Finite Group Databasebeta

← #365330

Subgroups — #365330

Order 512.

1414 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1940C211yesmaximal, characteristic, complemented
2C2×#1924C211yesmaximal, characteristic
3C2×#1923C211yesmaximal, characteristic
4C2×#1797C211yesmaximal, characteristic
5C2×#1771C211yesmaximal, characteristic, complemented
6C2×#1749C211yesmaximal, characteristic
7C4×#380C211yesmaximal, characteristic
8#11298C211yesmaximal, characteristic, complemented
9#11298C211yesmaximal, characteristic, complemented
10#11147C211yesmaximal, characteristic
11#11147C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10835C211yesmaximal, characteristic, complemented
15#10835C211yesmaximal, characteristic, complemented
16C23×C42C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#380C411yescharacteristic
30C2×#380C411yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35#1940—24no—
36#1924—24no—
37#1923—24no—
38#1797—24no—
39#1771—24no—
40#1749—24no—
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
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C4⋊#95C411yescharacteristic
58C4⋊#95C411yescharacteristic
59#1434C411yescharacteristic
60#1434C411yescharacteristic
61C22⋊#95C411yescharacteristic
62C22⋊#95C411yescharacteristic
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C22⋊C4C2×C411yescharacteristic
82C22×C22⋊C4C2×C411yescharacteristic
83C22×C22⋊C4C2×C411yescharacteristic
84C22×C42—22no—
85C22×C42—22no—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42C2×C411yescharacteristic
91C22×C42C2×C411yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8D414yes—
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—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8D414yes—
122C2×#97—22no—
123C2×#97—22no—
124C2×#97—22no—
125C2×#97—22no—
126C2×#97—22no—
127C2×#97—22no—
128C2×#97—22no—
129C2×#97—41no—
130C2×#97D414yes—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—41no—
134#380—24no—
135#380—24no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C22⋊C4—22no—
141C4×C22⋊C4—22no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—22no—
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
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
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—
176C25C22×C411yescharacteristic
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
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—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—41no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4—41no—
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C2×D412yes—
217C23×C4#4112yes—
218C23×C4C2411yescharacteristic
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—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×C8C2×D412yes—
268C22×C8C2×D412yes—
269C22×C8C2×D412yes—
270C22×C8C2×D412yes—
271C22×C8C2×D412yes—
272C22×C8C2×D412yes—
273C22×C8#4112yes—
274C22×C8#4112yes—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—41no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4M1614yes—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—22no—
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—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
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—44no—
336C2×C42—44no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42C2×D412yes—
340C2×C42C2×D412yes—
341C2×C42#4112yes—
342C2×C42#4112yes—
343C2×C42#4112yes—
344C2×C42#4112yes—
345C4⋊C8—28no—
346C4⋊C8—44no—
347C4⋊C8—44no—
348C4⋊C8—44no—
349C22⋊C8—28no—
350C22⋊C8—28no—
351C22⋊C8—44no—
352C22⋊C8—44no—
353#97—28no—
354#97—44no—
355#97—44no—
356C4×C8—44no—
357#95—22no—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—41no—
371#95—41no—
372#95M1614yes—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24C4×D412yes—
386C24C2×M1612yes—
387C24#13112yes—
388C24C23×C411yescharacteristic
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—28no—
398C22×C4—28no—
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—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
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—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—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4#11712yes—
510C22×C4#11712yes—
511C22×C4C4×D412yes—
512C22×C4C4×D412yes—
513C22×C4C4×D412yes—
514C22×C4C4×D412yes—
515C22×C4C4×D412yes—
516C22×C4C2×M1612yes—
517C22×C4C2×M1612yes—
518C22×C4C2×M1612yes—
519C22×C4C2×M1612yes—
520C22×C4C2×M1612yes—
521C22×C4#13112yes—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4H(5,𝔽2)11yescharacteristic
533C22×C42−1+411yescharacteristic
