Finite Group Databasebeta

← C2×#15757 #609405

Subgroups — C2×#15757 #609405

Order 512.

3886 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3#15757C2116yesmaximal, direct product factor
4C2×#1445C211yesmaximal, characteristic, complemented
5C2×#1442C211yesmaximal, characteristic, complemented
6C2×#1441C211yesmaximal, characteristic, complemented
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic
9C2×#1440C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1439C211yesmaximal, characteristic
12C2×#1437C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#397—28no—
31C2×#397C2218yes—
32C2×#388—28no—
33C2×#388C2218yes—
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1445C2218yescomplemented
57#1442C2218yescomplemented
58#1441C2218yescomplemented
59#1441C2218yescomplemented
60#1440C2218yes—
61#1440C2218yes—
62#1439C2218yes—
63#1439C2218yes—
64#1437C2218yes—
65#1436C2218yescomplemented
66#1436C2218yescomplemented
67#1434C2218yescomplemented
68#1434C2218yescomplemented
69C26C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C22×C4⋊C4—24no—
85C22×C4⋊C4—24no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—42no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4—42no—
94C22×C4⋊C4—42no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4C2314yes—
97C22×C4⋊C4C2314yes—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2314yes—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—42no—
113C22×C22⋊C4—42no—
114C22×C22⋊C4—42no—
115C22×C22⋊C4—42no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4—42no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4D418yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C42—24no—
129C22×C42—24no—
130C22×C42—24no—
131C22×C42—42no—
132C22×C42—42no—
133C22×C42—42no—
134C22×C42C2314yes—
135C22×C42C2314yes—
136#397—232no—
137#388—232no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C25—22no—
183C25—22no—
184C25—22no—
185C25—22no—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25C2×D414yes—
197C25C2412yes—
198C25C2411yescharacteristic
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4#4114yes—
290C23×C4#4114yes—
291C23×C4#4114yes—
292C23×C4#4114yes—
293C23×C4#4114yes—
294C23×C4#4114yes—
295C23×C4#4114yes—
296C23×C4#4114yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—416no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—416no—
326C2×C4⋊C4—416no—
327C2×C22⋊C4—232no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—416no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—416no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—416no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—416no—
354C2×C22⋊C4C2×D4116yes—
355C2×C42—28no—
356C2×C42—28no—
357C2×C42—28no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42—44no—
361C2×C42—416no—
362C2×C42—416no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385C24—28no—
386C24—28no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—28no—
391C24—28no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—44no—
407C24—44no—
408C24—44no—
409C24—44no—
410C24—44no—
411C24—44no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—44no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24C22×D414yes—
435C24C22×D412yes—
436C24C2×#4112yes—
437C24C2×#4112yes—
438C24C2×#4112yes—
439C24C2×#4112yes—
440C24C2×#4112yes—
441C24C2×#4112yes—
442C24C2×#4112yes—
443C24C2×#4112yes—
444C24H(5,𝔽2)12yes—
445C24H(5,𝔽2)12yes—
446C24H(5,𝔽2)12yes—
447C24H(5,𝔽2)12yes—
448C242−1+412yes—
449C242−1+412yes—
450C24C2511yescharacteristic
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
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—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4114yes—
646C22×C4C2×#4114yes—
647C4⋊C4—416no—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C4⋊C4—416no—
651C22⋊C4—232no—
652C22⋊C4—416no—
653C22⋊C4—416no—
654C22⋊C4—416no—
655C22⋊C4—416no—
656C22⋊C4—416no—
657C22⋊C4—416no—
658C42—416no—
659C42—416no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—416no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—416no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—416no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—416no—
697C23—416no—
698C23—42no—
699C23—42no—
700C23—416no—
701C23—416no—
702C23—88no—
703C23—88no—
704C23—88no—
705C23—88no—
706C23—88no—
707C23—88no—
708C23—88no—
