Finite Group Databasebeta

← #6477674

Subgroups — #6477674

Order 512.

2026 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3096C212yesmaximal, complemented
2#37297C211yesmaximal, characteristic
3#34253C211yesmaximal, characteristic, complemented
4#33116C212yesmaximal, complemented
5#33113C211yesmaximal, characteristic, complemented
6#33113C211yesmaximal, characteristic, complemented
7#29763C212yesmaximal, complemented
8#29755C211yesmaximal, characteristic, complemented
9#29754C211yesmaximal, characteristic, complemented
10#24591C212yesmaximal, complemented
11#24589C212yesmaximal, complemented
12#24587C212yesmaximal, complemented
13#24585C212yesmaximal, complemented
14#24494C212yesmaximal, complemented
15#24492C212yesmaximal, complemented
16#24478C212yesmaximal, complemented
17#24476C212yesmaximal, complemented
18#21936C211yesmaximal, characteristic, complemented
19#21770C212yesmaximal, complemented
20C2×#535C2212yes—
21C2×#520C2211yescharacteristic
22#3096—216no—
23C2×#481C2212yes—
24C2×#481C2212yescomplemented
25C2×#482C2212yes—
26C2×#482C2212yes—
27C2×#482C2212yescomplemented
28C2×#482C2212yescomplemented
29C2×#480C2212yes—
30C2×#480C2212yescomplemented
31C2×#428C2212yescomplemented
32C2×#427C2212yescomplemented
33C2×#418C2212yescomplemented
34C22×#102C2212yescomplemented
35C2×#408C2212yes—
36#2856C2211yescharacteristic
37#2856C2211yescharacteristic
38#2733—21no—
39#2733—21no—
40#2679—21no—
41#2679—21no—
42#2669—22no—
43#2669—22no—
44#2619C2212yes—
45#2500C2212yes—
46#2500C2212yes—
47#2433C2212yes—
48#2433C2212yes—
49#2353—22no—
50#2352—22no—
51#2347C2212yescomplemented
52#2346C2212yescomplemented
53#2345C2212yescomplemented
54#2344C2212yescomplemented
55#2320—21no—
56#2319—21no—
57#2316C2211yescharacteristic, complemented
58#2311C2211yescharacteristic
59#2297C2211yescharacteristic
60#2295—21no—
61#2293—21no—
62C2×#389C2211yescharacteristic, complemented
63#2274C2211yescharacteristic, complemented
64C4×#117C2211yescharacteristic, complemented
65#2085C2212yescomplemented
66#2085C2212yescomplemented
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2067C2212yescomplemented
70#2067C2212yescomplemented
71#2067C2212yescomplemented
72#2067C2212yescomplemented
73#2065C2212yescomplemented
74#2065C2212yescomplemented
75#2065C2212yescomplemented
76#2065C2212yescomplemented
77#2041C2212yes—
78#2041C2212yes—
79#2041C2212yes—
80#2041C2212yes—
81#1982C2211yescharacteristic
82#1982C2211yescharacteristic
83#1982C2211yescharacteristic
84#1982C2211yescharacteristic
85#1982C2212yes—
86#1982C2212yes—
87#1949C2212yescomplemented
88#1949C2212yescomplemented
89#1948C2211yescharacteristic, complemented
90#1948C2211yescharacteristic, complemented
91#1947C2211yescharacteristic, complemented
92#1947C2211yescharacteristic, complemented
93#1926C2212yescomplemented
94#1926C2212yescomplemented
95#1926C2212yescomplemented
96#1926C2212yescomplemented
97#1925C2212yescomplemented
98#1925C2212yescomplemented
99#1925C2212yescomplemented
100#1925C2212yescomplemented
101#1895C2212yes—
102#1895C2212yes—
103#1893C2212yes—
104#1893C2212yes—
105#1875C2212yescomplemented
106#1875C2212yescomplemented
107#1874C2212yescomplemented
108#1874C2212yescomplemented
109#1851C2212yescomplemented
110#1851C2212yescomplemented
111#1850C2212yescomplemented
112#1850C2212yescomplemented
113#1825C2212yescomplemented
114#1825C2212yescomplemented
115#1798C2212yescomplemented
116#1797C2211yescharacteristic, complemented
117#1797C2211yescharacteristic, complemented
118#1786C2212yescomplemented
119#1786C2212yescomplemented
120C22×#41C2311yescharacteristic
121C23×D4C2312yes—
122C22×M16C2312yes—
123C23×C8C2312yes—
124#535—28no—
125#535—28no—
126C2×#127—22no—
127C2×#127C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#127C2312yes—
130C2×#124—22no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×#120—22no—
140C2×#120—22no—
141C2×#120—22no—
142C2×#120—22no—
143C2×#120—22no—
144C2×#120—22no—
145#520—24no—
146#520D418yescomplemented
147C2×C4×Q8—21no—
148C2×C4×D4—21no—
149C2×C4×D4—22no—
150C2×#117—22no—
151C2×#117C2312yes—
152C2×#117C2312yes—
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#482—28no—
162#482—28no—
163#482—28no—
164#482—28no—
165#481—28no—
166#481—28no—
167#480—28no—
168#480—28no—
169#428—28no—
170#427—28no—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185#418—28no—
186C2×#102—28no—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203#408—28no—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208#394—22no—
