Finite Group Databasebeta

← #391475

Subgroups — #391475

Order 512.

1000 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2065C211yesmaximal, characteristic
2#14266C211yesmaximal, characteristic, complemented
3#14260C211yesmaximal, characteristic
4#11378C211yesmaximal, characteristic, complemented
5#11328C211yesmaximal, characteristic, complemented
6#11316C211yesmaximal, characteristic, complemented
7#11232C211yesmaximal, characteristic, complemented
8#11227C211yesmaximal, characteristic, complemented
9#11220C211yesmaximal, characteristic, complemented
10#11189C211yesmaximal, characteristic
11#11189C211yesmaximal, characteristic
12#11123C211yesmaximal, characteristic
13#11076C211yesmaximal, characteristic
14#11066C211yesmaximal, characteristic
15#10833C211yesmaximal, characteristic, complemented
16C22×#107C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C2×#390C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#376C2211yescharacteristic
31#2065C418yescomplemented
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46#1445—21no—
47#1443—21no—
48#1442—21no—
49#1441—21no—
50#1440—21no—
51#1440—21no—
52#1439—21no—
53#1439—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
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×C42C2311yescharacteristic
82C22×C42C2311yescharacteristic
83C22×C42C2311yescharacteristic
84C2×#107—41no—
85C2×#107—41no—
86C2×#107—41no—
87C2×#106—41no—
88C2×#106—41no—
89C2×#106C2×C414yes—
90C2×C4⋊C8—22no—
91C2×C4⋊C8—41no—
92C2×C4⋊C8—41no—
93C2×C4⋊C8—41no—
94C2×C4⋊C8—41no—
95C2×C4⋊C8C2×C414yes—
96C2×#102—41no—
97C2×#102—41no—
98C2×#102—41no—
99C2×#102—41no—
100C2×#102—41no—
101C2×#102—41no—
102C2×#102—41no—
103C2×#102—41no—
104C2×#102—41no—
105C2×#102—41no—
106C2×#102C2×C414yes—
107C2×#102C2×C414yes—
108#390—22no—
109#390—41no—
110#390—41no—
111#390—41no—
112#390—41no—
113#390C2×C414yes—
114#389—22no—
115#389—41no—
116#389—41no—
117#389—41no—
118#389—41no—
119#389C2×C414yes—
120#376—41no—
121#376—41no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
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×#95D411yescharacteristic
138C2×#95D411yescharacteristic
139C2×#95D411yescharacteristic
140C2×#95D411yescharacteristic
141#340—41no—
142#340—41no—
143#340—41no—
144#340—41no—
145#340—41no—
146#340—41no—
147#340—41no—
148#340—41no—
149#340—41no—
150#340C2×C414yes—
151#336—41no—
152#336—41no—
153#336—41no—
154#336—41no—
155C25—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—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×D4C22×C412yes—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2411yescharacteristic
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
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×C8—21no—
210C22×C8C22×C412yes—
211C22×C8C22×C412yes—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
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—21no—
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—24no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—81no—
255C2×C4⋊C4—81no—
256C2×C4⋊C4—81no—
257C2×C4⋊C4—81no—
258C2×C4⋊C4—81no—
259C2×C4⋊C4—81no—
260C2×C4⋊C4C22×C412yes—
261C2×C4⋊C4C22×C412yes—
262C2×C4⋊C4C22×C412yes—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—42no—
266C2×C22⋊C4—42no—
267C2×C22⋊C4—42no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—81no—
270C2×C22⋊C4—81no—
271C2×C22⋊C4—81no—
272C2×C22⋊C4—81no—
273C2×C22⋊C4—81no—
274C2×C22⋊C4—81no—
275C2×C22⋊C4—81no—
276C2×C22⋊C4—81no—
277C2×C22⋊C4—81no—
278C2×C22⋊C4—81no—
279C2×C22⋊C4—81no—
280C2×C22⋊C4—81no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42C22×C412yes—
298C2×C42#4112yes—
299#107—44no—
300#106—44no—
301C4⋊C8—44no—
302C4⋊C8—44no—
303#102—44no—
304#102—44no—
305#102—44no—
306#102—44no—
307#95—24no—
308#95—41no—
309#95—41no—
310#95—41no—
311#95—41no—
312#95—42no—
313#95—42no—
314#95—81no—
315#95—81no—
316#95—81no—
317#95—81no—
318#95—81no—
319#95—81no—
320#95—81no—
321#95—81no—
322#95—81no—
323#95—81no—
324#95—81no—
325#95—81no—
326C24—22no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24—41no—
339C24—41no—
340C24—41no—
341C24C22×D411yescharacteristic
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
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—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
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—41no—
414C22×C4—41no—
415C22×C4—41no—
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×C4C4×D412yes—
460C22×C4C4×D412yes—
461C22×C4C23×C411yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4H(5,𝔽2)11yescharacteristic
464C22×C4H(5,𝔽2)11yescharacteristic
465C22×C4H(5,𝔽2)11yescharacteristic
466C22×C4H(5,𝔽2)11yescharacteristic
467C22×C4H(5,𝔽2)11yescharacteristic
468C22×C4H(5,𝔽2)11yescharacteristic
469C22×C4H(5,𝔽2)11yescharacteristic
470C22×C42−1+411yescharacteristic
