Finite Group Databasebeta

← C2×#14375 #520675

Subgroups — C2×#14375 #520675

Order 512.

6410 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C22×#381C211yesmaximal, characteristic, complemented
4#14375C2116yesmaximal, direct product factor
5C2×#1443C211yesmaximal, characteristic, complemented
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1438C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic, complemented
12C2×#1437C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×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×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#386—28no—
33C2×#386C4116yescomplemented
34C2×#386C2218yes—
35C2×#386C2218yes—
36C2×#381—28no—
37C2×#381C2218yescomplemented
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
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58#1443C2218yescomplemented
59#1443C2218yescomplemented
60#1442C2218yescomplemented
61#1439C2218yescomplemented
62#1439C2218yescomplemented
63#1438C2218yes—
64#1437C2218yescomplemented
65#1437C2218yescomplemented
66#1434C2218yescomplemented
67C22⋊#95C2218yescomplemented
68C22⋊#95C2218yescomplemented
69C22⋊#95C2218yescomplemented
70C26C2311yescharacteristic
71C26C2311yescharacteristic
72C23×D4—24no—
73C23×D4—24no—
74C23×D4—24no—
75C23×D4—24no—
76C23×D4—42no—
77C23×D4—42no—
78C23×D4C2×C418yes—
79C23×D4C2314yes—
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4—42no—
92C24×C4—42no—
93C24×C4C2×C418yescomplemented
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2314yes—
108C24×C4C2314yes—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4C2314yes—
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—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
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⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4C2×C418yes—
140C22×C22⋊C4C2×C418yes—
141C22×C22⋊C4C2×C418yescomplemented
142C22×C22⋊C4D418yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C42—24no—
154C22×C42—42no—
155C22×C42—42no—
156C22×C42C2314yes—
157#386—232no—
158#386C2×C4164yescomplemented
159#381—232no—
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×#95—42no—
177C2×#95—42no—
178C2×#95C2×C418yescomplemented
179C2×#95C2×C418yescomplemented
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—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
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—
222C25—22no—
223C25—22no—
224C25C22×C414yes—
225C25C22×C414yes—
226C25C2×D414yes—
227C25#4114yes—
228C25#4114yes—
229C25#4114yes—
230C25C2412yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C22×D4—232no—
234C22×D4—232no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—416no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—416no—
243C22×D4—416no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4C22×C4116yes—
247C23×C4—232no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—28no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—28no—
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—28no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—28no—
334C23×C4—28no—
335C23×C4—416no—
336C23×C4—416no—
337C23×C4—44no—
338C23×C4—44no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4—416no—
346C23×C4—416no—
347C23×C4—416no—
348C23×C4—416no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
354C23×C4—416no—
355C23×C4—416no—
356C23×C4C22×C414yes—
357C23×C4C22×C414yes—
358C23×C4C22×C414yes—
359C23×C4C22×C414yes—
360C23×C4C22×C414yes—
361C23×C4C22×C4116yescomplemented
362C23×C4C2×D414yes—
363C23×C4C2×D414yes—
364C23×C4#4114yes—
365C23×C4#4114yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—416no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—416no—
394C2×C22⋊C4—416no—
395C2×C22⋊C4—416no—
