Finite Group Databasebeta

← #6433153

Subgroups — #6433153

Order 512.

2712 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35250C211yesmaximal, characteristic
2C2×#2311C211yesmaximal, characteristic, complemented
3#29899C214yesmaximal, complemented
4#29898C214yesmaximal, complemented
5#29892C212yesmaximal, complemented
6#29891C212yesmaximal, complemented
7#29891C212yesmaximal, complemented
8#29890C212yesmaximal, complemented
9#23643C212yesmaximal, complemented
10#23641C212yesmaximal, complemented
11#23486C212yesmaximal, complemented
12#23483C212yesmaximal, complemented
13#20912C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15#20844C211yesmaximal, characteristic, complemented
16#20843C211yesmaximal, characteristic, complemented
17#20581C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C2×#535C2211yescharacteristic
20C2×#535C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C2×#428C2212yescomplemented
25C2×#427C2212yescomplemented
26C2×#418C2212yescomplemented
27C22×#102C2212yescomplemented
28C2×#408C2212yes—
29C2×#408C2212yes—
30C2×#407C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32#2847C2212yes—
33#2847C2212yes—
34#2615C2212yes—
35#2615C2212yes—
36#2436—21no—
37#2433—21no—
38#2431—21no—
39#2431—21no—
40#2404—22no—
41#2403—22no—
42#2311—22no—
43#2311—21no—
44#2311—21no—
45#2311C2211yescharacteristic
46#2311C2212yes—
47#2311C2211yescharacteristic
48#2311C2212yes—
49#2311C2214yescomplemented
50C2×#391—21no—
51C2×#390—21no—
52C2×#386—22no—
53#2280C2211yescharacteristic
54C2×#380C2212yescomplemented
55C2×#380C2212yescomplemented
56#2077C2214yescomplemented
57#2077C2214yescomplemented
58#2077C2214yescomplemented
59#2077C2214yescomplemented
60#2076C2214yescomplemented
61#2076C2214yescomplemented
62#2075C2214yescomplemented
63#2075C2214yescomplemented
64#2034C2214yescomplemented
65#2034C2214yescomplemented
66#2034C2214yescomplemented
67#2034C2214yescomplemented
68#2033C2214yescomplemented
69#2033C2214yescomplemented
70#2033C2214yescomplemented
71#2033C2214yescomplemented
72#1875C2214yescomplemented
73#1874C2212yes—
74#1874C2212yes—
75#1874C2212yes—
76#1874C2212yes—
77#1874C2214yescomplemented
78#1854C2212yescomplemented
79#1854C2212yescomplemented
80#1853C2211yescharacteristic, complemented
81#1853C2211yescharacteristic, complemented
82#1853C2212yescomplemented
83#1853C2212yescomplemented
84#1852C2211yescharacteristic, complemented
85#1852C2211yescharacteristic, complemented
86#1852C2212yescomplemented
87#1852C2212yescomplemented
88#1780C2214yescomplemented
89#1779C2212yescomplemented
90#1779C2212yescomplemented
91#1736C2212yescomplemented
92#1736C2212yescomplemented
93#1735C2212yescomplemented
94C2×#340C2212yescomplemented
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—44no—
98C22×#41—44no—
99C22×#41D412yes—
100C22×#41D411yescharacteristic
101C22×#41D411yescharacteristic
102C22×#41C2311yescharacteristic
103C22×#41C2311yescharacteristic
104C22×#41C2312yes—
105C23×Q8D411yescharacteristic
106C23×D4—21no—
107C23×D4D412yes—
108C23×D4D411yescharacteristic
109C23×D4C2311yescharacteristic
110C24×C4—21no—
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C22×M16C2312yes—
114C23×C8C2312yes—
115#535—44no—
116#535—44no—
117C2×#127—21no—
118C2×#127—21no—
119C2×#124—21no—
120C2×#124—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—24no—
124C2×#121—24no—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#120—22no—
132C2×#120—22no—
133C2×#120—22no—
134C2×#120—22no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—44no—
138C2×#117C2312yes—
139C2×#117C2311yescharacteristic
140C2×#117C2311yescharacteristic
141C2×#117C2312yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—44no—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—22no—
155C22×C22⋊C4—22no—
156C22×C42—21no—
157#428—44no—
158#427—44no—
159C2×#107C2312yes—
160C2×#107C2314yes—
161C2×#107C2312yes—
162C2×#106C2314yes—
163C2×#106C2312yes—
164C2×#106C2312yes—
165#418—44no—
166C2×#102—44no—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171#408—44no—
172#408—44no—
173#407—24no—
174C2×C22⋊C8—24no—
175C2×C22⋊C8C2311yescharacteristic
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2311yescharacteristic
