Finite Group Databasebeta

← #6445381

Subgroups — #6445381

Order 512.

3262 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#544C211yesmaximal, characteristic, complemented
2C2×#3084C212yesmaximal, complemented
3#34202C211yesmaximal, characteristic
4#24310C214yesmaximal, complemented
5#24309C214yesmaximal, complemented
6#24307C212yesmaximal, complemented
7#24305C212yesmaximal, complemented
8#24301C212yesmaximal, complemented
9#24299C212yesmaximal, complemented
10#23556C212yesmaximal, complemented
11#23458C212yesmaximal, complemented
12#21315C212yesmaximal, complemented
13#20909C211yesmaximal, characteristic
14#20908C211yesmaximal, characteristic
15#20846C211yesmaximal, characteristic, complemented
16C2×#1853C211yesmaximal, characteristic, complemented
17#20628C211yesmaximal, characteristic, complemented
18C2×#544—216no—
19C2×#544—21no—
20C2×#544—21no—
21C2×#544—22no—
22C2×#544C2212yes—
23C2×#544C2214yes—
24C2×#544C2212yes—
25C22×C4⋊Q8—21no—
26C22×C4⋊Q8C2212yes—
27C22×#125—21no—
28C22×#125C2212yes—
29C2×#525C2211yescharacteristic
30C22×C22⋊Q8—22no—
31C2×#520C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#3084—216no—
36C2×#479C2214yescomplemented
37C2×#475C2214yescomplemented
38C2×#478C2214yescomplemented
39C2×#476C2214yescomplemented
40C2×#428C2212yes—
41C22×#106C2212yes—
42C2×#424C2212yes—
43C2×#417C2212yes—
44C2×#416C2212yes—
45C2×#407C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47#2359—22no—
48#2358—22no—
49#2354—21no—
50#2352—21no—
51#2352—21no—
52D4×C4⋊C4—21no—
53#2324C2212yes—
54#2323C2212yes—
55#2317C2211yescharacteristic
56#2311C2211yescharacteristic
57C4×C22⋊Q8C2212yes—
58C4×#121C2212yes—
59C2×#380C2211yescharacteristic
60#2274C2211yescharacteristic
61#2059C2214yescomplemented
62#2059C2214yescomplemented
63#2058C2214yescomplemented
64#2058C2214yescomplemented
65#2026C2214yescomplemented
66#2025C2214yescomplemented
67#2024C2214yescomplemented
68#2023C2214yescomplemented
69#1989C2214yescomplemented
70#1989C2214yescomplemented
71#1988C2214yescomplemented
72#1987C2214yescomplemented
73#1875C2212yes—
74#1874C2211yescharacteristic
75#1874C2211yescharacteristic
76#1874C2212yes—
77#1874C2212yes—
78#1873C2212yes—
79#1872C2211yescharacteristic
80#1872C2211yescharacteristic
81#1872C2212yes—
82#1872C2212yes—
83#1854C2214yes—
84#1853C2212yes—
85#1853C2212yes—
86#1853C2214yes—
87#1853C2212yes—
88#1852C2212yes—
89#1798C2214yes—
90#1797C2212yes—
91#1797C2212yes—
92#1736C2212yes—
93#1736C2212yes—
94#1735C2212yes—
95C2×#340C2212yes—
96#1729C2212yes—
97C22×#41C2311yescharacteristic
98C23×Q8—22no—
99C24×C4—21no—
100C24×C4C2311yescharacteristic
101C22×M16C2312yes—
102C23×C8C2312yes—
103#544—216no—
104#544—216no—
105#544—232no—
106#544—216no—
107#544—216no—
108#544—28no—
109#544—28no—
110#544—28no—
111#544D4116yescomplemented
112C2×C4⋊Q8—216no—
113C2×C4⋊Q8—216no—
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8C2314yes—
120C2×C4⋊Q8C2314yes—
121C2×#125—216no—
122C2×#125—216no—
123C2×#125—22no—
124C2×#125—24no—
125C2×#125—22no—
126C2×#125—22no—
127C2×#125—22no—
128C2×#125C2314yes—
129C2×#125C2314yes—
130#525—24no—
131#525Q818yescomplemented
132C2×#123—21no—
133C2×C22⋊Q8—232no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8C2311yescharacteristic
139C2×C22⋊Q8C2311yescharacteristic
140C2×#121C2311yescharacteristic
141C2×#121C2311yescharacteristic
142C2×#120—21no—
143#520—28no—
144C2×C4×Q8C2312yes—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4C2312yes—
150C2×#117—21no—
151C2×#117—21no—
152C2×#117—28no—
153C2×#117—28no—
154C2×#117—21no—
155C2×#117D411yescharacteristic
156C2×#117D411yescharacteristic
157C2×#117D412yes—
158C2×#117C2312yes—
159C2×#117C2312yes—
160C2×#117C2311yescharacteristic
161C2×#117C2312yes—
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4—22no—
168C22×C4⋊C4—22no—
169C22×C4⋊C4—22no—
170C22×C4⋊C4—28no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4D411yescharacteristic
173C22×C4⋊C4D411yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4—21no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4D412yes—
