Finite Group Databasebeta

← #387454

Subgroups — #387454

Order 512.

1170 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#125C211yesmaximal, characteristic
2C2×#1917C211yesmaximal, characteristic
3C2×#1916C211yesmaximal, characteristic
4#11346C211yesmaximal, characteristic
5#11346C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic
7#11346C211yesmaximal, characteristic
8#11202C211yesmaximal, characteristic
9#11202C211yesmaximal, characteristic
10#10875C211yesmaximal, characteristic
11#10874C211yesmaximal, characteristic
12#10835C211yesmaximal, characteristic
13#10834C211yesmaximal, characteristic
14#10795C211yesmaximal, characteristic
15#10795C211yesmaximal, characteristic
16C22×#125C411yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#97C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21C4×#125—24no—
22C4×#125—24no—
23C2×#389C411yescharacteristic
24C2×#389C411yescharacteristic
25C2×#387C411yescharacteristic
26C2×#387C411yescharacteristic
27C2×#387C411yescharacteristic
28C2×#387C411yescharacteristic
29C2×#382C411yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C43C2211yescharacteristic
37#1917—24no—
38#1916—24no—
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#125—24no—
72C2×#125—24no—
73C2×#125—24no—
74C22×C4⋊C4C2×C411yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C4⋊C4C2×C411yescharacteristic
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4C2×C411yescharacteristic
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—41no—
102C2×C4⋊C8—41no—
103C2×#97—22no—
104C2×#97—22no—
105C2×#97—41no—
106C2×C4×C8—22no—
107C2×C4×C8—22no—
108C2×C4×C8—41no—
109#389—24no—
110#389—24no—
111#387—24no—
112#387—24no—
113#387—24no—
114#387—24no—
115#382—24no—
116C4×C4⋊C4—22no—
117C4×C4⋊C4—22no—
118C4×C4⋊C4—22no—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4D414yes—
127C4×C4⋊C4D414yes—
128C2×#95C2×C411yescharacteristic
129C2×#95C2×C411yescharacteristic
130C2×#95C2×C411yescharacteristic
131C2×#95C2×C411yescharacteristic
132C2×#95C2×C411yescharacteristic
133C2×#95C2×C411yescharacteristic
134C2×#95C2×C411yescharacteristic
135C2×#95C2×C411yescharacteristic
136C2×#95C2×C411yescharacteristic
137C2×#95C2×C411yescharacteristic
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C43—22no—
141C43—22no—
142#336—22no—
143#336—22no—
144#336—22no—
145#336—22no—
146#336—22no—
147#336—22no—
148#336—22no—
149#336—22no—
150#336—22no—
151#336—22no—
152#336—22no—
153#336—22no—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—41no—
159#336—41no—
160#336—41no—
161#336—41no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336—41no—
166C23×C4C22×C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C22×C411yescharacteristic
169C23×C4C22×C411yescharacteristic
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C22×C411yescharacteristic
173C23×C4C22×C411yescharacteristic
174C23×C4C22×C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C22×C411yescharacteristic
177C23×C4C22×C411yescharacteristic
178C23×C4C22×C411yescharacteristic
179C23×C4C22×C411yescharacteristic
180C23×C4C2411yescharacteristic
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—21no—
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×C8—21no—
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#4112yes—
234C22×C8#4112yes—
235C22×C8#4112yes—
236C22×C8#4112yes—
237#125—232no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4C22⋊C414yes—
271C2×C4⋊C4C22⋊C414yes—
272C2×C4⋊C4M1614yes—
273C2×C4⋊C4M1614yes—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
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—22no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
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—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—41no—
321C2×C42—41no—
322C2×C42C2×D412yes—
323C2×C42C2×D412yes—
324C2×C42C2×D412yes—
325C2×C42C2×D412yes—
326C2×C42C2×D412yes—
327C2×C42C2×D412yes—
328C4⋊C8—44no—
329C4⋊C8—44no—
330#97—44no—
331C4×C8—44no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95C22⋊C414yes—
343#95C22⋊C414yes—
344C24C23×C411yescharacteristic
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
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—21no—
379C22×C4—21no—
380C22×C4—21no—
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—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×C4C2×C22⋊C412yes—
428C22×C4C2×C22⋊C412yes—
429C22×C4C2×C22⋊C412yes—
430C22×C4C2×C22⋊C412yes—
431C22×C4C2×C22⋊C412yes—
432C22×C4C2×C22⋊C412yes—
433C22×C4C2×M1612yes—
434C22×C4C2×M1612yes—
435C22×C4C2×M1612yes—
436C22×C4C2×M1612yes—
437C22×C4C2×M1612yes—
438C22×C4C2×M1612yes—
439C22×C4#13112yes—
440C22×C4#13112yes—
441C22×C4#13112yes—
442C22×C4#13112yes—
443C22×C4C22×D411yescharacteristic
444C22×C4C22×D411yescharacteristic
445C22×C4C2×#4111yescharacteristic
