Finite Group Databasebeta

← #6447642

Subgroups — #6447642

Order 512.

3253 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#544C211yesmaximal, characteristic, complemented
2C2×#3137C212yesmaximal, complemented
3#35306C211yesmaximal, characteristic
4#25916C214yesmaximal, complemented
5#25914C214yesmaximal, complemented
6#25912C212yesmaximal, complemented
7#25908C212yesmaximal, complemented
8#25907C212yesmaximal, complemented
9#25902C212yesmaximal, complemented
10#23458C212yesmaximal, complemented
11#23457C212yesmaximal, complemented
12#21326C212yesmaximal, complemented
13#20911C211yesmaximal, characteristic, complemented
14#20909C211yesmaximal, characteristic
15#20908C211yesmaximal, characteristic
16C2×#1872C211yesmaximal, characteristic, complemented
17#20379C211yesmaximal, characteristic, complemented
18C2×#544—216no—
19C2×#544—22no—
20C2×#544—21no—
21C2×#544—21no—
22C2×#544C2214yes—
23C2×#544C2212yes—
24C2×#544C2212yes—
25C2×#536C2211yescharacteristic
26C22×C4⋊Q8—21no—
27C22×C4⋊Q8C2212yes—
28C22×#125—21no—
29C22×#125C2212yes—
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8—22no—
32C22×C22⋊Q8C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#3137—216no—
37C2×#491C2214yescomplemented
38C2×#489C2214yescomplemented
39C2×#488C2214yescomplemented
40C2×#487C2214yescomplemented
41C2×#417C2212yes—
42C2×#419C2212yes—
43C2×#416C2212yes—
44C22×#103C2212yes—
45C2×#407C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47C2×#405C2212yes—
48#2857C2212yes—
49#2850C2212yes—
50#2621C2212yes—
51#2620C2212yes—
52#2417—21no—
53#2417—21no—
54#2415—21no—
55#2415—21no—
56#2413—22no—
57#2412—22no—
58#2317C2211yescharacteristic
59#2311C2211yescharacteristic
60#2310C2211yescharacteristic
61#2026C2214yescomplemented
62#2026C2214yescomplemented
63#2026C2214yescomplemented
64#2025C2214yescomplemented
65#2024C2214yescomplemented
66#2024C2214yescomplemented
67#2024C2214yescomplemented
68#2023C2214yescomplemented
69#1993C2214yescomplemented
70#1992C2214yescomplemented
71#1991C2214yescomplemented
72#1990C2214yescomplemented
73#1875C2212yes—
74#1874C2211yescharacteristic
75#1874C2212yes—
76#1874C2211yescharacteristic
77#1874C2212yes—
78#1873C2212yes—
79#1873C2214yes—
80#1872C2211yescharacteristic
81#1872C2212yes—
82#1872C2212yes—
83#1872C2212yes—
84#1872C2212yes—
85#1872C2212yes—
86#1872C2211yescharacteristic
87#1872C2212yes—
88#1872C2214yes—
89#1750C2214yes—
90#1749C2212yes—
91C4×C22⋊C8C2212yes—
92#1736C2212yes—
93#1736C2212yes—
94#1735C2212yes—
95C2×#340C2212yes—
96#1729C2212yes—
97C22×#41C2311yescharacteristic
98C23×Q8—22no—
99C23×Q8C2311yescharacteristic
100C24×C4—21no—
101C24×C4C2311yescharacteristic
102C22×M16C2312yes—
103C23×C8C2312yes—
104#544—216no—
105#544—216no—
106#544—232no—
107#544—216no—
108#544—216no—
109#544—28no—
110#544—28no—
111#544—28no—
112#544D4116yescomplemented
113#536—28no—
114C2×C4⋊Q8—216no—
115C2×C4⋊Q8—216no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—22no—
120C2×C4⋊Q8—22no—
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2314yes—
123C2×C4⋊Q8C2314yes—
124C2×#125—216no—
125C2×#125—216no—
126C2×#125—22no—
127C2×#125—24no—
128C2×#125—22no—
129C2×#125—22no—
130C2×#125—22no—
131C2×#125C2314yes—
132C2×#125C2314yes—
133C2×#124C2312yes—
134#525—24no—
135#525—24no—
136C2×#123—21no—
137C2×#123—22no—
138C2×C22⋊Q8—232no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8C2312yes—
150C2×C22⋊Q8C2311yescharacteristic
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2311yescharacteristic
153C2×#121C2311yescharacteristic
154C2×#121C2311yescharacteristic
155C2×#120—21no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×#117—21no—
159C2×#117—21no—
160C2×#117—28no—
161C2×#117—28no—
162C2×#117D412yes—
163C2×#117D411yescharacteristic
164C2×#117D411yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2312yes—
167C2×#117C2312yes—
168C2×#117C2311yescharacteristic
169C2×#117C2312yes—
170C2×#117C2311yescharacteristic
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—22no—
175C22×C4⋊C4—22no—
