Finite Group Databasebeta

← #6436520

Subgroups — #6436520

Order 512.

3369 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#3108C211yesmaximal, characteristic, complemented
3C2×#3105C211yesmaximal, characteristic, complemented
4#36621C211yesmaximal, characteristic, complemented
5#29693C214yesmaximal, complemented
6#29666C214yesmaximal, complemented
7#29643C211yesmaximal, characteristic, complemented
8#29640C211yesmaximal, characteristic, complemented
9#29626C211yesmaximal, characteristic, complemented
10#29623C211yesmaximal, characteristic, complemented
11#29597C211yesmaximal, characteristic, complemented
12#29596C211yesmaximal, characteristic, complemented
13#29593C211yesmaximal, characteristic, complemented
14#29592C211yesmaximal, characteristic
15#23572C214yesmaximal, complemented
16#23569C214yesmaximal, complemented
17#20735C211yesmaximal, characteristic, complemented
18#20733C211yesmaximal, characteristic, complemented
19#20714C211yesmaximal, characteristic, complemented
20C2×#529—22no—
21C2×#529—22no—
22C2×#529—28no—
23C2×#529—28no—
24C2×#529C2211yescharacteristic
25C2×#529C2214yes—
26C2×#529C2214yes—
27C22×#126—21no—
28C22×#125C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#123—21no—
31C22×C22⋊Q8C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4—21no—
35C22×C4×D4C2211yescharacteristic
36C22×#117—21no—
37C23×C42C2211yescharacteristic
38#3108—28no—
39#3105—28no—
40C2×#484C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#483C2211yescharacteristic
43C2×#480C2211yescharacteristic
44C2×#479C2212yescomplemented
45C2×#478C2212yescomplemented
46C2×#464C2212yescomplemented
47C2×#463C2212yescomplemented
48C2×#451C2211yescharacteristic
49C2×#448C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#447C2211yescharacteristic
52C2×C4×Q16C2212yescomplemented
53C2×C4×SD16C2212yescomplemented
54C2×C4×SD16C2212yescomplemented
55C2×C4×D8C2212yescomplemented
56C2×#431C2211yescharacteristic
57C2×#431C2211yescharacteristic
58#2855C2211yescharacteristic
59#2854C2211yescharacteristic
60#2853—21no—
61#2852—22no—
62#2851C2212yescomplemented
63#2850C2212yescomplemented
64#2849—21no—
65#2848C2211yescharacteristic
66#2847C2211yescharacteristic
67C4×C22⋊Q8C2212yescomplemented
68C4×#123—21no—
69C4×#121C2212yescomplemented
70C4×#120—21no—
71#2290—22no—
72#2283C2211yescharacteristic
73#2059C2214yescomplemented
74#2059C2214yescomplemented
75#2042C2214yescomplemented
76#2042C2214yescomplemented
77#2036C2214yescomplemented
78#2035C2214yescomplemented
79#2034C2214yes—
80#2033C2214yes—
81#2026C2214yescomplemented
82#2025C2214yescomplemented
83#2015C2214yescomplemented
84#2012C2214yescomplemented
85#2001C2214yescomplemented
86#2000C2214yes—
87#2000C2214yescomplemented
88#1999C2214yes—
89#1824C2211yescharacteristic
90#1824C2211yescharacteristic
91#1823C2211yescharacteristic
92#1823C2211yescharacteristic
93#1817C2211yescharacteristic
94#1817C2211yescharacteristic
95#1805C2214yescomplemented
96#1804C2214yescomplemented
97#1797C2214yescomplemented
98#1787C2211yescharacteristic
99#1787C2211yescharacteristic
100#1786C2211yescharacteristic
101#1786C2211yescharacteristic
102#1779C2211yescharacteristic
103#1779C2211yescharacteristic
104C4×#103C2214yescomplemented
105C4×#102C2214yescomplemented
106C4×C22⋊C8C2214yescomplemented
107C23×Q8C2311yescharacteristic
108C23×D4—21no—
109C23×D4C2311yescharacteristic
110C24×C4—21no—
111C24×C4D411yescharacteristic
112C24×C4D411yescharacteristic
113C24×C4C2311yescharacteristic
114C22×Q16C2312yes—
115C22×SD16C2312yes—
116C22×SD16C2312yes—
117C22×D8C2312yes—
118#529—232no—
119#529—232no—
120#529—216no—
121#529—216no—
122#529—216no—
