Finite Group Databasebeta

← #6635559

Subgroups — #6635559

Order 512.

1798 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37451C211yesmaximal, characteristic
2#35672C211yesmaximal, characteristic, complemented
3#32918C212yesmaximal, complemented
4#31960C212yesmaximal, complemented
5#31956C212yesmaximal, complemented
6#31936C212yesmaximal, complemented
7#31932C212yesmaximal, complemented
8#31014C212yesmaximal, complemented
9#31012C212yesmaximal, complemented
10#30998C212yesmaximal, complemented
11#30996C212yesmaximal, complemented
12#29769C212yesmaximal, complemented
13#28324C212yesmaximal, complemented
14#27984C212yesmaximal, complemented
15#24010C211yesmaximal, characteristic, complemented
16#24009C211yesmaximal, characteristic
17#23921C211yesmaximal, characteristic, complemented
18#23919C211yesmaximal, characteristic
19#21908C211yesmaximal, characteristic, complemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C2×#519C2211yescharacteristic, complemented
24C2×#485C2212yescomplemented
25C2×#482C2212yes—
26C2×#464C2212yescomplemented
27C2×#464C2212yescomplemented
28C2×#451C2212yescomplemented
29C2×#451C2212yescomplemented
30C2×#448C2212yes—
31C2×#450C2212yes—
32#2816—22no—
33#2626—21no—
34#2626—21no—
35#2620C2212yes—
36#2620C2212yes—
37#2618—21no—
38#2618—21no—
39#2502C2212yes—
40#2501C2212yes—
41#2484—22no—
42#2482—22no—
43#2436C2212yes—
44#2435C2212yes—
45#2423—21no—
46#2423—21no—
47#2423C2212yes—
48#2423C2212yescomplemented
49#2421—21no—
50#2421—21no—
51#2421C2212yes—
52#2421C2212yescomplemented
53#2405—22no—
54#2317C2211yescharacteristic, complemented
55#2317C2211yescharacteristic, complemented
56#2310C2211yescharacteristic, complemented
57#2280C2211yescharacteristic
58#2280C2211yescharacteristic
59#2096C2212yescomplemented
60#2095C2212yescomplemented
61#2084C2212yescomplemented
62#2083C2212yescomplemented
63#2074C2212yescomplemented
64#2073C2212yescomplemented
65#2072C2212yescomplemented
66#2071C2212yescomplemented
67#2068C2212yescomplemented
68#2067C2212yescomplemented
69#2066C2212yescomplemented
70#2065C2212yescomplemented
71#2042C2212yescomplemented
72#2042C2212yescomplemented
73#2036C2212yes—
74#2035C2212yes—
75#2034C2212yes—
76#2033C2212yes—
77#2015C2212yescomplemented
78#2015C2212yescomplemented
79#2001C2212yes—
80#2001C2212yes—
81#2000C2212yes—
82#2000C2212yes—
83#1973C2212yescomplemented
84#1971C2212yescomplemented
85#1969C2212yescomplemented
86#1968C2212yescomplemented
87#1959C2212yescomplemented
88#1958C2212yescomplemented
89#1924C2212yes—
90#1924C2212yescomplemented
91#1923C2212yes—
92#1923C2212yescomplemented
93#1880C2212yescomplemented
94#1880C2212yescomplemented
95#1878C2212yescomplemented
96#1878C2212yescomplemented
97#1875C2212yes—
98#1874C2212yes—
99#1873C2212yescomplemented
100#1872C2212yes—
101#1872C2212yescomplemented
102#1872C2212yescomplemented
103#1853C2211yescharacteristic
104#1853C2211yescharacteristic, complemented
105#1852C2211yescharacteristic
106#1852C2211yescharacteristic, complemented
107#1836C2212yescomplemented
108#1834C2212yescomplemented
109#1803C2212yescomplemented
110#1803C2212yescomplemented
111#1798C2212yescomplemented
112#1787C2211yescharacteristic, complemented
113#1787C2211yescharacteristic, complemented
114#1786C2211yescharacteristic
115#1786C2211yescharacteristic
116#1779C2211yescharacteristic
117#1779C2211yescharacteristic
118#1750C2212yescomplemented
119C23×Q8C2311yescharacteristic
120C23×Q8C2311yescharacteristic
121C23×D4—21no—
122C23×D4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C22×Q16C2312yes—
125C22×Q16C2312yes—
126C22×SD16C2312yes—
127C22×SD16C2312yes—
128C2×#124C2312yes—
129C2×#124C2312yes—
130C2×#123—22no—
131C2×#123—22no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—44no—
137C2×C22⋊Q8—44no—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121—44no—
145C2×#121C2312yes—
146C2×#121C2312yes—
147#519—44no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×#117—22no—
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165#485—44no—
166#482—44no—
167#464—44no—
168#464—44no—
