Finite Group Databasebeta

← #368524

Subgroups — #368524

Order 512.

1560 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1893C211yesmaximal, characteristic
2C2×#1875C211yesmaximal, characteristic
3C2×#1735C211yesmaximal, characteristic, complemented
4#14136C211yesmaximal, characteristic
5#13801C211yesmaximal, characteristic, complemented
6#11316C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11189C211yesmaximal, characteristic, complemented
9#11189C211yesmaximal, characteristic, complemented
10#10931C211yesmaximal, characteristic, complemented
11#10931C211yesmaximal, characteristic, complemented
12#10807C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10714C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31#1893C418yescomplemented
32#1875—24no—
33#1735—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
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1438—21no—
51#1438—21no—
52#1437—21no—
53#1437—21no—
54#1437—21no—
55#1437—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60#1434—21no—
61C4×#95—21no—
62C23×D4—21no—
63C23×D4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—41no—
68C23×C8—41no—
69C23×C8—41no—
70C23×C8—41no—
71C23×C8C2×C414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×#121—22no—
77C2×#121—22no—
78C2×#121—22no—
79C2×#121—22no—
80C2×#121—22no—
81C2×#121C2×C414yes—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—41no—
90C2×#117—41no—
91C2×#117—41no—
92C2×#117—41no—
93C2×#117D414yes—
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⋊C4—21no—
109C22×C22⋊C4D411yescharacteristic
110C22×C22⋊C4D411yescharacteristic
111C22×C42—21no—
112C22×C42—21no—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—41no—
122C2×#102—41no—
123C2×#102—41no—
124C2×#102—41no—
125C2×#102—41no—
126C2×#102—41no—
127C2×#102C2×C414yes—
128C2×#102C2×C414yes—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132#390—22no—
133#390—22no—
134#390—41no—
135#390—41no—
136#380—22no—
137#380C2×C414yes—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—22no—
144C2×#95—21no—
145C2×#95—21no—
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×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340C2×C414yes—
168#340C2×C414yes—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
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—21no—
210C23×C4—21no—
211C23×C4C22×C412yes—
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D412yes—
218C23×C4#4112yes—
219C23×C4#4112yes—
220C23×C4#4112yes—
221C23×C4#4112yes—
222C23×C4C2411yescharacteristic
223C22×C8—28no—
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×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—44no—
251C22×C8—44no—
252C22×C8—44no—
253C22×C8—44no—
254C22×C8—44no—
255C22×C8—44no—
256C22×C8C22×C412yes—
257C22×C8C22×C412yes—
258#121—28no—
259#121—28no—
260#121—44no—
261#121—44no—
262#117—28no—
263#117—28no—
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—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⋊C4C22×C412yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4#4112yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C4⋊C4#4112yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4—81no—
338C2×C22⋊C4—81no—
339C2×C22⋊C4—81no—
340C2×C22⋊C4—81no—
341C2×C22⋊C4—81no—
342C2×C42—24no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—81no—
365C2×C42—81no—
366#102—44no—
367#102—44no—
368#102—44no—
369#102—44no—
370C22⋊C8—44no—
371#95—24no—
372#95—22no—
373#95—22no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—81no—
379#95—81no—
380#95—81no—
381#95—81no—
382#95—81no—
383#95—81no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24C4×D412yes—
412C24#12112yes—
413C24#12312yes—
414C24C22×D411yescharacteristic
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—48no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
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—84no—
445C2×D4—84no—
446C2×D4—84no—
447C2×D4—84no—
448C2×D4—84no—
449C2×D4—84no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
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—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—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
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—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
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—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
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#11714yes—
554C22×C4C4×D414yes—
555C22×C4C4×D412yes—
556C22×C4#12112yes—
557C22×C4#12312yes—
558C22×C4#12414yes—
559C22×C4#12614yes—
560C22×C4#13512yes—
561C22×C4#13512yes—
562C22×C4C23×C411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4C2×#4111yescharacteristic
569C22×C4C2×#4111yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4H(5,𝔽2)11yescharacteristic
573C22×C4H(5,𝔽2)11yescharacteristic
574C22×C4H(5,𝔽2)11yescharacteristic
