Finite Group Databasebeta

← #388018

Subgroups — #388018

Order 512.

1162 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#388C211yesmaximal, characteristic
2#11346C211yesmaximal, characteristic, complemented
3#11298C211yesmaximal, characteristic, complemented
4#11298C211yesmaximal, characteristic, complemented
5#11255C211yesmaximal, characteristic, complemented
6#11147C211yesmaximal, characteristic
7#11042C211yesmaximal, characteristic
8#10921C211yesmaximal, characteristic
9#10876C211yesmaximal, characteristic, complemented
10#10874C211yesmaximal, characteristic, complemented
11#10795C211yesmaximal, characteristic, complemented
12#10795C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic
14#10714C211yesmaximal, characteristic
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22C2×#388C411yescharacteristic
23C2×#388C411yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C22⋊C4C2211yescharacteristic
26C2×C4×C22⋊C4C2211yescharacteristic
27C2×C4×C22⋊C4C2211yescharacteristic
28C2×C43C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31C2×#336C2211yescharacteristic
32C2×#336C2211yescharacteristic
33C2×#336C2211yescharacteristic
34C2×#336C2211yescharacteristic
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1437C411yescharacteristic
52#1437C411yescharacteristic
53#1436C411yescharacteristic
54#1436C411yescharacteristic
55#1434C411yescharacteristic
56#1434C411yescharacteristic
57C4×#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59C24×C4C2311yescharacteristic
60C23×C8—22no—
61C23×C8—22no—
62C23×C8—22no—
63C23×C8—41no—
64C23×C8—41no—
65C23×C8—41no—
66C23×C8—41no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C22⋊C4C2×C411yescharacteristic
78C22×C22⋊C4C2×C411yescharacteristic
79C22×C22⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C42C2×C411yescharacteristic
84C22×C42C2×C411yescharacteristic
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C2×C4⋊C8—22no—
94C2×C4⋊C8—41no—
95C2×C4⋊C8—41no—
96C2×C22⋊C8—22no—
97C2×C22⋊C8—22no—
98C2×C22⋊C8—22no—
99C2×C22⋊C8—22no—
100C2×C22⋊C8—22no—
101C2×C22⋊C8—41no—
102C2×C22⋊C8—41no—
103C2×C22⋊C8—41no—
104C2×C22⋊C8—41no—
105C2×C4×C8—41no—
106C2×C4×C8—41no—
107C2×C4×C8—41no—
108#388—24no—
109#388C818yescomplemented
110C4×C4⋊C4—41no—
111C4×C4⋊C4—41no—
112C4×C22⋊C4—22no—
113C4×C22⋊C4—22no—
114C4×C22⋊C4—41no—
115C4×C22⋊C4—41no—
116C4×C22⋊C4—41no—
117C4×C22⋊C4—41no—
118C2×#95C2×C411yescharacteristic
119C2×#95C2×C411yescharacteristic
120C2×#95C2×C411yescharacteristic
121C2×#95C2×C411yescharacteristic
122C2×#95C2×C411yescharacteristic
123C2×#95C2×C411yescharacteristic
124C2×#95C2×C411yescharacteristic
125C2×#95C2×C411yescharacteristic
126C2×#95C2×C411yescharacteristic
127C2×#95C2×C411yescharacteristic
128C2×#95C2×C411yescharacteristic
129C2×#95C2×C411yescharacteristic
130C2×#95C2×C411yescharacteristic
131C2×#95C2×C411yescharacteristic
132C2×#95C2×C411yescharacteristic
133C2×#95C2×C411yescharacteristic
134C43—41no—
135C43—41no—
136#336—22no—
137#336—22no—
138#336—22no—
139#336—22no—
140#336—22no—
141#336—22no—
142#336—22no—
143#336—41no—
144#336—41no—
145#336—41no—
146#336—41no—
147#336—41no—
148#336—41no—
149#336—41no—
150#336—41no—
151#336—41no—
152#336—41no—
153#336—41no—
154#336—41no—
155#336—41no—
156#336—41no—
157#336—41no—
158C25C22×C411yescharacteristic
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×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×C4C22×C411yescharacteristic
181C23×C4C22×C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4#4112yes—
185C23×C4#4112yes—
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×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—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—44no—
240C22×C8—44no—
241C22×C8—44no—
242C22×C8—44no—
243C22×C8—44no—
244C22×C8—44no—
245C22×C8—44no—
246C22×C8#4112yes—
247C22×C8#4112yes—
248C22×C8#4112yes—
249C22×C8#4112yes—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4C2×C814yescomplemented
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4—41no—
266C2×C22⋊C4—41no—
267C2×C22⋊C4—41no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4—41no—
270C2×C22⋊C4C2×C814yes—
271C2×C22⋊C4C2×C814yes—
272C2×C22⋊C4C2×C814yes—
273C2×C22⋊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—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
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—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—41no—
314C2×C42—41no—
315C2×C42—41no—
316C2×C42—41no—
317C2×C42—41no—
318C2×C42—41no—
319C2×C42—41no—
320C2×C42—41no—
321C2×C42C2×C814yescomplemented
322C4⋊C8—44no—
323C22⋊C8—44no—
324C22⋊C8—44no—
325C22⋊C8—44no—
326C4×C8—44no—
327#95—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—41no—
333#95—41no—
334#95—41no—
335#95—41no—
336#95—41no—
337#95—41no—
338#95—41no—
339#95—41no—
340#95—41no—
341#95C2×C814yescomplemented
342#95C2×C814yescomplemented
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24#11712yes—
356C24C22×C812yes—
357C24C2×M1612yes—
358C24C23×C411yescharacteristic
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—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