184C22×C42—21no—
185C22×C42C2312yes—
186#479—216no—
187#478—216no—
188#476—216no—
189#475—216no—
190#428—28no—
191C2×#107C2314yes—
192C2×#106—28no—
193C2×#106C2314yes—
194C2×#106C2314yes—
195C2×#106C2314yes—
196#424—28no—
197C2×C4⋊C8C2314yes—
198C2×C4⋊C8C2314yes—
199#417—28no—
200#416—28no—
201C2×#103C2312yes—
202C2×#103C2314yes—
203C2×#103C2312yes—
204C2×#102C2312yes—
205C2×#102C2314yes—
206C2×#102C2312yes—
207#407—24no—
208C2×C22⋊C8—24no—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214#391C2312yes—
215#390—22no—
216#390C2312yes—
217#389—22no—
218#389C2312yes—
219#389C2312yes—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#384—21no—
233#382—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380C2312yes—
239#380C2312yes—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C2×#95—21no—
249#340C2312yes—
250#340C2312yes—
251#340C2314yes—
252#340C2314yes—
253#340C2312yes—
254#340C2312yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—22no—
263C2×#41—24no—
264C2×#41—24no—
265C2×#41C2×Q814yescomplemented
266C22×Q8—216no—
267C22×Q8—24no—
268C22×Q8—24no—
269C22×Q8—84no—
270C22×Q8—84no—
271C22×Q8C2411yescharacteristic
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4C2411yescharacteristic
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—28no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—82no—
289C23×C4—82no—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×Q814yes—
296C23×C4#4114yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C22×C8—24no—
304C22×C8—24no—
305C22×C8—24no—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2414yes—
309C4⋊Q8—232no—
310C4⋊Q8—216no—
311C4⋊Q8—216no—
312C4⋊Q8—216no—
313C4⋊Q8—216no—
314C4⋊Q8—28no—
315C4⋊Q8—28no—
316C4⋊Q8—28no—
317C4⋊Q8C2×D4116yes—
318#125—232no—
319#125—216no—
320#125—216no—
321#125—216no—
322#125—216no—
323#125—28no—
324#125—28no—
325#125—28no—
326#125C2×D4116yes—
327#123—28no—
328C22⋊Q8—232no—
329C22⋊Q8—232no—
330C22⋊Q8—232no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—232no—
334C22⋊Q8C2×Q814yes—
335C22⋊Q8C2×Q814yescomplemented
336#121—22no—
337#121—22no—
338#121C2×Q814yes—
339#121C2×Q814yescomplemented
340#120—28no—
341C4×Q8—28no—
342C4×D4—28no—
343C4×D4—28no—
344C4×D4—28no—
345C4×D4—48no—
346C4×D4—84no—
347#117—28no—
348#117—28no—
349#117—24no—
350#117—24no—
351#117—22no—
352#117—24no—
353#117—24no—
354#117—24no—
355#117—24no—
356#117—28no—
357#117—28no—
358#117—44no—
359#117C2×D418yes—
360#117C2×D418yes—
361#117C2×Q814yescomplemented
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—216no—
366C2×C4⋊C4—216no—
367C2×C4⋊C4—216no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D412yes—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D412yes—
400C2×C4⋊C4C2×D418yes—
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2414yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2411yescharacteristic
409C2×C4⋊C4C2411yescharacteristic
410C2×C22⋊C4—28no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—82no—
425C2×C22⋊C4C2×D412yes—
426C2×C22⋊C4C2×D412yes—
427C2×C22⋊C4C2×D412yes—
428C2×C22⋊C4C2×D412yes—
429C2×C42—28no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—21no—
433C2×C42—28no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×D412yes—
438C2×C42C2×D412yes—
439C2×C42C2412yes—
440C2×C42C2412yes—
441#107—28no—
442#106—28no—
443#106—28no—
444#106—28no—
445C4⋊C8—28no—
446C4⋊C8—28no—
447#103—24no—
448#103—24no—
449#103—28no—
450#102—24no—
451#102—24no—
452#102—28no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—41no—
472C24—41no—
473C24C22⋊Q814yes—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477#41—216no—
478#41—48no—
479C2×Q8—216no—
480C2×Q8—216no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—84no—
485C2×Q8—84no—
486C2×Q8—84no—
487C2×Q8—84no—
488C2×Q8—832no—
489C2×Q8C22×Q812yes—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4C22×Q812yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—28no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—44no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—44no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—816no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4C22⋊Q814yes—
