Finite Group Databasebeta

← #6503229

Subgroups — #6503229

Order 512.

1822 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37437C211yesmaximal, characteristic
2#34361C211yesmaximal, characteristic, complemented
3#27869C212yesmaximal, complemented
4#27868C212yesmaximal, complemented
5#26213C212yesmaximal, complemented
6#26199C212yesmaximal, complemented
7#26137C212yesmaximal, complemented
8#26131C212yesmaximal, complemented
9#24958C212yesmaximal, complemented
10#24950C212yesmaximal, complemented
11#24890C212yesmaximal, complemented
12#24882C212yesmaximal, complemented
13#24567C212yesmaximal, complemented
14#24562C212yesmaximal, complemented
15#21939C211yesmaximal, characteristic, complemented
16#21761C211yesmaximal, characteristic, complemented
17#20973C211yesmaximal, characteristic, complemented
18#20897C211yesmaximal, characteristic, complemented
19#20660C211yesmaximal, characteristic, complemented
20C23×M16C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C2×#482C2212yescomplemented
24C2×#480C2212yescomplemented
25C2×#427C2211yescharacteristic, complemented
26C2×#427C2211yescharacteristic, complemented
27C2×#418C2211yescharacteristic
28C2×#418C2211yescharacteristic
29C2×#408C2211yescharacteristic, complemented
30C2×#408C2211yescharacteristic, complemented
31C22×C22⋊C8C2211yescharacteristic
32#2816—21no—
33#2815—21no—
34#2661—22no—
35#2624C2212yes—
36#2615C2212yes—
37#2613—22no—
38#2561—21no—
39#2539—21no—
40#2486C2212yes—
41#2414C2212yes—
42#2414C2212yes—
43#2408C2212yes—
44#2375—22no—
45#2374—22no—
46#2354C2212yes—
47#2354C2212yescomplemented
48#2352C2212yes—
49#2352C2212yescomplemented
50#2333—21no—
51#2333—21no—
52#2332—21no—
53#2332—21no—
54#2314C2212yescomplemented
55#2311C2212yescomplemented
56#2280C2211yescharacteristic
57#2280C2211yescharacteristic
58#2280C2211yescharacteristic
59#2101C2212yescomplemented
60#2100C2212yescomplemented
61#2093C2212yescomplemented
62#2092C2212yescomplemented
63#2085C2212yescomplemented
64#2084C2212yescomplemented
65#2077C2212yescomplemented
66#2076C2212yescomplemented
67#2075C2212yescomplemented
68#2075C2212yescomplemented
69#2073C2212yescomplemented
70#2071C2212yescomplemented
71#2034C2212yescomplemented
72#2034C2212yescomplemented
73#2034C2212yescomplemented
74#2033C2212yescomplemented
75#1926C2212yescomplemented
76#1926C2212yescomplemented
77#1926C2212yescomplemented
78#1925C2212yescomplemented
79#1921C2212yescomplemented
80#1920C2212yescomplemented
81#1918C2212yescomplemented
82#1918C2212yescomplemented
83#1895C2212yes—
84#1895C2212yes—
85#1893C2212yes—
86#1893C2212yes—
87#1893C2212yes—
88#1893C2212yes—
89#1875C2212yes—
90#1875C2212yes—
91#1875C2212yescomplemented
92#1874C2212yescomplemented
93#1870C2212yes—
94#1870C2212yes—
95#1869C2212yescomplemented
96#1869C2212yescomplemented
97#1854C2212yes—
98#1854C2212yes—
99#1854C2212yescomplemented
100#1854C2212yescomplemented
101#1854C2212yescomplemented
102#1853C2212yescomplemented
103#1825C2212yescomplemented
104#1824C2212yes—
105#1824C2212yescomplemented
106#1809C2212yes—
107#1809C2212yes—
108#1809C2212yescomplemented
109#1809C2212yescomplemented
110#1808C2212yescomplemented
111#1807C2212yescomplemented
112#1786C2212yes—
113#1736C2211yescharacteristic
114#1736C2211yescharacteristic
115#1735C2211yescharacteristic, complemented
116#1735C2211yescharacteristic, complemented
117#1729C2211yescharacteristic, complemented
118#1729C2211yescharacteristic, complemented
119C22×#41C2311yescharacteristic
120C23×D4—21no—
121C23×D4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C22×M16—24no—
124C22×M16—42no—
125C22×M16—42no—
126C22×M16C2311yescharacteristic
127C22×M16C2311yescharacteristic
128C22×M16C2311yescharacteristic
129C22×M16C2311yescharacteristic
130C23×C8C2311yescharacteristic
131C23×C8C2311yescharacteristic
132C23×C8C2311yescharacteristic
133C23×C8C2311yescharacteristic
134#525—24no—
135#525—24no—
136C2×#123—22no—
137C2×#123D412yes—
138C2×C22⋊Q8D411yescharacteristic
139C2×C22⋊Q8D411yescharacteristic
