414yes—
171#336—22no—
172#336—22no—
173C25—21no—
174C25C2×D411yescharacteristic
175C22×D4—24no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—42no—
190C22×D4—42no—
191C22×D4—81no—
192C22×D4—81no—
193C22×D4—81no—
194C22×D4—81no—
195C22×D4C22×C412yes—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
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—24no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—81no—
215C23×C4—81no—
216C23×C4—81no—
217C23×C4—81no—
218C23×C4C22×C412yes—
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D412yes—
225C23×C4#4112yes—
226C23×C4#4112yes—
227C23×C4#4112yes—
228C23×C4#4112yes—
229C23×C4C2411yescharacteristic
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×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8C22×C412yes—
255C22×C8C22×C412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258#121—28no—
259#121—28no—
260#121—44no—
261#121—44no—
262#117—44no—
263#117—44no—
264#117—44no—
265#117—44no—
266#117—44no—
267#117—44no—
268#117—44no—
269#117—44no—
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—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
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—21no—
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—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4C22×C412yes—
321C2×C4⋊C4C22×C412yes—
322C2×C4⋊C4C22×C412yes—
323C2×C4⋊C4#4112yes—
324C2×C4⋊C4#4112yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—81no—
343C2×C22⋊C4—81no—
344C2×C22⋊C4—81no—
345C2×C22⋊C4—81no—
346C2×C22⋊C4—81no—
347C2×C22⋊C4—81no—
348C2×C22⋊C4—81no—
349C2×C22⋊C4—81no—
350C2×C22⋊C4—81no—
351C2×C22⋊C4—81no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—24no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42#4112yes—
366C2×C42#4112yes—
367#102—44no—
368#102—44no—
369#102—44no—
370#102—44no—
371C22⋊C8—28no—
372C22⋊C8—28no—
373#97—44no—
374C4×C8—44no—
375#95—42no—
376#95—81no—
377#95—81no—
378#95—81no—
379#95—81no—
380#95—81no—
381#95—81no—
382#95—81no—
383#95—81no—
384#95—81no—
385#95—81no—
386#95—81no—
387#95—81no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24—41no—
412C24—41no—
413C24—41no—
414C24—41no—
415C24C4×D412yes—
416C24#12112yes—
417C24#12412yes—
418C24C22×D411yescharacteristic
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—48no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—84no—
449C2×D4—84no—
450C2×D4—84no—
451C2×D4—84no—
452C2×D4—84no—
453C2×D4—84no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
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—21no—
483C22×C4—21no—
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—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
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—48no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
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—41no—
536C22×C4—41no—
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—84no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—84no—
564C22×C4#11714yes—
565C22×C4C4×D414yes—
566C22×C4C4×D412yes—
567C22×C4#12112yes—
568C22×C4#12312yes—
569C22×C4#12312yes—
570C22×C4#12314yes—
571C22×C4#12412yes—
572C22×C4#12614yes—
573C22×C4C23×C411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4C2×#4111yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4C2×#4111yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4C2×#4111yescharacteristic
582C22×C4C2×#4111yescharacteristic
583C22×C4H(5,𝔽2)11yescharacteristic
584C22×C4H(5,𝔽2)11yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—48no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—81no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23#38814yes—
734C23C2×C4×D411yescharacteristic
735C23C2×#12111yescharacteristic
736C23C2×#12311yescharacteristic
737C23#52511yescharacteristic
738C23C2×#12411yescharacteristic
739C23#53411yescharacteristic
740C23#53511yescharacteristic
741C23#57611yescharacteristic
742C23#57611yescharacteristic
743C23#57611yescharacteristic
