Finite Group Databasebeta

← #384267

Subgroups — #384267

Order 512.

1314 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1954C211yesmaximal, characteristic
2C2×#1818C211yesmaximal, characteristic, complemented
3#13839C211yesmaximal, characteristic
4#11255C211yesmaximal, characteristic, complemented
5#11147C211yesmaximal, characteristic, complemented
6#11147C211yesmaximal, characteristic, complemented
7#11042C211yesmaximal, characteristic, complemented
8#11042C211yesmaximal, characteristic, complemented
9#10964C211yesmaximal, characteristic
10#10921C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10876C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10797C211yesmaximal, characteristic, complemented
15#10713C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33#1954—24no—
34#1818—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
51#1441C411yescharacteristic
52#1441C411yescharacteristic
53#1440C411yescharacteristic
54#1440C411yescharacteristic
55#1439C411yescharacteristic
56#1439C411yescharacteristic
57#1438C411yescharacteristic
58#1438C411yescharacteristic
59C4×#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C23×D4C2×C411yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—41no—
77C2×C4×D4—41no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—41no—
81C2×#117—41no—
82C2×#117—41no—
83C2×#117—41no—
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C22⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—41no—
106C2×C4⋊C8—41no—
107C2×C4⋊C8—41no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—41no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8—41no—
122C2×C22⋊C8—41no—
123C2×C22⋊C8—41no—
124C2×C22⋊C8—41no—
125C2×C22⋊C8—41no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8D414yes—
132C2×C4×C8—22no—
133C2×C4×C8—22no—
134C2×C4×C8—41no—
135C2×C4×C8—41no—
136C2×C4×C8—41no—
137C2×C4×C8—41no—
138C4×C22⋊C4—41no—
139C4×C22⋊C4—41no—
140C4×C22⋊C4—41no—
141C4×C22⋊C4—41no—
142C4×C22⋊C4—41no—
143C4×C22⋊C4—41no—
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—41no—
166#336—41no—
167#336—41no—
168#336—41no—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
173#336—41no—
174C25C22×C411yescharacteristic
175C25C22×C411yescharacteristic
176C22×D4—22no—
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—22no—
181C22×D4—41no—
182C22×D4—41no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
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×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C2×D412yes—
222C23×C4#4112yes—
223C23×C4C2411yescharacteristic
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—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×C8C2×D412yes—
277C22×C8C2×D412yes—
278C22×C8#4112yes—
279C22×C8#4112yes—
280C4×D4—44no—
281C4×D4—44no—
282C4×D4—44no—
283C4×D4—44no—
284#117—44no—
285#117—44no—
286#117—44no—
287#117—44no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—41no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
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#4112yes—
356C2×C42#4112yes—
357C4⋊C8—44no—
358C4⋊C8—44no—
359C22⋊C8—44no—
360C22⋊C8—44no—
361C22⋊C8—44no—
362C22⋊C8—44no—
363C22⋊C8—44no—
364C22⋊C8—44no—
365C22⋊C8—44no—
366C22⋊C8—44no—
367C4×C8—44no—
368C4×C8—44no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—41no—
377#95—41no—
378#95—41no—
379#95—41no—
380#95—41no—
381#95—41no—
382#95—41no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
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—
411C24C4×D412yes—
412C24#13112yes—
413C24C23×C411yescharacteristic
414C2×D4—28no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
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—21no—
434C22×C4—21no—
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—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
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—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
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#11712yes—
554C22×C4#11712yes—
555C22×C4C4×D412yes—
556C22×C4#13112yes—
557C22×C4#13112yes—
558C22×C4#13112yes—
559C22×C4#13112yes—
560C22×C4#13112yes—
561C22×C4C22×D411yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C22×C4H(5,𝔽2)11yescharacteristic
573C22×C4H(5,𝔽2)11yescharacteristic
574C22×C42−1+411yescharacteristic
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
