Finite Group Databasebeta

← C2×#16159 #610259

Subgroups — C2×#16159 #610259

Order 512.

3550 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16159C2116yesmaximal, direct product factor
2C2×#1443C211yesmaximal, characteristic, complemented
3C2×#1442C211yesmaximal, characteristic, complemented
4C2×#1442C211yesmaximal, characteristic, complemented
5C2×#1441C211yesmaximal, characteristic, complemented
6C2×#1440C211yesmaximal, characteristic
7C2×#1440C211yesmaximal, characteristic
8C2×#1440C211yesmaximal, characteristic
9C2×#1439C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic
12C2×#1437C211yesmaximal, characteristic
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×#1434C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
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
52#1443C2218yescomplemented
53#1442C2218yescomplemented
54#1442C2218yescomplemented
55#1441C2218yescomplemented
56#1440C2218yes—
57#1440C2218yes—
58#1440C2218yes—
59#1439C2218yes—
60#1439C2218yes—
61#1437C2218yes—
62#1437C2218yes—
63#1434C2218yescomplemented
64#1434C2218yescomplemented
65#1434C2218yescomplemented
66#1434C2218yescomplemented
67C26C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C22×C4⋊C4—24no—
83C22×C4⋊C4—42no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4—42no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4—42no—
88C22×C4⋊C4C2314yes—
89C22×C4⋊C4C2314yes—
90C22×C22⋊C4—24no—
91C22×C22⋊C4—24no—
92C22×C22⋊C4—24no—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—24no—
95C22×C22⋊C4—24no—
96C22×C22⋊C4—24no—
97C22×C22⋊C4—24no—
98C22×C22⋊C4—24no—
99C22×C22⋊C4—24no—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—42no—
102C22×C22⋊C4—42no—
103C22×C22⋊C4—42no—
104C22×C22⋊C4—42no—
105C22×C22⋊C4—42no—
106C22×C22⋊C4—42no—
107C22×C22⋊C4—42no—
108C22×C22⋊C4—42no—
109C22×C22⋊C4—42no—
110C22×C22⋊C4—42no—
111C22×C22⋊C4C2314yes—
112C22×C22⋊C4C2314yes—
113C22×C22⋊C4C2314yes—
114C22×C22⋊C4C2314yes—
115C22×C22⋊C4C2314yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2314yes—
118C22×C42—24no—
119C22×C42—24no—
120C22×C42—24no—
121C22×C42—24no—
122C22×C42—42no—
123C22×C42—42no—
124C22×C42C2314yes—
125C22×C42C2314yes—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95—42no—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
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—
174C25—22no—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25—22no—
180C25—22no—
181C25—22no—
182C25—22no—
183C25—22no—
184C25—22no—
185C25—22no—
186C25—22no—
187C25—22no—
188C25#4114yes—
189C25C2412yes—
190C25C2411yescharacteristic
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
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#4114yes—
282C23×C4#4114yes—
283C23×C4#4114yes—
284C23×C4#4114yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—416no—
310C2×C4⋊C4—416no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—416no—
333C2×C22⋊C4—416no—
334C2×C22⋊C4—416no—
335C2×C22⋊C4—416no—
336C2×C22⋊C4—416no—
337C2×C22⋊C4—416no—
338C2×C22⋊C4—416no—
339C2×C42—28no—
340C2×C42—28no—
341C2×C42—28no—
342C2×C42—28no—
343C2×C42—44no—
344C2×C42—44no—
345C2×C42—416no—
346C2×C42—416no—
347#95—28no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—28no—
352#95—28no—
353#95—28no—
354#95—28no—
355#95—28no—
356#95—28no—
357#95—28no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371C24—28no—
372C24—28no—
373C24—28no—
374C24—28no—
375C24—28no—
376C24—28no—
377C24—28no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—44no—
393C24—44no—
394C24—44no—
395C24—44no—
396C24—44no—
397C24—44no—
398C24—44no—
399C24—44no—
400C24—44no—
401C24—44no—
402C24—44no—
403C24—44no—
404C24—44no—
405C24—44no—
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—
420C24C2×#4114yes—
421C24C2×#4112yes—
422C24C2×#4112yes—
423C24C2×#4112yes—
424C24C2×#4112yes—
425C24C2×#4112yes—
426C24C2×#4112yes—
427C24C2×#4112yes—
428C24C2×#4112yes—
429C24C2×#4112yes—
430C24H(5,𝔽2)12yes—
431C24H(5,𝔽2)12yes—
432C24H(5,𝔽2)12yes—
433C24H(5,𝔽2)12yes—
434C24H(5,𝔽2)12yes—
435C242−1+412yes—
436C24C2511yescharacteristic
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
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—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
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—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—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
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×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4114yes—
633C4⋊C4—416no—
634C4⋊C4—416no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—416no—
638C22⋊C4—416no—
639C22⋊C4—416no—
640C22⋊C4—416no—
641C22⋊C4—416no—
642C42—416no—
643C42—416no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—416no—
