Finite Group Databasebeta

← #6499898

Subgroups — #6499898

Order 512.

3500 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#3189C211yesmaximal, characteristic, complemented
3C2×#3187C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic, complemented
5#25541C214yesmaximal, complemented
6#25535C214yesmaximal, complemented
7#24431C214yesmaximal, complemented
8#24426C214yesmaximal, complemented
9#24067C212yesmaximal, complemented
10#24007C212yesmaximal, complemented
11#23937C212yesmaximal, complemented
12#23922C212yesmaximal, complemented
13#21738C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16#3505—28no—
17#3505—28no—
18C2×#553—22no—
19C2×#553C2212yes—
20C2×#552C2212yes—
21C2×#551—22no—
22C2×#548C2212yes—
23C2×#546C2212yes—
24C2×#539—21no—
25C2×#538—21no—
26C2×#534—21no—
27C2×#529C2212yes—
28C2×#525C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic, complemented
32C22×#121C2211yescharacteristic
33C2×#518—21no—
34C22×C4×D4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#3189—28no—
37#3187—28no—
38C2×#484C2212yescomplemented
39C2×#484C2212yescomplemented
40C2×#481C2212yes—
41C2×#483C2212yescomplemented
42C2×#467C2214yescomplemented
43C2×#465C2214yescomplemented
44C2×#452C2214yescomplemented
45C2×#451C2212yescomplemented
46C2×#451C2212yescomplemented
47C2×#448C2212yes—
48C2×#450C2212yescomplemented
49C22×#103C2212yescomplemented
50C22×#102C2212yescomplemented
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53#2417—22no—
54#2417—22no—
55#2417C2214yes—
56#2417C2214yescomplemented
57C2×#398—21no—
58C2×#396—21no—
59C2×#391C2211yescharacteristic, complemented
60C2×#389C2211yescharacteristic, complemented
61C2×#386—21no—
62C2×#380—21no—
63C2×#380C2211yescharacteristic, complemented
64#2059C2214yescomplemented
65#2042C2214yescomplemented
66#2035C2214yescomplemented
67#2033C2214yescomplemented
68#2026C2214yescomplemented
69#2015C2214yescomplemented
70#2001C2214yescomplemented
71#2000C2214yescomplemented
72#1878C2214yescomplemented
73#1877C2214yescomplemented
74#1874C2212yes—
75#1874C2212yes—
76#1874C2214yescomplemented
77#1873C2214yescomplemented
78#1872C2212yescomplemented
79#1872C2214yescomplemented
80#1872C2212yescomplemented
81#1869C2214yes—
82#1869C2214yescomplemented
83#1865C2214yescomplemented
84#1862C2214yescomplemented
85#1854C2214yescomplemented
86#1817C2212yescomplemented
87#1788C2214yescomplemented
88#1779C2212yescomplemented
89C2×#340C2212yescomplemented
90C2×#340C2212yescomplemented
91C22×#41C2312yes—
92C23×Q8C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4—21no—
95C23×D4D411yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4—21no—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C22×Q16C2314yes—
101C22×SD16C2314yes—
102C23×C8C2312yes—
103C23×C8C2312yes—
104#553—232no—
105#553—28no—
106#553—28no—
107#552—28no—
108#552—28no—
109#551—232no—
110#548—28no—
111#548—28no—
112#546—28no—
113#546—28no—
114#539—216no—
115#538—216no—
116#534—216no—
117#529—28no—
118#529—28no—
119C2×#126—22no—
120C2×#126—22no—
121C2×#126—22no—
122C2×#125—22no—
123C2×#125C2312yes—
124C2×#124—22no—
125C2×#124C2312yes—
126#525—28no—
127#525—28no—
128C2×#123—22no—
129C2×#123—22no—
130C2×#123—22no—
131C2×#123—22no—
132C2×#123—22no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—22no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—44no—
143C2×C22⋊Q8D418yes—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2314yes—
148C2×C22⋊Q8C2312yes—
149C2×C22⋊Q8C2312yes—
150C2×#121—22no—
151C2×#121—22no—
152C2×#121—21no—
153C2×#121—21no—
