Finite Group Databasebeta

← #428745

Subgroups — #428745

Order 512.

1506 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2076C211yesmaximal, characteristic, complemented
2C2×#1869C211yesmaximal, characteristic
3C2×#1852C211yesmaximal, characteristic, complemented
4C2×#1808C211yesmaximal, characteristic, complemented
5#15181C211yesmaximal, characteristic
6#13872C211yesmaximal, characteristic
7#11377C211yesmaximal, characteristic, complemented
8#11316C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11219C211yesmaximal, characteristic, complemented
11#11200C211yesmaximal, characteristic, complemented
12#11200C211yesmaximal, characteristic, complemented
13#11096C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#386—21no—
27C2×#380C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34#2076—24no—
35#1869—24no—
36#1852—24no—
37#1808—24no—
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1442—21no—
54#1441—21no—
55#1439—21no—
56#1439—21no—
57#1439—21no—
58#1438—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—21no—
63C23×D4D411yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—41no—
83C2×C4×D4—41no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—41no—
89C22×C4⋊C4—41no—
90C22×C4⋊C4—41no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4D411yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4—21no—
108C22×C22⋊C4D411yescharacteristic
109C22×C22⋊C4D411yescharacteristic
110C22×C42C2311yescharacteristic
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—41no—
117C2×#107—41no—
118C2×#107—41no—
119C2×#107D414yescomplemented
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8D414yes—
129#389—41no—
130#389—41no—
131#386—44no—
132#380—22no—
133#380—22no—
134#380—22no—
135#380—22no—
136#380—22no—
137#380—22no—
138#380—22no—
139#380—22no—
140#380—22no—
141#380—22no—
142#380—41no—
143#380—41no—
144#380—41no—
145#380—41no—
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—
159C2×#95—21no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340—41no—
172#340—41no—
173#336—22no—
174#336—22no—
175C25C2×D411yescharacteristic
176C25C2×D411yescharacteristic
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—22no—
181C22×D4—41no—
182C22×D4—41no—
183C22×D4Q1614yes—
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—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—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—81no—
222C23×C4—81no—
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D412yes—
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4#4112yes—
229C23×C4#4112yes—
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—28no—
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×C8—21no—
255C22×C8—21no—
256C22×C8—44no—
257C22×C8—44no—
258C22×C8—44no—
259C22×C8—44no—
260C22×C8—44no—
261C22×C8—44no—
262C22×C8C2×D412yes—
263C22×C8C2×D412yes—
264C22×C8C2×D412yes—
265C22×C8#4112yes—
266C22×C8#4112yes—
267C4×D4—44no—
268C4×D4—44no—
269C4×D4—44no—
270C4×D4—44no—
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—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
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—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—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—81no—
328C2×C4⋊C4—81no—
329C2×C4⋊C4C2×D412yes—
330C2×C4⋊C4C2×D412yes—
331C2×C4⋊C4#4112yes—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—81no—
352C2×C22⋊C4—81no—
353C2×C22⋊C4—81no—
354C2×C22⋊C4—81no—
355C2×C22⋊C4—81no—
356C2×C22⋊C4—81no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4—81no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365#107—44no—
366#107—44no—
367#107—44no—
368C22⋊C8—28no—
369C22⋊C8—44no—
370C22⋊C8—44no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—81no—
383#95—81no—
384#95—81no—
385C24—21no—
386C24—21no—
387C24—21no—
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—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24#12112yes—
410C24#12312yes—
411C24C2×Q1612yes—
412C24C2×Q1612yes—
413C24#13512yes—
414C24AGL(1,ℤ/8)12yes—
415C24C22×D411yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
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—48no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
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—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4#12112yes—
568C22×C4#12312yes—
569C22×C4C2×Q1612yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4C2×#4111yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4H(5,𝔽2)11yescharacteristic
579C22×C4H(5,𝔽2)11yescharacteristic
580C22×C4H(5,𝔽2)11yescharacteristic
581C22×C4H(5,𝔽2)11yescharacteristic
582C22×C42−1+411yescharacteristic
583C22×C42−1+411yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
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—416no—
597C2×C8—41no—
598C2×C8—41no—
