Finite Group Databasebeta

← C2×#15756 #609404

Subgroups — C2×#15756 #609404

Order 512.

4930 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#394C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic, complemented
3#15756C2116yesmaximal, direct product factor
4C2×#1442C211yesmaximal, characteristic, complemented
5C2×#1442C211yesmaximal, characteristic, complemented
6C2×#1440C211yesmaximal, characteristic, complemented
7C2×#1440C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1438C211yesmaximal, characteristic
11C2×#1438C211yesmaximal, characteristic
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#394—28no—
35C2×#394C2218yes—
36C2×#388—28no—
37C2×#388C2218yescomplemented
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#1442C2218yescomplemented
57#1442C2218yescomplemented
58#1440C2218yescomplemented
59#1440C2218yescomplemented
60#1440C2218yescomplemented
61#1439C2218yescomplemented
62#1438C2218yes—
63#1438C2218yes—
64#1437C2218yescomplemented
65#1437C2218yescomplemented
66#1437C2218yescomplemented
67#1436C2218yescomplemented
68#1434C2218yescomplemented
69C26C2311yescharacteristic
70C26C2311yescharacteristic
71C23×D4—24no—
72C23×D4—24no—
73C23×D4—24no—
74C23×D4—42no—
75C23×D4—42no—
76C23×D4—42no—
77C23×D4—42no—
78C23×D4C2314yes—
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
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—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4—42no—
127C22×C22⋊C4—42no—
128C22×C22⋊C4—42no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4D418yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42—42no—
151C22×C42—42no—
152C22×C42—42no—
153C22×C42—42no—
154C22×C42C2314yes—
155C22×C42C2314yes—
156#394—232no—
157#388—232no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25C2×D414yes—
223C25#4114yes—
224C25C2412yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—28no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—416no—
235C22×D4—416no—
236C22×D4—416no—
237C22×D4—416no—
238C22×D4—416no—
239C22×D4—416no—
240C22×D4—416no—
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×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4C2×D414yes—
324C23×C4C2×D414yes—
325C23×C4#4114yes—
326C23×C4#4114yes—
327C23×C4#4114yes—
328C23×C4#4114yes—
329C23×C4#4114yes—
330C23×C4#4114yes—
331C23×C4#4114yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—416no—
352C2×C4⋊C4—416no—
353C2×C22⋊C4—232no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—416no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—416no—
391C2×C22⋊C4—416no—
392C2×C22⋊C4—416no—
393C2×C22⋊C4—416no—
394C2×C22⋊C4—416no—
395C2×C22⋊C4—416no—
396C2×C22⋊C4—416no—
397C2×C22⋊C4—416no—
398C2×C22⋊C4—416no—
399C2×C22⋊C4—416no—
400C2×C22⋊C4C2×D4116yes—
401C2×C42—28no—
402C2×C42—28no—
403C2×C42—44no—
404C2×C42—44no—
405C2×C42—44no—
406C2×C42—44no—
407C2×C42—416no—
408C2×C42—416no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24C22×D414yes—
526C24C22×D412yes—
527C24C2×#4114yes—
528C24C2×#4112yes—
529C24C2×#4112yes—
530C24C2×#4112yes—
531C24C2×#4112yes—
532C24C2×#4112yes—
533C24C2×#4112yes—
534C24C2×#4112yes—
535C24C2×#4112yes—
536C24H(5,𝔽2)12yes—
537C24H(5,𝔽2)12yes—
538C24H(5,𝔽2)12yes—
539C24H(5,𝔽2)12yes—
540C24H(5,𝔽2)12yes—
541C24H(5,𝔽2)12yes—
542C24C2511yescharacteristic
543C2×D4—416no—
544C2×D4—416no—
545C2×D4—416no—
546C2×D4—416no—
547C2×D4—416no—
548C2×D4—416no—
549C2×D4—4128no—
550C2×D4—416no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
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—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4C22×D414yes—
725C22×C4C22×D414yes—
726C22×C4C2×#4114yes—
727C22×C4C2×#4114yes—
728C22×C4C2×#4114yes—
729C22×C4C2×#4114yes—
730C22×C4C2×#4114yes—
731C22×C4C2×#4114yes—
732C22×C4C2×#4114yes—
733C4⋊C4—416no—
734C4⋊C4—416no—
735C22⋊C4—232no—
736C22⋊C4—416no—
737C22⋊C4—416no—
738C22⋊C4—416no—
739C22⋊C4—416no—
740C22⋊C4—416no—
741C22⋊C4—416no—
742C22⋊C4—416no—
743C22⋊C4—416no—
744C22⋊C4—416no—
745C22⋊C4—416no—
746C22⋊C4—416no—
747C42—416no—
748C42—416no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—416no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—416no—
781C23—416no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—416no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—416no—
820C23—416no—
821C23—416no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—416no—
827C23—416no—
828C23—416no—
829C23—416no—
830C23—416no—
831C23—416no—
832C23—416no—
833C23—88no—
834C23—88no—
835C23—88no—
836C23—88no—
837C23—88no—
838C23—88no—
839C23—88no—
840C23—88no—
841C23—88no—
842C23—88no—
843C23—88no—
844C23—88no—
845C23—88no—
846C23—88no—
847C23—88no—
848C23—88no—
849C23#52514yes—
850C23#52914yes—
851C23#52914yes—
852C23#52914yes—
853C23#52914yes—