169#451—44no—
170#451—44no—
171#450—44no—
172#448—44no—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2311yescharacteristic
198C2×C22⋊C8C2311yescharacteristic
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×#97C2312yes—
204C2×C4×C8C2312yes—
205#400—22no—
206#400—22no—
207#399—22no—
208#399—22no—
209#399—22no—
210#399—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#398—22no—
215#397—22no—
216#397—22no—
217#396—22no—
218#396—22no—
219#396—22no—
220#396—22no—
221#394—22no—
222#394—22no—
223#394—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#393—22no—
228#393—22no—
229#391—21no—
230#391—21no—
231#391C2312yes—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#390C2312yes—
236#390C2312yes—
237#389—21no—
238#389—21no—
239#389C2312yes—
240#389C2312yes—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#386—22no—
250#386—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#384—21no—
256#384C2312yes—
257#384C2312yes—
258#384C2312yes—
259#382—21no—
260#382C2312yes—
261#381—21no—
262#381—22no—
263#381D412yes—
264#380D411yescharacteristic
265#380D411yescharacteristic
266#380D411yescharacteristic
267#380D411yescharacteristic
268#380C2311yescharacteristic
269#380C2311yescharacteristic
270#380C2311yescharacteristic
271#380C2311yescharacteristic
272#379—21no—
273#379—22no—
274#379—22no—
275#379D412yes—
276C4×C22⋊C4—21no—
277C4×C22⋊C4—21no—
278C4×C22⋊C4C2312yes—
279C4×C22⋊C4C2312yes—
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
294C22×Q8—24no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—24no—
298C22×Q8—41no—
299C22×Q8—41no—
300C22×Q8—42no—
301C22×Q8—41no—
302C22×Q8—41no—
303C22×Q8—42no—
304C22×Q8C2412yes—
305C22×Q8C2412yes—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—42no—
310C22×D4—41no—
311C22×D4—41no—
312C22×D4—42no—
313C22×D4—44no—
314C22×D4—82no—
315C22×D4—82no—
316C22×D4C2412yes—
317C23×C4—21no—
318C23×C4—24no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—42no—
324C23×C4—41no—
325C23×C4—41no—
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C2×Q16—24no—
333C2×Q16—24no—
334C2×Q16—42no—
335C2×Q16—42no—
336C2×Q16—42no—
337C2×Q16—42no—
338C2×SD16—24no—
339C2×SD16—24no—
340C2×SD16—42no—
341C2×SD16—42no—
342C2×SD16—42no—
343C2×SD16—42no—
344C22×C8C2412yes—
345C22×C8C2412yes—
346C22×C8C2412yes—
347C22×C8C2412yes—
348#124—42no—
349#124—42no—
350#124—42no—
351#124—42no—
352#123—84no—
353#123—84no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—42no—
359C22⋊Q8—42no—
360C22⋊Q8—42no—
361C22⋊Q8—42no—
362C22⋊Q8—44no—
363C22⋊Q8—44no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366#121—24no—
367#121—24no—
368#121—42no—
369#121—42no—
370#121—44no—
371#121—44no—
372C4×Q8—24no—
373C4×Q8—24no—
374C4×Q8—42no—
375C4×Q8—42no—
376C4×Q8—44no—
377C4×Q8—44no—
378#117—24no—
379#117—41no—
380#117—41no—
381#117—42no—
382#117—42no—
383#117—48no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2411yescharacteristic
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C2412yes—
451C2×C42C2412yes—
452#107—42no—
453#107—42no—
454#106—42no—
455#106—42no—
456C4⋊C8—42no—
457C4⋊C8—42no—
458#103—42no—
459#103—42no—
460#103—42no—
461#103—42no—
462#103—42no—
463#103—42no—
464#103—42no—
465#103—42no—
466#103—42no—
467#103—42no—
468#102—42no—
469#102—42no—
470#102—42no—
471#102—42no—
472#102—42no—
473#102—42no—
474C22⋊C8—24no—
475C22⋊C8—24no—
476C22⋊C8—41no—
477C22⋊C8—41no—
478C22⋊C8—41no—
479C22⋊C8—41no—
480C22⋊C8—42no—
481C22⋊C8—42no—
482#97—42no—
483C4×C8—42no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
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#95C2×D412yes—
501#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—41no—
509C24—41no—
510C24—41no—
511C24—41no—
512C24—42no—
513C24—42no—
514C24—42no—
515C24—81no—
516C24—81no—
517C24—81no—
518C24—81no—
519C24C22×D411yescharacteristic
520C24C22×D411yescharacteristic
521C24C22×D411yescharacteristic
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—48no—
535C2×Q8—48no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8—81no—
540C2×Q8—81no—
541C2×Q8—84no—
