Finite Group Databasebeta

← #380910

Subgroups — #380910

Order 512.

1162 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1934C211yesmaximal, characteristic
2#14700C211yesmaximal, characteristic
3#14699C211yesmaximal, characteristic, complemented
4#11328C211yesmaximal, characteristic, complemented
5#11315C211yesmaximal, characteristic, complemented
6#11292C211yesmaximal, characteristic, complemented
7#11256C211yesmaximal, characteristic, complemented
8#11189C211yesmaximal, characteristic
9#11123C211yesmaximal, characteristic
10#11123C211yesmaximal, characteristic
11#11066C211yesmaximal, characteristic
12#10925C211yesmaximal, characteristic
13#10880C211yesmaximal, characteristic, complemented
14#10862C211yesmaximal, characteristic, complemented
15C4×#336C211yesmaximal, characteristic, complemented
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#102C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C2×#390C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#388—21no—
31C2×#388—21no—
32C2×#387—21no—
33C2×C43C2211yescharacteristic
34#1934C418yescomplemented
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1437—21no—
50#1437—21no—
51#1436—21no—
52#1436—21no—
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60C23×D4C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C22⋊C4—21no—
76C22×C22⋊C4—21no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4—21no—
81C22×C42D411yescharacteristic
82C22×C42D411yescharacteristic
83C22×C42D411yescharacteristic
84C22×C42D411yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C2×#107—22no—
89C2×#107—22no—
90C2×#107—41no—
91C2×#107—41no—
92C2×#107—41no—
93C2×#107—41no—
94C2×#102—22no—
95C2×#102—22no—
96C2×#102—22no—
97C2×#102—22no—
98C2×#102—41no—
99C2×#102—41no—
100C2×#102—41no—
101C2×#102—41no—
102C2×#102—41no—
103C2×#102—41no—
104C2×#102C2×C414yes—
105C2×#102C2×C414yes—
106C2×C4×C8—22no—
107C2×C4×C8—41no—
108C2×C4×C8—41no—
109C2×C4×C8—41no—
110C2×C4×C8—41no—
111C2×C4×C8C2×C414yes—
112#390—22no—
113#390—41no—
114#390—41no—
115#390—41no—
116#390—41no—
117#390C2×C414yes—
118#389—22no—
119#389—41no—
120#389—41no—
121#389—41no—
122#389—41no—
123#389C2×C414yes—
124#388—44no—
125#388—44no—
126#387—44no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C43—41no—
143C43—41no—
144#340—22no—
145#340—22no—
146#340—41no—
147#340—41no—
148#340—41no—
149#340—41no—
150#340—41no—
151#340—41no—
152#340C2×C414yes—
153#340C2×C414yes—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158C25—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4C22×C412yes—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2411yescharacteristic
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8C22×C412yes—
210C22×C8C22×C412yes—
211C22×C8#4112yes—
212C22×C8#4112yes—
213C22×C8#4112yes—
214C22×C8#4112yes—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
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—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4C22×C412yes—
264C2×C4⋊C4C22×C412yes—
265C2×C4⋊C4C22×C412yes—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—41no—
306C2×C42—41no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42D814yes—
312C2×C42C22×C412yes—
313C2×C42#4112yes—
314#107—44no—
315#107—44no—
316#102—28no—
317#102—44no—
318#102—44no—
319#102—44no—
320C4×C8—44no—
321C4×C8—44no—
322#95—24no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—42no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337C24—22no—
338C24—41no—
339C24—41no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24C22×D411yescharacteristic
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
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×C4C4×D412yes—
463C22×C4C4×D412yes—
464C22×C4C2×D812yes—
465C22×C4C2×D812yes—
466C22×C4C2×D812yes—
467C22×C4#13512yes—
468C22×C4#13512yes—
469C22×C4#13512yes—
470C22×C4AGL(1,ℤ/8)12yes—
471C22×C4#13712yes—
472C22×C4C23×C411yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4H(5,𝔽2)11yescharacteristic
479C22×C4H(5,𝔽2)11yescharacteristic
480C22×C4H(5,𝔽2)11yescharacteristic
481C22×C4H(5,𝔽2)11yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C42−1+411yescharacteristic
484C22×C42−1+411yescharacteristic
485C22×C42−1+411yescharacteristic
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8#11714yes—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—48no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—84no—
548C22⋊C4—84no—
549C22⋊C4—84no—
