Finite Group Databasebeta

← #381606

Subgroups — #381606

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2034C211yesmaximal, characteristic
2#14257C211yesmaximal, characteristic
3#13777C211yesmaximal, characteristic, complemented
4#11378C211yesmaximal, characteristic, complemented
5#11315C211yesmaximal, characteristic, complemented
6#11199C211yesmaximal, characteristic, complemented
7#11189C211yesmaximal, characteristic, complemented
8#11121C211yesmaximal, characteristic, complemented
9#11095C211yesmaximal, characteristic, complemented
10#10969C211yesmaximal, characteristic
11#10931C211yesmaximal, characteristic, complemented
12#10931C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10908C211yesmaximal, characteristic, complemented
15#10713C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33#2034C418yescomplemented
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48#1439—21no—
49#1439—21no—
50#1438—21no—
51#1438—21no—
52#1437—21no—
53#1437—21no—
54#1436—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C23×D4—21no—
61C23×D4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×#121—22no—
68C2×#121—41no—
69C2×#121—41no—
70C2×#121—41no—
71C2×#121—41no—
72C2×#121C2×C414yes—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—41no—
76C2×#117—41no—
77C2×#117—41no—
78C2×#117—41no—
79C22×C4⋊C4D411yescharacteristic
80C22×C4⋊C4D411yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4D411yescharacteristic
97C22×C22⋊C4D411yescharacteristic
98C22×C42—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C2×#106—22no—
103C2×#106—41no—
104C2×#106—41no—
105C2×#106—41no—
106C2×#106—41no—
107C2×#106C2×C414yes—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102—41no—
116C2×#102—41no—
117C2×#102—41no—
118C2×#102C2×C414yes—
119C2×#102C2×C414yes—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—41no—
122C2×C22⋊C8—41no—
123C2×C22⋊C8—41no—
124C2×C22⋊C8—41no—
125C2×C22⋊C8C2×C414yes—
126#390—22no—
127#390—22no—
128#390—41no—
129#390—41no—
130#380—22no—
131#380—22no—
132#380—22no—
133#380—41no—
134#380—41no—
135#380C2×C414yes—
136C4×C4⋊C4—41no—
137C4×C4⋊C4—41no—
138C4×C4⋊C4—41no—
139C4×C4⋊C4—41no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
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—
153#340—22no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340C2×C414yes—
163#336—22no—
164#336—22no—
165#336—41no—
166#336—41no—
167C25—21no—
168C25C2×D411yescharacteristic
169C22×D4—24no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—42no—
184C22×D4—42no—
185C22×D4—81no—
186C22×D4—81no—
187C22×D4—81no—
188C22×D4—81no—
189C22×D4C22×C412yes—
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×C4C22×C412yes—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4#4112yes—
216C23×C4C2411yescharacteristic
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×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8C22×C412yes—
244C22×C8C22×C412yes—
245#121—44no—
246#121—44no—
247#121—44no—
248#121—44no—
249#117—44no—
250#117—44no—
251#117—44no—
252#117—44no—
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—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
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—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4C22×C412yes—
297C2×C4⋊C4C22×C412yes—
298C2×C4⋊C4C22×C412yes—
299C2×C4⋊C4#4112yes—
300C2×C4⋊C4#4112yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—41no—
308C2×C22⋊C4—41no—
309C2×C22⋊C4—41no—
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—81no—
318C2×C22⋊C4—81no—
319C2×C22⋊C4—81no—
320C2×C22⋊C4—81no—
321C2×C22⋊C4—81no—
322C2×C22⋊C4—81no—
323C2×C22⋊C4—81no—
324C2×C22⋊C4—81no—
325C2×C22⋊C4—81no—
326C2×C22⋊C4—81no—
327C2×C22⋊C4—81no—
328C2×C22⋊C4—81no—
329C2×C22⋊C4—81no—
330C2×C22⋊C4—81no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42—81no—
344C2×C42—81no—
345C2×C42—81no—
346C2×C42—81no—
347C2×C42#4112yes—
348C2×C42#4112yes—
349#106—44no—
350#106—44no—
351#102—44no—
352#102—44no—
353#102—44no—
354#102—44no—
355C22⋊C8—44no—
356C22⋊C8—44no—
357#95—24no—
358#95—24no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—81no—
363#95—81no—
364#95—81no—
365#95—81no—
366#95—81no—
367#95—81no—
368#95—81no—
369#95—81no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24C4×D412yes—
400C24C22×D411yescharacteristic
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—48no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
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—84no—
431C2×D4—84no—
432C2×D4—84no—
433C2×D4—84no—
434C2×D4—84no—
435C2×D4—84no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
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—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—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
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—41no—