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121D411yescharacteristic
145C2×#121D411yescharacteristic
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×#121C2312yes—
149C2×#121C2312yes—
150C2×#120—22no—
151C2×#120D412yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×#117C2312yes—
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C22⋊C4—21no—
165#482—44no—
166#480—44no—
167#427—42no—
168#427—42no—
169C2×#107C2312yes—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177#418—42no—
178#418—42no—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187#408—42no—
188#408—42no—
189C2×C22⋊C8—24no—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196#399—22no—
197#398—22no—
198#397—22no—
199#397—22no—
200#394—22no—
201#394—22no—
202#394—22no—
203#394—22no—
204#394—22no—
205#393—22no—
206#392—22no—
207#392—22no—
208#392—22no—
209#392—22no—
210#392—22no—
211#392—22no—
212#391—22no—
213#390—22no—
214#390—22no—
215#390—22no—
216#390—22no—
217#390—22no—
218#390C2312yes—
219#390C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#384C2312yes—
241#382C2312yes—
242#381—21no—
243#381—21no—
244#381—21no—
245#381—22no—
246#380C2312yes—
247#380C2312yes—
248#380C2312yes—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#379—21no—
257#379—21no—
258#379—21no—
259#379—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272#340C2312yes—
273#340C2312yes—
274#340C2312yes—
275#340C2312yes—
276#340C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C25—21no—
293C25C2×D411yescharacteristic
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—41no—
297C2×#41—41no—
298C2×#41—41no—
299C2×#41—41no—
300C22×Q8C2×D411yescharacteristic
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—41no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—41no—
312C22×D4—44no—
313C22×D4—84no—
314C22×D4C2×D412yes—
315C22×D4C2×D412yes—
316C22×D4C2×D412yes—
317C22×D4C2×D411yescharacteristic
318C22×D4C2412yes—
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—41no—
322C23×C4—41no—
323C23×C4—41no—
324C23×C4—41no—
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4#4114yes—
329C23×C4#4114yes—
330C23×C4C2412yes—
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—41no—
343C2×M16—41no—
344C2×M16—41no—
345C2×M16—41no—
346C2×M16—416no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—41no—
354C22×C8—41no—
355C22×C8—41no—
356C22×C8—41no—
357C22×C8—41no—
358C22×C8—41no—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365#123—28no—
366#123—84no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—24no—
373#121—24no—
374#121—24no—
375#121—44no—
376#121—44no—
377#121—42no—
378#121—42no—
379#121—42no—
380#121—42no—
381#120—28no—
382#120—84no—
383C4×D4—24no—
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—24no—
387#117—22no—
388#117—22no—
389#117—41no—
390#117—41no—
391#117—42no—
392#117—41no—
393#117—41no—
394#117—41no—
395#117—41no—
396#117—41no—
397#117—41no—
398#117—41no—
399#117—41no—
400#117—41no—
401#117—41no—
402#117—42no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
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—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42C2412yes—
465#107—24no—
466#107—24no—
467#107—42no—
468#107—42no—
469#106—42no—
470#106—42no—
471#106—42no—
472#106—42no—
473#102—24no—
474#102—24no—
475#102—42no—
476#102—42no—
477#102—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C22⋊C8—42no—
486C22⋊C8—42no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
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#95—22no—
501#95—22no—
502#95—22no—
503C24—22no—
504C24—41no—
505C24—41no—
506C24—42no—
507C24—42no—
508C24—44no—
509C24—42no—
510C24—81no—
511C24—81no—
512C24—82no—
513C24#12314yes—
514C24C22×D412yes—
515C24C22×D411yescharacteristic
516C24C22×D411yescharacteristic
517C24C22×D411yescharacteristic
518#41—82no—
519#41—82no—
520#41—82no—
521#41—82no—
522C2×Q8—22no—
523C2×Q8—41no—