550C22⋊C4—84no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—44no—
556C42—44no—
557C42—44no—
558C42—44no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23—81no—
590C23—81no—
591C23—81no—
592C23—81no—
593C23—81no—
594C23—81no—
595C23—81no—
596C23—81no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23—81no—
602C23C2×C4×D411yescharacteristic
603C23#53211yescharacteristic
604C23#53211yescharacteristic
605C23#53411yescharacteristic
606C23#53511yescharacteristic
607C23#53611yescharacteristic
608C23#53711yescharacteristic
609C23C22×D811yescharacteristic
610C23C2×#13511yescharacteristic
611C23C2×#13511yescharacteristic
612C23C2×#13511yescharacteristic
613C23C2×AGL(1,ℤ/8)11yescharacteristic
614C23C2×#13711yescharacteristic
615C23#57511yescharacteristic
616C23#57511yescharacteristic
617D4—42no—
618D4—42no—
619D4—42no—
620D4—42no—
621D4—81no—
622D4—81no—
623D4—81no—
624D4—81no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4C4×D814yes—
715C2×C4#44014yes—
716C2×C4C2×#11711yescharacteristic
717C2×C4C4×#4111yescharacteristic
718C2×C4#51811yescharacteristic
719C2×C4#52011yescharacteristic
720C2×C4#52011yescharacteristic
721C2×C4#52011yescharacteristic
722C2×C4#52911yescharacteristic
723C2×C4#52911yescharacteristic
724C2×C4#53811yescharacteristic
725C2×C4#53811yescharacteristic
726C2×C4#53811yescharacteristic
727C2×C4#53811yescharacteristic
728C2×C4#53811yescharacteristic
729C2×C4#53911yescharacteristic
730C2×C4#53911yescharacteristic
731C2×C4#53911yescharacteristic
732C2×C4#53911yescharacteristic
733C2×C4#53911yescharacteristic
734C2×C4#54011yescharacteristic
735C2×C4#54011yescharacteristic
736C2×C4#54111yescharacteristic
737C2×C4#54111yescharacteristic
738C2×C4#54211yescharacteristic
739C2×C4#54211yescharacteristic
740C2×C4#54211yescharacteristic
741C2×C4#54211yescharacteristic
742C2×C4#54211yescharacteristic
743C2×C4#54211yescharacteristic
744C8—24no—
745C8—42no—
746C8—42no—
747C8—42no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—161no—
756C22—161no—
757C22—161no—
758C22—161no—
759C22—161no—
760C22—161no—
761C22—161no—
762C22—161no—
763C22#229311yescharacteristic
764C22#232511yescharacteristic
765C22#232611yescharacteristic
766C22#266111yescharacteristic
767C22#266211yescharacteristic
768C22#266311yescharacteristic
769C22#266411yescharacteristic
770C22C2×C4×D811yescharacteristic
771C22C4×#13511yescharacteristic
772C22C2×#44011yescharacteristic
773C22#294311yescharacteristic
774C22#316811yescharacteristic
775C22#316811yescharacteristic
776C22#316911yescharacteristic
777C22#316911yescharacteristic
778C22#317111yescharacteristic
779C22#317111yescharacteristic
780C22#317211yescharacteristic
781C22#317211yescharacteristic
782C22#318611yescharacteristic
783C22#318811yescharacteristic
784C22#319011yescharacteristic
785C22#319111yescharacteristic
786C22#320511yescharacteristic
787C22#321011yescharacteristic
788C22#321111yescharacteristic
789C22#321211yescharacteristic
790C22#322611yescharacteristic
791C22#322811yescharacteristic
792C22#323211yescharacteristic
793C22#323311yescharacteristic
794C22#324511yescharacteristic
795C22#324711yescharacteristic
796C22#324811yescharacteristic
797C22#325011yescharacteristic
798C4—24no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—161no—
808C4—161no—
809C4—161no—
810C4—161no—
811C4#231411yescharacteristic
812C4#231811yescharacteristic
813C4#233411yescharacteristic
814C4#233511yescharacteristic
815C4#264911yescharacteristic
816C4#265011yescharacteristic
817C4#265311yescharacteristic
818C4#265411yescharacteristic
819C2—162no—
820C2#1427911yescharacteristic
821C2#2127511yescharacteristic
822C2#2127911yescharacteristic
823C2#2218111yescharacteristic
824C2#2218511yescharacteristic
825C2#2222011yescharacteristic
826C2#2222211yescharacteristic
827C2#3031611yescharacteristic
828C2#3032111yescharacteristic
829C2#3033611yescharacteristic
830C2#3034111yescharacteristic
831C2#3035611yescharacteristic
832C2#3036011yescharacteristic
833C2#3037611yescharacteristic
834C2#3038111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #14699C2semidirect
4. #11328C2semidirect
5. #11315C2semidirect
6. #11292C2semidirect
7. #11256C2semidirect
13. #10880C2semidirect
14. #10862C2semidirect
15. C4×#336C2semidirect
34. #1934C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19342
#147002
#146992
#113282
#113152
#112922
#112562
#111892
#111232
#110662
#109252
#108802
#108622
C4×#3362