Finite Group Databasebeta

← #414882

Subgroups — #414882

Order 512.

1440 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#478C211yesmaximal, characteristic
2C2×#1992C211yesmaximal, characteristic, complemented
3C2×#1940C211yesmaximal, characteristic, complemented
4C2×#1762C211yesmaximal, characteristic
5#14160C211yesmaximal, characteristic, complemented
6#13906C211yesmaximal, characteristic
7#11257C211yesmaximal, characteristic, complemented
8#11256C211yesmaximal, characteristic, complemented
9#11232C211yesmaximal, characteristic, complemented
10#11231C211yesmaximal, characteristic, complemented
11#11189C211yesmaximal, characteristic
12#11189C211yesmaximal, characteristic
13#11076C211yesmaximal, characteristic
14#11076C211yesmaximal, characteristic
15#10849C211yesmaximal, characteristic, complemented
16C22×#125C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C2×#478—24no—
19C2×#478—24no—
20C2×#478—24no—
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×#380—21no—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#1992—24no—
39#1940—24no—
40#1762—24no—
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#1441—21no—
54#1441—21no—
55#1439—21no—
56#1439—21no—
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—22no—
75C2×#125—22no—
76C2×#125D414yes—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4D414yes—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4D411yescharacteristic
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C42—21no—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105#478—232no—
106C2×#107—22no—
107C2×#107—22no—
108C2×#107—22no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—41no—
119C2×C4⋊C8—41no—
120C2×C4⋊C8D414yes—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102Q814yes—
133C2×#97—22no—
134C2×#97—22no—
135C2×#97—22no—
136#390—22no—
137#390—22no—
138#390—41no—
139#390—41no—
140#384—22no—
141#384—22no—
142#380—44no—
143#380—44no—
144C4×C4⋊C4—22no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—22no—
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—
160C2×#95—21no—
161C2×#95D411yescharacteristic
162C2×#95D411yescharacteristic
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—41no—
172#340—41no—
173#336—22no—
174#336—22no—
175C25—21no—
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×D4C2×D412yes—
188C22×D4C2×Q812yes—
189C22×D4#4112yes—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—24no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2411yescharacteristic
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
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×C8C2×D412yes—
236C22×C8C2×D412yes—
237C22×C8C2×Q812yes—
238C22×C8#4112yes—
239#125—28no—
240#125—28no—
241#125—44no—
242#125—44no—
243C4×D4—28no—
244C4×D4—28no—
245C4×D4—44no—
246C4×D4—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
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—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4C2×D412yes—
303C2×C4⋊C4C2×D412yes—
304C2×C4⋊C4C2×D412yes—
305C2×C4⋊C4C2×Q812yes—
306C2×C4⋊C4#4112yes—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—81no—
319C2×C22⋊C4—81no—
320C2×C22⋊C4—81no—
321C2×C22⋊C4—81no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—42no—
335C2×C42—81no—
336C2×C42—81no—
337C2×C42C2×D412yes—
338C2×C42C2×D412yes—
339C2×C42C2×D412yes—
340C2×C42#4112yes—
341C2×C42#4112yes—
342C2×C42#4112yes—
343#107—28no—
344#106—28no—
345C4⋊C8—28no—
346C4⋊C8—44no—
347C4⋊C8—44no—
348#102—28no—
349#102—28no—
350#102—28no—
351#102—28no—
352#97—44no—
353#95—22no—
354#95—22no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—81no—
365#95—81no—
366#95—81no—
367#95—81no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24C22×D411yescharacteristic
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C22⋊Q814yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
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—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
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—48no—
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—84no—
499C22×C4—84no—
500C22×C4—84no—
501C22×C4—84no—
502C22×C4#12112yes—
503C22×C4#12112yes—
504C22×C4#12112yes—
505C22×C4#12112yes—
506C22×C4#12112yes—
507C22×C4#12112yes—
508C22×C4AGL(1,ℤ/8)12yes—
509C22×C4AGL(1,ℤ/8)12yes—
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×Q811yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C42−1+411yescharacteristic