123#529—216no—
124#529—24no—
125#529—24no—
126C2×#126—216no—
127C2×#126—24no—
128C2×#126—24no—
129C2×#126—21no—
130C2×#125—24no—
131C2×#125—24no—
132C2×#125—22no—
133C2×#125C2311yescharacteristic
134C2×#125C2314yes—
135C2×#124—24no—
136C2×#124—24no—
137C2×#124—22no—
138C2×#124C2311yescharacteristic
139C2×#124C2314yes—
140C2×#123—216no—
141C2×#123—24no—
142C2×#123—24no—
143C2×#123—21no—
144C2×#123—21no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8C2311yescharacteristic
149C2×C22⋊Q8C2314yes—
150C2×C22⋊Q8C2312yes—
151C2×#121—24no—
152C2×#121—22no—
153C2×#121—24no—
154C2×#121C2311yescharacteristic
155C2×#121C2314yes—
156C2×#121C2312yes—
157C2×#120—21no—
158C2×C4×Q8—24no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8D418yescomplemented
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2312yes—
165C2×C4×D4—216no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—21no—
169C2×C4×D4—22no—
170C2×C4×D4—21no—
171C2×C4×D4—21no—
172C2×C4×D4—24no—
173C2×C4×D4D418yescomplemented
174C2×C4×D4C2311yescharacteristic
175C2×C4×D4C2312yes—
176C2×C4×D4C2312yes—
177C2×#117—216no—
178C2×#117—24no—
179C2×#117—24no—
180C2×#117—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4—21no—
184C22×C4⋊C4—21no—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C22⋊C4—21no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C42—21no—
193C22×C42—24no—
194C22×C42—24no—
195C22×C42D412yes—
196C22×C42D411yescharacteristic
197C22×C42D411yescharacteristic
198C22×C42D412yes—
199C22×C42C2312yes—
200C22×C42C2311yescharacteristic
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203#484—24no—
204#483—24no—
205#481—24no—
206#480—24no—
207#479—28no—
208#478—28no—
209#464—28no—
210#463—28no—
211#451—24no—
212#450—24no—
213#448—24no—
214#447—24no—
215C4×Q16—28no—
216C4×SD16—28no—
217C4×SD16—28no—
218C4×D8—28no—
219#431—24no—
220#431—24no—
221C2×#107C2312yes—
222C2×#107C2312yes—
223C2×#106C2312yes—
224C2×#106C2312yes—
225C2×C4⋊C8C2312yes—
226C2×C4⋊C8C2312yes—
227C2×#103C2312yes—
228C2×#103C2312yes—
229C2×#103C2312yes—
230C2×#103C2312yes—
231C2×#103C2314yes—
232C2×#103C2314yes—
233C2×#102C2312yes—
234C2×#102C2312yes—
235C2×#102C2312yes—
236C2×#102C2312yes—
237C2×#102C2314yes—
238C2×#102C2314yes—
239C2×C22⋊C8C2311yescharacteristic
240C2×C22⋊C8C2311yescharacteristic
241C2×C22⋊C8C2311yescharacteristic
242C2×C22⋊C8C2311yescharacteristic
243C2×C22⋊C8C2314yes—
244C2×C22⋊C8C2314yes—
245C2×C4×C8C2312yes—
246C2×C4×C8C2312yes—
247#391C2312yes—
248#390C2312yes—
249#389C2312yes—
250#389C2312yes—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#386—22no—
260#386—21no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—21no—
265#385—22no—
266#385—21no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—21no—
271#383—21no—
272#382C2312yes—
273#381—21no—
274#381—21no—
275#380C2311yescharacteristic
276#380C2311yescharacteristic
277#380C2312yes—
278#380C2312yes—
279#379—21no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4C2312yes—
282C4×C22⋊C4—21no—
283C4×C22⋊C4—22no—
284C4×C22⋊C4—22no—
285#376—21no—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#336C2314yes—
291#336C2314yes—
292C25—21no—
293C25C2×D411yescharacteristic
294C22×Q8—22no—
295C22×Q8—21no—
296C22×Q8—44no—
297C22×Q8C2×D414yes—
298C22×Q8C2411yescharacteristic
299C22×Q8C2412yes—
300C22×D4—28no—
301C22×D4—24no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—22no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4C2×D414yes—
310C22×D4C2411yescharacteristic
311C22×D4C2412yes—
312C23×C4—24no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—28no—
317C23×C4—24no—
318C23×C4—24no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—21no—