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—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
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—
734C23C2×#11711yescharacteristic
735C23C2×C4×D411yescharacteristic
736C23C4×#4111yescharacteristic
737C23#51811yescharacteristic
738C23#51811yescharacteristic
739C23#51811yescharacteristic
740C23#52011yescharacteristic
741C23C2×#13111yescharacteristic
742C23C2×#13111yescharacteristic
743C23C2×#13111yescharacteristic
744C23C2×#13111yescharacteristic
745C23C2×#13111yescharacteristic
746C23C2×#13111yescharacteristic
747C23#56811yescharacteristic
748C23#56811yescharacteristic
749D4—416no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
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—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
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—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4#43314yes—
850C2×C4#53411yescharacteristic
851C2×C4#53511yescharacteristic
852C2×C4#53811yescharacteristic
853C2×C4#53811yescharacteristic
854C2×C4#53811yescharacteristic
855C2×C4#53811yescharacteristic
856C2×C4#54011yescharacteristic
857C2×C4#54011yescharacteristic
858C2×C4#54011yescharacteristic
859C2×C4#54011yescharacteristic
860C2×C4#54211yescharacteristic
861C2×C4#54211yescharacteristic
862C2×C4#54611yescharacteristic
863C2×C4#54611yescharacteristic
864C2×C4#54611yescharacteristic
865C2×C4#54711yescharacteristic
866C2×C4#55111yescharacteristic
867C2×C4#55111yescharacteristic
868C2×C4#55111yescharacteristic
869C2×C4#55211yescharacteristic
870C2×C4#55311yescharacteristic
871C2×C4#55311yescharacteristic
872C2×C4#55911yescharacteristic
873C2×C4#55911yescharacteristic
874C2×C4#56011yescharacteristic
875C2×C4#56011yescharacteristic
876C2×C4#56211yescharacteristic
877C2×C4#56211yescharacteristic
878C8—42no—
879C8—42no—
880C8—42no—
881C8—42no—
882C8—81no—
883C8—81no—
884C8—81no—
885C8—81no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22#231911yescharacteristic
917C22#232111yescharacteristic
918C22#233311yescharacteristic
919C22#234211yescharacteristic
920C22#235711yescharacteristic
921C22#235911yescharacteristic
922C22#237711yescharacteristic
923C22C2×#43311yescharacteristic
924C22#292211yescharacteristic
925C22#292411yescharacteristic
926C22#292511yescharacteristic
927C22#292911yescharacteristic
928C22#293111yescharacteristic
929C22#293311yescharacteristic
930C22#293511yescharacteristic
931C22#296611yescharacteristic
932C22#296611yescharacteristic
933C22#296911yescharacteristic
934C22#296911yescharacteristic
935C22#297611yescharacteristic
936C22#297611yescharacteristic
937C22#297611yescharacteristic
938C22#297711yescharacteristic
939C22#297711yescharacteristic
940C22#297711yescharacteristic
941C22#297711yescharacteristic
942C22#297811yescharacteristic
943C22#297911yescharacteristic
944C22#297911yescharacteristic
945C22#297911yescharacteristic
946C22#298111yescharacteristic
947C22#299211yescharacteristic
948C22#299311yescharacteristic
949C22#299411yescharacteristic
950C22#299411yescharacteristic
951C4—24no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C4—81no—
962C4—81no—
963C4#270111yescharacteristic
964C4#270311yescharacteristic
965C4#270911yescharacteristic
966C4#271011yescharacteristic
967C4#274911yescharacteristic
968C4#275111yescharacteristic
969C4#275211yescharacteristic
970C4#276111yescharacteristic
971C2—82no—
972C2—82no—
973C2#1437611yescharacteristic
974C2#2200911yescharacteristic
975C2#2201711yescharacteristic
976C2#2202911yescharacteristic
977C2#2203911yescharacteristic
978C2#2233011yescharacteristic
979C2#2233211yescharacteristic
980C2#2255811yescharacteristic
981C2#2256011yescharacteristic
982C2#2283611yescharacteristic
983C2#2284011yescharacteristic
984C2#2290111yescharacteristic
985C2#2291511yescharacteristic
986C2#2332811yescharacteristic
987C2#2333011yescharacteristic
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
2. C2×#1818C2semidirect
4. #11255C2semidirect
5. #11147C2semidirect
6. #11147C2semidirect
7. #11042C2semidirect
8. #11042C2semidirect
10. #10921C2semidirect
11. #10921C2semidirect
12. #10876C2semidirect
13. #10876C2semidirect
14. #10797C2semidirect
15. #10713C2semidirect

Maximal subgroups

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

subgroupindex
C2×#19542
C2×#18182
#138392
#112552
#111472
#110422
#109642
#109212
#108762
#107972
#107132