176C22×C4⋊C4—22no—
177C22×C4⋊C4—28no—
178C22×C4⋊C4—21no—
179C22×C4⋊C4D411yescharacteristic
180C22×C4⋊C4D411yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C22⋊C4—21no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4D412yes—
190C22×C42—21no—
191C22×C42C2312yes—
192#491—216no—
193#489—216no—
194#488—216no—
195#487—216no—
196#419—28no—
197#417—28no—
198#416—28no—
199C2×#103—28no—
200C2×#103C2312yes—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#103C2314yes—
205C2×#103C2314yes—
206C2×#103C2312yes—
207C2×#102C2312yes—
208C2×#102C2314yes—
209C2×#102C2312yes—
210#407—24no—
211C2×C22⋊C8—24no—
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217#405—28no—
218C2×#97C2314yes—
219C2×C4×C8C2314yes—
220#398—22no—
221#398—22no—
222#397—22no—
223#397—22no—
224#396—22no—
225#396—22no—
226#394—22no—
227#394—22no—
228#391—21no—
229#391—21no—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#390C2312yes—
234#389—21no—
235#389—21no—
236#389—22no—
237#389—22no—
238#388—22no—
239#388—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#385—22no—
244#384C2312yes—
245#382C2312yes—
246#381—22no—
247#380—22no—
248#380—22no—
249#380—21no—
250#380—21no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2312yes—
258#340C2312yes—
259#340C2312yes—
260#340C2312yes—
261#336C2314yes—
262#336C2314yes—
263C25C2×D411yescharacteristic
264C2×#41—24no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—24no—
268C22×Q8—216no—
269C22×Q8—24no—
270C22×Q8—24no—
271C22×Q8—21no—
272C22×Q8—24no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—24no—
276C22×Q8—84no—
277C22×Q8—84no—
278C22×Q8C2412yes—
279C22×Q8C2411yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2411yescharacteristic
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—28no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—82no—
296C23×C4—82no—
297C23×C4C2×D412yes—
298C23×C4C2×D412yes—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4#4114yes—
303C23×C4#4114yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—24no—
310C22×C8—24no—
311C22×C8—24no—
312C22×C8—24no—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2414yes—
316C4⋊Q8—232no—
317C4⋊Q8—216no—
318C4⋊Q8—216no—
319C4⋊Q8—216no—
320C4⋊Q8—216no—
321C4⋊Q8—28no—
322C4⋊Q8—28no—
323C4⋊Q8—28no—
324C4⋊Q8—28no—
325C4⋊Q8C2×D4116yes—
326#125—232no—
327#125—216no—
328#125—216no—
329#125—216no—
330#125—216no—
331#125—28no—
332#125—28no—
333#125—28no—
334#125C2×D4116yes—
335#124—28no—
336#123—44no—
337#123—48no—
338C22⋊Q8—232no—
339C22⋊Q8—232no—
340C22⋊Q8—232no—
341C22⋊Q8—232no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#120—44no—
359C4×D4—44no—
360C4×D4—44no—
361#117—28no—
362#117—28no—
363#117—24no—
364#117—24no—
365#117—24no—
366#117—24no—
367#117—24no—
368#117—24no—
369#117—28no—
370#117—28no—
371#117—22no—
372#117—22no—
373#117C2×D418yes—
374#117C2×D418yes—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—216no—
379C2×C4⋊C4—216no—
380C2×C4⋊C4—216no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2×D418yes—
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2411yescharacteristic
421C2×C4⋊C4C2414yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C42—28no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—28no—
448C2×C42—21no—
449C2×C42C2×D412yes—
450C2×C42C2×D412yes—
451C2×C42C2412yes—
452C2×C42C2412yes—
453#103—28no—
454#103—28no—
455#103—24no—
456#103—24no—
457#103—28no—
458#103—28no—
459#103—28no—
460#102—24no—
461#102—24no—
462#102—28no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468#97—28no—
469C4×C8—28no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—41no—
484C24—41no—
485C24#12414yes—
486C24C22×D411yescharacteristic
487C24C22×D411yescharacteristic
488C24C22×D411yescharacteristic
489#41—48no—
490#41—48no—
491C2×Q8—216no—
492C2×Q8—216no—
493C2×Q8—24no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—48no—
505C2×Q8—48no—
506C2×Q8—84no—
507C2×Q8—84no—
508C2×Q8—84no—
509C2×Q8—84no—
510C2×Q8—832no—