534C22×C42−1+411yescharacteristic
535C22×C42−1+411yescharacteristic
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8#12114yes—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C22⋊C4—28no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—44no—
621C42—44no—
622C42#12114yes—
623C42#12314yes—
624C42#12414yes—
625C42#12614yes—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23#43514yes—
661C23C2×#11711yescharacteristic
662C23C2×C4×D411yescharacteristic
663C23C2×C4×D411yescharacteristic
664C23C2×C4×D411yescharacteristic
665C23C4×#4111yescharacteristic
666C23#51911yescharacteristic
667C23#52011yescharacteristic
668C23C22×M1611yescharacteristic
669C23C22×M1611yescharacteristic
670C23C2×#13111yescharacteristic
671C23C2×#13111yescharacteristic
672C23#56811yescharacteristic
673C23#56811yescharacteristic
674C23#56811yescharacteristic
675C23#56811yescharacteristic
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—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—416no—
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—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—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4#38814yes—
776C2×C4#38814yes—
777C2×C4C2×#12111yescharacteristic
778C2×C4C2×#12111yescharacteristic
779C2×C4C2×#12311yescharacteristic
780C2×C4#52511yescharacteristic
781C2×C4C2×#12411yescharacteristic
782C2×C4C2×#12611yescharacteristic
783C2×C4#52911yescharacteristic
784C2×C4#53211yescharacteristic
785C2×C4#53611yescharacteristic
786C2×C4#53711yescharacteristic
787C2×C4#54111yescharacteristic
788C2×C4#54211yescharacteristic
789C2×C4D4211yescharacteristic
790C2×C4#54711yescharacteristic
791C2×C4#54711yescharacteristic
792C2×C4#54711yescharacteristic
793C2×C4#54711yescharacteristic
794C2×C4#54811yescharacteristic
795C2×C4#54811yescharacteristic
796C2×C4#55211yescharacteristic
797C2×C4#55211yescharacteristic
798C2×C4#55211yescharacteristic
799C2×C4#55311yescharacteristic
800C2×C4#55311yescharacteristic
801C2×C4#55311yescharacteristic
802C2×C4#55611yescharacteristic
803C2×C4#55611yescharacteristic
804C2×C4#55611yescharacteristic
805C8—24no—
806C8—42no—
807C8—42no—
808C8—42no—
809C8—42no—
810C8—42no—
811C8—81no—
812C8—81no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22C2×#38811yescharacteristic
829C22C4×#12111yescharacteristic
830C22#232311yescharacteristic
831C22#234411yescharacteristic
832C22#234711yescharacteristic
833C22#236111yescharacteristic
834C22#236211yescharacteristic
835C22#292011yescharacteristic
836C22#292111yescharacteristic
837C22#292411yescharacteristic
838C22#292411yescharacteristic
839C22C2×#43511yescharacteristic
840C22#292911yescharacteristic
841C22#293011yescharacteristic
842C22#293211yescharacteristic
843C22#293311yescharacteristic
844C22#293311yescharacteristic
845C22D4×M1611yescharacteristic
846C22D4×M1611yescharacteristic
847C22D4×M1611yescharacteristic
848C22D4×M1611yescharacteristic
849C22D4×M1611yescharacteristic
850C22#293511yescharacteristic
851C22#296511yescharacteristic
852C22#296711yescharacteristic
853C22#296811yescharacteristic
854C22#297011yescharacteristic
855C22#298311yescharacteristic
856C22#298411yescharacteristic
857C22#298511yescharacteristic
858C22#298711yescharacteristic
859C22#298911yescharacteristic
860C22#299011yescharacteristic
861C22#299211yescharacteristic
862C22#299511yescharacteristic
863C4—24no—
864C4—24no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4#241511yescharacteristic
877C4#241611yescharacteristic
878C4#242111yescharacteristic
879C4#242211yescharacteristic
880C4#249411yescharacteristic
881C4#249611yescharacteristic
882C4#254711yescharacteristic
883C4#256211yescharacteristic
884C2—44no—
885C2#1397411yescharacteristic
886C2#2104911yescharacteristic
887C2#2105011yescharacteristic
888C2#2148911yescharacteristic
889C2#2149011yescharacteristic
890C2#2210611yescharacteristic
891C2#2210811yescharacteristic
892C2#2260111yescharacteristic
893C2#2260211yescharacteristic
894C2#2264111yescharacteristic
895C2#2264211yescharacteristic
896C2#2298711yescharacteristic
897C2#2298811yescharacteristic
898C2#2305211yescharacteristic
899C2#2305311yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC25C22×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×#1940C2semidirect
5. C2×#1771C2semidirect
8. #11298C2semidirect
9. #11298C2semidirect
12. #10877C2semidirect
13. #10876C2semidirect
14. #10835C2semidirect
15. #10835C2semidirect

Maximal subgroups

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

subgroupindex
C2×#19402
C2×#19242
C2×#19232
C2×#17972
C2×#17712
C2×#17492
C4×#3802
#112982
#111472
#108772
#108762
#108352