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—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—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4#11712yes—
468C22×C4C22×C812yes—
469C22×C4C22×C812yes—
470C22×C4C22×C812yes—
471C22×C4C22×C812yes—
472C22×C4C22×C812yes—
473C22×C4C22×C812yes—
474C22×C4C2×M1612yes—
475C22×C4C2×M1612yes—
476C22×C4#13112yes—
477C22×C4#13112yes—
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C4H(5,𝔽2)11yescharacteristic
486C22×C4H(5,𝔽2)11yescharacteristic
487C22×C4H(5,𝔽2)11yescharacteristic
488C22×C4H(5,𝔽2)11yescharacteristic
489C22×C4H(5,𝔽2)11yescharacteristic
490C22×C42−1+411yescharacteristic
491C22×C42−1+411yescharacteristic
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—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—416no—
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—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C22⋊C4—28no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—44no—
557C42—44no—
558C42—44no—
559C42—44no—
560C42—44no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23#43114yes—
620C23C2×#11711yescharacteristic
621C23C4×#4111yescharacteristic
622C23C4×#4111yescharacteristic
623C23#51811yescharacteristic
624C23#51811yescharacteristic
625C23#52011yescharacteristic
626C23#52011yescharacteristic
627C23C23×C811yescharacteristic
628C23C22×M1611yescharacteristic
629C23C2×#13111yescharacteristic
630C23C2×#13111yescharacteristic
631C23#56811yescharacteristic
632C23#56811yescharacteristic
633C23#56811yescharacteristic
634C23#56811yescharacteristic
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—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4#53811yescharacteristic
735C2×C4#53811yescharacteristic
736C2×C4#53811yescharacteristic
737C2×C4#53811yescharacteristic
738C2×C4#53811yescharacteristic
739C2×C4#53911yescharacteristic
740C2×C4#53911yescharacteristic
741C2×C4#53911yescharacteristic
742C2×C4#54111yescharacteristic
743C2×C4#54211yescharacteristic
744C2×C4#54211yescharacteristic
745C2×C4#54211yescharacteristic
746C2×C4#55111yescharacteristic
747C2×C4#55111yescharacteristic
748C2×C4#55111yescharacteristic
749C2×C4#55111yescharacteristic
750C2×C4#55111yescharacteristic
751C2×C4#55211yescharacteristic
752C2×C4#55211yescharacteristic
753C2×C4#55311yescharacteristic
754C2×C4#55311yescharacteristic
755C2×C4#55311yescharacteristic
756C2×C4#55311yescharacteristic
757C2×C4#55911yescharacteristic
758C2×C4#56011yescharacteristic
759C2×C4#56011yescharacteristic
760C2×C4#56211yescharacteristic
761C2×C4#56211yescharacteristic
762C8—42no—
763C8—42no—
764C8—42no—
765C8—42no—
766C8—81no—
767C8—81no—
768C8—81no—
769C8—81no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22#231811yescharacteristic
786C22#233411yescharacteristic
787C22#233711yescharacteristic
788C22#234311yescharacteristic
789C22#235311yescharacteristic
790C22#237411yescharacteristic
791C22#237711yescharacteristic
792C22C2×#43111yescharacteristic
793C22#292311yescharacteristic
794C22#292411yescharacteristic
795C22#292511yescharacteristic
796C22C8×#4111yescharacteristic
797C22C8×#4111yescharacteristic
798C22#296711yescharacteristic
799C22#296711yescharacteristic
800C22#296911yescharacteristic
801C22#296911yescharacteristic
802C22#297011yescharacteristic
803C22#297011yescharacteristic
804C22#297211yescharacteristic
805C22#297211yescharacteristic
806C22#297311yescharacteristic
807C22#297411yescharacteristic
808C22#297711yescharacteristic
809C22#297811yescharacteristic
810C22#298011yescharacteristic
811C22#298111yescharacteristic
812C22#298811yescharacteristic
813C22#298811yescharacteristic
814C22#298911yescharacteristic
815C22#299011yescharacteristic
816C22#299211yescharacteristic
817C22#299211yescharacteristic
818C22#299311yescharacteristic
819C22#299511yescharacteristic
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4#273511yescharacteristic
834C4#273911yescharacteristic
835C4#274611yescharacteristic
836C4#274711yescharacteristic
837C4#275111yescharacteristic
838C4#277811yescharacteristic
839C4#277911yescharacteristic
840C4#279611yescharacteristic
841C2—44no—
842C2#1450911yescharacteristic
843C2#2199611yescharacteristic
844C2#2200611yescharacteristic
845C2#2234111yescharacteristic
846C2#2235111yescharacteristic
847C2#2238511yescharacteristic
848C2#2239111yescharacteristic
849C2#2258911yescharacteristic
850C2#2259411yescharacteristic
851C2#2278511yescharacteristic
852C2#2279011yescharacteristic
853C2#2329411yescharacteristic
854C2#2330211yescharacteristic
855C2#2332611yescharacteristic
856C2#2333311yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #11346C2semidirect
3. #11298C2semidirect
4. #11298C2semidirect
5. #11255C2semidirect
9. #10876C2semidirect
10. #10874C2semidirect
11. #10795C2semidirect
12. #10795C2semidirect
109. #388C8semidirect
255. C2×C4⋊C4C2×C8semidirect
321. C2×C42C2×C8semidirect
341. #95C2×C8semidirect
342. #95C2×C8semidirect

Maximal subgroups

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

subgroupindex
C4×#3882
#113462
#112982
#112552
#111472
#110422
#109212
#108762
#108742
#107952
#107142