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184#393—22no—
185#393—22no—
186#392—22no—
187#392—22no—
188#392—22no—
189#392—22no—
190#392—22no—
191#392—22no—
192#391—22no—
193#391—22no—
194#391—24no—
195#391—21no—
196#391—21no—
197#390—22no—
198#390—22no—
199#390—24no—
200#390—21no—
201#390—21no—
202#386—24no—
203#386—24no—
204#386—24no—
205#386—24no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#381—21no—
215#380—22no—
216#380—22no—
217#380—22no—
218#380—22no—
219#380C2314yes—
220#380C2314yes—
221#380C2314yes—
222#380C2314yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2311yescharacteristic
228#380C2311yescharacteristic
229#380C2311yescharacteristic
230#380C2311yescharacteristic
231#379—21no—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—21no—
234C2×#95—22no—
235C2×#95—22no—
236#340C2314yes—
237#340C2314yes—
238#340C2312yes—
239#340C2314yes—
240#340C2314yes—
241#340C2312yes—
242#340C2314yes—
243#340C2314yes—
244#340C2312yes—
245#340C2312yes—
246C25—21no—
247C25C2×D411yescharacteristic
248C25C2×D412yes—
249C2×#41—28no—
250C2×#41—24no—
251C2×#41—24no—
252C2×#41—24no—
253C2×#41—24no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—24no—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—24no—
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C2×#41—44no—
266C2×#41—42no—
267C2×#41—42no—
268C2×#41—42no—
269C2×#41—42no—
270C2×#41—432no—
271C2×#41—432no—
272C22×Q8—24no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8C2×D411yescharacteristic
276C22×Q8C2×D411yescharacteristic
277C22×Q8C2×D412yes—
278C22×D4—28no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—24no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—24no—
290C22×D4—24no—
291C22×D4—42no—
292C22×D4—42no—
293C22×D4—44no—
294C22×D4—44no—
295C22×D4—44no—
296C22×D4—82no—
297C22×D4—82no—
298C22×D4C2×D412yes—
299C22×D4C2×D412yes—
300C22×D4C2×D411yescharacteristic
301C22×D4C2×D411yescharacteristic
302C22×D4C2×D412yes—
303C22×D4C2×D412yes—
304C22×D4C2×D412yes—
305C22×D4C2412yes—
306C23×C4—24no—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—22no—
313C23×C4—21no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—44no—
317C23×C4—44no—
318C23×C4—44no—
319C23×C4—82no—
320C23×C4—82no—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D412yes—
325C23×C4C2×D412yes—
326C23×C4C2×D412yes—
327C23×C4#4114yes—
328C23×C4#4114yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—24no—
337C22×C8—24no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2414yes—
343#127—44no—
344#127—44no—
345#124—44no—
346#124—44no—
347#121—24no—
348#121—24no—
349#121—24no—
350#121—24no—
351#121—44no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—44no—
357#120—48no—
358#120—48no—
359#120—84no—
360#120—84no—
361#117—24no—
362#117—24no—
363#117—24no—
364#117—24no—
365#117—42no—
366#117—42no—
367#117—44no—
368#117—44no—
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—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4C2414yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—84no—
419C2×C22⋊C4—84no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—44no—
425#107—42no—
426#107—42no—
427#107—44no—
428#106—42no—
429#106—42no—
430#106—44no—
431#102—44no—
432#102—44no—
433#102—44no—
434#102—44no—
435C22⋊C8—22no—
436C22⋊C8—22no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—44no—
441C22⋊C8—44no—
442C22⋊C8—44no—
443C22⋊C8—44no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—81no—
474C24—81no—
475C24—81no—
476C24—81no—
477C24#12314yes—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483#41—432no—
484#41—416no—
485#41—416no—
486#41—416no—
487#41—416no—
488#41—48no—
489#41—48no—
490#41—48no—
491#41—48no—
492C2×Q8—24no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—416no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—416no—
528C2×D4—432no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—816no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—216no—
560C22×C4—216no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—816no—
611C22×C4#12314yes—
612C22×C4#12314yes—
613C22×C4#12314yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4H(5,𝔽2)14yes—