542C2×Q8—84no—
543C2×Q8H(5,𝔽2)14yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—84no—
558C2×D4—84no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—816no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D411yescharacteristic
615C22×C4H(5,𝔽2)14yes—
616C22×C4C2511yescharacteristic
617Q16—84no—
618Q16—84no—
619SD16—84no—
620SD16—84no—
621C2×C8—22no—
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—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4—82no—
660C4⋊C4—82no—
661C4⋊C4—82no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—44no—
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—81no—
689C22⋊C4—81no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—44no—
695C42—44no—
696C42—42no—
697C42—42no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—82no—
727C23—82no—
728C23—82no—
729C23—84no—
730C23—82no—
731C23—84no—
732C23—84no—
733C23—162no—
734C23—162no—
735C23—162no—
736C23—162no—
737C23#53512yes—
738C23#57712yes—
739C23#57812yes—
740C23C23×D411yescharacteristic
741Q8—24no—
742Q8—24no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—84no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—84no—
756D4—88no—
757D4—88no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4#53512yes—
820C2×C4C2×H(5,𝔽2)12yes—
821C2×C4C2×H(5,𝔽2)12yes—
822C2×C4#58511yescharacteristic
823C2×C4#58511yescharacteristic
824C8—42no—
825C8—42no—
826C8—42no—
827C8—42no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—88no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—168no—
858C22C2×#53511yescharacteristic
859C22#348411yescharacteristic
860C22#348511yescharacteristic
861C22C2×#57711yescharacteristic
862C22C2×#57811yescharacteristic
863C22#358511yescharacteristic
864C22#358611yescharacteristic
865C4—22no—
866C4—42no—
867C4—42no—
868C4—41no—
869C4—41no—
870C4—44no—
871C4—42no—
872C4—42no—
873C4—82no—
874C4—81no—
875C4—82no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4—82no—
881C4#353412yes—
882C4#353412yes—
883C2—42no—
884C2—42no—
885C2—42no—
886C2—162no—
887C2#3672111yescharacteristic
888C2#6081211yescharacteristic
889C2#6081411yescharacteristic
890C2#6163211yescharacteristic
891C2#6165011yescharacteristic
892C2#6175411yescharacteristic
893C2#6175511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35672C2semidirect
3. #32918C2semidirect
4. #31960C2semidirect
5. #31956C2semidirect
6. #31936C2semidirect
7. #31932C2semidirect
8. #31014C2semidirect
9. #31012C2semidirect
10. #30998C2semidirect
11. #30996C2semidirect
12. #29769C2semidirect
13. #28324C2semidirect
14. #27984C2semidirect
15. #24010C2semidirect
17. #23921C2semidirect
19. #21908C2semidirect
23. C2×#519C22semidirect
24. C2×#485C22semidirect
26. C2×#464C22semidirect
27. C2×#464C22semidirect
28. C2×#451C22semidirect
29. C2×#451C22semidirect
48. #2423C22semidirect
52. #2421C22semidirect
54. #2317C22semidirect
55. #2317C22semidirect
56. #2310C22semidirect
59. #2096C22semidirect
60. #2095C22semidirect
61. #2084C22semidirect
62. #2083C22semidirect
63. #2074C22semidirect
64. #2073C22semidirect
65. #2072C22semidirect
66. #2071C22semidirect
67. #2068C22semidirect
68. #2067C22semidirect
69. #2066C22semidirect
70. #2065C22semidirect
71. #2042C22semidirect
72. #2042C22semidirect
77. #2015C22semidirect
78. #2015C22semidirect
83. #1973C22semidirect
84. #1971C22semidirect
85. #1969C22semidirect
86. #1968C22semidirect
87. #1959C22semidirect
88. #1958C22semidirect
90. #1924C22semidirect
92. #1923C22semidirect
93. #1880C22semidirect
94. #1880C22semidirect
95. #1878C22semidirect
96. #1878C22semidirect
99. #1873C22semidirect
101. #1872C22semidirect
102. #1872C22semidirect
104. #1853C22semidirect
106. #1852C22semidirect
107. #1836C22semidirect
108. #1834C22semidirect
109. #1803C22semidirect
110. #1803C22semidirect
111. #1798C22semidirect
112. #1787C22semidirect
113. #1787C22semidirect
118. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#374512
#356722
#329182
#319602
#319562
#319362
#319322
#310142
#310122
#309982
#309962
#297692
#283242
#279842
#240102
#240092
#239212
#239192
#219082