652C23—416no—
653C23—416no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—416no—
681C23—416no—
682C23—42no—
683C23—42no—
684C23—416no—
685C23—416no—
686C23—88no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—88no—
691C23—88no—
692C23—88no—
693C23—88no—
694C23#52914yes—
695C23#52914yes—
696C23#52914yes—
697C23#52914yes—
698C23#52914yes—
699C23#52914yes—
700C23#53814yes—
701C23#53814yes—
702C23#53914yes—
703C23#53914yes—
704C23#53914yes—
705C23#54014yes—
706C23#54014yes—
707C23#54014yes—
708C23#54014yes—
709C23#55114yes—
710C23#55114yes—
711C23#55114yes—
712C23#55114yes—
713C23#55114yes—
714C23#55114yes—
715C23#55114yes—
716C23#55214yes—
717C23#55314yes—
718C23#55314yes—
719C23#55314yes—
720C23#55314yes—
721C23#55314yes—
722C23#55514yes—
723C23#55514yes—
724C23#55514yes—
725C23#55614yes—
726C23#55614yes—
727C23H(3,𝔽4)14yes—
728C23#56214yes—
729C23C22×#4111yescharacteristic
730C23C22×#4111yescharacteristic
731C23C22×#4111yescharacteristic
732C23C22×#4111yescharacteristic
733C23C22×#4111yescharacteristic
734C23C22×#4111yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4111yescharacteristic
737C23C22×#4111yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)11yescharacteristic
742C23C2×H(5,𝔽2)11yescharacteristic
743C23C2×2−1+411yescharacteristic
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
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—416no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—416no—
798C2×C4—416no—
799C2×C4—416no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—416no—
805C2×C4—416no—
806C2×C4—416no—
807C2×C4—416no—
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—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
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—88no—
851C2×C4—88no—
852C2×C4—88no—
853C2×C4—88no—
854C2×C4—88no—
855C2×C4—88no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—82no—
864C22—82no—
865C22—832no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22#251818yes—
873C22#252618yes—
874C22#253118yes—
875C22#253118yes—
876C22#253118yes—
877C22#257218yes—
878C22#257318yes—
879C22#257718yes—
880C22#259418yes—
881C22#274018yes—
882C22#274318yes—
883C22#275318yes—
884C22#275318yes—
885C22#278518yes—
886C22#278618yes—
887C22C2×#52911yescharacteristic
888C22C2×#52911yescharacteristic
889C22C2×#52911yescharacteristic
890C22C2×#52911yescharacteristic
891C22C2×#52911yescharacteristic
892C22C2×#52911yescharacteristic
893C22C2×#53811yescharacteristic
894C22C2×#53811yescharacteristic
895C22C2×#53911yescharacteristic
896C22C2×#53911yescharacteristic
897C22C2×#53911yescharacteristic
898C22C2×#54011yescharacteristic
899C22C2×#54011yescharacteristic
900C22C2×#54011yescharacteristic
901C22C2×#54011yescharacteristic
902C22C2×#55111yescharacteristic
903C22C2×#55111yescharacteristic
904C22C2×#55111yescharacteristic
905C22C2×#55111yescharacteristic
906C22C2×#55111yescharacteristic
907C22C2×#55111yescharacteristic
908C22C2×#55111yescharacteristic
909C22C2×#55211yescharacteristic
910C22C2×#55311yescharacteristic
911C22C2×#55311yescharacteristic
912C22C2×#55311yescharacteristic
913C22C2×#55311yescharacteristic
914C22C2×#55311yescharacteristic
915C22C2×#55511yescharacteristic
916C22C2×#55511yescharacteristic
917C22C2×#55511yescharacteristic
918C22C2×#55611yescharacteristic
919C22C2×#55611yescharacteristic
920C22C2×H(3,𝔽4)11yescharacteristic
921C22C2×#56211yescharacteristic
922C4—44no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4—44no—
929C4—44no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C2—84no—
937C2#16159116yesdirect product factor
938C2C2×#251811yescharacteristic
939C2C2×#253111yescharacteristic
940C2C2×#253111yescharacteristic
941C2C2×#253111yescharacteristic
942C2C2×#252611yescharacteristic
943C2C2×#257211yescharacteristic
944C2C2×#257311yescharacteristic
945C2C2×#257711yescharacteristic
946C2C2×#259411yescharacteristic
947C2C2×#274011yescharacteristic
948C2C2×#274311yescharacteristic
949C2C2×#275311yescharacteristic
950C2C2×#275311yescharacteristic
951C2C2×#278511yescharacteristic
952C2C2×#278611yescharacteristic
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
1. #16159C2direct (N × H)
2. C2×#1443C2semidirect
3. C2×#1442C2semidirect
4. C2×#1442C2semidirect
5. C2×#1441C2semidirect
13. C2×#1434C2semidirect
14. C2×#1434C2semidirect
15. C2×#1434C2semidirect
16. C2×#1434C2semidirect
52. #1443C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1441C22semidirect
63. #1434C22semidirect
64. #1434C22semidirect
65. #1434C22semidirect
66. #1434C22semidirect
937. C2#16159direct (N × H)

Maximal subgroups

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

subgroupindex
#161592
C2×#14432
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14372
C2×#14342