Finite Group Databasebeta

← #6447643

Subgroups — #6447643

Order 512.

3383 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#544C211yesmaximal, characteristic, complemented
2C2×#3136C212yesmaximal, complemented
3#35252C211yesmaximal, characteristic
4#25916C214yesmaximal, complemented
5#25915C214yesmaximal, complemented
6#25913C212yesmaximal, complemented
7#25908C212yesmaximal, complemented
8#25907C212yesmaximal, complemented
9#25903C212yesmaximal, complemented
10#23458C212yesmaximal, complemented
11#23456C212yesmaximal, complemented
12#21326C212yesmaximal, complemented
13#20912C211yesmaximal, characteristic, complemented
14#20909C211yesmaximal, characteristic, complemented
15#20908C211yesmaximal, characteristic, complemented
16C2×#1874C211yesmaximal, characteristic, complemented
17#20379C211yesmaximal, characteristic, complemented
18C2×#544—216no—
19C2×#544—22no—
20C2×#544—21no—
21C2×#544—21no—
22C2×#544C2212yes—
23C2×#544C2212yes—
24C2×#544C2214yescomplemented
25C2×#535C2211yescharacteristic
26C22×C4⋊Q8—21no—
27C22×C4⋊Q8C2212yescomplemented
28C22×#125—21no—
29C22×#125C2212yescomplemented
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8—22no—
32C22×#121C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#3136—216no—
37C2×#490C2214yescomplemented
38C2×#489C2214yescomplemented
39C2×#488C2214yescomplemented
40C2×#486C2214yescomplemented
41C2×#417C2212yes—
42C2×#418C2212yes—
43C2×#416C2212yes—
44C22×#102C2212yes—
45C2×#407C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47C2×#405C2212yes—
48#2856C2212yes—
49#2850C2212yes—
50#2620C2212yes—
51#2619C2212yes—
52#2416—21no—
53#2416—21no—
54#2414—21no—
55#2414—21no—
56#2411—22no—
57#2410—22no—
58#2317C2211yescharacteristic
59#2311C2211yescharacteristic
60#2309C2211yescharacteristic
61#2026C2214yescomplemented
62#2025C2214yescomplemented
63#2025C2214yescomplemented
64#2025C2214yescomplemented
65#2024C2214yescomplemented
66#2023C2214yescomplemented
67#2023C2214yescomplemented
68#2023C2214yescomplemented
69#1993C2214yescomplemented
70#1992C2214yescomplemented
71#1991C2214yescomplemented
72#1990C2214yescomplemented
73#1875C2214yes—
74#1875C2212yescomplemented
75#1874C2212yes—
76#1874C2212yes—
77#1874C2212yes—
78#1874C2212yes—
79#1874C2214yes—
80#1874C2211yescharacteristic, complemented
81#1874C2212yescomplemented
82#1874C2211yescharacteristic, complemented
83#1874C2212yescomplemented
84#1873C2212yescomplemented
85#1872C2211yescharacteristic, complemented
86#1872C2212yescomplemented
87#1872C2211yescharacteristic, complemented
88#1872C2212yescomplemented
89#1750C2214yescomplemented
90#1749C2212yescomplemented
91C4×C22⋊C8C2212yescomplemented
92#1736C2212yes—
93#1736C2212yes—
94#1735C2212yes—
95C2×#340C2212yes—
96#1729C2212yes—
97C22×#41C2311yescharacteristic
98C23×Q8—22no—
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4C2311yescharacteristic
103C22×M16C2312yes—
104C23×C8C2312yes—
105#544—216no—
106#544—216no—
107#544—232no—
108#544—216no—
109#544—216no—
110#544—28no—
111#544—28no—
112#544—28no—
113#544D4116yescomplemented
114#535—28no—
115C2×C4⋊Q8—216no—
116C2×C4⋊Q8—216no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—22no—
121C2×C4⋊Q8—22no—
122C2×C4⋊Q8C2314yes—
123C2×C4⋊Q8C2314yes—
124C2×#127C2312yes—
125C2×#125—216no—
126C2×#125—216no—
127C2×#125—22no—
128C2×#125—22no—
129C2×#125—24no—
130C2×#125—22no—
131C2×#125—22no—
132C2×#125C2314yes—
133C2×#125C2314yes—
134C2×#124C2312yes—
135#525—24no—
136#525—24no—
137C2×#123—21no—
138C2×C22⋊Q8—232no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8C2311yescharacteristic
144C2×C22⋊Q8C2311yescharacteristic
145C2×#121—21no—
146C2×#121—21no—
147C2×#121—22no—
148C2×#121—22no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121—24no—
152C2×#121—24no—
153C2×#121C2312yes—
154C2×#121C2311yescharacteristic
155C2×#121C2311yescharacteristic
156C2×#121C2312yes—
157C2×#120—21no—
158C2×#120—22no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×#117—21no—
162C2×#117—21no—
163C2×#117—28no—
164C2×#117—28no—
165C2×#117D412yes—
166C2×#117D411yescharacteristic
167C2×#117D411yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2312yes—
170C2×#117C2312yes—
171C2×#117C2311yescharacteristic
172C2×#117C2312yes—
173C2×#117C2311yescharacteristic
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—22no—
178C22×C4⋊C4—22no—
179C22×C4⋊C4—22no—
180C22×C4⋊C4—28no—
181C22×C4⋊C4D411yescharacteristic
182C22×C4⋊C4D411yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4D412yes—
192C22×C42—21no—
193C22×C42C2312yes—
194#490—216no—