209#394—22no—
210#394—22no—
211#394—22no—
212#394—22no—
213#394—22no—
214#392—22no—
215#392—22no—
216#392—22no—
217#392—22no—
218#392—22no—
219#392—22no—
220#391—21no—
221#391D411yescharacteristic
222#391D411yescharacteristic
223#390—21no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390D411yescharacteristic
229#390D411yescharacteristic
230#390C2312yes—
231#390C2312yes—
232#390C2312yes—
233#390C2312yes—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#386—22no—
255#386D412yes—
256#386D412yes—
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#383—22no—
260#382—22no—
261#382C2312yes—
262#381—22no—
263#380—22no—
264#380—22no—
265#380C2312yes—
266#380C2312yes—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—22no—
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4—21no—
277C4×C22⋊C4—21no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4C2312yes—
281C4×C22⋊C4C2312yes—
282#376—21no—
283#376—22no—
284C2×#95—21no—
285C43—21no—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298C25—22no—
299C2×#41—41no—
300C2×#41—41no—
301C2×#41—41no—
302C2×#41—41no—
303C2×#41C2×D414yes—
304C2×#41#4114yes—
305C22×Q8C2×D411yescharacteristic
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—24no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—24no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4—42no—
323C22×D4C2×D411yescharacteristic
324C22×D4C2×D412yes—
325C22×D4C2412yes—
326C22×D4C2412yes—
327C23×C4—21no—
328C23×C4—22no—
329C23×C4—21no—
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2412yes—
334C2×M16—24no—
335C2×M16—42no—
336C2×M16—42no—
337C22×C8—24no—
338C22×C8—42no—
339C22×C8—42no—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C22×C8C2412yes—
344#127—41no—
345#127—41no—
346#127—41no—
347#127—41no—
348#127—42no—
349#127—42no—
350#127—48no—
351#124—48no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—24no—
360#121—82no—
361#121—82no—
362#121—82no—
363#121—82no—
364#120—48no—
365#120—48no—
366#120—84no—
367#120—84no—
368#120—84no—
369#120—84no—
370C4×Q8—28no—
371C4×D4—28no—
372C4×D4—216no—
373#117—24no—
374#117—22no—
375#117—24no—
376#117—24no—
377#117—41no—
378#117—41no—
379#117—41no—
380#117—41no—
381#117—84no—
382#117C2×D418yes—
383#117C2×D414yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—82no—
400C2×C4⋊C4C2×D418yes—
401C2×C4⋊C4C2×D414yes—
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2411yescharacteristic
408C2×C4⋊C4C2411yescharacteristic
409C2×C4⋊C4C2411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2411yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4C2×D412yes—
431C2×C22⋊C4C2×D412yes—
432C2×C22⋊C4C2×D412yes—
433C2×C22⋊C4C2×D412yes—
434C2×C22⋊C4C2×D412yes—
435C2×C42—21no—
436C2×C42—22no—
437C2×C42—21no—
438C2×C42—22no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—22no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—22no—
445C2×C42—41no—
446C2×C42—41no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2412yes—
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—24no—
453#107—24no—
454#107—24no—
455#107—24no—
456#106—24no—
457#106—24no—
458#106—24no—
459#106—24no—
460C4⋊C8—41no—
461C4⋊C8—41no—
462C4⋊C8—41no—
463C4⋊C8—41no—
464C4⋊C8—42no—
465C4⋊C8—42no—
466#102—24no—
467#102—24no—
468#102—24no—
469#102—24no—
470#102—24no—
471#102—24no—
472#102—24no—
473#102—24no—
474#102—42no—
475#102—42no—
476#102—42no—
477#102—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481#102—42no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C22⋊C8—24no—
486#95—22no—
487#95—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95C2×D412yes—
501#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504C24—22no—
505C24—22no—
506C24—44no—
507C24—82no—
508C24—82no—
509C24—82no—
510C24—82no—
511C24—82no—
512C24—82no—
513C24C22×D412yes—
514C24C22×D411yescharacteristic
515#41—44no—
516#41—44no—
517#41—44no—
518#41—44no—
519C2×Q8—41no—
520C2×Q8—41no—
521C2×Q8#12114yes—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—84no—
550C2×D4—84no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—82no—
568C2×D4—82no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4#12114yes—
576C2×D4#12118yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D414yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C2×#4114yes—
619C22×C4C2×#4112yes—
620C22×C4C2511yescharacteristic
621M16—48no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—48no—
635C4⋊C4—28no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
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—41no—
