Finite Group Databasebeta

← #462385

Subgroups — #462385

Order 512.

1134 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15183C211yesmaximal, characteristic
2#13880C211yesmaximal, characteristic
3#11377C211yesmaximal, characteristic, complemented
4#11371C211yesmaximal, characteristic, complemented
5#11357C211yesmaximal, characteristic, complemented
6#11316C211yesmaximal, characteristic, complemented
7#11293C211yesmaximal, characteristic, complemented
8#11267C211yesmaximal, characteristic, complemented
9#11256C211yesmaximal, characteristic, complemented
10#11207C211yesmaximal, characteristic, complemented
11#11200C211yesmaximal, characteristic
12#11147C211yesmaximal, characteristic
13#11096C211yesmaximal, characteristic
14#10730C211yesmaximal, characteristic
15#10730C211yesmaximal, characteristic
16C23×C4⋊C4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#385—21no—
22C2×#385—21no—
23C2×#384C2211yescharacteristic
24C2×#384C2211yescharacteristic
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×C4×C22⋊C4C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
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#1445—21no—
49#1444—21no—
50#1444—21no—
51#1443—21no—
52#1440—21no—
53#1439—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C24×C4—21no—
60C24×C4C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—41no—
74C22×C4⋊C4—41no—
75C22×C4⋊C4—41no—
76C22×C4⋊C4—41no—
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C22⋊C4D411yescharacteristic
89C22×C22⋊C4D411yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×#107—22no—
93C2×#107—41no—
94C2×#107—41no—
95C2×C22⋊C8—22no—
96C2×C22⋊C8—22no—
97C2×C22⋊C8—22no—
98C2×C22⋊C8—41no—
99C2×C22⋊C8—41no—
100C2×C22⋊C8—41no—
101#389—22no—
102#389—41no—
103#385—44no—
104#385—44no—
105#384—22no—
106#384—22no—
107#384—41no—
108#384—41no—
109#380—22no—
110#380—22no—
111#380—22no—
112#380—41no—
113#380—41no—
114#380—41no—
115C4×C22⋊C4—22no—
116C4×C22⋊C4—22no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
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×#95D411yescharacteristic
132C2×#95D411yescharacteristic
133#340—22no—
134#340—22no—
135#340—22no—
136#340—41no—
137#340—41no—
138#340—41no—
139#340—41no—
140#340—41no—
141#340—41no—
142#340—41no—
143#340—41no—
144#340—41no—
145#340—41no—
146#340—41no—
147#340—41no—
148#336—22no—
149#336—41no—
150#336—41no—
151#336—41no—
152C25C2×D411yescharacteristic
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—42no—
174C23×C4—42no—
175C23×C4—42no—
176C23×C4—42no—
177C23×C4—42no—
178C23×C4—81no—
179C23×C4—81no—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4#4112yes—
186C23×C4#4112yes—
187C23×C4C2411yescharacteristic
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×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8#4112yes—
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—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—44no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—81no—
279C2×C4⋊C4—81no—
280C2×C4⋊C4—81no—
281C2×C4⋊C4—81no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4#4112yes—
284C2×C4⋊C4#4112yes—
285C2×C4⋊C4#4112yes—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—81no—
298C2×C22⋊C4—81no—
299C2×C22⋊C4—81no—
300C2×C22⋊C4Q1614yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313#107—44no—
314C22⋊C8—44no—
315C22⋊C8—44no—
316#95—22no—
317#95—22no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95—42no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—81no—
328#95—81no—
329#95—81no—
330#95—81no—
331#95—81no—
332C24—21no—
333C24—21no—
334C24—21no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—21no—
339C24—21no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24#12312yes—
345C24C2×Q1612yes—
346C24AGL(1,ℤ/8)12yes—
347C24C22×D411yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
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—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—48no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
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×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—84no—
464C22×C4—84no—
465C22×C4—84no—
466C22×C4—84no—
467C22×C4—84no—
468C22×C4—84no—
469C22×C4#12312yes—
470C22×C4C2×Q1612yes—
471C22×C4C2×Q1612yes—
472C22×C4AGL(1,ℤ/8)12yes—
473C22×C4#13712yes—
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4H(5,𝔽2)11yescharacteristic
481C22×C4H(5,𝔽2)11yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C42−1+411yescharacteristic
486C22×C42−1+411yescharacteristic
487C22×C42−1+411yescharacteristic
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
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—