744C23#57711yescharacteristic
745C23#57711yescharacteristic
746C23#57711yescharacteristic
747C23#57711yescharacteristic
748C23#57811yescharacteristic
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—816no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—816no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4#38814yes—
851C2×C4C2×#11711yescharacteristic
852C2×C4C2×C4×D411yescharacteristic
853C2×C4C4×#4111yescharacteristic
854C2×C4C4×#4111yescharacteristic
855C2×C4#51811yescharacteristic
856C2×C4#51811yescharacteristic
857C2×C4C2×#12311yescharacteristic
858C2×C4C2×#12611yescharacteristic
859C2×C4#52911yescharacteristic
860C2×C4#52911yescharacteristic
861C2×C4#53811yescharacteristic
862C2×C4#53811yescharacteristic
863C2×C4#54611yescharacteristic
864C2×C4#54611yescharacteristic
865C2×C4#54611yescharacteristic
866C2×C4#54611yescharacteristic
867C2×C4#55111yescharacteristic
868C2×C4#55111yescharacteristic
869C2×C4#55111yescharacteristic
870C2×C4#55111yescharacteristic
871C2×C4#55311yescharacteristic
872C2×C4#55311yescharacteristic
873C2×C4#55311yescharacteristic
874C2×C4#55311yescharacteristic
875C2×C4#55311yescharacteristic
876C2×C4#55311yescharacteristic
877C2×C4#55311yescharacteristic
878C2×C4#55311yescharacteristic
879C8—42no—
880C8—42no—
881C8—42no—
882C8—42no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—161no—
906C22—161no—
907C22—161no—
908C22—161no—
909C22—161no—
910C22—161no—
911C22—161no—
912C22—161no—
913C22C2×#38811yescharacteristic
914C22C4×#12311yescharacteristic
915C22#232111yescharacteristic
916C22#241111yescharacteristic
917C22#241211yescharacteristic
918C22#250411yescharacteristic
919C22#259111yescharacteristic
920C22#294611yescharacteristic
921C22#294711yescharacteristic
922C22#294811yescharacteristic
923C22#294911yescharacteristic
924C22#306011yescharacteristic
925C22#306111yescharacteristic
926C22#306211yescharacteristic
927C22#306211yescharacteristic
928C22#309611yescharacteristic
929C22#309611yescharacteristic
930C22#309811yescharacteristic
931C22#309911yescharacteristic
932C22#311911yescharacteristic
933C22#311911yescharacteristic
934C22#312411yescharacteristic
935C22#312511yescharacteristic
936C22#313611yescharacteristic
937C22#313611yescharacteristic
938C22#313611yescharacteristic
939C22#313711yescharacteristic
940C22#319811yescharacteristic
941C22#319911yescharacteristic
942C22#320011yescharacteristic
943C22#320111yescharacteristic
944C22#322011yescharacteristic
945C22#322111yescharacteristic
946C22#322411yescharacteristic
947C22#322511yescharacteristic
948C4—24no—
949C4—42no—
950C4—42no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—82no—
955C4—82no—
956C4—81no—
957C4—81no—
958C4—161no—
959C4—161no—
960C4#235311yescharacteristic
961C4#235311yescharacteristic
962C4#236411yescharacteristic
963C4#236411yescharacteristic
964C4#244411yescharacteristic
965C4#244411yescharacteristic
966C4#251011yescharacteristic
967C4#251011yescharacteristic
968C2—44no—
969C2—162no—
970C2#1402011yescharacteristic
971C2#2108911yescharacteristic
972C2#2109211yescharacteristic
973C2#2158411yescharacteristic
974C2#2158611yescharacteristic
975C2#2205611yescharacteristic
976C2#2205811yescharacteristic
977C2#2451311yescharacteristic
978C2#2451911yescharacteristic
979C2#2456511yescharacteristic
980C2#2456711yescharacteristic
981C2#2798411yescharacteristic
982C2#2798611yescharacteristic
983C2#2934311yescharacteristic
984C2#2934511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×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
3. C2×#1750C2semidirect
5. #13795C2semidirect
6. #11316C2semidirect
7. #11315C2semidirect
8. #11189C2semidirect
9. #11189C2semidirect
10. #10927C2semidirect
11. #10925C2semidirect
12. #10821C2semidirect
13. #10820C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
32. #1874C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18752
C2×#18742
C2×#17502
#142572
#137952
#113162
#113152
#111892
#109272
#109252
#108212
#108202
#107312
#107302