154C2×#121—24no—
155C2×#121—22no—
156C2×#121D418yes—
157C2×#121C2312yes—
158C2×#121C2312yes—
159C2×#121C2312yes—
160C2×#120—22no—
161C2×#120—22no—
162#518—216no—
163C2×C4×Q8C2312yes—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—22no—
167C2×C4×D4—22no—
168C2×C4×D4—22no—
169C2×C4×D4—22no—
170C2×C4×D4—22no—
171C2×C4×D4D412yes—
172C2×C4×D4D412yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2312yes—
175C2×C4×D4C2312yes—
176C2×#117—22no—
177C2×#117—22no—
178C2×#117C2312yes—
179C22×C4⋊C4—21no—
180C22×C4⋊C4—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4—21no—
184C22×C4⋊C4—21no—
185C22×C4⋊C4—21no—
186C22×C4⋊C4—44no—
187C22×C4⋊C4D411yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C22⋊C4—21no—
196C22×C22⋊C4—21no—
197C22×C22⋊C4—22no—
198C22×C22⋊C4—21no—
199C22×C22⋊C4—21no—
200C22×C22⋊C4—21no—
201C22×C22⋊C4D411yescharacteristic
202C22×C22⋊C4D411yescharacteristic
203C22×C42C2311yescharacteristic
204#484—28no—
205#484—28no—
206#483—28no—
207#481—28no—
208#467—216no—
209#465—216no—
210#452—48no—
211#451—28no—
212#451—28no—
213#450—28no—
214#448—28no—
215C2×#107C2314yes—
216C2×#106C2314yes—
217C2×#103—44no—
218C2×#103C2314yes—
219C2×#103C2314yes—
220C2×#103C2314yes—
221C2×#103C2314yes—
222C2×#103C2314yes—
223C2×#102—44no—
224C2×#102C2314yes—
225C2×#102C2314yes—
226C2×#102C2314yes—
227C2×C22⋊C8—24no—
228C2×C22⋊C8—24no—
229C2×C22⋊C8C2312yes—
230C2×C22⋊C8C2312yes—
231C2×C22⋊C8C2312yes—
232C2×C22⋊C8C2312yes—
233C2×C22⋊C8C2314yes—
234C2×C22⋊C8C2314yes—
235#398—24no—
236#398—24no—
237#396—24no—
238#396—24no—
239#391—22no—
240#391C2314yes—
241#389—22no—
242#389C2314yes—
243#386—24no—
244#386—24no—
245#380—22no—
246#380—24no—
247#380—24no—
248#380C2314yes—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#336C2314yes—
258#336C2314yes—
259C25—21no—
260C25C2×D411yescharacteristic
261C25C2×D411yescharacteristic
262C2×#41—24no—
263C2×#41—24no—
264C2×#41—44no—
265C2×#41—44no—
266C22×Q8—21no—
267C22×Q8—22no—
268C22×Q8—21no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—42no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8C2×D414yes—
276C22×Q8C2412yes—
277C22×Q8C2412yes—
278C22×D4—24no—
279C22×D4—28no—
280C22×D4—24no—
281C22×D4—24no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—42no—
289C22×D4—42no—
290C22×D4—44no—
291C22×D4—44no—
292C22×D4C2×D412yes—
293C22×D4C2×D412yes—
294C22×D4C2×D414yes—
295C22×D4C2412yes—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—44no—
314C23×C4—44no—
315C23×C4—82no—
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D412yes—
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D414yes—
324C23×C4C2×D414yes—
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C2×Q16—28no—
330C2×Q16—44no—
331C2×Q16—44no—
332C2×SD16—28no—
333C2×SD16—44no—
334C2×SD16—44no—
335C22×C8—24no—
336C22×C8—24no—
337C22×C8—42no—
338C22×C8—42no—
339C22×C8—42no—
340C22×C8—42no—
341C22×C8C2414yes—
342C22×C8C2414yes—
343#126—216no—
344#126—216no—
345#126—216no—
346#125—216no—
347#125—24no—
348#125—24no—
349#124—216no—
350#124—24no—
351#124—24no—
352#123—216no—
353#123—216no—
354#123—216no—
355#123—216no—
356#123—216no—
357C22⋊Q8—216no—
358C22⋊Q8—24no—
359C22⋊Q8—28no—
360C22⋊Q8—28no—
361C22⋊Q8—24no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—28no—
369C22⋊Q8—44no—
370C22⋊Q8—48no—
371C22⋊Q8—44no—
372C22⋊Q8—44no—
373C22⋊Q8C2×D418yes—
374C22⋊Q8C2×D418yes—
375#121—216no—
376#121—216no—
377#121—216no—
378#121—24no—
379#121—28no—
380#121—28no—
381#121—24no—
382#121—24no—
383#121—24no—
384#121C2×D418yes—
385#121C2×D418yes—