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×C4C4×D412yes—
546C22×C4#12312yes—
547C22×C4#12312yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4H(5,𝔽2)11yescharacteristic
555C22×C4H(5,𝔽2)11yescharacteristic
556C22×C4H(5,𝔽2)11yescharacteristic
557C22×C4H(5,𝔽2)11yescharacteristic
558C22×C4H(5,𝔽2)11yescharacteristic
559C22×C4H(5,𝔽2)11yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C42−1+411yescharacteristic
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—48no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—84no—
639C42—84no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
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—
710C23C2×C4×D411yescharacteristic
711C23C2×#12311yescharacteristic
712C23#52511yescharacteristic
713C23#53411yescharacteristic
714C23#53411yescharacteristic
715C23#53511yescharacteristic
716C23#53711yescharacteristic
717C23#57611yescharacteristic
718C23#57611yescharacteristic
719C23#57711yescharacteristic
720C23#57711yescharacteristic
721C23#57711yescharacteristic
722C23#57711yescharacteristic
723C23#57711yescharacteristic
724C23#57711yescharacteristic
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—816no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
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×C4C4×#4111yescharacteristic
827C2×C4C4×#4111yescharacteristic
828C2×C4#51811yescharacteristic
829C2×C4#51811yescharacteristic
830C2×C4#51811yescharacteristic
831C2×C4#52011yescharacteristic
832C2×C4#52911yescharacteristic
833C2×C4#52911yescharacteristic
834C2×C4#53811yescharacteristic
835C2×C4#53811yescharacteristic
836C2×C4#53811yescharacteristic
837C2×C4#53811yescharacteristic
838C2×C4#53811yescharacteristic
839C2×C4#53811yescharacteristic
840C2×C4#53811yescharacteristic
841C2×C4#53811yescharacteristic
842C2×C4#53811yescharacteristic
843C2×C4#53811yescharacteristic
844C2×C4#53911yescharacteristic
845C2×C4#53911yescharacteristic
846C2×C4#54011yescharacteristic
847C2×C4#54011yescharacteristic
848C2×C4#54011yescharacteristic
849C2×C4#54011yescharacteristic
850C2×C4#54011yescharacteristic
851C2×C4#54211yescharacteristic
852C2×C4#54211yescharacteristic
853C2×C4#54211yescharacteristic
854C8—42no—
855C8—42no—
856C8—81no—
857C8—81no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—161no—
881C22—161no—
882C22—161no—
883C22—161no—
884C22—161no—
885C22—161no—
886C22—161no—
887C22—161no—
888C22C4×#12311yescharacteristic
889C22#232111yescharacteristic
890C22#232511yescharacteristic
891C22#262211yescharacteristic
892C22#262411yescharacteristic
893C22#263011yescharacteristic
894C22#263511yescharacteristic
895C22#294611yescharacteristic
896C22#294611yescharacteristic
897C22#294911yescharacteristic
898C22#295211yescharacteristic
899C22#309611yescharacteristic
900C22#309611yescharacteristic
901C22#309911yescharacteristic
902C22#309911yescharacteristic
903C22#311811yescharacteristic
904C22#311911yescharacteristic
905C22#312511yescharacteristic
906C22#312611yescharacteristic
907C22#319811yescharacteristic
908C22#319811yescharacteristic
909C22#319811yescharacteristic
910C22#319811yescharacteristic
911C22#320011yescharacteristic
912C22#320011yescharacteristic
913C22#320411yescharacteristic
914C22#320411yescharacteristic
915C22#322111yescharacteristic
916C22#322211yescharacteristic
917C22#322411yescharacteristic
918C22#322411yescharacteristic
919C22#325911yescharacteristic
920C22#326011yescharacteristic
921C22#326311yescharacteristic
922C22#326311yescharacteristic
923C4—42no—
924C4—42no—
925C4—42no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—81no—
932C4—81no—
933C4—161no—
934C4—161no—
935C4#233311yescharacteristic
936C4#233311yescharacteristic
937C4#233511yescharacteristic
938C4#233711yescharacteristic
939C4#264811yescharacteristic
940C4#264811yescharacteristic
941C4#264911yescharacteristic
942C4#265311yescharacteristic
943C2—82no—
944C2—162no—
945C2#1430311yescharacteristic
946C2#2158411yescharacteristic
947C2#2158811yescharacteristic
948C2#2205211yescharacteristic
949C2#2205311yescharacteristic
950C2#2219511yescharacteristic
951C2#2219911yescharacteristic
952C2#2989911yescharacteristic
953C2#2989911yescharacteristic
954C2#2992911yescharacteristic
955C2#2993211yescharacteristic
956C2#3003011yescharacteristic
957C2#3003511yescharacteristic
958C2#3011711yescharacteristic
959C2#3012211yescharacteristic
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. #13777C2semidirect
4. #11378C2semidirect
5. #11315C2semidirect
6. #11199C2semidirect
7. #11189C2semidirect
8. #11121C2semidirect
9. #11095C2semidirect
11. #10931C2semidirect
12. #10931C2semidirect
13. #10908C2semidirect
14. #10908C2semidirect
15. #10713C2semidirect
33. #2034C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20342
#142572
#137772
#113782
#113152
#111992
#111892
#111212
#110952
#109692
#109312
#109082
#107132