626C22×C4H(5,𝔽2)14yes—
627C22×C4C2511yescharacteristic
628M16—48no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—24no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—24no—
635C2×C8—22no—
636C2×C8—24no—
637C2×C8—22no—
638C2×C8—48no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—81no—
670C22⋊C4—81no—
671C22⋊C4—84no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C22⋊C4—84no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C42—44no—
680C42—44no—
681C42—42no—
682C42—42no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—28no—
694C23—28no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—48no—
719C23—48no—
720C23—48no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—162no—
736C23—162no—
737C23—162no—
738C23—162no—
739C23C2×#12312yes—
740C23C2×#12312yes—
741C23C2×#12312yes—
742C23#53412yes—
743C23#53412yes—
744C23#57612yes—
745C23#57712yes—
746C23C23×D411yescharacteristic
747Q8—48no—
748Q8—44no—
749Q8—44no—
750D4—48no—
751D4—48no—
752D4—48no—
753D4—48no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—44no—
759D4—88no—
760D4—88no—
761D4—84no—
762D4—164no—
763D4—164no—
764D4—164no—
765D4—164no—
766C2×C4—28no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—44no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—88no—
817C2×C4—88no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4C2×#12312yes—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4#53412yes—
824C2×C4#53412yes—
825C2×C4#53818yes—
826C2×C4#53818yes—
827C2×C4C22×#4111yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C2×H(5,𝔽2)12yes—
830C2×C4C2×H(5,𝔽2)12yes—
831C8—42no—
832C8—42no—
833C8—44no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—416no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—816no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—168no—
877C22#262214yes—
878C22#309614yes—
879C22C22×#12311yescharacteristic
880C22C2×#53411yescharacteristic
881C22C2×#53411yescharacteristic
882C22C2×#57611yescharacteristic
883C22C2×#57711yescharacteristic
884C22#358511yescharacteristic
885C22#358611yescharacteristic
886C4—22no—
887C4—22no—
888C4—42no—
889C4—42no—
890C4—84no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—81no—
895C4—82no—
896C4—81no—
897C4—82no—
898C4#262214yes—
899C4C2×#53812yes—
900C4C2×#53812yes—
901C2—24no—
902C2—24no—
903C2—42no—
904C2—82no—
905C2—82no—
906C2—162no—
907C2C2×#262211yescharacteristic
908C2C2×#309611yescharacteristic
909C2#6051711yescharacteristic
910C2#6075611yescharacteristic
911C2#6075811yescharacteristic
912C2#6076211yescharacteristic
913C2#6076511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35250C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2311C2semidirect
3. #29899C2semidirect
4. #29898C2semidirect
5. #29892C2semidirect
6. #29891C2semidirect
7. #29891C2semidirect
8. #29890C2semidirect
9. #23643C2semidirect
10. #23641C2semidirect
11. #23486C2semidirect
12. #23483C2semidirect
13. #20912C2semidirect
14. C2×#1874C2semidirect
15. #20844C2semidirect
16. #20843C2semidirect
17. #20581C2semidirect
24. C2×#428C22semidirect
25. C2×#427C22semidirect
26. C2×#418C22semidirect
27. C22×#102C22semidirect
49. #2311C22semidirect
54. C2×#380C22semidirect
55. C2×#380C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2077C22semidirect
59. #2077C22semidirect
60. #2076C22semidirect
61. #2076C22semidirect
62. #2075C22semidirect
63. #2075C22semidirect
64. #2034C22semidirect
65. #2034C22semidirect
66. #2034C22semidirect
67. #2034C22semidirect
68. #2033C22semidirect
69. #2033C22semidirect
70. #2033C22semidirect
71. #2033C22semidirect
72. #1875C22semidirect
77. #1874C22semidirect
78. #1854C22semidirect
79. #1854C22semidirect
80. #1853C22semidirect
81. #1853C22semidirect
82. #1853C22semidirect
83. #1853C22semidirect
84. #1852C22semidirect
85. #1852C22semidirect
86. #1852C22semidirect
87. #1852C22semidirect
88. #1780C22semidirect
89. #1779C22semidirect
90. #1779C22semidirect
91. #1736C22semidirect
92. #1736C22semidirect
93. #1735C22semidirect
94. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#352502
C2×#23112
#298992
#298982
#298922
#298912
#298902
#236432
#236412
#234862
#234832
#209122
C2×#18742
#208442
#208432
#205812