471C22×C42−1+411yescharacteristic
472C22×C42−1+411yescharacteristic
473C22×C42−1+411yescharacteristic
474C22×C42−1+411yescharacteristic
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—84no—
532C4⋊C4—84no—
533C4⋊C4—84no—
534C22⋊C4—84no—
535C22⋊C4—84no—
536C22⋊C4—84no—
537C22⋊C4—84no—
538C22⋊C4—84no—
539C22⋊C4—84no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—81no—
560C23—81no—
561C23—81no—
562C23—81no—
563C23—81no—
564C23—81no—
565C23—81no—
566C23—81no—
567C23—81no—
568C23—81no—
569C23—81no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23—81no—
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—
587C23C2×C4×D411yescharacteristic
588C23#53411yescharacteristic
589C23#53511yescharacteristic
590C23#53611yescharacteristic
591C23#53711yescharacteristic
592C23#53711yescharacteristic
593C23#53711yescharacteristic
594C23#57611yescharacteristic
595C23#57611yescharacteristic
596C23#57611yescharacteristic
597C23#57711yescharacteristic
598C23#57711yescharacteristic
599C23#57711yescharacteristic
600C23#57711yescharacteristic
601C23#57811yescharacteristic
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—81no—
607D4—81no—
608D4—81no—
609D4—81no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
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—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
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#51811yescharacteristic
702C2×C4#51811yescharacteristic
703C2×C4#51911yescharacteristic
704C2×C4#52011yescharacteristic
705C2×C4#52011yescharacteristic
706C2×C4#52011yescharacteristic
707C2×C4#53811yescharacteristic
708C2×C4#53911yescharacteristic
709C2×C4#54011yescharacteristic
710C2×C4#54111yescharacteristic
711C2×C4#54211yescharacteristic
712C2×C4#54211yescharacteristic
713C2×C4#56011yescharacteristic
714C2×C4#56011yescharacteristic
715C2×C4#56011yescharacteristic
716C2×C4#56211yescharacteristic
717C2×C4#56211yescharacteristic
718C2×C4#56211yescharacteristic
719C2×C4#56211yescharacteristic
720C2×C4#56211yescharacteristic
721C2×C4#56211yescharacteristic
722C2×C4#56311yescharacteristic
723C2×C4#56311yescharacteristic
724C2×C4#56311yescharacteristic
725C2×C4#56311yescharacteristic
726C2×C4#56311yescharacteristic
727C2×C4#56311yescharacteristic
728C2×C4#56311yescharacteristic
729C8—42no—
730C8—42no—
731C8—81no—
732C8—81no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—161no—
741C22—161no—
742C22—161no—
743C22—161no—
744C22—161no—
745C22—161no—
746C22—161no—
747C22—161no—
748C22#232311yescharacteristic
749C22#232411yescharacteristic
750C22#232511yescharacteristic
751C22#281311yescharacteristic
752C22#281411yescharacteristic
753C22#282011yescharacteristic
754C22#282311yescharacteristic
755C22#294611yescharacteristic
756C22#294611yescharacteristic
757C22#294911yescharacteristic
758C22#295111yescharacteristic
759C22#319811yescharacteristic
760C22#319911yescharacteristic
761C22#320111yescharacteristic
762C22#320411yescharacteristic
763C22#322011yescharacteristic
764C22#322211yescharacteristic
765C22#322411yescharacteristic
766C22#322511yescharacteristic
767C22#324111yescharacteristic
768C22#324111yescharacteristic
769C22#324311yescharacteristic
770C22#324411yescharacteristic
771C22#325711yescharacteristic
772C22#325711yescharacteristic
773C22#325711yescharacteristic
774C22#325711yescharacteristic
775C22#325711yescharacteristic
776C22#325711yescharacteristic
777C22#325811yescharacteristic
778C22#325811yescharacteristic
779C22#325911yescharacteristic
780C22#326011yescharacteristic
781C22#326211yescharacteristic
782C22#326311yescharacteristic
783C4—42no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—161no—
793C4—161no—
794C4—161no—
795C4—161no—
796C4#237711yescharacteristic
797C4#237811yescharacteristic
798C4#237811yescharacteristic
799C4#238311yescharacteristic
800C4#282911yescharacteristic
801C4#283111yescharacteristic
802C4#283611yescharacteristic
803C4#283811yescharacteristic
804C2—162no—
805C2#1463311yescharacteristic
806C2#2212311yescharacteristic
807C2#2212611yescharacteristic
808C2#2215711yescharacteristic
809C2#2216011yescharacteristic
810C2#2219411yescharacteristic
811C2#2220211yescharacteristic
812C2#3273011yescharacteristic
813C2#3273711yescharacteristic
814C2#3275011yescharacteristic
815C2#3275611yescharacteristic
816C2#3283111yescharacteristic
817C2#3283311yescharacteristic
818C2#3286411yescharacteristic
819C2#3286511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14266C2semidirect
4. #11378C2semidirect
5. #11328C2semidirect
6. #11316C2semidirect
7. #11232C2semidirect
8. #11227C2semidirect
9. #11220C2semidirect
15. #10833C2semidirect
31. #2065C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20652
#142662
#142602
#113782
#113282
#113162
#112322
#112272
#112202
#111892
#111232
#110762
#110662
#108332