Finite Group Databasebeta

← #373248

Subgroups — #373248

Order 512.

1314 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1923C211yesmaximal, characteristic
2C2×C8×C22⋊C4C211yesmaximal, characteristic
3C4×#388C211yesmaximal, characteristic
4#11255C211yesmaximal, characteristic, complemented
5#11202C211yesmaximal, characteristic, complemented
6#11042C211yesmaximal, characteristic
7#11042C211yesmaximal, characteristic
8#10876C211yesmaximal, characteristic, complemented
9#10876C211yesmaximal, characteristic, complemented
10#10876C211yesmaximal, characteristic, complemented
11#10834C211yesmaximal, characteristic, complemented
12#10795C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic
14#10714C211yesmaximal, characteristic
15C4×#336C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#388C411yescharacteristic
27C2×#388C411yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C43C2211yescharacteristic
33#1923—24no—
34C8×C22⋊C4—24no—
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
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1437C411yescharacteristic
54#1437C411yescharacteristic
55#1436C411yescharacteristic
56#1436C411yescharacteristic
57#1434C411yescharacteristic
58#1434C411yescharacteristic
59C4×#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C24×C4C2311yescharacteristic
62C23×C8—22no—
63C23×C8—22no—
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—41no—
68C23×C8—41no—
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C22⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C22⋊C4C2×C411yescharacteristic
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×C4⋊C8—22no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—41no—
101C2×C4⋊C8—41no—
102C2×C4⋊C8—41no—
103C2×C4⋊C8—41no—
104C2×C22⋊C8—22no—
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—41no—
112C2×C22⋊C8—41no—
113C2×C4×C8—22no—
114C2×C4×C8—22no—
115C2×C4×C8—22no—
116C2×C4×C8—22no—
117C2×C4×C8—22no—
118C2×C4×C8—22no—
119C2×C4×C8—41no—
120C2×C4×C8—41no—
121C2×C4×C8—41no—
122#388—24no—
123#388C818yescomplemented
124C4×C4⋊C4—41no—
125C4×C4⋊C4—41no—
126C4×C22⋊C4—41no—
127C4×C22⋊C4—41no—
128C4×C22⋊C4—41no—
129C4×C22⋊C4—41no—
130C4×C22⋊C4D414yes—
131C4×C22⋊C4Q814yes—
132C2×#95C2×C411yescharacteristic
133C2×#95C2×C411yescharacteristic
134C2×#95C2×C411yescharacteristic
135C2×#95C2×C411yescharacteristic
136C2×#95C2×C411yescharacteristic
137C2×#95C2×C411yescharacteristic
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C2×#95C2×C411yescharacteristic
141C2×#95C2×C411yescharacteristic
142C2×#95C2×C411yescharacteristic
143C2×#95C2×C411yescharacteristic
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C43—41no—
149C43—41no—
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—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—41no—
164#336—41no—
165#336—41no—
166#336—41no—
167#336—41no—
168C25C22×C411yescharacteristic
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4C22×C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4C22×C411yescharacteristic
185C23×C4C22×C411yescharacteristic
186C23×C4C22×C411yescharacteristic
187C23×C4C22×C411yescharacteristic
188C23×C4C22×C411yescharacteristic
189C23×C4C22×C411yescharacteristic
190C23×C4C22×C411yescharacteristic
191C23×C4C22×C411yescharacteristic
192C23×C4C22×C411yescharacteristic
193C23×C4C22×C411yescharacteristic
194C23×C4C2×D412yes—
195C23×C4C2×Q812yes—
196C23×C4C2411yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—28no—
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—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—44no—
247C22×C8—44no—
248C22×C8—44no—
249C22×C8—44no—
250C22×C8—44no—
251C22×C8—44no—
252C22×C8#4112yes—
253C22×C8#4112yes—
254C22×C8#4112yes—
255C22×C8#4112yes—
256C22×C8#4112yes—
257C22×C8#4112yes—
258C22×C8#4112yes—
259C22×C8#4112yes—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4C2×C814yescomplemented
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—41no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4—41no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4C4⋊C414yes—
279C2×C22⋊C4C4⋊C414yes—
280C2×C22⋊C4C2×C814yes—
281C2×C22⋊C4C2×C814yes—
282C2×C22⋊C4C2×C814yes—
283C2×C22⋊C4M1614yes—
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—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
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—21no—
321C2×C42—41no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—41no—
325C2×C42—41no—
326C2×C42—41no—
327C2×C42C2×C814yescomplemented
328C2×C42C2×D412yes—
329C2×C42C2×D412yes—
330C2×C42C2×Q812yes—
331C2×C42C2×Q812yes—
332C4⋊C8—44no—
333C4⋊C8—44no—
334C4⋊C8—44no—
335C22⋊C8—28no—
336C22⋊C8—44no—
337C22⋊C8—44no—
338C4×C8—44no—
339C4×C8—44no—
340C4×C8—44no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—41no—
347#95—41no—
348#95—41no—
349#95—41no—
350#95—41no—
351#95—41no—
352#95—41no—
353#95C4⋊C414yes—
354#95C4⋊C414yes—
355#95C2×C814yescomplemented
356#95C2×C814yescomplemented
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24C2×C4⋊C412yes—
370C24C22×C812yes—
371C24C2×M1612yes—
372C24C23×C411yescharacteristic