446C22×C4C2×#4111yescharacteristic
447C22×C4C2×#4111yescharacteristic
448C22×C4C2×#4111yescharacteristic
449C22×C4H(5,𝔽2)11yescharacteristic
450C22×C4H(5,𝔽2)11yescharacteristic
451C22×C42−1+411yescharacteristic
452C22×C42−1+411yescharacteristic
453C22×C42−1+411yescharacteristic
454C22×C42−1+411yescharacteristic
455C22×C42−1+411yescharacteristic
456C22×C42−1+411yescharacteristic
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
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—
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—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—28no—
518C4⋊C4—28no—
519C4⋊C4—28no—
520C4⋊C4—44no—
521C4⋊C4—44no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C42—28no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—44no—
539C42—44no—
540C42—41no—
541C42—41no—
542C42—41no—
543C42—41no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—44no—
557C23C22×C22⋊C411yescharacteristic
558C23C4×#4111yescharacteristic
559C23C4×#4111yescharacteristic
560C23#51911yescharacteristic
561C23#51911yescharacteristic
562C23#52011yescharacteristic
563C23#52011yescharacteristic
564C23C22×M1611yescharacteristic
565C23C22×M1611yescharacteristic
566C23C2×#13111yescharacteristic
567C23C2×#13111yescharacteristic
568C23C2×#13111yescharacteristic
569C23C2×#13111yescharacteristic
570C23#56811yescharacteristic
571C23#56811yescharacteristic
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—41no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
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—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—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4#40714yes—
669C2×C4#40814yes—
670C2×C4#53611yescharacteristic
671C2×C4#53611yescharacteristic
672C2×C4#53611yescharacteristic
673C2×C4#53611yescharacteristic
674C2×C4#53911yescharacteristic
675C2×C4#53911yescharacteristic
676C2×C4#53911yescharacteristic
677C2×C4#53911yescharacteristic
678C2×C4#54111yescharacteristic
679C2×C4#54111yescharacteristic
680C2×C4#54111yescharacteristic
681C2×C4#54111yescharacteristic
682C2×C4#54611yescharacteristic
683C2×C4#54611yescharacteristic
684C2×C4#54711yescharacteristic
685C2×C4#54711yescharacteristic
686C2×C4#54811yescharacteristic
687C2×C4#54811yescharacteristic
688C2×C4#55011yescharacteristic
689C2×C4#55011yescharacteristic
690C2×C4#55211yescharacteristic
691C2×C4#55211yescharacteristic
692C2×C4#55211yescharacteristic
693C2×C4#55211yescharacteristic
694C2×C4#56211yescharacteristic
695C2×C4#56311yescharacteristic
696C2×C4#56311yescharacteristic
697C2×C4#56411yescharacteristic
698C8—42no—
699C8—42no—
700C8—42no—
701C8—42no—
702C8—81no—
703C8—81no—
704C8—81no—
705C8—81no—
706C22#231011yescharacteristic
707C22#233611yescharacteristic
708C22#233611yescharacteristic
709C22#233911yescharacteristic
710C22#234111yescharacteristic
711C22#237111yescharacteristic
712C22#238211yescharacteristic
713C22C2×#40711yescharacteristic
714C22C2×#40811yescharacteristic
715C22#288011yescharacteristic
716C22#288011yescharacteristic
717C22#296511yescharacteristic
718C22#296511yescharacteristic
719C22#296611yescharacteristic
720C22#296611yescharacteristic
721C22#296911yescharacteristic
722C22#296911yescharacteristic
723C22#297011yescharacteristic
724C22#297011yescharacteristic
725C22#298411yescharacteristic
726C22#298411yescharacteristic
727C22#298411yescharacteristic
728C22#298411yescharacteristic
729C22#298511yescharacteristic
730C22#298511yescharacteristic
731C22#298611yescharacteristic
732C22#298711yescharacteristic
733C22#298911yescharacteristic
734C22#298911yescharacteristic
735C22#299011yescharacteristic
736C22#299011yescharacteristic
737C22#299311yescharacteristic
738C22#299311yescharacteristic
739C22#299411yescharacteristic
740C22#299411yescharacteristic
741C4—24no—
742C4—24no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—81no—
754C4—81no—
755C4#269011yescharacteristic
756C4#269011yescharacteristic
757C4#269411yescharacteristic
758C4#269411yescharacteristic
759C4#271911yescharacteristic
760C4#271911yescharacteristic
761C4#272111yescharacteristic
762C4#272111yescharacteristic
763C2#1447411yescharacteristic
764C2#2182011yescharacteristic
765C2#2182411yescharacteristic
766C2#2237711yescharacteristic
767C2#2237711yescharacteristic
768C2#2237911yescharacteristic
769C2#2237911yescharacteristic
770C2#2247111yescharacteristic
771C2#2247411yescharacteristic
772C2#2253111yescharacteristic
773C2#2253211yescharacteristic
774C2#2326411yescharacteristic
775C2#2326411yescharacteristic
776C2#2337011yescharacteristic
777C2#2337011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socle, prime radicalC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×C4×#1252
C2×#19172
C2×#19162
#113462
#112022
#108752
#108742
#108352
#108342
#107952