396C2×C22⋊C4—416no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—416no—
414C2×C22⋊C4—416no—
415C2×C22⋊C4—416no—
416C2×C22⋊C4—416no—
417C2×C22⋊C4—416no—
418C2×C22⋊C4—416no—
419C2×C22⋊C4C22×C4116yes—
420C2×C22⋊C4C22×C4116yes—
421C2×C22⋊C4C22×C4116yescomplemented
422C2×C22⋊C4C2×D4116yes—
423C2×C42—28no—
424C2×C42—44no—
425C2×C42—44no—
426C2×C42—416no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95C22×C4116yescomplemented
446#95C22×C4116yescomplemented
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
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—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24#117116yes—
540C24C4×D4116yes—
541C24C23×C414yes—
542C24C23×C414yes—
543C24C23×C412yes—
544C24C22×D414yes—
545C24C22×D412yes—
546C24C2×#4114yes—
547C24C2×#4114yes—
548C24C2×#4114yes—
549C24C2×#4112yes—
550C24C2×#4112yes—
551C24C2×#4112yes—
552C24C2×#4112yes—
553C24C2×#4112yes—
554C24H(5,𝔽2)12yes—
555C24H(5,𝔽2)12yes—
556C24H(5,𝔽2)12yes—
557C24H(5,𝔽2)12yes—
558C24H(5,𝔽2)12yes—
559C24H(5,𝔽2)12yes—
560C24H(5,𝔽2)12yes—
561C242−1+412yes—
562C24C2511yescharacteristic
563C2×D4—232no—
564C2×D4—232no—
565C2×D4—416no—
566C2×D4—4128no—
567C2×D4—416no—
568C2×D4—416no—
569C2×D4—416no—
570C2×D4—416no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—232no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
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—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4—416no—
687C22×C4—416no—
688C22×C4—4128no—
689C22×C4—416no—
690C22×C4—416no—
691C22×C4—416no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4—4128no—
695C22×C4—416no—
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×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C23×C414yes—
761C22×C4C23×C414yes—
762C22×C4C23×C414yes—
763C22×C4C23×C414yes—
764C22×C4C23×C414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C2×#4114yes—
768C22×C4C2×#4114yes—
769C4⋊C4—416no—
770C22⋊C4—416no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C22⋊C4—416no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C22⋊C4—416no—
779C22⋊C4—416no—
780C42—416no—
781C23—232no—
782C23—232no—
783C23—232no—
784C23—232no—
785C23—232no—
786C23—232no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—416no—
824C23—416no—
825C23—416no—
826C23—416no—
827C23—416no—
828C23—416no—
829C23—416no—
830C23—416no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—416no—
850C23—416no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—416no—
856C23—416no—
857C23—42no—
858C23—42no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—416no—
878C23—416no—
879C23C2×#11718yes—
880C23C2×#11714yes—
881C23C2×C4×D418yes—
882C23C2×C4×D414yes—
883C23C4×#4114yes—
884C23#51814yes—
885C23#51814yes—
886C23#51814yes—
887C23#52014yes—
888C23#53414yes—
889C23#53514yes—
890C23#53814yes—
891C23#53814yes—
892C23#53814yes—
893C23#53814yes—
894C23#53814yes—
895C23#53814yes—
896C23#53914yes—
897C23#53914yes—
898C23#54014yes—
899C23#54014yes—
900C23#54614yes—
901C23#54614yes—
902C23#54614yes—
903C23#54714yes—
904C23#55114yes—
905C23#55114yes—
906C23#55114yes—
907C23#55114yes—
908C23#55114yes—
909C23#55214yes—
910C23#55314yes—
911C23#55314yes—
912C23#56014yes—
913C23#56014yes—
914C23#56214yes—
915C23#56214yes—
916C23C24×C411yescharacteristic
917C23C23×D411yescharacteristic
918C23C22×#4111yescharacteristic
919C23C22×#4111yescharacteristic
920C23C22×#4111yescharacteristic
921C23C22×#4111yescharacteristic
922C23C22×#4111yescharacteristic
923C23C2×H(5,𝔽2)11yescharacteristic
924C23C2×H(5,𝔽2)11yescharacteristic
925C23C2×H(5,𝔽2)11yescharacteristic
926C23C2×H(5,𝔽2)11yescharacteristic
927C23C2×H(5,𝔽2)11yescharacteristic
928C23C2×H(5,𝔽2)11yescharacteristic
929C23C2×H(5,𝔽2)11yescharacteristic
930C23C2×2−1+411yescharacteristic
931D4—464no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—464no—