854C23#53214yes—
855C23#53414yes—
856C23#53814yes—
857C23#53814yes—
858C23#53814yes—
859C23#53814yes—
860C23#54014yes—
861C23#54014yes—
862C23#54014yes—
863C23#54014yes—
864C23#54614yes—
865C23#54614yes—
866C23#54614yes—
867C23#54614yes—
868C23#55114yes—
869C23#55114yes—
870C23#55114yes—
871C23#55114yes—
872C23#55314yes—
873C23#55314yes—
874C23#55314yes—
875C23#55314yes—
876C23#55314yes—
877C23#55314yes—
878C23#55514yes—
879C23#55514yes—
880C23#55914yes—
881C23#55914yes—
882C23#56014yes—
883C23H(3,𝔽4)14yes—
884C23C23×D411yescharacteristic
885C23C22×#4111yescharacteristic
886C23C22×#4111yescharacteristic
887C23C22×#4111yescharacteristic
888C23C22×#4111yescharacteristic
889C23C22×#4111yescharacteristic
890C23C22×#4111yescharacteristic
891C23C22×#4111yescharacteristic
892C23C22×#4111yescharacteristic
893C23C2×H(5,𝔽2)11yescharacteristic
894C23C2×H(5,𝔽2)11yescharacteristic
895C23C2×H(5,𝔽2)11yescharacteristic
896C23C2×H(5,𝔽2)11yescharacteristic
897C23C2×H(5,𝔽2)11yescharacteristic
898C23C2×H(5,𝔽2)11yescharacteristic
899D4—464no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—416no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—416no—
939C2×C4—416no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—416no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—416no—
963C2×C4—416no—
964C2×C4—416no—
965C2×C4—416no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—416no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—88no—
1001C2×C4—88no—
1002C2×C4—88no—
1003C2×C4—88no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—82no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—82no—
1023C22—82no—
1024C22—82no—
1025C22—832no—
1026C22—832no—
1027C22—82no—
1028C22—82no—
1029C22—82no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22—82no—
1035C22—82no—
1036C22#245718yes—
1037C22#247618yes—
1038C22#251618yes—
1039C22#251818yes—
1040C22#253118yes—
1041C22#255718yes—
1042C22#255918yes—
1043C22#259318yes—
1044C22#260218yes—
1045C22#268418yes—
1046C22#269918yes—
1047C22#275318yes—
1048C22#275318yes—
1049C22#279718yes—
1050C22#280318yes—
1051C22C2×#52511yescharacteristic
1052C22C2×#52911yescharacteristic
1053C22C2×#52911yescharacteristic
1054C22C2×#52911yescharacteristic
1055C22C2×#52911yescharacteristic
1056C22C2×#53211yescharacteristic
1057C22C2×#53411yescharacteristic
1058C22C2×#53811yescharacteristic
1059C22C2×#53811yescharacteristic
1060C22C2×#53811yescharacteristic
1061C22C2×#53811yescharacteristic
1062C22C2×#54011yescharacteristic
1063C22C2×#54011yescharacteristic
1064C22C2×#54011yescharacteristic
1065C22C2×#54011yescharacteristic
1066C22C2×#54611yescharacteristic
1067C22C2×#54611yescharacteristic
1068C22C2×#54611yescharacteristic
1069C22C2×#54611yescharacteristic
1070C22C2×#55111yescharacteristic
1071C22C2×#55111yescharacteristic
1072C22C2×#55111yescharacteristic
1073C22C2×#55111yescharacteristic
1074C22C2×#55311yescharacteristic
1075C22C2×#55311yescharacteristic
1076C22C2×#55311yescharacteristic
1077C22C2×#55311yescharacteristic
1078C22C2×#55311yescharacteristic
1079C22C2×#55311yescharacteristic
1080C22C2×#55511yescharacteristic
1081C22C2×#55511yescharacteristic
1082C22C2×#55911yescharacteristic
1083C22C2×#55911yescharacteristic
1084C22C2×#56011yescharacteristic
1085C22C2×H(3,𝔽4)11yescharacteristic
1086C4—44no—
1087C4—44no—
1088C4—44no—
1089C4—44no—
1090C4—44no—
1091C4—44no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—82no—
1096C4—82no—
1097C4—82no—
1098C4—82no—
1099C2—84no—
1100C2—84no—
1101C2#15756116yesdirect product factor
1102C2C2×#245711yescharacteristic
1103C2C2×#247611yescharacteristic
1104C2C2×#251811yescharacteristic
1105C2C2×#251611yescharacteristic
1106C2C2×#253111yescharacteristic
1107C2C2×#255711yescharacteristic
1108C2C2×#255911yescharacteristic
1109C2C2×#259311yescharacteristic
1110C2C2×#260211yescharacteristic
1111C2C2×#268411yescharacteristic
1112C2C2×#269911yescharacteristic
1113C2C2×#275311yescharacteristic
1114C2C2×#275311yescharacteristic
1115C2C2×#279711yescharacteristic
1116C2C2×#280311yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#388C2semidirect
3. #15756C2direct (N × H)
4. C2×#1442C2semidirect
5. C2×#1442C2semidirect
6. C2×#1440C2semidirect
7. C2×#1440C2semidirect
8. C2×#1440C2semidirect
9. C2×#1439C2semidirect
12. C2×#1437C2semidirect
13. C2×#1437C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×#1434C2semidirect
37. C2×#388C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1440C22semidirect
59. #1440C22semidirect
60. #1440C22semidirect
61. #1439C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. #1434C22semidirect
1101. C2#15756direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3942
C22×#3882
#157562
C2×#14422
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×#14342