Finite Group Databasebeta

← #390379

Subgroups — #390379

Order 512.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1924C211yesmaximal, characteristic, complemented
2C2×#1924C211yesmaximal, characteristic, complemented
3C2×#1870C211yesmaximal, characteristic
4C2×#1869C211yesmaximal, characteristic
5C4×#394C211yesmaximal, characteristic
6#11346C211yesmaximal, characteristic, complemented
7#11255C211yesmaximal, characteristic, complemented
8#11255C211yesmaximal, characteristic, complemented
9#11042C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#10875C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10714C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C2×#394C411yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34#1924—24no—
35#1924—24no—
36#1870—24no—
37#1869—24no—
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
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1442C411yescharacteristic
56#1441C411yescharacteristic
57#1440C411yescharacteristic
58#1440C411yescharacteristic
59#1439C411yescharacteristic
60#1439C411yescharacteristic
61#1438C411yescharacteristic
62C4×#95C2211yescharacteristic
63C23×D4C2×C411yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16—41no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8—41no—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—41no—
93C2×C4×D4—41no—
94C22×C4⋊C4C2×C411yescharacteristic
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C4⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C22⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C411yescharacteristic
102C22×C22⋊C4C2×C411yescharacteristic
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C411yescharacteristic
106C22×C22⋊C4C2×C411yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—41no—
115C2×C4⋊C8—41no—
116C2×C4⋊C8—41no—
117C2×C4⋊C8—41no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8—41no—
134C2×C22⋊C8D414yes—
135C2×C22⋊C8D414yes—
136C2×#97—22no—
137C2×#97—22no—
138C2×#97—41no—
139#394—24no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—22no—
144C4×C22⋊C4—22no—
145C4×C22⋊C4—22no—
146C4×C22⋊C4—41no—
147C4×C22⋊C4—41no—
148C4×C22⋊C4—41no—
149C4×C22⋊C4—41no—
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162C2×#95C2×C411yescharacteristic
163C2×#95C2×C411yescharacteristic
164#336—22no—
165#336—22no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—41no—
175#336—41no—
176#336—41no—
177#336—41no—
178#336—41no—
179#336—41no—
180#336—41no—
181C25C22×C411yescharacteristic
182C25C22×C411yescharacteristic
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—41no—
189C22×D4—41no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C2×D412yes—
227C23×C4C2×D412yes—
228C23×C4#4112yes—
229C23×C4#4112yes—
230C23×C4C2411yescharacteristic
231C2×M16—44no—
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C2×M16—44no—
236C2×M16—44no—
237C2×M16—44no—
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—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—44no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299C22×C8#4112yes—
300C22×C8#4112yes—
301C4×D4—44no—
302C4×D4—44no—
303C4×D4—44no—
304C4×D4—44no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4M1614yescomplemented
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C4⋊C8—44no—
375C4⋊C8—44no—
376C22⋊C8—44no—
377C22⋊C8—44no—
378C22⋊C8—44no—
379C22⋊C8—44no—
380C22⋊C8—44no—
381C22⋊C8—44no—
382#97—44no—
383#95—22no—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—41no—
391#95—41no—
392#95—41no—
393#95—41no—
394#95—41no—
395#95—41no—
396#95—41no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24C4×D412yes—
424C24C4×D412yes—
425C24C2×M1612yes—
426C24#13112yes—
427C24C23×C411yescharacteristic
428C2×D4—28no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C22×C4—21no—
436C22×C4—21no—
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—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4C4×D412yes—
570C22×C4C4×D412yes—
571C22×C4C2×M1612yes—
572C22×C4C2×M1612yes—
573C22×C4#13112yes—
574C22×C4#13112yes—
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4111yescharacteristic
578C22×C4C2×#4111yescharacteristic
579C22×C4C2×#4111yescharacteristic
580C22×C4C2×#4111yescharacteristic
581C22×C4H(5,𝔽2)11yescharacteristic
582C22×C4H(5,𝔽2)11yescharacteristic