960C2×C4—464no—
961C2×C4—416no—
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—42no—
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—416no—
990C2×C4—416no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—416no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—416no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—88no—
1035C2×C4—88no—
1036C2×C4—88no—
1037C2×C4—88no—
1038C22—28no—
1039C22—28no—
1040C22—28no—
1041C22—28no—
1042C22—28no—
1043C22—28no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—464no—
1051C22—464no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22#231818yes—
1071C22#232118yes—
1072C22#233318yes—
1073C22#234218yes—
1074C22#235318yes—
1075C22#235918yes—
1076C22#237718yes—
1077C22#269718yes—
1078C22#270318yes—
1079C22#270618yes—
1080C22#270818yes—
1081C22#274318yes—
1082C22#274918yes—
1083C22#275018yes—
1084C22#276018yes—
1085C22C22×#11711yescharacteristic
1086C22C22×C4×D411yescharacteristic
1087C22C2×C4×#4111yescharacteristic
1088C22C2×#51811yescharacteristic
1089C22C2×#51811yescharacteristic
1090C22C2×#51811yescharacteristic
1091C22C2×#52011yescharacteristic
1092C22C2×#53411yescharacteristic
1093C22C2×#53511yescharacteristic
1094C22C2×#53811yescharacteristic
1095C22C2×#53811yescharacteristic
1096C22C2×#53811yescharacteristic
1097C22C2×#53811yescharacteristic
1098C22C2×#53811yescharacteristic
1099C22C2×#53811yescharacteristic
1100C22C2×#53911yescharacteristic
1101C22C2×#53911yescharacteristic
1102C22C2×#54011yescharacteristic
1103C22C2×#54011yescharacteristic
1104C22C2×#54611yescharacteristic
1105C22C2×#54611yescharacteristic
1106C22C2×#54611yescharacteristic
1107C22C2×#54711yescharacteristic
1108C22C2×#55111yescharacteristic
1109C22C2×#55111yescharacteristic
1110C22C2×#55111yescharacteristic
1111C22C2×#55111yescharacteristic
1112C22C2×#55111yescharacteristic
1113C22C2×#55211yescharacteristic
1114C22C2×#55311yescharacteristic
1115C22C2×#55311yescharacteristic
1116C22C2×#56011yescharacteristic
1117C22C2×#56011yescharacteristic
1118C22C2×#56211yescharacteristic
1119C22C2×#56211yescharacteristic
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—82no—
1130C4—82no—
1131C4—82no—
1132C4—82no—
1133C2—48no—
1134C2—48no—
1135C2#14375116yesdirect product factor
1136C2C2×#231811yescharacteristic
1137C2C2×#232111yescharacteristic
1138C2C2×#233311yescharacteristic
1139C2C2×#234211yescharacteristic
1140C2C2×#235311yescharacteristic
1141C2C2×#235911yescharacteristic
1142C2C2×#237711yescharacteristic
1143C2C2×#269711yescharacteristic
1144C2C2×#270311yescharacteristic
1145C2C2×#270611yescharacteristic
1146C2C2×#270811yescharacteristic
1147C2C2×#274311yescharacteristic
1148C2C2×#274911yescharacteristic
1149C2C2×#275011yescharacteristic
1150C2C2×#276011yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#381C2semidirect
4. #14375C2direct (N × H)
5. C2×#1443C2semidirect
6. C2×#1443C2semidirect
7. C2×#1442C2semidirect
8. C2×#1439C2semidirect
9. C2×#1439C2semidirect
11. C2×#1437C2semidirect
12. C2×#1437C2semidirect
13. C2×#1434C2semidirect
14. C2×C22⋊#95C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
33. C2×#386C4semidirect
37. C2×#381C22semidirect
58. #1443C22semidirect
59. #1443C22semidirect
60. #1442C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1434C22semidirect
67. C22⋊#95C22semidirect
68. C22⋊#95C22semidirect
69. C22⋊#95C22semidirect
93. C24×C4C2×C4semidirect
141. C22×C22⋊C4C2×C4semidirect
158. #386C2×C4semidirect
178. C2×#95C2×C4semidirect
179. C2×#95C2×C4semidirect
361. C23×C4C22×C4semidirect
421. C2×C22⋊C4C22×C4semidirect
445. #95C22×C4semidirect
446. #95C22×C4semidirect
1135. C2#14375direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3862
C22×#3812
#143752
C2×#14432
C2×#14422
C2×#14392
C2×#14382
C2×#14372
C2×#14342
C2×C22⋊#952