Finite Group Databasebeta

← #366827

Subgroups — #366827

Order 512.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2395C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic
4C2×#1850C211yesmaximal, characteristic, complemented
5C2×#1818C211yesmaximal, characteristic, complemented
6C2×#1753C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#11346C211yesmaximal, characteristic, complemented
9#11346C211yesmaximal, characteristic, complemented
10#11042C211yesmaximal, characteristic, complemented
11#11042C211yesmaximal, characteristic, complemented
12#10922C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10835C211yesmaximal, characteristic, complemented
15#10834C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30#2395—24no—
31#2395—24no—
32C2×#400C411yescharacteristic
33C2×#399C411yescharacteristic
34C2×#398C411yescharacteristic
35C2×#397C411yescharacteristic
36C2×#397C411yescharacteristic
37C2×#397C411yescharacteristic
38C2×#394C411yescharacteristic
39C2×#394C411yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45#1870—24no—
46#1869—24no—
47#1850—24no—
48#1818—24no—
49#1753—24no—
50#1729—24no—
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C23×D4C2×C411yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C22×M16D414yes—
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—41no—
83C23×C8—41no—
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C4⋊C4C2×C411yescharacteristic
110C22×C4⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C411yescharacteristic
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C22⋊C4C2×C411yescharacteristic
118C22×C22⋊C4C2×C411yescharacteristic
119C22×C22⋊C4C2×C411yescharacteristic
120C22×C22⋊C4C2×C411yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126C2×C4⋊C8—22no—
127C2×C4⋊C8—22no—
128C2×C4⋊C8—22no—
129C2×C4⋊C8—22no—
130C2×C4⋊C8—41no—
131C2×C4⋊C8—41no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—22no—
141C2×C22⋊C8—22no—
142C2×C22⋊C8—22no—
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C2×C22⋊C8—41no—
146C2×C22⋊C8—41no—
147C2×C22⋊C8—41no—
148C2×C22⋊C8—41no—
149C2×C22⋊C8D414yes—
150C2×#97—22no—
151C2×#97—22no—
152C2×#97—41no—
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—41no—
156#400—24no—
157#399—24no—
158#398—24no—
159#397—24no—
160#397—24no—
161#397—24no—
162#394—24no—
163#394—24no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4—22no—
167C4×C4⋊C4—22no—
168C4×C22⋊C4—22no—
169C4×C22⋊C4—22no—
170C4×C22⋊C4—22no—
171C4×C22⋊C4—22no—
172C4×C22⋊C4D414yes—
173C4×C22⋊C4D414yes—
174C2×#95C2×C411yescharacteristic
175C2×#95C2×C411yescharacteristic
176C2×#95C2×C411yescharacteristic
177C2×#95C2×C411yescharacteristic
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180C2×#95C2×C411yescharacteristic
181C2×#95C2×C411yescharacteristic
182C2×#95C2×C411yescharacteristic
183C2×#95C2×C411yescharacteristic
184#336—22no—
185#336—22no—
186#336—22no—
187#336—22no—
188#336—22no—
189#336—22no—
190#336—22no—
191#336—22no—
192#336—22no—
193#336—22no—
194#336—22no—
195#336—22no—
196#336—22no—
197#336—22no—
198#336—22no—
199#336—22no—
200C25C22×C411yescharacteristic
201C25C22×C411yescharacteristic
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—41no—
208C22×D4—41no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C22×C411yescharacteristic
232C23×C4C22×C411yescharacteristic
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C411yescharacteristic
235C23×C4C22×C411yescharacteristic
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D412yes—
246C23×C4C2×D412yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4C2411yescharacteristic
250C2×M16—28no—
251C2×M16—28no—
252C2×M16—44no—
253C2×M16—44no—
254C2×M16—44no—
255C2×M16—44no—
256C2×M16—44no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—28no—
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—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—44no—
307C22×C8—44no—
308C22×C8—44no—
309C22×C8—44no—
310C22×C8—44no—
311C22×C8—44no—
312C22×C8C2×D412yes—
313C22×C8C2×D412yes—
314C22×C8C2×D412yes—
315C22×C8C2×D412yes—
316C22×C8#4112yes—
317C22×C8#4112yes—
318C22×C8#4112yes—
319C22×C8#4112yes—
320C4×D4—44no—
321C4×D4—44no—
322C4×D4—44no—
323C4×D4—44no—
324#117—44no—
325#117—44no—
326#117—44no—
327#117—44no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4C22⋊C414yes—
378C2×C22⋊C4C22⋊C414yes—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407C2×C42C2×D412yes—
408C2×C42C2×D412yes—
409C4⋊C8—44no—
410C4⋊C8—44no—
411C22⋊C8—28no—
412C22⋊C8—44no—
413C22⋊C8—44no—
414C22⋊C8—44no—
415C22⋊C8—44no—
416C22⋊C8—44no—
417#97—44no—
418C4×C8—44no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95C22⋊C414yes—
428#95C22⋊C414yes—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24C2×C22⋊C412yes—
456C24C4×D412yes—
457C24C4×D412yes—
458C24#13112yes—
459C24C23×C411yescharacteristic
460C2×D4—28no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
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—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—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
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—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4C2×C22⋊C412yes—