583C22×C4H(5,𝔽2)11yescharacteristic
584C22×C4H(5,𝔽2)11yescharacteristic
585C22×C4H(5,𝔽2)11yescharacteristic
586C22×C4H(5,𝔽2)11yescharacteristic
587C22×C42−1+411yescharacteristic
588C22×C42−1+411yescharacteristic
589M16—416no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—416no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—41no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23#43614yes—
750C23C2×C4×D411yescharacteristic
751C23C2×C4×D411yescharacteristic
752C23C4×#4111yescharacteristic
753C23#51811yescharacteristic
754C23#51811yescharacteristic
755C23#52011yescharacteristic
756C23#52011yescharacteristic
757C23C22×M1611yescharacteristic
758C23C2×#13111yescharacteristic
759C23C2×#13111yescharacteristic
760C23C2×#13111yescharacteristic
761C23#56811yescharacteristic
762C23#56811yescharacteristic
763C23#56811yescharacteristic
764C23#56811yescharacteristic
765D4—416no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4#53411yescharacteristic
867C2×C4#53411yescharacteristic
868C2×C4#53711yescharacteristic
869C2×C4#53711yescharacteristic
870C2×C4#53811yescharacteristic
871C2×C4#53811yescharacteristic
872C2×C4#53811yescharacteristic
873C2×C4#53811yescharacteristic
874C2×C4#53911yescharacteristic
875C2×C4#53911yescharacteristic
876C2×C4#54011yescharacteristic
877C2×C4#54011yescharacteristic
878C2×C4D4211yescharacteristic
879C2×C4#54611yescharacteristic
880C2×C4#54611yescharacteristic
881C2×C4#54611yescharacteristic
882C2×C4#54611yescharacteristic
883C2×C4#54711yescharacteristic
884C2×C4#54711yescharacteristic
885C2×C4#55111yescharacteristic
886C2×C4#55111yescharacteristic
887C2×C4#55111yescharacteristic
888C2×C4#55211yescharacteristic
889C2×C4#55211yescharacteristic
890C2×C4H(3,𝔽4)11yescharacteristic
891C2×C4#56211yescharacteristic
892C2×C4#56211yescharacteristic
893C2×C4#56311yescharacteristic
894C8—42no—
895C8—42no—
896C8—42no—
897C8—42no—
898C8—42no—
899C8—42no—
900C8—81no—
901C8—81no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22#232511yescharacteristic
933C22#232511yescharacteristic
934C22#233311yescharacteristic
935C22#235811yescharacteristic
936C22#235911yescharacteristic
937C22#235911yescharacteristic
938C22#237911yescharacteristic
939C22C2×#43611yescharacteristic
940C22#292911yescharacteristic
941C22#293011yescharacteristic
942C22#293211yescharacteristic
943C22#293311yescharacteristic
944C22#293311yescharacteristic
945C22D4×M1611yescharacteristic
946C22#293511yescharacteristic
947C22#296611yescharacteristic
948C22#296711yescharacteristic
949C22#296911yescharacteristic
950C22#297011yescharacteristic
951C22#297311yescharacteristic
952C22#297411yescharacteristic
953C22#297611yescharacteristic
954C22#297611yescharacteristic
955C22#297611yescharacteristic
956C22#297811yescharacteristic
957C22#298111yescharacteristic
958C22#298111yescharacteristic
959C22#298911yescharacteristic
960C22#299011yescharacteristic
961C22#299211yescharacteristic
962C22#299211yescharacteristic
963C22#299311yescharacteristic
964C22#299411yescharacteristic
965C22#299511yescharacteristic
966C22#299511yescharacteristic
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4#267111yescharacteristic
980C4#267111yescharacteristic
981C4#268411yescharacteristic
982C4#268411yescharacteristic
983C4#269511yescharacteristic
984C4#269511yescharacteristic
985C4#274311yescharacteristic
986C4#274311yescharacteristic
987C2—44no—
988C2—82no—
989C2#1457111yescharacteristic
990C2#2217011yescharacteristic
991C2#2217311yescharacteristic
992C2#2217511yescharacteristic
993C2#2217611yescharacteristic
994C2#2233411yescharacteristic
995C2#2233511yescharacteristic
996C2#2284811yescharacteristic
997C2#2284911yescharacteristic
998C2#2290111yescharacteristic
999C2#2290711yescharacteristic
1000C2#2291011yescharacteristic
1001C2#2291211yescharacteristic
1002C2#2334911yescharacteristic
1003C2#2335411yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1924C2semidirect
2. C2×#1924C2semidirect
6. #11346C2semidirect
7. #11255C2semidirect
8. #11255C2semidirect
9. #11042C2semidirect
10. #11042C2semidirect
11. #10875C2semidirect
12. #10715C2semidirect
13. #10715C2semidirect
14. #10714C2semidirect
15. #10714C2semidirect
343. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×#19242
C2×#18702
C2×#18692
C4×#3942
#113462
#112552
#110422
#108752
#107152
#107142