Finite Group Databasebeta

← #6457212

Subgroups — #6457212

Order 512.

2192 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3093C211yesmaximal, characteristic
2C2×#3092C211yesmaximal, characteristic
3#34065C211yesmaximal, characteristic
4C2×#2317C211yesmaximal, characteristic, complemented
5#27657C214yesmaximal, complemented
6#27656C214yesmaximal, complemented
7#27655C214yesmaximal, complemented
8#27654C214yesmaximal, complemented
9#23659C211yesmaximal, characteristic, complemented
10#23658C211yesmaximal, characteristic, complemented
11#23631C211yesmaximal, characteristic, complemented
12#23630C211yesmaximal, characteristic, complemented
13#21172C211yesmaximal, characteristic, complemented
14#21171C211yesmaximal, characteristic, complemented
15#20701C211yesmaximal, characteristic, complemented
16#20700C211yesmaximal, characteristic, complemented
17#20649C211yesmaximal, characteristic, complemented
18#20648C211yesmaximal, characteristic, complemented
19#20627C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#3093—28no—
26#3092—28no—
27C2×#484C2212yes—
28C2×#481C2212yes—
29C2×#485C2212yes—
30C2×#485C2212yes—
31C2×#482C2212yes—
32C2×#482C2212yes—
33C2×#483C2212yes—
34C2×#480C2212yes—
35C2×#428C2211yescharacteristic
36C2×#428C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#423C2211yescharacteristic
40C2×#423C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#407C2211yescharacteristic
46C2×#407C2211yescharacteristic
47#2324C2212yes—
48#2324C2212yes—
49#2323C2212yes—
50#2323C2212yes—
51#2322—22no—
52#2321—22no—
53#2317—21no—
54#2317—21no—
55#2317—21no—
56#2317—21no—
57#2317C2214yes—
58#2317C2214yes—
59#2297C2211yescharacteristic
60#2296C2211yescharacteristic
61#2293—21no—
62#2293—21no—
63C2×#389—22no—
64#2290—21no—
65#2290—21no—
66C2×#385—22no—
67C2×#384C2211yescharacteristic
68C2×#384C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C2×#382C2211yescharacteristic
71#2280C2211yescharacteristic
72C4×#117C2211yescharacteristic
73#2085C2214yescomplemented
74#2085C2214yescomplemented
75#2084C2214yescomplemented
76#2083C2214yescomplemented
77#2074C2214yescomplemented
78#2073C2214yescomplemented
79#2072C2214yescomplemented
80#2071C2214yescomplemented
81#1949C2214yescomplemented
82#1949C2214yescomplemented
83#1948C2214yescomplemented
84#1947C2214yescomplemented
85#1825C2214yes—
86#1825C2214yes—
87#1824C2214yes—
88#1823C2214yes—
89#1805C2214yescomplemented
90#1804C2214yescomplemented
91#1803C2214yescomplemented
92#1802C2214yescomplemented
93#1798C2214yes—
94#1798C2214yes—
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1736C2211yescharacteristic
102#1736C2211yescharacteristic
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C24×C4—21no—
107C24×C4C2311yescharacteristic
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C22×M16C2311yescharacteristic
112#525—24no—
113#525D418yes—
114C2×#123—21no—
115C2×C22⋊Q8C2311yescharacteristic
116C2×C22⋊Q8C2311yescharacteristic
117C2×#121C2311yescharacteristic
118C2×#121C2311yescharacteristic
119C2×#120—21no—
120C4×#41—24no—
121C4×#41—24no—
122C2×C4×Q8C2312yes—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—22no—
126C2×C4×D4C2312yes—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117D411yescharacteristic
135C2×#117D411yescharacteristic
136C2×#117D411yescharacteristic
137C2×#117D411yescharacteristic
138C2×#117C2312yes—
139C2×#117C2312yes—
140C2×#117C2311yescharacteristic
141C2×#117C2311yescharacteristic
142C2×#117C2311yescharacteristic
143C2×#117C2312yes—
144C2×#117C2312yes—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—24no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4—22no—
152C22×C4⋊C4D412yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C22⋊C4—21no—
160C22×C22⋊C4D412yes—
161C22×C42—21no—
162C22×C42—21no—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#485—28no—
166#485—28no—
167#484—28no—
168#483—28no—
169#482—28no—
170#482—28no—
171#481—28no—
172#480—28no—
173#428—24no—
174#428—24no—
175#428—24no—
176#428—24no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185#423—24no—
186#423—24no—
187C2×C4⋊C8C2314yes—
188C2×C4⋊C8C2314yes—
189#417—24no—
190#417—24no—
191#417—24no—
192#417—24no—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201#407—24no—
202#407—24no—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207#391C2312yes—
208#390—22no—
209#390—22no—
210#390C2312yes—
211#389—24no—
212#389—24no—
213#389—24no—
214#389—24no—
215#389—22no—
216#389—22no—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#387—22no—
226#387—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—24no—
234#385—24no—
235#385—24no—
236#385—24no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384—21no—
241#384C2314yes—
242#384C2314yes—
243#382—21no—
244#382—21no—
245#382—21no—
246#382—21no—
247#382C2314yes—
248#382C2314yes—
249#381—21no—
250#380C2312yes—
251#380C2312yes—
252#379—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4C2312yes—
256C4×C4⋊C4C2312yes—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262#376—21no—
263C2×#95—22no—
264C2×#95—22no—
265C43—21no—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2314yes—
275#336C2314yes—
276C25C2×D411yescharacteristic
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41C2×D414yes—
283C22×Q8C2411yescharacteristic
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C2411yescharacteristic
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—44no—