594C22×C4C2×C22⋊C412yes—
595C22×C4C2×C22⋊C412yes—
596C22×C4C2×C22⋊C412yes—
597C22×C4C2×C22⋊C412yes—
598C22×C4C4×D412yes—
599C22×C4C4×D412yes—
600C22×C4#12114yes—
601C22×C4#12114yes—
602C22×C4#12414yes—
603C22×C4#12714yes—
604C22×C4#13112yes—
605C22×C4#13112yes—
606C22×C4#13112yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4H(5,𝔽2)11yescharacteristic
618C22×C4H(5,𝔽2)11yescharacteristic
619C22×C42−1+411yescharacteristic
620C22×C42−1+411yescharacteristic
621M16—416no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—416no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8—41no—
674C2×C8—41no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8#12314yes—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C22⋊C4—28no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—41no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—41no—
715C42—41no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23#39014yes—
786C23C22×C22⋊C411yescharacteristic
787C23C2×C4×D411yescharacteristic
788C23C2×C4×D411yescharacteristic
789C23C4×#4111yescharacteristic
790C23C4×#4111yescharacteristic
791C23#52011yescharacteristic
792C23#52011yescharacteristic
793C23C2×#13111yescharacteristic
794C23C2×#13111yescharacteristic
795C23C2×#13111yescharacteristic
796C23C2×#13111yescharacteristic
797C23#56811yescharacteristic
798C23#56811yescharacteristic
799C23#56811yescharacteristic
800C23#56811yescharacteristic
801D4—416no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
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—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4#39014yes—
901C2×C4#40814yes—
902C2×C4C2×#12111yescharacteristic
903C2×C4C2×#12111yescharacteristic
904C2×C4C2×#12311yescharacteristic
905C2×C4#52511yescharacteristic
906C2×C4C2×#12411yescharacteristic
907C2×C4#52911yescharacteristic
908C2×C4#52911yescharacteristic
909C2×C4C2×#12711yescharacteristic
910C2×C4#53411yescharacteristic
911C2×C4#53611yescharacteristic
912C2×C4#53911yescharacteristic
913C2×C4#53911yescharacteristic
914C2×C4#54611yescharacteristic
915C2×C4#54611yescharacteristic
916C2×C4#54611yescharacteristic
917C2×C4#54611yescharacteristic
918C2×C4#54611yescharacteristic
919C2×C4#54611yescharacteristic
920C2×C4#54711yescharacteristic
921C2×C4#54711yescharacteristic
922C2×C4#54711yescharacteristic
923C2×C4#54711yescharacteristic
924C2×C4#54711yescharacteristic
925C2×C4#54711yescharacteristic
926C2×C4#55111yescharacteristic
927C2×C4#55111yescharacteristic
928C2×C4#55211yescharacteristic
929C2×C4#55211yescharacteristic
930C8—24no—
931C8—42no—
932C8—42no—
933C8—42no—
934C8—42no—
935C8—42no—
936C8—81no—
937C8—81no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22C2×#39011yescharacteristic
969C22C4×#12311yescharacteristic
970C22#232211yescharacteristic
971C22#233911yescharacteristic
972C22#233911yescharacteristic
973C22#235911yescharacteristic
974C22#235911yescharacteristic
975C22C2×#40811yescharacteristic
976C22#287911yescharacteristic
977C22#288011yescharacteristic
978C22#288011yescharacteristic
979C22#292911yescharacteristic
980C22#293011yescharacteristic
981C22#293311yescharacteristic
982C22#293311yescharacteristic
983C22#293511yescharacteristic
984C22#293511yescharacteristic
985C22#293511yescharacteristic
986C22#293511yescharacteristic
987C22#296611yescharacteristic
988C22#296611yescharacteristic
989C22#296711yescharacteristic
990C22#296711yescharacteristic
991C22#296811yescharacteristic
992C22#296811yescharacteristic
993C22#296911yescharacteristic
994C22#296911yescharacteristic
995C22#299211yescharacteristic
996C22#299211yescharacteristic
997C22#299311yescharacteristic
998C22#299311yescharacteristic
999C22#299411yescharacteristic
1000C22#299411yescharacteristic
1001C22#299511yescharacteristic
1002C22#299511yescharacteristic
1003C4—24no—
1004C4—24no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C4—81no—
1014C4—81no—
1015C4#241211yescharacteristic
1016C4#241311yescharacteristic
1017C4#242511yescharacteristic
1018C4#242511yescharacteristic
1019C4#248811yescharacteristic
1020C4#248811yescharacteristic
1021C4#250111yescharacteristic
1022C4#253911yescharacteristic
1023C2—44no—
1024C2—82no—
1025C2#1399611yescharacteristic
1026C2#2118911yescharacteristic
1027C2#2119111yescharacteristic
1028C2#2156811yescharacteristic
1029C2#2157111yescharacteristic
1030C2#2207211yescharacteristic
1031C2#2207411yescharacteristic
1032C2#2247011yescharacteristic
1033C2#2247211yescharacteristic
1034C2#2247411yescharacteristic
1035C2#2247511yescharacteristic
1036C2#2290111yescharacteristic
1037C2#2290311yescharacteristic
1038C2#2290911yescharacteristic
1039C2#2291111yescharacteristic
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
4. C2×#1850C2semidirect
5. C2×#1818C2semidirect
6. C2×#1753C2semidirect
7. C2×#1729C2semidirect
8. #11346C2semidirect
9. #11346C2semidirect
10. #11042C2semidirect
11. #11042C2semidirect
12. #10922C2semidirect
13. #10921C2semidirect
14. #10835C2semidirect
15. #10834C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23952
C2×#18702
C2×#18692
C2×#18502
C2×#18182
C2×#17532
C2×#17292
#113462
#110422
#109222
#109212
#108352
#108342