324C23×C4—44no—
325C23×C4—44no—
326C23×C4—42no—
327C23×C4—48no—
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D412yes—
330C23×C4C2×D412yes—
331C23×C4C2×D412yes—
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D411yescharacteristic
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D412yes—
337C23×C4C2×D412yes—
338C23×C4C2412yes—
339C23×C4C2411yescharacteristic
340C2×Q16—24no—
341C2×Q16—44no—
342C2×SD16—24no—
343C2×SD16—24no—
344C2×SD16—44no—
345C2×SD16—44no—
346C2×D8—24no—
347C2×D8—44no—
348C22×C8C2412yes—
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2412yes—
352#126—232no—
353#126—232no—
354#126—44no—
355#125—216no—
356#125—28no—
357#125—28no—
358#125—22no—
359#125—22no—
360#124—216no—
361#124—28no—
362#124—28no—
363#124—22no—
364#124—22no—
365#123—232no—
366#123—232no—
367#123—44no—
368#123—44no—
369C22⋊Q8—216no—
370C22⋊Q8—28no—
371C22⋊Q8—28no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—44no—
375#121—216no—
376#121—28no—
377#121—28no—
378#121—22no—
379#121—22no—
380#121—44no—
381#120—44no—
382C4×Q8—28no—
383C4×Q8—28no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8C2×D418yes—
389C4×Q8C2×D418yes—
390C4×D4—232no—
391C4×D4—232no—
392C4×D4—28no—
393C4×D4—28no—
394C4×D4—24no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—48no—
399C4×D4—44no—
400C4×D4C2×D418yes—
401C4×D4C2×D418yes—
402#117—232no—
403#117—232no—
404#117—44no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4C2×D414yes—
426C2×C4⋊C4C2×D414yes—
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C42—24no—
458C2×C42—28no—
459C2×C42—24no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—28no—
465C2×C42—28no—
466C2×C42—24no—
467C2×C42—24no—
468C2×C42—24no—
469C2×C42—24no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42C2×D412yes—
473C2×C42C2×D412yes—
474C2×C42C2×D412yes—
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D414yes—
480C2×C42C2×D414yes—
481C2×C42C2412yes—
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107—24no—
485#107—24no—
486#106—24no—
487#106—24no—
488C4⋊C8—24no—
489C4⋊C8—24no—
490#103—24no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—44no—
495#103—44no—
496#102—24no—
497#102—24no—
498#102—24no—
499#102—24no—
500#102—44no—
501#102—44no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—44no—
507C22⋊C8—44no—
508C4×C8—24no—
509C4×C8—24no—
510#95—21no—
511#95—21no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521C24—22no—
522C24—22no—
523C24—24no—
524C24—22no—
525C24—21no—
526C24—42no—
527C24—42no—
528C24—44no—
529C24—44no—
530C24—42no—
531C24—42no—
532C24#13514yes—
533C24C22×D412yes—
534C24C22×D411yescharacteristic
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—24no—
540C2×Q8—24no—
541C2×Q8—24no—
542C2×Q8—48no—
543C2×Q8—44no—
544C2×Q8—48no—
545C2×Q8C22×D414yes—
546C2×D4—216no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—48no—
555C2×D4—44no—
556C2×D4—48no—
557C2×D4—432no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—42no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4C22×D414yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—416no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—416no—
615C22×C4—432no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—48no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4#12014yes—
624C22×C4#12014yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D411yescharacteristic
635C22×C4C2511yescharacteristic
636Q16—48no—
637SD16—48no—
638SD16—48no—
639D8—48no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
648C4⋊C4—216no—
649C4⋊C4—216no—
650C4⋊C4—216no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C22×D414yes—