709C23—88no—
710C23#52514yes—
711C23#52914yes—
712C23#52914yes—
713C23#52914yes—
714C23#52914yes—
715C23#53214yes—
716C23#53414yes—
717C23#53814yes—
718C23#53914yes—
719C23#54014yes—
720C23#54014yes—
721C23#54114yes—
722C23#54214yes—
723C23#54214yes—
724C23#54214yes—
725C23#54614yes—
726C23#54614yes—
727C23#54714yes—
728C23#54714yes—
729C23#55114yes—
730C23#55114yes—
731C23#55114yes—
732C23#55114yes—
733C23#55214yes—
734C23#55214yes—
735C23#55314yes—
736C23#55314yes—
737C23#55314yes—
738C23#55314yes—
739C23#55514yes—
740C23#55614yes—
741C23#55614yes—
742C23#55914yes—
743C23#56214yes—
744C23#56214yes—
745C23C23×D411yescharacteristic
746C23C22×#4111yescharacteristic
747C23C22×#4111yescharacteristic
748C23C22×#4111yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4111yescharacteristic
751C23C22×#4111yescharacteristic
752C23C22×#4111yescharacteristic
753C23C22×#4111yescharacteristic
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×H(5,𝔽2)11yescharacteristic
756C23C2×H(5,𝔽2)11yescharacteristic
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×2−1+411yescharacteristic
759C23C2×2−1+411yescharacteristic
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—416no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—416no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—416no—
838C2×C4—416no—
839C2×C4—416no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—88no—
869C2×C4—88no—
870C2×C4—88no—
871C2×C4—88no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—82no—
880C22—82no—
881C22—832no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22#245718yes—
889C22#247818yes—
890C22#252118yes—
891C22#252518yes—
892C22#253118yes—
893C22#253218yes—
894C22#255318yes—
895C22#259518yes—
896C22#260218yes—
897C22#268618yes—
898C22#270118yes—
899C22#274018yes—
900C22#276118yes—
901C22#277218yes—
902C22#279818yes—
903C22C2×#52511yescharacteristic
904C22C2×#52911yescharacteristic
905C22C2×#52911yescharacteristic
906C22C2×#52911yescharacteristic
907C22C2×#52911yescharacteristic
908C22C2×#53211yescharacteristic
909C22C2×#53411yescharacteristic
910C22C2×#53811yescharacteristic
911C22C2×#53911yescharacteristic
912C22C2×#54011yescharacteristic
913C22C2×#54011yescharacteristic
914C22C2×#54111yescharacteristic
915C22C2×#54211yescharacteristic
916C22C2×#54211yescharacteristic
917C22C2×#54211yescharacteristic
918C22C2×#54611yescharacteristic
919C22C2×#54611yescharacteristic
920C22C2×#54711yescharacteristic
921C22C2×#54711yescharacteristic
922C22C2×#55111yescharacteristic
923C22C2×#55111yescharacteristic
924C22C2×#55111yescharacteristic
925C22C2×#55111yescharacteristic
926C22C2×#55211yescharacteristic
927C22C2×#55211yescharacteristic
928C22C2×#55311yescharacteristic
929C22C2×#55311yescharacteristic
930C22C2×#55311yescharacteristic
931C22C2×#55311yescharacteristic
932C22C2×#55511yescharacteristic
933C22C2×#55611yescharacteristic
934C22C2×#55611yescharacteristic
935C22C2×#55911yescharacteristic
936C22C2×#56211yescharacteristic
937C22C2×#56211yescharacteristic
938C4—44no—
939C4—44no—
940C4—44no—
941C4—44no—
942C4—44no—
943C4—44no—
944C4—44no—
945C4—44no—
946C4—44no—
947C4—44no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C2—84no—
953C2#15757116yesdirect product factor
954C2C2×#245711yescharacteristic
955C2C2×#247811yescharacteristic
956C2C2×#252111yescharacteristic
957C2C2×#252511yescharacteristic
958C2C2×#253111yescharacteristic
959C2C2×#253211yescharacteristic
960C2C2×#255311yescharacteristic
961C2C2×#259511yescharacteristic
962C2C2×#260211yescharacteristic
963C2C2×#268611yescharacteristic
964C2C2×#270111yescharacteristic
965C2C2×#274011yescharacteristic
966C2C2×#276111yescharacteristic
967C2C2×#277211yescharacteristic
968C2C2×#279811yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #15757C2direct (N × H)
4. C2×#1445C2semidirect
5. C2×#1442C2semidirect
6. C2×#1441C2semidirect
7. C2×#1441C2semidirect
13. C2×#1436C2semidirect
14. C2×#1436C2semidirect
15. C2×#1434C2semidirect
16. C2×#1434C2semidirect
56. #1445C22semidirect
57. #1442C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
65. #1436C22semidirect
66. #1436C22semidirect
67. #1434C22semidirect
68. #1434C22semidirect
953. C2#15757direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3972
C22×#3882
#157572
C2×#14452
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×#14342