558C22×C4C22⋊Q814yes—
559C22×C4C22⋊Q814yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D414yes—
568C22×C4C22×Q812yes—
569C22×C4C22×Q812yes—
570C22×C4C22×Q812yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C42−1+414yes—
575C22×C4C2511yescharacteristic
576M16—48no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—24no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—24no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—48no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—216no—
592C4⋊C4—216no—
593C4⋊C4—216no—
594C4⋊C4—28no—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—216no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4#12014yes—
617C4⋊C4#12014yes—
618C4⋊C4C22×D418yes—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C4⋊C4C22×Q812yes—
622C4⋊C4C22×Q812yes—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—82no—
636C22⋊C4—82no—
637C22⋊C4—82no—
638C22⋊C4#12018yes—
639C42—28no—
640C42—28no—
641C42—24no—
642C42—24no—
643C42—24no—
644C42—24no—
645C42—44no—
646C42—82no—
647C42—82no—
648C42C22×D418yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—28no—
660C23—21no—
661C23—28no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C2×#12012yes—
678C23C2×C22⋊Q812yes—
679C23C2×C22⋊Q812yes—
680C23C2×C22⋊Q812yes—
681C23#53612yes—
682C23#57712yes—
683C23#57712yes—
684C23C23×D411yescharacteristic
685Q8—24no—
686Q8—42no—
687Q8—816no—
688Q8—816no—
689D4—24no—
690D4—48no—
691D4—48no—
692D4—42no—
693D4—84no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—28no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—416no—
725C2×C4—48no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—88no—
746C2×C4—88no—
747C2×C4—164no—
748C2×C4—162no—
749C2×C4—162no—
750C2×C4C2×#12014yes—
751C2×C4C2×#12014yes—
752C2×C4C2×#12012yes—
753C2×C4C2×C22⋊Q812yes—
754C2×C4C2×C22⋊Q812yes—
755C2×C4C2×C22⋊Q812yes—
756C2×C4#53612yes—
757C2×C4#54818yes—
758C2×C4D4×Q818yes—
759C2×C4C23×D412yes—
760C2×C4C23×Q811yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×2−1+412yes—
763C8—42no—
764C8—42no—
765C8—44no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22#240914yes—
794C22#308414yescomplemented
795C22C22×#12011yescharacteristic
796C22C22×C22⋊Q811yescharacteristic
797C22C2×#53611yescharacteristic
798C22C2×#57711yescharacteristic
799C22C2×#57711yescharacteristic
800C22#358511yescharacteristic
801C22#358611yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—48no—
811C4—44no—
812C4—42no—
813C4—44no—
814C4—82no—
815C4—82no—
816C4#240914yes—
817C4C2×#54812yes—
818C4C2×D4×Q812yes—
819C2—24no—
820C2—24no—
821C2—42no—
822C2—82no—
823C2C2×#240911yescharacteristic
824C2#6037311yescharacteristic
825C2#6037411yescharacteristic
826C2C2×#308411yescharacteristic
827C2#6049311yescharacteristic
828C2#6087211yescharacteristic
829C2#6087311yescharacteristic
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×#3084C2semidirect
4. #24310C2semidirect
5. #24309C2semidirect
6. #24307C2semidirect
7. #24305C2semidirect
8. #24301C2semidirect
9. #24299C2semidirect
10. #23556C2semidirect
11. #23458C2semidirect
12. #21315C2semidirect
15. #20846C2semidirect
16. C2×#1853C2semidirect
17. #20628C2semidirect
36. C2×#479C22semidirect
37. C2×#475C22semidirect
38. C2×#478C22semidirect
39. C2×#476C22semidirect
61. #2059C22semidirect
62. #2059C22semidirect
63. #2058C22semidirect
64. #2058C22semidirect
65. #2026C22semidirect
66. #2025C22semidirect
67. #2024C22semidirect
68. #2023C22semidirect
69. #1989C22semidirect
70. #1989C22semidirect
71. #1988C22semidirect
72. #1987C22semidirect
111. #544D4semidirect
131. #525Q8semidirect
265. C2×#41C2×Q8semidirect
335. C22⋊Q8C2×Q8semidirect
339. #121C2×Q8semidirect
361. #117C2×Q8semidirect
794. C22#3084semidirect

Maximal subgroups

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

subgroupindex
C22×#5442
C2×#30842
#342022
#243102
#243092
#243072
#243052
#243012
#242992
#235562
#234582
#213152
#209092
#209082
#208462
C2×#18532
#206282