671C4⋊C4C22×D414yes—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—44no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C42—24no—
692C42—24no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—28no—
697C42—28no—
698C42—22no—
699C42—22no—
700C42—42no—
701C42—44no—
702C42#12014yes—
703C42#12014yes—
704C42C22×D412yes—
705C42C22×D412yes—
706C42C22×D412yes—
707C42C22×D412yes—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—48no—
719C23—44no—
720C23—44no—
721C23—48no—
722C23—48no—
723C23—48no—
724C23—44no—
725C23—48no—
726C23—42no—
727C23—44no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—88no—
735C23—88no—
736C23C2×#12012yes—
737C23C2×#13514yes—
738C23C2×#13512yes—
739C23#57512yes—
740C23C23×D411yescharacteristic
741Q8—24no—
742Q8—24no—
743Q8—48no—
744Q8—44no—
745Q8—42no—
746Q8—42no—
747D4—24no—
748D4—24no—
749D4—48no—
750D4—432no—
751D4—44no—
752D4—42no—
753D4—42no—
754D4—88no—
755D4—84no—
756C2×C4—22no—
757C2×C4—28no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—48no—
796C2×C4—416no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—84no—
811C2×C4C2×#12012yes—
812C2×C4C2×#12012yes—
813C2×C4C2×#12012yes—
814C2×C4C2×#12012yes—
815C2×C4C2×#12012yes—
816C2×C4#57514yes—
817C2×C4C23×D411yescharacteristic
818C2×C4C23×D411yescharacteristic
819C2×C4#58514yes—
820C8—42no—
821C8—42no—
822C8—42no—
823C8—42no—
824C22—24no—
825C22—24no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—416no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—816no—
840C22—84no—
841C22—84no—
842C22—82no—
843C22—82no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22#300214yes—
848C22C22×#12011yescharacteristic
849C22#344912yes—
850C22C22×#13511yescharacteristic
851C22C2×#57512yes—
852C22C2×#57511yescharacteristic
853C4—22no—
854C4—22no—
855C4—22no—
856C4—22no—
857C4—42no—
858C4—44no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—44no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4#300514yes—
869C4#344912yes—
870C4#344912yes—
871C2—24no—
872C2—44no—
873C2—84no—
874C2—161no—
875C2#3463211yescharacteristic
876C2C2×#300211yescharacteristic
877C2C2×#300511yescharacteristic
878C2#6094512yes—
879C2#6095412yes—
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#29592C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C2×#3108C2semidirect
3. C2×#3105C2semidirect
4. #36621C2semidirect
5. #29693C2semidirect
6. #29666C2semidirect
7. #29643C2semidirect
8. #29640C2semidirect
9. #29626C2semidirect
10. #29623C2semidirect
11. #29597C2semidirect
12. #29596C2semidirect
13. #29593C2semidirect
15. #23572C2semidirect
16. #23569C2semidirect
17. #20735C2semidirect
18. #20733C2semidirect
19. #20714C2semidirect
44. C2×#479C22semidirect
45. C2×#478C22semidirect
46. C2×#464C22semidirect
47. C2×#463C22semidirect
52. C2×C4×Q16C22semidirect
53. C2×C4×SD16C22semidirect
54. C2×C4×SD16C22semidirect
55. C2×C4×D8C22semidirect
62. #2851C22semidirect
63. #2850C22semidirect
67. C4×C22⋊Q8C22semidirect
69. C4×#121C22semidirect
73. #2059C22semidirect
74. #2059C22semidirect
75. #2042C22semidirect
76. #2042C22semidirect
77. #2036C22semidirect
78. #2035C22semidirect
81. #2026C22semidirect
82. #2025C22semidirect
83. #2015C22semidirect
84. #2012C22semidirect
85. #2001C22semidirect
87. #2000C22semidirect
95. #1805C22semidirect
96. #1804C22semidirect
97. #1797C22semidirect
104. C4×#103C22semidirect
105. C4×#102C22semidirect
106. C4×C22⋊C8C22semidirect
161. C2×C4×Q8D4semidirect
173. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#31082
C2×#31052
#366212
#296932
#296662
#296432
#296402
#296262
#296232
#295972
#295962
#295932
#295922
#235722
#235692
#207352
#207332
#207142