301C23×C4—84no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D414yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4#4114yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328#123—28no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8C2×D414yes—
332C22⋊Q8C2×D414yes—
333#121—22no—
334#121—22no—
335#121C2×D414yes—
336#121C2×D414yes—
337#120—28no—
338C4×Q8—24no—
339C4×Q8—24no—
340C4×D4—28no—
341C4×D4—28no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—48no—
345#117—22no—
346#117—24no—
347#117—24no—
348#117—24no—
349#117—24no—
350#117—24no—
351#117—24no—
352#117—24no—
353#117—24no—
354#117—24no—
355#117—24no—
356#117—24no—
357#117—24no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—44no—
363#117—44no—
364#117—44no—
365#117C2×D414yes—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—84no—
398C2×C4⋊C4—84no—
399C2×C4⋊C4C2×D412yes—
400C2×C4⋊C4C2×D412yes—
401C2×C4⋊C4C2×D412yes—
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2411yescharacteristic
410C2×C4⋊C4C2411yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4C2×D412yes—
428C2×C22⋊C4C2×D412yes—
429C2×C22⋊C4C2×D412yes—
430C2×C22⋊C4C2×D412yes—
431C2×C42—21no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—21no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—21no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—44no—
442C2×C42—44no—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42#4114yes—
448C2×C42#4114yes—
449C2×C42C2412yes—
450C2×C42C2412yes—
451#107—24no—
452#107—24no—
453#107—24no—
454#107—24no—
455#106—24no—
456#106—24no—
457#106—24no—
458#106—24no—
459C4⋊C8—28no—
460C4⋊C8—28no—
461#103—24no—
462#103—24no—
463#103—24no—
464#103—24no—
465#102—24no—
466#102—24no—
467#102—24no—
468#102—24no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—42no—
489C24—42no—
490C24#12114yes—
491C24C22×D411yescharacteristic
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494#41—28no—
495#41—28no—
496#41—44no—
497#41—44no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C22×D412yes—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—82no—
515C2×D4—82no—
516C2×D4C22×D412yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—816no—
568C22×C4#12114yes—
569C22×C4#12114yes—
570C22×C4#12114yes—
571C22×C4#12318yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D412yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C42−1+412yes—
588C22×C42−1+412yes—
589C22×C4C2511yescharacteristic
590M16—44no—
591M16—44no—
592M16—44no—
593M16—44no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4C22×D412yes—
640C4⋊C4C22×D412yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—44no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C42—24no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—44no—
665C42—44no—
666C42—42no—
667C42—44no—
668C42—42no—
669C42—82no—
670C42—82no—
671C42#12314yes—
672C42#12314yes—
673C42C2×#4114yes—
674C42C2×#4114yes—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—28no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—48no—
690C23—48no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—41no—
695C23C2×#12112yes—
696C23C2×#12112yes—
697C23C2×#12112yes—
698C23C2×#12312yes—
699C23#53612yes—
700C23C23×D411yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—41no—
704Q8—41no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—88no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—88no—
767C2×C4—88no—
768C2×C4C2×#12112yes—
769C2×C4C2×#12112yes—
770C2×C4C2×#12112yes—
771C2×C4C2×#12314yes—
772C2×C4C2×#12314yes—
773C2×C4C2×#12312yes—
774C2×C4#53612yes—
775C2×C4#54714yes—
776C2×C4#54714yes—
777C2×C4#55214yes—
778C2×C4#55214yes—
779C2×C4C23×D411yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C22×#4111yescharacteristic
782C2×C4C22×#4111yescharacteristic
783C2×C4C2×2−1+411yescharacteristic
784C2×C4C2×2−1+411yescharacteristic
785C8—42no—
786C8—42no—
787C8—42no—
788C8—42no—
789C22—22no—
790C22—22no—
791C22—24no—
792C22—24no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—416no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—82no—
808C22—82no—
809C22#248614yes—
810C22C22×#12111yescharacteristic
811C22C22×#12311yescharacteristic
812C22C2×#53611yescharacteristic
813C22#358512yes—
814C22#358612yes—
815C4—24no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4#248614yes—
831C4C2×#54711yescharacteristic
832C4C2×#54711yescharacteristic
833C4C2×#55211yescharacteristic
834C4C2×#55211yescharacteristic
835C2—24no—
836C2—42no—
837C2—42no—
838C2—82no—
839C2C2×#248611yescharacteristic
840C2#6042611yescharacteristic
841C2#6042711yescharacteristic
842C2#6051712yes—
843C2#6086712yes—
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
4. C2×#2317C2semidirect
5. #27657C2semidirect
6. #27656C2semidirect
7. #27655C2semidirect
8. #27654C2semidirect
9. #23659C2semidirect
10. #23658C2semidirect
11. #23631C2semidirect
12. #23630C2semidirect
13. #21172C2semidirect
14. #21171C2semidirect
15. #20701C2semidirect
16. #20700C2semidirect
17. #20649C2semidirect
18. #20648C2semidirect
19. #20627C2semidirect
73. #2085C22semidirect
74. #2085C22semidirect
75. #2084C22semidirect
76. #2083C22semidirect
77. #2074C22semidirect
78. #2073C22semidirect
79. #2072C22semidirect
80. #2071C22semidirect
81. #1949C22semidirect
82. #1949C22semidirect
83. #1948C22semidirect
84. #1947C22semidirect
89. #1805C22semidirect
90. #1804C22semidirect
91. #1803C22semidirect
92. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30932
C2×#30922
#340652
C2×#23172
#276572
#276562
#276552
#276542
#236592
#236582
#236312
#236302
#211722
#211712
#207012
#207002
#206492
#206482
#206272