386#120—216no—
387#120—216no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×D4—216no—
391C4×D4—216no—
392C4×D4—216no—
393C4×D4—216no—
394C4×D4—216no—
395C4×D4—24no—
396C4×D4—28no—
397C4×D4—28no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—24no—
401C4×D4—24no—
402C4×D4—24no—
403#117—216no—
404#117—216no—
405#117—24no—
406#117—24no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4—44no—
441C2×C4⋊C4—82no—
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D414yes—
445C2×C4⋊C4C2×D414yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C22⋊C4—216no—
452C2×C22⋊C4—28no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—28no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—44no—
471C2×C22⋊C4—44no—
472C2×C22⋊C4—82no—
473C2×C22⋊C4C2×D412yes—
474C2×C22⋊C4C2×D412yes—
475C2×C22⋊C4C2×D412yes—
476C2×C22⋊C4C2×D412yes—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42C2×D412yes—
482C2×C42C2412yes—
483#107—28no—
484#106—28no—
485#103—28no—
486#103—28no—
487#103—28no—
488#103—28no—
489#103—44no—
490#102—28no—
491#102—28no—
492#102—44no—
493C22⋊C8—24no—
494C22⋊C8—24no—
495C22⋊C8—24no—
496C22⋊C8—24no—
497C22⋊C8—44no—
498C22⋊C8—44no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—24no—
503C24—22no—
504C24—22no—
505C24—24no—
506C24—22no—
507C24—22no—
508C24—41no—
509C24—41no—
510C24—41no—
511C24—41no—
512C24—41no—
513C24—41no—
514C24—41no—
515C24—41no—
516C24—42no—
517C24—42no—
518C24—81no—
519C24—81no—
520C24—81no—
521C24—81no—
522C24#12014yes—
523C24#13514yes—
524C24#13714yes—
525C24C22×D412yes—
526C24C22×D411yescharacteristic
527C24C22×D411yescharacteristic
528C24C22×D411yescharacteristic
529#41—88no—
530#41—88no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8—24no—
538C2×Q8—24no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8—48no—
542C2×Q8—42no—
543C2×Q8—81no—
544C2×Q8—81no—
545C2×Q8—84no—
546C2×Q8—84no—
547C2×Q8—84no—
548C2×Q8C22×D414yes—
549C2×D4—24no—
550C2×D4—28no—
551C2×D4—24no—
552C2×D4—28no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—416no—
569C2×D4—432no—
570C2×D4—84no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4C22×D414yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—42no—
638C22×C4—84no—
639C22×C4—84no—
640C22×C4—82no—
641C22×C4—82no—
642C22×C4—82no—
643C22×C4—82no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4—82no—
647C22×C4—82no—
648C22×C4—81no—
649C22×C4—81no—
650C22×C4—816no—
651C22×C4#12014yes—
652C22×C4#12014yes—
653C22×C4#12014yes—
654C22×C4C22×D412yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D412yes—
661C22×C4C22×D412yes—
662C22×C4C22×D412yes—
663C22×C4C22×D412yes—
664C22×C4C22×D412yes—
665C22×C4C22×D412yes—
666C22×C4C2511yescharacteristic
667Q16—88no—
668SD16—88no—
669C2×C8—24no—
670C2×C8—24no—
671C2×C8—24no—
672C2×C8—24no—
673C2×C8—24no—
674C2×C8—24no—
675C2×C8—84no—
676C2×C8—84no—
677C4⋊C4—24no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—48no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—84no—
703C4⋊C4C22×D414yes—
704C4⋊C4C22×D414yes—
705C4⋊C4H(5,𝔽2)14yes—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—24no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—24no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—48no—
721C22⋊C4—44no—
722C22⋊C4—44no—
723C22⋊C4—84no—
724C42—28no—
725C42—28no—
726C42—24no—
727C42—22no—
728C42—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—44no—
762C23—42no—
763C23—42no—
764C23—48no—
765C23—82no—
766C23—82no—
767C23—82no—
768C23—82no—
769C23—84no—
770C23—84no—
771C23—162no—
772C23—162no—