522C22×C42−1+411yescharacteristic
523C22×C42−1+411yescharacteristic
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C22⋊C4—48no—
587C22⋊C4—84no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—84no—
600C42#12014yes—
601C42#12314yes—
602C42#12314yes—
603C42#12414yes—
604C23—24no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23C2×#12111yescharacteristic
640C23C2×#12111yescharacteristic
641C23C2×#12111yescharacteristic
642C23#54611yescharacteristic
643C23#54711yescharacteristic
644C23#54811yescharacteristic
645C23D4×Q811yescharacteristic
646C23C2×AGL(1,ℤ/8)11yescharacteristic
647C23C2×AGL(1,ℤ/8)11yescharacteristic
648C23#57511yescharacteristic
649C23#57511yescharacteristic
650C23#57611yescharacteristic
651C23#57711yescharacteristic
652C23#57711yescharacteristic
653C23#57811yescharacteristic
654D4—24no—
655D4—24no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—816no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4#39414yes—
753C2×C4#39414yes—
754C2×C4C2×#12011yescharacteristic
755C2×C4C2×C22⋊Q811yescharacteristic
756C2×C4C2×#12311yescharacteristic
757C2×C4C2×#12311yescharacteristic
758C2×C4#52511yescharacteristic
759C2×C4C2×#12411yescharacteristic
760C2×C4#52911yescharacteristic
761C2×C4#52911yescharacteristic
762C2×C4#53311yescharacteristic
763C2×C4#53311yescharacteristic
764C2×C4#53611yescharacteristic
765C2×C4#53711yescharacteristic
766C2×C4#54111yescharacteristic
767C2×C4#54111yescharacteristic
768C2×C4#54211yescharacteristic
769C2×C4#54211yescharacteristic
770C2×C4#54611yescharacteristic
771C2×C4#54711yescharacteristic
772C2×C4#54811yescharacteristic
773C2×C4#54811yescharacteristic
774C2×C4#54811yescharacteristic
775C2×C4D4×Q811yescharacteristic
776C2×C4D4×Q811yescharacteristic
777C2×C4#55011yescharacteristic
778C2×C4#55211yescharacteristic
779C2×C4#55211yescharacteristic
780C2×C4#55411yescharacteristic
781C2×C4#55611yescharacteristic
782C8—42no—
783C8—42no—
784C8—42no—
785C8—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22C2×#39411yescharacteristic
802C22#241511yescharacteristic
803C22#241711yescharacteristic
804C22#242611yescharacteristic
805C22#242711yescharacteristic
806C22#242911yescharacteristic
807C22#242911yescharacteristic
808C22#303611yescharacteristic
809C22#303611yescharacteristic
810C22#303811yescharacteristic
811C22#304011yescharacteristic
812C22#304511yescharacteristic
813C22#304511yescharacteristic
814C22#304611yescharacteristic
815C22#304611yescharacteristic
816C22#305511yescharacteristic
817C22#305511yescharacteristic
818C22#306011yescharacteristic
819C22#306111yescharacteristic
820C22#330711yescharacteristic
821C22#331011yescharacteristic
822C22#331511yescharacteristic
823C22#331811yescharacteristic
824C22#334311yescharacteristic
825C22#334511yescharacteristic
826C22#334711yescharacteristic
827C22#334811yescharacteristic
828C22#336611yescharacteristic
829C22#336811yescharacteristic
830C22#337611yescharacteristic
831C22#337711yescharacteristic
832C22#338411yescharacteristic
833C22#338611yescharacteristic
834C22#338811yescharacteristic
835C22#338911yescharacteristic
836C4—24no—
837C4—24no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—161no—
848C4—161no—
849C4#240711yescharacteristic
850C4#240911yescharacteristic
851C4#242111yescharacteristic
852C4#242311yescharacteristic
853C4#248911yescharacteristic
854C4#249211yescharacteristic
855C4#262511yescharacteristic
856C4#285511yescharacteristic
857C2—84no—
858C2#1517911yescharacteristic
859C2#2354311yescharacteristic
860C2#2354611yescharacteristic
861C2#2468811yescharacteristic
862C2#2469011yescharacteristic
863C2#2482311yescharacteristic
864C2#2482511yescharacteristic
865C2#2528811yescharacteristic
866C2#2528911yescharacteristic
867C2#2535111yescharacteristic
868C2#2535511yescharacteristic
869C2#2546511yescharacteristic
870C2#2546611yescharacteristic
871C2#2548211yescharacteristic
872C2#2548611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1992C2semidirect
3. C2×#1940C2semidirect
5. #14160C2semidirect
7. #11257C2semidirect
8. #11256C2semidirect
9. #11232C2semidirect
10. #11231C2semidirect
15. #10849C2semidirect

Maximal subgroups

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

subgroupindex
C22×#4782
C2×#19922
C2×#19402
C2×#17622
#141602
#139062
#112572
#112562
#112322
#112312
#111892
#110762
#108492