524C2×Q8—41no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—42no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4—816no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4#12314yes—
604C22×C4#12314yes—
605C22×C4#12314yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2511yescharacteristic
619M16—44no—
620M16—44no—
621M16—44no—
622M16—44no—
623C2×C8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—44no—
641C2×C8—82no—
642C2×C8—82no—
643C2×C8H(5,𝔽2)12yes—
644C2×C8H(5,𝔽2)12yes—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—42no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—82no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—22no—
700C42—22no—
701C42—82no—
702C42—82no—
703C42—81no—
704C42—81no—
705C42—81no—
706C42—81no—
707C42—81no—
708C42—81no—
709C42—82no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23—164no—
745C23—164no—
746C23C2×#12312yes—
747C23C2×#12312yes—
748C23C2×#12312yes—
749C23C23×D411yescharacteristic
750Q8—82no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—82no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—88no—
761D4—88no—
762D4—164no—
763D4—164no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—84no—
820C2×C4—164no—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4C2×#12312yes—
824C2×C4C22×#4111yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4C2×H(5,𝔽2)11yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4#58511yescharacteristic
829C2×C4#58511yescharacteristic
830C8—22no—
831C8—22no—
832C8—41no—
833C8—41no—
834C8—42no—
835C8—42no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—88no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—168no—
867C22C22×#12311yescharacteristic
868C22#349611yescharacteristic
869C22#349611yescharacteristic
870C22#358412yes—
871C22#358512yes—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4#349011yescharacteristic
886C4#349111yescharacteristic
887C4#350511yescharacteristic
888C4#350511yescharacteristic
889C2—42no—
890C2—42no—
891C2—42no—
892C2—82no—
893C2—162no—
894C2#3536011yescharacteristic
895C2#6051611yescharacteristic
896C2#6051811yescharacteristic
897C2#6231812yes—
898C2#6232012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37437C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34361C2semidirect
3. #27869C2semidirect
4. #27868C2semidirect
5. #26213C2semidirect
6. #26199C2semidirect
7. #26137C2semidirect
8. #26131C2semidirect
9. #24958C2semidirect
10. #24950C2semidirect
11. #24890C2semidirect
12. #24882C2semidirect
13. #24567C2semidirect
14. #24562C2semidirect
15. #21939C2semidirect
16. #21761C2semidirect
17. #20973C2semidirect
18. #20897C2semidirect
19. #20660C2semidirect
23. C2×#482C22semidirect
24. C2×#480C22semidirect
25. C2×#427C22semidirect
26. C2×#427C22semidirect
29. C2×#408C22semidirect
30. C2×#408C22semidirect
47. #2354C22semidirect
49. #2352C22semidirect
54. #2314C22semidirect
55. #2311C22semidirect
59. #2101C22semidirect
60. #2100C22semidirect
61. #2093C22semidirect
62. #2092C22semidirect
63. #2085C22semidirect
64. #2084C22semidirect
65. #2077C22semidirect
66. #2076C22semidirect
67. #2075C22semidirect
68. #2075C22semidirect
69. #2073C22semidirect
70. #2071C22semidirect
71. #2034C22semidirect
72. #2034C22semidirect
73. #2034C22semidirect
74. #2033C22semidirect
75. #1926C22semidirect
76. #1926C22semidirect
77. #1926C22semidirect
78. #1925C22semidirect
79. #1921C22semidirect
80. #1920C22semidirect
81. #1918C22semidirect
82. #1918C22semidirect
91. #1875C22semidirect
92. #1874C22semidirect
95. #1869C22semidirect
96. #1869C22semidirect
99. #1854C22semidirect
100. #1854C22semidirect
101. #1854C22semidirect
102. #1853C22semidirect
103. #1825C22semidirect
105. #1824C22semidirect
108. #1809C22semidirect
109. #1809C22semidirect
110. #1808C22semidirect
111. #1807C22semidirect
115. #1735C22semidirect
116. #1735C22semidirect
117. #1729C22semidirect
118. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#374372
#343612
#278692
#278682
#262132
#261992
#261372
#261312
#249582
#249502
#248902
#248822
#245672
#245622
#219392
#217612
#209732
#208972
#206602