511C2×D4—22no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—22no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C2×D4—81no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—28no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—42no—
558C22×C4—44no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—816no—
575C22×C4#12414yes—
576C22×C4#12414yes—
577C22×C4#12414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D414yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C42−1+414yes—
593C22×C4C2511yescharacteristic
594M16—48no—
595C2×C8—22no—
596C2×C8—24no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—24no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—24no—
604C2×C8—48no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—24no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—82no—
637C4⋊C4—82no—
638C4⋊C4#12014yes—
639C4⋊C4#12014yes—
640C4⋊C4C22×D418yes—
641C4⋊C4C22×D414yes—
642C4⋊C4C22×D414yes—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C22⋊C4#12018yes—
660C42—28no—
661C42—28no—
662C42—24no—
663C42—24no—
664C42—24no—
665C42—42no—
666C42C22×D418yes—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—28no—
678C23—21no—
679C23—21no—
680C23—28no—
681C23—21no—
682C23—21no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C2×#12012yes—
696C23C2×#12412yes—
697C23C2×#12412yes—
698C23C2×#12412yes—
699C23#53612yes—
700C23#57712yes—
701C23#57812yes—
702C23C23×D411yescharacteristic
703Q8—44no—
704Q8—44no—
705Q8—42no—
706Q8—42no—
707Q8—816no—
708Q8—816no—
709Q8—84no—
710D4—42no—
711D4—42no—
712D4—84no—
713D4—84no—
714D4—84no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—416no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—88no—
766C2×C4—88no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4C2×#12014yes—
771C2×C4C2×#12014yes—
772C2×C4C2×#12012yes—
773C2×C4C2×#12412yes—
774C2×C4C2×#12412yes—
775C2×C4C2×#12412yes—
776C2×C4#53612yes—
777C2×C4#54818yes—
778C2×C4#54818yes—
779C2×C4C23×D412yes—
780C2×C4C22×#4111yescharacteristic
781C2×C4C22×#4111yescharacteristic
782C2×C4C2×2−1+412yes—
783C8—42no—
784C8—42no—
785C8—44no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—416no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#243614yes—
814C22#313714yescomplemented
815C22C22×#12011yescharacteristic
816C22C22×#12411yescharacteristic
817C22C2×#53611yescharacteristic
818C22C2×#57711yescharacteristic
819C22C2×#57811yescharacteristic
820C22#358511yescharacteristic
821C22#358611yescharacteristic
822C4—22no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—42no—
827C4—48no—
828C4—44no—
829C4—42no—
830C4—44no—
831C4—81no—
832C4—82no—
833C4—81no—
834C4—82no—
835C4—81no—
836C4#243614yes—
837C4C2×#54812yes—
838C4C2×#54812yes—
839C2—24no—
840C2—24no—
841C2—42no—
842C2—161no—
843C2C2×#243611yescharacteristic
844C2#6037311yescharacteristic
845C2#6037511yescharacteristic
846C2C2×#313711yescharacteristic
847C2#6062111yescharacteristic
848C2#6087211yescharacteristic
849C2#6087411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
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×#3137C2semidirect
4. #25916C2semidirect
5. #25914C2semidirect
6. #25912C2semidirect
7. #25908C2semidirect
8. #25907C2semidirect
9. #25902C2semidirect
10. #23458C2semidirect
11. #23457C2semidirect
12. #21326C2semidirect
13. #20911C2semidirect
16. C2×#1872C2semidirect
17. #20379C2semidirect
37. C2×#491C22semidirect
38. C2×#489C22semidirect
39. C2×#488C22semidirect
40. C2×#487C22semidirect
61. #2026C22semidirect
62. #2026C22semidirect
63. #2026C22semidirect
64. #2025C22semidirect
65. #2024C22semidirect
66. #2024C22semidirect
67. #2024C22semidirect
68. #2023C22semidirect
69. #1993C22semidirect
70. #1992C22semidirect
71. #1991C22semidirect
72. #1990C22semidirect
112. #544D4semidirect
814. C22#3137semidirect

Maximal subgroups

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

subgroupindex
C22×#5442
C2×#31372
#353062
#259162
#259142
#259122
#259082
#259072
#259022
#234582
#234572
#213262
#209112
#209092
#209082
C2×#18722
#203792