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#12114yes—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—44no—
620C4⋊C4—48no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
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—
646C4⋊C4—41no—
647C4⋊C4—84no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C23—22no—
662C23—22no—
663C23—22no—
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—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23#46714yes—
730C23#48414yes—
731C23C2×#12111yescharacteristic
732C23C2×#12311yescharacteristic
733C23#53411yescharacteristic
734C23D4211yescharacteristic
735C23#54611yescharacteristic
736C23#54711yescharacteristic
737C23#54711yescharacteristic
738C23C22×Q1611yescharacteristic
739C23C2×#13511yescharacteristic
740C23C2×AGL(1,ℤ/8)11yescharacteristic
741C23#57511yescharacteristic
742C23#57611yescharacteristic
743C23#57611yescharacteristic
744C23#57711yescharacteristic
745C23#57811yescharacteristic
746D4—416no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—816no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
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×C4C2×#12111yescharacteristic
849C2×C4#52511yescharacteristic
850C2×C4#52911yescharacteristic
851C2×C4#52911yescharacteristic
852C2×C4#53411yescharacteristic
853C2×C4#53711yescharacteristic
854C2×C4#53811yescharacteristic
855C2×C4#53911yescharacteristic
856C2×C4#53911yescharacteristic
857C2×C4#53911yescharacteristic
858C2×C4#54211yescharacteristic
859C2×C4#54211yescharacteristic
860C2×C4#54611yescharacteristic
861C2×C4#54611yescharacteristic
862C2×C4#54611yescharacteristic
863C2×C4#54611yescharacteristic
864C2×C4#54711yescharacteristic
865C2×C4#54811yescharacteristic
866C2×C4#54811yescharacteristic
867C2×C4#55111yescharacteristic
868C2×C4#55111yescharacteristic
869C2×C4#55111yescharacteristic
870C2×C4#55111yescharacteristic
871C2×C4#55211yescharacteristic
872C2×C4#55311yescharacteristic
873C2×C4#55311yescharacteristic
874C2×C4#56011yescharacteristic
875C2×C4#56311yescharacteristic
876C8—24no—
877C8—42no—
878C8—42no—
879C8—81no—
880C22—24no—
881C22—24no—
882C22—24no—
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—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22#241211yescharacteristic
911C22#241611yescharacteristic
912C22#241911yescharacteristic
913C22#242511yescharacteristic
914C22#244311yescharacteristic
915C22#266811yescharacteristic
916C22#271711yescharacteristic
917C22C2×#46711yescharacteristic
918C22#305511yescharacteristic
919C22#306111yescharacteristic
920C22#306211yescharacteristic
921C22C2×#48411yescharacteristic
922C22#309111yescharacteristic
923C22#309611yescharacteristic
924C22#309811yescharacteristic
925C22#318811yescharacteristic
926C22#318911yescharacteristic
927C22#319911yescharacteristic
928C22#320111yescharacteristic
929C22#326411yescharacteristic
930C22#327111yescharacteristic
931C22#328011yescharacteristic
932C22D4×Q1611yescharacteristic
933C22#329711yescharacteristic
934C22#329911yescharacteristic
935C22#331311yescharacteristic
936C22#331811yescharacteristic
937C22#333611yescharacteristic
938C22#333711yescharacteristic
939C22#333811yescharacteristic
940C22#333811yescharacteristic
941C22#334311yescharacteristic
942C22#334511yescharacteristic
943C22#334711yescharacteristic
944C22#334711yescharacteristic
945C4—42no—
946C4—42no—
947C4—42no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—81no—
952C4—161no—
953C4—161no—
954C4—161no—
955C4—161no—
956C4—161no—
957C4#242711yescharacteristic
958C4#247711yescharacteristic
959C4#253411yescharacteristic
960C4#257811yescharacteristic
961C4#269111yescharacteristic
962C4#269511yescharacteristic
963C4#272811yescharacteristic
964C4#274611yescharacteristic
965C2—44no—
966C2—44no—
967C2#1539011yescharacteristic
968C2#2455211yescharacteristic
969C2#2456511yescharacteristic
970C2#2478111yescharacteristic
971C2#2479011yescharacteristic
972C2#2493911yescharacteristic
973C2#2494011yescharacteristic
974C2#2523411yescharacteristic
975C2#2524311yescharacteristic
976C2#2613111yescharacteristic
977C2#2613211yescharacteristic
978C2#3040011yescharacteristic
979C2#3040711yescharacteristic
980C2#3226111yescharacteristic
981C2#3226411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C23×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
1. C2×#2076C2semidirect
3. C2×#1852C2semidirect
4. C2×#1808C2semidirect
7. #11377C2semidirect
8. #11316C2semidirect
9. #11219C2semidirect
10. #11219C2semidirect
11. #11200C2semidirect
12. #11200C2semidirect
13. #11096C2semidirect
14. #10730C2semidirect
15. #10721C2semidirect
119. C2×#107D4semidirect

Maximal subgroups

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

subgroupindex
C2×#20762
C2×#18692
C2×#18522
C2×#18082
#151812
#138722
#113772
#113162
#112192
#112002
#110962
#107302
#107212