195#489—216no—
196#488—216no—
197#486—216no—
198#418—28no—
199#417—28no—
200#416—28no—
201C2×#103C2312yes—
202C2×#103C2314yes—
203C2×#103C2312yes—
204C2×#102—28no—
205C2×#102C2312yes—
206C2×#102C2314yes—
207C2×#102C2314yes—
208C2×#102C2314yes—
209C2×#102C2314yes—
210C2×#102C2314yes—
211C2×#102C2312yes—
212#407—24no—
213C2×C22⋊C8—24no—
214C2×C22⋊C8C2311yescharacteristic
215C2×C22⋊C8C2311yescharacteristic
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2312yes—
219#405—28no—
220C2×#97C2314yes—
221C2×C4×C8C2314yes—
222#396—22no—
223#396—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#392—22no—
229#392—22no—
230#391C2312yes—
231#390—21no—
232#390—21no—
233#390—22no—
234#390—22no—
235#390C2312yes—
236#390C2312yes—
237#390C2312yes—
238#389—21no—
239#389—21no—
240#388—22no—
241#388—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#385—22no—
246#384C2312yes—
247#382C2312yes—
248#380—21no—
249#380—21no—
250#379—22no—
251#340C2314yes—
252#340C2314yes—
253#340C2312yes—
254#340C2312yes—
255#340C2312yes—
256#340C2312yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2314yes—
262#336C2314yes—
263C25—21no—
264C25C2×D411yescharacteristic
265C2×#41—24no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—24no—
269C22×Q8—216no—
270C22×Q8—24no—
271C22×Q8—24no—
272C22×Q8—84no—
273C22×Q8—84no—
274C22×Q8C2411yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—22no—
280C22×D4—24no—
281C22×D4—21no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—24no—
287C22×D4—44no—
288C22×D4—82no—
289C22×D4—82no—
290C22×D4C2412yes—
291C22×D4C2411yescharacteristic
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—28no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—82no—
303C23×C4—82no—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C22×C8—24no—
318C22×C8—24no—
319C22×C8—24no—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2414yes—
323C4⋊Q8—232no—
324C4⋊Q8—216no—
325C4⋊Q8—216no—
326C4⋊Q8—216no—
327C4⋊Q8—216no—
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—28no—
331C4⋊Q8C2×D4116yescomplemented
332#127—28no—
333#125—232no—
334#125—216no—
335#125—216no—
336#125—216no—
337#125—216no—
338#125—28no—
339#125—28no—
340#125—28no—
341#125C2×D4116yescomplemented
342#124—28no—
343#123—44no—
344C22⋊Q8—232no—
345C22⋊Q8—232no—
346C22⋊Q8—232no—
347C22⋊Q8—232no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—24no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—44no—
361#121—44no—
362#121—44no—
363#121—44no—
364#121—84no—
365#121—84no—
366#120—44no—
367#120—48no—
368C4×D4—44no—
369C4×D4—44no—
370#117—28no—
371#117—28no—
372#117—24no—
373#117—24no—
374#117—24no—
375#117—24no—
376#117—24no—
377#117—24no—
378#117—28no—
379#117—28no—
380#117—22no—
381#117—22no—
382#117C2×D418yes—
383#117C2×D418yes—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—216no—
388C2×C4⋊C4—216no—
389C2×C4⋊C4—216no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D412yes—
419C2×C4⋊C4C2×D418yes—
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2411yescharacteristic
425C2×C4⋊C4C2414yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4C2×D412yes—
449C2×C22⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C42—28no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—28no—
456C2×C42—21no—
457C2×C42C2×D412yes—
458C2×C42C2×D412yes—
459C2×C42C2412yes—
460C2×C42C2412yes—
461#103—24no—
462#103—24no—
463#103—28no—
464#102—28no—
465#102—28no—
466#102—24no—
467#102—24no—
468#102—28no—
469#102—28no—
470#102—28no—
471C22⋊C8—22no—
472C22⋊C8—22no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C22⋊C8—24no—
476#97—28no—
477C4×C8—28no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—41no—
489C24—41no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24—81no—
494C24—81no—
495C24—81no—
496C24—81no—
497C24#12414yes—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501#41—48no—
502#41—48no—
503C2×Q8—216no—
504C2×Q8—216no—
505C2×Q8—22no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—84no—
510C2×Q8—84no—
511C2×Q8—84no—
512C2×Q8—84no—
513C2×Q8—832no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—24no—
521C2×D4—22no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—44no—
531C2×D4—42no—
532C2×D4—44no—
533C2×D4—42no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—82no—
547C2×D4—82no—
548C2×D4—816no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—216no—
556C22×C4—216no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—28no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—816no—
596C22×C4#12414yes—