575C22×C4H(5,𝔽2)11yescharacteristic
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—416no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—41no—
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#12314yes—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C42—48no—
644C42—48no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—84no—
654C42—84no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
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—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
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#38814yes—
725C23C2×C4×D411yescharacteristic
726C23C2×#12111yescharacteristic
727C23C2×#12311yescharacteristic
728C23#54611yescharacteristic
729C23#54611yescharacteristic
730C23#54611yescharacteristic
731C23#54611yescharacteristic
732C23C2×#13511yescharacteristic
733C23C2×#13511yescharacteristic
734C23#57511yescharacteristic
735C23#57511yescharacteristic
736C23#57611yescharacteristic
737C23#57611yescharacteristic
738C23#57711yescharacteristic
739C23#57711yescharacteristic
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—816no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
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#38814yes—
841C2×C4C2×#11711yescharacteristic
842C2×C4C2×C4×D411yescharacteristic
843C2×C4C4×#4111yescharacteristic
844C2×C4C4×#4111yescharacteristic
845C2×C4#51811yescharacteristic
846C2×C4#51811yescharacteristic
847C2×C4C2×#12311yescharacteristic
848C2×C4#52511yescharacteristic
849C2×C4C2×#12411yescharacteristic
850C2×C4C2×#12611yescharacteristic
851C2×C4#52911yescharacteristic
852C2×C4#52911yescharacteristic
853C2×C4#53411yescharacteristic
854C2×C4#53511yescharacteristic
855C2×C4#53811yescharacteristic
856C2×C4#53811yescharacteristic
857C2×C4#55111yescharacteristic
858C2×C4#55111yescharacteristic
859C2×C4#55111yescharacteristic
860C2×C4#55111yescharacteristic
861C2×C4#55311yescharacteristic
862C2×C4#55311yescharacteristic
863C2×C4#55311yescharacteristic
864C2×C4#55311yescharacteristic
865C2×C4#55311yescharacteristic
866C2×C4#55311yescharacteristic
867C2×C4#55311yescharacteristic
868C2×C4#55311yescharacteristic
869C8—42no—
870C8—42no—
871C8—81no—
872C8—81no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—161no—
896C22—161no—
897C22—161no—
898C22—161no—
899C22—161no—
900C22—161no—
901C22—161no—
902C22—161no—
903C22C2×#38811yescharacteristic
904C22#236411yescharacteristic
905C22#236411yescharacteristic
906C22#241111yescharacteristic
907C22#241211yescharacteristic
908C22#244411yescharacteristic
909C22#244411yescharacteristic
910C22C4×#13511yescharacteristic
911C22#294311yescharacteristic
912C22#294811yescharacteristic
913C22#294911yescharacteristic
914C22#303511yescharacteristic
915C22#303511yescharacteristic
916C22#304511yescharacteristic
917C22#304511yescharacteristic
918C22#309111yescharacteristic
919C22#309111yescharacteristic
920C22#309611yescharacteristic
921C22#309611yescharacteristic
922C22#329611yescharacteristic
923C22#329711yescharacteristic
924C22#329711yescharacteristic
925C22#330111yescharacteristic
926C22#330311yescharacteristic
927C22#330411yescharacteristic
928C22#330511yescharacteristic
929C22#330511yescharacteristic
930C22#330711yescharacteristic
931C22#330911yescharacteristic
932C22#330911yescharacteristic
933C22#331111yescharacteristic
934C22#331711yescharacteristic
935C22#331911yescharacteristic
936C22#331911yescharacteristic
937C22#332111yescharacteristic
938C4—24no—
939C4—42no—
940C4—42no—
941C4—44no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—81no—
946C4—81no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4C4×#12311yescharacteristic
951C4#232111yescharacteristic
952C4#235311yescharacteristic
953C4#235311yescharacteristic
954C4#250411yescharacteristic
955C4#251011yescharacteristic
956C4#251011yescharacteristic
957C4#259111yescharacteristic
958C2—44no—
959C2—162no—
960C2#1402011yescharacteristic
961C2#2105811yescharacteristic
962C2#2106511yescharacteristic
963C2#2313011yescharacteristic
964C2#2313111yescharacteristic
965C2#2313511yescharacteristic
966C2#2313711yescharacteristic
967C2#2448411yescharacteristic
968C2#2448611yescharacteristic
969C2#2453511yescharacteristic
970C2#2453711yescharacteristic
971C2#2619911yescharacteristic
972C2#2620311yescharacteristic
973C2#2620911yescharacteristic
974C2#2621311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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
3. C2×#1735C2semidirect
5. #13801C2semidirect
6. #11316C2semidirect
7. #11315C2semidirect
8. #11189C2semidirect
9. #11189C2semidirect
10. #10931C2semidirect
11. #10931C2semidirect
12. #10807C2semidirect
13. #10806C2semidirect
14. #10731C2semidirect
15. #10714C2semidirect
31. #1893C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18932
C2×#18752
C2×#17352
#141362
#138012
#113162
#113152
#111892
#109312
#108072
#108062
#107312
#107142