651C4⋊C4—41no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—81no—
658C4⋊C4—81no—
659C4⋊C4—81no—
660C4⋊C4—81no—
661C4⋊C4C22×D412yes—
662C4⋊C4C22×D414yes—
663C4⋊C4C22×D412yes—
664C22⋊C4—28no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—42no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C42—28no—
688C42—24no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—22no—
694C42—22no—
695C42—41no—
696C42—41no—
697C42—42no—
698C42—44no—
699C42—42no—
700C42—42no—
701C42—81no—
702C42—81no—
703C42—82no—
704C42—82no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—22no—
716C23—21no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—88no—
732C23—164no—
733C23—164no—
734C23—164no—
735C23—164no—
736C23—164no—
737C23—164no—
738C23C2×#12114yes—
739C23C2×#12112yes—
740C23C23×D411yescharacteristic
741Q8—44no—
742D4—48no—
743D4—44no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—88no—
753D4—162no—
754D4—162no—
755D4—162no—
756D4—162no—
757D4—164no—
758D4—164no—
759D4—164no—
760D4—164no—
761D4—164no—
762D4—164no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—84no—
818C2×C4—88no—
819C2×C4—162no—
820C2×C4C2×#12114yes—
821C2×C4C2×#12112yes—
822C2×C4#57612yes—
823C2×C4#57712yes—
824C2×C4C23×D411yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4#58511yescharacteristic
827C2×C4#58511yescharacteristic
828C2×C4#58511yescharacteristic
829C2×C4#58511yescharacteristic
830C8—42no—
831C8—42no—
832C8—42no—
833C8—42no—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—22no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—1616no—
863C22C22×#12111yescharacteristic
864C22#348511yescharacteristic
865C22#348511yescharacteristic
866C22C2×#57611yescharacteristic
867C22C2×#57711yescharacteristic
868C22#358511yescharacteristic
869C22#358511yescharacteristic
870C4—24no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—42no—
875C4—44no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—42no—
880C4—42no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—81no—
885C4—81no—
886C4#344911yescharacteristic
887C4#344911yescharacteristic
888C4#349111yescharacteristic
889C4#349111yescharacteristic
890C2—42no—
891C2—44no—
892C2—162no—
893C2—162no—
894C2#3508911yescharacteristic
895C2#6042811yescharacteristic
896C2#6043111yescharacteristic
897C2#6175211yescharacteristic
898C2#6175611yescharacteristic
899C2#6178811yescharacteristic
900C2#6179711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37297C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3096C2semidirect
3. #34253C2semidirect
4. #33116C2semidirect
5. #33113C2semidirect
6. #33113C2semidirect
7. #29763C2semidirect
8. #29755C2semidirect
9. #29754C2semidirect
10. #24591C2semidirect
11. #24589C2semidirect
12. #24587C2semidirect
13. #24585C2semidirect
14. #24494C2semidirect
15. #24492C2semidirect
16. #24478C2semidirect
17. #24476C2semidirect
18. #21936C2semidirect
19. #21770C2semidirect
24. C2×#481C22semidirect
27. C2×#482C22semidirect
28. C2×#482C22semidirect
30. C2×#480C22semidirect
31. C2×#428C22semidirect
32. C2×#427C22semidirect
33. C2×#418C22semidirect
34. C22×#102C22semidirect
51. #2347C22semidirect
52. #2346C22semidirect
53. #2345C22semidirect
54. #2344C22semidirect
57. #2316C22semidirect
62. C2×#389C22semidirect
63. #2274C22semidirect
64. C4×#117C22semidirect
65. #2085C22semidirect
66. #2085C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
69. #2067C22semidirect
70. #2067C22semidirect
71. #2067C22semidirect
72. #2067C22semidirect
73. #2065C22semidirect
74. #2065C22semidirect
75. #2065C22semidirect
76. #2065C22semidirect
87. #1949C22semidirect
88. #1949C22semidirect
89. #1948C22semidirect
90. #1948C22semidirect
91. #1947C22semidirect
92. #1947C22semidirect
93. #1926C22semidirect
94. #1926C22semidirect
95. #1926C22semidirect
96. #1926C22semidirect
97. #1925C22semidirect
98. #1925C22semidirect
99. #1925C22semidirect
100. #1925C22semidirect
105. #1875C22semidirect
106. #1875C22semidirect
107. #1874C22semidirect
108. #1874C22semidirect
109. #1851C22semidirect
110. #1851C22semidirect
111. #1850C22semidirect
112. #1850C22semidirect
113. #1825C22semidirect
114. #1825C22semidirect
115. #1798C22semidirect
116. #1797C22semidirect
117. #1797C22semidirect
118. #1786C22semidirect
119. #1786C22semidirect
146. #520D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30962
#372972
#342532
#331162
#331132
#297632
#297552
#297542
#245912
#245892
#245872
#245852
#244942
#244922
#244782
#244762
#219362
#217702