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—41no—
514C2×C8—41no—
515C2×C8—41no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—48no—
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—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—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—84no—
550C4⋊C4—84no—
551C4⋊C4—84no—
552C4⋊C4—84no—
553C4⋊C4—84no—
554C22⋊C4—28no—
555C22⋊C4—28no—
556C22⋊C4—84no—
557C22⋊C4—84no—
558C22⋊C4—84no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#48414yes—
602C23C2×#12311yescharacteristic
603C23#53511yescharacteristic
604C23#53611yescharacteristic
605C23#54611yescharacteristic
606C23#54611yescharacteristic
607C23#54611yescharacteristic
608C23#54711yescharacteristic
609C23C22×Q1611yescharacteristic
610C23C2×AGL(1,ℤ/8)11yescharacteristic
611C23C2×AGL(1,ℤ/8)11yescharacteristic
612C23C2×#13711yescharacteristic
613C23#57611yescharacteristic
614C23#57711yescharacteristic
615C23#57711yescharacteristic
616C23#57711yescharacteristic
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
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—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—816no—
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—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×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4#52911yescharacteristic
718C2×C4#52911yescharacteristic
719C2×C4#53811yescharacteristic
720C2×C4#53811yescharacteristic
721C2×C4#53811yescharacteristic
722C2×C4#53811yescharacteristic
723C2×C4#53911yescharacteristic
724C2×C4#53911yescharacteristic
725C2×C4#53911yescharacteristic
726C2×C4#53911yescharacteristic
727C2×C4#53911yescharacteristic
728C2×C4#53911yescharacteristic
729C2×C4#54111yescharacteristic
730C2×C4#54211yescharacteristic
731C2×C4#54211yescharacteristic
732C2×C4#54211yescharacteristic
733C2×C4#55111yescharacteristic
734C2×C4#55111yescharacteristic
735C2×C4#55211yescharacteristic
736C2×C4#55211yescharacteristic
737C2×C4#55211yescharacteristic
738C2×C4#55311yescharacteristic
739C2×C4#55311yescharacteristic
740C2×C4#55911yescharacteristic
741C2×C4#56011yescharacteristic
742C2×C4#56211yescharacteristic
743C2×C4#56211yescharacteristic
744C2×C4#56311yescharacteristic
745C8—42no—
746C8—81no—
747C8—81no—
748C8—81no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22#241911yescharacteristic
765C22#244411yescharacteristic
766C22#262311yescharacteristic
767C22#268511yescharacteristic
768C22#268711yescharacteristic
769C22#269811yescharacteristic
770C22#271011yescharacteristic
771C22C2×#48411yescharacteristic
772C22#309211yescharacteristic
773C22#309611yescharacteristic
774C22#309911yescharacteristic
775C22#320911yescharacteristic
776C22#321711yescharacteristic
777C22#322111yescharacteristic
778C22#322411yescharacteristic
779C22#323011yescharacteristic
780C22#323811yescharacteristic
781C22#324111yescharacteristic
782C22#324411yescharacteristic
783C22#329911yescharacteristic
784C22#329911yescharacteristic
785C22#329911yescharacteristic
786C22#330611yescharacteristic
787C22#331011yescharacteristic
788C22#331011yescharacteristic
789C22#331411yescharacteristic
790C22#331811yescharacteristic
791C22#332011yescharacteristic
792C22#332511yescharacteristic
793C22#332911yescharacteristic
794C22#333211yescharacteristic
795C22#333811yescharacteristic
796C22#334511yescharacteristic
797C22#334511yescharacteristic
798C22#335611yescharacteristic
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—161no—
808C4—161no—
809C4—161no—
810C4—161no—
811C4—161no—
812C4#251711yescharacteristic
813C4#265211yescharacteristic
814C4#265311yescharacteristic
815C4#274711yescharacteristic
816C4#275011yescharacteristic
817C4#277011yescharacteristic
818C4#279611yescharacteristic
819C4#282711yescharacteristic
820C2—44no—
821C2#1642911yescharacteristic
822C2#2493911yescharacteristic
823C2#2494911yescharacteristic
824C2#2620411yescharacteristic
825C2#2621811yescharacteristic
826C2#2990911yescharacteristic
827C2#2991611yescharacteristic
828C2#3129211yescharacteristic
829C2#3131411yescharacteristic
830C2#3135611yescharacteristic
831C2#3137411yescharacteristic
832C2#3169211yescharacteristic
833C2#3170611yescharacteristic
834C2#3205211yescharacteristic
835C2#3207211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×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. #11377C2semidirect
4. #11371C2semidirect
5. #11357C2semidirect
6. #11316C2semidirect
7. #11293C2semidirect
8. #11267C2semidirect
9. #11256C2semidirect
10. #11207C2semidirect

Maximal subgroups

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

subgroupindex
#151832
#138802
#113772
#113712
#113572
#113162
#112932
#112672
#112562
#112072
#112002
#111472
#110962
#107302