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×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
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—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4C2×C4⋊C412yes—
476C22×C4C2×C4⋊C412yes—
477C22×C4C2×C4⋊C412yes—
478C22×C4C2×C4⋊C412yes—
479C22×C4C2×C4⋊C412yes—
480C22×C4C22×C812yes—
481C22×C4C22×C812yes—
482C22×C4C22×C812yes—
483C22×C4C22×C812yes—
484C22×C4C22×C812yes—
485C22×C4C22×C812yes—
486C22×C4C2×M1612yes—
487C22×C4C2×M1612yes—
488C22×C4#13112yes—
489C22×C4#13112yes—
490C22×C4#13112yes—
491C22×C4#13112yes—
492C22×C4C22×D411yescharacteristic
493C22×C4C22×Q811yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C4H(5,𝔽2)11yescharacteristic
504C22×C4H(5,𝔽2)11yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—416no—
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—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8#12614yes—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4C4⋊C8116yescomplemented
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—44no—
580C42—44no—
581C42—44no—
582C42—44no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C4⋊C814yes—
634C23C22×C4⋊C411yescharacteristic
635C23C4×#4111yescharacteristic
636C23C4×#4111yescharacteristic
637C23C4×#4111yescharacteristic
638C23C4×#4111yescharacteristic
639C23#51811yescharacteristic
640C23#51811yescharacteristic
641C23C23×C811yescharacteristic
642C23C22×M1611yescharacteristic
643C23C2×#13111yescharacteristic
644C23C2×#13111yescharacteristic
645C23C2×#13111yescharacteristic
646C23C2×#13111yescharacteristic
647C23#56811yescharacteristic
648C23#56811yescharacteristic
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—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4C2×C4⋊C814yes—
746C2×C4C2×C4⋊C814yes—
747C2×C4#42414yes—
748C2×C4#52511yescharacteristic
749C2×C4#52511yescharacteristic
750C2×C4C2×#12611yescharacteristic
751C2×C4#52911yescharacteristic
752C2×C4#52911yescharacteristic
753C2×C4#52911yescharacteristic
754C2×C4#53311yescharacteristic
755C2×C4#53311yescharacteristic
756C2×C4#53811yescharacteristic
757C2×C4#53811yescharacteristic
758C2×C4#54011yescharacteristic
759C2×C4#54011yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#55111yescharacteristic
765C2×C4#55111yescharacteristic
766C2×C4#55111yescharacteristic
767C2×C4#55311yescharacteristic
768C2×C4#55311yescharacteristic
769C2×C4#55411yescharacteristic
770C2×C4#55411yescharacteristic
771C2×C4#55411yescharacteristic
772C2×C4#55411yescharacteristic
773C2×C4#55511yescharacteristic
774C2×C4#55511yescharacteristic
775C2×C4#55911yescharacteristic
776C8—24no—
777C8—42no—
778C8—42no—
779C8—42no—
780C8—42no—
781C8—42no—
782C8—81no—
783C8—81no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22#229611yescharacteristic
800C22C4×#12611yescharacteristic
801C22#233311yescharacteristic
802C22#234911yescharacteristic
803C22#234911yescharacteristic
804C22#237211yescharacteristic
805C22#237411yescharacteristic
806C22C22×C4⋊C811yescharacteristic
807C22C2×#42411yescharacteristic
808C22#290611yescharacteristic
809C22#290611yescharacteristic
810C22C8×#4111yescharacteristic
811C22C8×#4111yescharacteristic
812C22C8×#4111yescharacteristic
813C22C8×#4111yescharacteristic
814C22#296511yescharacteristic
815C22#296511yescharacteristic
816C22#296611yescharacteristic
817C22#296611yescharacteristic
818C22#296611yescharacteristic
819C22#296711yescharacteristic
820C22#296811yescharacteristic
821C22#296811yescharacteristic
822C22#296911yescharacteristic
823C22#296911yescharacteristic
824C22#297011yescharacteristic
825C22#297011yescharacteristic
826C22#297211yescharacteristic
827C22#297211yescharacteristic
828C22#297411yescharacteristic
829C22#297411yescharacteristic
830C22#297611yescharacteristic
831C22#297711yescharacteristic
832C22#297911yescharacteristic
833C22#298111yescharacteristic
834C4—24no—
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—81no—
846C4—81no—
847C4#245711yescharacteristic
848C4#245911yescharacteristic
849C4#247611yescharacteristic
850C4#248011yescharacteristic
851C4#249711yescharacteristic
852C4#252211yescharacteristic
853C4#257411yescharacteristic
854C4#258911yescharacteristic
855C2—44no—
856C2#1411411yescharacteristic
857C2#2134911yescharacteristic
858C2#2135711yescharacteristic
859C2C8×#12611yescharacteristic
860C2#2166511yescharacteristic
861C2#2232911yescharacteristic
862C2#2233311yescharacteristic
863C2#2269611yescharacteristic
864C2#2269611yescharacteristic
865C2#2269711yescharacteristic
866C2#2270111yescharacteristic
867C2#2326911yescharacteristic
868C2#2327011yescharacteristic
869C2#2329411yescharacteristic
870C2#2330011yescharacteristic
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
4. #11255C2semidirect
5. #11202C2semidirect
8. #10876C2semidirect
9. #10876C2semidirect
10. #10876C2semidirect
11. #10834C2semidirect
12. #10795C2semidirect
15. C4×#336C2semidirect
123. #388C8semidirect
265. C2×C4⋊C4C2×C8semidirect
327. C2×C42C2×C8semidirect
355. #95C2×C8semidirect
356. #95C2×C8semidirect
570. C22⋊C4C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#19232
C2×C8×C22⋊C42
C4×#3882
#112552
#112022
#110422
#108762
#108342
#107952
#107142
C4×#3362