773C23—162no—
774C23—162no—
775C23#452116yescomplemented
776C23C2×#12012yes—
777C23C2×#12012yes—
778C23C2×#12012yes—
779C23C2×#13512yes—
780C23C2×#13512yes—
781C23C2×#13512yes—
782C23C2×#13712yes—
783C23C2×#13712yes—
784C23C2×#13712yes—
785C23C23×D411yescharacteristic
786Q8—28no—
787Q8—44no—
788Q8—44no—
789Q8—44no—
790Q8—84no—
791Q8—84no—
792D4—28no—
793D4—48no—
794D4—48no—
795D4—416no—
796D4—416no—
797D4—44no—
798D4—84no—
799D4—88no—
800D4—88no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—48no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—48no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—44no—
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—84no—
852C2×C4—82no—
853C2×C4—82no—
854C2×C4—84no—
855C2×C4—84no—
856C2×C4—88no—
857C2×C4—88no—
858C2×C4—88no—
859C2×C4—88no—
860C2×C4—84no—
861C2×C4—84no—
862C2×C4—84no—
863C2×C4C2×#12012yes—
864C2×C4C2×#12012yes—
865C2×C4C2×#12012yes—
866C2×C4C23×D411yescharacteristic
867C2×C4C23×D411yescharacteristic
868C2×C4C2×H(5,𝔽2)12yes—
869C2×C4#58512yes—
870C8—44no—
871C8—44no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—416no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—44no—
900C22—42no—
901C22—88no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—168no—
907C22C2×#45214yes—
908C22C2×#45214yes—
909C22C2×#45214yes—
910C22C22×#12011yescharacteristic
911C22#348411yescharacteristic
912C22#348511yescharacteristic
913C22C22×#13511yescharacteristic
914C22C22×#13711yescharacteristic
915C22#358511yescharacteristic
916C22#358611yescharacteristic
917C4—22no—
918C4—22no—
919C4—22no—
920C4—42no—
921C4—44no—
922C4—44no—
923C4—42no—
924C4—44no—
925C4—42no—
926C4—44no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4#349612yes—
931C4#349612yes—
932C2—24no—
933C2—24no—
934C2—24no—
935C2—82no—
936C2—84no—
937C2#3534711yescharacteristic
938C2C22×#45211yescharacteristic
939C2#6037111yescharacteristic
940C2#6156111yescharacteristic
941C2#6157411yescharacteristic
942C2#6169611yescharacteristic
943C2#6170911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3189C2semidirect
3. C2×#3187C2semidirect
4. C2×#2417C2semidirect
5. #25541C2semidirect
6. #25535C2semidirect
7. #24431C2semidirect
8. #24426C2semidirect
9. #24067C2semidirect
10. #24007C2semidirect
11. #23937C2semidirect
12. #23922C2semidirect
13. #21738C2semidirect
14. C2×#1874C2semidirect
15. C2×#1872C2semidirect
31. C22×C22⋊Q8C22semidirect
38. C2×#484C22semidirect
39. C2×#484C22semidirect
41. C2×#483C22semidirect
42. C2×#467C22semidirect
43. C2×#465C22semidirect
44. C2×#452C22semidirect
45. C2×#451C22semidirect
46. C2×#451C22semidirect
48. C2×#450C22semidirect
49. C22×#103C22semidirect
50. C22×#102C22semidirect
56. #2417C22semidirect
59. C2×#391C22semidirect
60. C2×#389C22semidirect
63. C2×#380C22semidirect
64. #2059C22semidirect
65. #2042C22semidirect
66. #2035C22semidirect
67. #2033C22semidirect
68. #2026C22semidirect
69. #2015C22semidirect
70. #2001C22semidirect
71. #2000C22semidirect
72. #1878C22semidirect
73. #1877C22semidirect
76. #1874C22semidirect
77. #1873C22semidirect
78. #1872C22semidirect
79. #1872C22semidirect
80. #1872C22semidirect
82. #1869C22semidirect
83. #1865C22semidirect
84. #1862C22semidirect
85. #1854C22semidirect
86. #1817C22semidirect
87. #1788C22semidirect
88. #1779C22semidirect
89. C2×#340C22semidirect
90. C2×#340C22semidirect
775. C23#452semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#31892
C2×#31872
C2×#24172
#255412
#255352
#244312
#244262
#240672
#240072
#239372
#239222
#217382
C2×#18742
C2×#18722