597C22×C4#12414yes—
598C22×C4#12414yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D414yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C42−1+414yes—
614C22×C4C2511yescharacteristic
615M16—48no—
616C2×C8—22no—
617C2×C8—24no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—24no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—24no—
625C2×C8—48no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—216no—
633C4⋊C4—28no—
634C4⋊C4—216no—
635C4⋊C4—216no—
636C4⋊C4—216no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4#12014yes—
656C4⋊C4#12014yes—
657C4⋊C4C22×D418yes—
658C4⋊C4C22×D414yes—
659C4⋊C4C22×D414yes—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4#12018yes—
681C42—28no—
682C42—28no—
683C42—24no—
684C42—24no—
685C42—24no—
686C42—42no—
687C42C22×D418yes—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—28no—
699C23—21no—
700C23—21no—
701C23—28no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—162no—
727C23—162no—
728C23—162no—
729C23—162no—
730C23C2×#12012yes—
731C23C2×#12412yes—
732C23C2×#12412yes—
733C23C2×#12412yes—
734C23#53612yes—
735C23#57612yes—
736C23#57712yes—
737C23C23×D411yescharacteristic
738Q8—42no—
739Q8—42no—
740Q8—816no—
741Q8—816no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—42no—
746D4—84no—
747D4—88no—
748D4—84no—
749D4—88no—
750D4—84no—
751D4—84no—
752D4—164no—
753D4—164no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4—416no—
782C2×C4—48no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—88no—
802C2×C4—88no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4C2×#12014yes—
806C2×C4C2×#12014yes—
807C2×C4C2×#12012yes—
808C2×C4C2×#12412yes—
809C2×C4C2×#12412yes—
810C2×C4C2×#12412yes—
811C2×C4#53612yes—
812C2×C4#54818yes—
813C2×C4#54818yes—
814C2×C4C23×D412yes—
815C2×C4C22×#4111yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C2×2−1+412yes—
818C8—42no—
819C8—42no—
820C8—44no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—416no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—81no—
842C22—82no—
843C22—82no—
844C22—81no—
845C22—81no—
846C22—82no—
847C22—81no—
848C22—82no—
849C22—81no—
850C22—82no—
851C22—81no—
852C22—82no—
853C22—81no—
854C22—82no—
855C22—168no—
856C22#243614yes—
857C22#313614yescomplemented
858C22C22×#12011yescharacteristic
859C22C22×#12411yescharacteristic
860C22C2×#53611yescharacteristic
861C22C2×#57611yescharacteristic
862C22C2×#57711yescharacteristic
863C22#358511yescharacteristic
864C22#358611yescharacteristic
865C4—22no—
866C4—22no—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—48no—
871C4—44no—
872C4—42no—
873C4—44no—
874C4—81no—
875C4—82no—
876C4—81no—
877C4—81no—
878C4#243614yes—
879C4C2×#54812yes—
880C4C2×#54812yes—
881C2—24no—
882C2—24no—
883C2—42no—
884C2—161no—
885C2—162no—
886C2C2×#243611yescharacteristic
887C2#6037211yescharacteristic
888C2#6037411yescharacteristic
889C2C2×#313611yescharacteristic
890C2#6062111yescharacteristic
891C2#6087111yescharacteristic
892C2#6087311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35252C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#544C2semidirect
2. C2×#3136C2semidirect
4. #25916C2semidirect
5. #25915C2semidirect
6. #25913C2semidirect
7. #25908C2semidirect
8. #25907C2semidirect
9. #25903C2semidirect
10. #23458C2semidirect
11. #23456C2semidirect
12. #21326C2semidirect
13. #20912C2semidirect
14. #20909C2semidirect
15. #20908C2semidirect
16. C2×#1874C2semidirect
17. #20379C2semidirect
24. C2×#544C22semidirect
27. C22×C4⋊Q8C22semidirect
29. C22×#125C22semidirect
37. C2×#490C22semidirect
38. C2×#489C22semidirect
39. C2×#488C22semidirect
40. C2×#486C22semidirect
61. #2026C22semidirect
62. #2025C22semidirect
63. #2025C22semidirect
64. #2025C22semidirect
65. #2024C22semidirect
66. #2023C22semidirect
67. #2023C22semidirect
68. #2023C22semidirect
69. #1993C22semidirect
70. #1992C22semidirect
71. #1991C22semidirect
72. #1990C22semidirect
74. #1875C22semidirect
80. #1874C22semidirect
81. #1874C22semidirect
82. #1874C22semidirect
83. #1874C22semidirect
84. #1873C22semidirect
85. #1872C22semidirect
86. #1872C22semidirect
87. #1872C22semidirect
88. #1872C22semidirect
89. #1750C22semidirect
90. #1749C22semidirect
91. C4×C22⋊C8C22semidirect
113. #544D4semidirect
331. C4⋊Q8C2×D4semidirect
341. #125C2×D4semidirect
857. C22#3136semidirect

Maximal subgroups

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

subgroupindex
C22×#5442
C2×#31362
#352522
#259162
#259152
#259132
#259082
#259072
#259032
#234582
#234562
#213262
#209122
#209092
#209082
C2×#18742
#203792