Finite Group Databasebeta

← #6814541

Subgroups — #6814541

Order 512.

2125 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3263C211yesmaximal, characteristic, complemented
2C2×#3192C211yesmaximal, characteristic
3#37664C212yesmaximal, complemented
4#33181C211yesmaximal, characteristic, complemented
5#31134C212yesmaximal, complemented
6#31086C212yesmaximal, complemented
7#31008C212yesmaximal, complemented
8#30448C212yesmaximal, complemented
9#29785C211yesmaximal, characteristic, complemented
10#29743C211yesmaximal, characteristic, complemented
11#28585C212yesmaximal, complemented
12#27243C212yesmaximal, complemented
13#26946C212yesmaximal, complemented
14#26788C212yesmaximal, complemented
15#25513C212yesmaximal, complemented
16#25160C212yesmaximal, complemented
17#24379C212yesmaximal, complemented
18#21536C211yesmaximal, characteristic, complemented
19#21050C211yesmaximal, characteristic, complemented
20C2×#542C2212yescomplemented
21C22×#121C2212yes—
22#3263—28no—
23#3192—28no—
24C2×#495C2211yescharacteristic, complemented
25C2×#481C2212yes—
26C2×#481C2212yes—
27C2×#475C2212yescomplemented
28C2×#476C2212yescomplemented
29C2×#470C2211yescharacteristic, complemented
30C2×#469C2211yescharacteristic
31C2×#469C2212yes—
32C2×#469C2211yescharacteristic
33C2×#465C2212yescomplemented
34C2×#465C2212yescomplemented
35C2×#464C2212yescomplemented
36C2×#463C2212yescomplemented
37C2×#450C2212yescomplemented
38C2×#447C2212yes—
39C2×#447C2212yes—
40C2×C4×D8C2211yescharacteristic, complemented
41C2×#424C2211yescharacteristic, complemented
42C2×#407C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C2×#405C2211yescharacteristic, complemented
45#2848C2212yes—
46#2701—22no—
47#2691—22no—
48#2686—22no—
49#2672—22no—
50#2624C2212yescomplemented
51#2620C2212yescomplemented
52#2491C2212yes—
53#2480—22no—
54#2440C2212yescomplemented
55#2437—22no—
56#2435—22no—
57#2435C2212yescomplemented
58#2427C2212yes—
59#2426C2212yes—
60#2422C2212yes—
61#2405—22no—
62#2360C2212yescomplemented
63D4×C22⋊C4C2212yescomplemented
64#2324C2212yescomplemented
65#2280C2211yescharacteristic
66#2088C2212yescomplemented
67#2084C2212yescomplemented
68#2077C2212yescomplemented
69#2071C2212yescomplemented
70#2067C2212yescomplemented
71#2065C2212yescomplemented
72#2058C2212yescomplemented
73#2054C2212yescomplemented
74#2042C2212yescomplemented
75#2042C2212yescomplemented
76#2036C2212yescomplemented
77#2035C2212yescomplemented
78#2034C2212yes—
79#2034C2212yes—
80#2023C2212yescomplemented
81#2012C2212yescomplemented
82#2012C2212yescomplemented
83#2001C2212yescomplemented
84#2000C2212yes—
85#2000C2212yes—
86#1972C2211yescharacteristic, complemented
87#1972C2211yescharacteristic, complemented
88#1971C2211yescharacteristic, complemented
89#1968C2212yescomplemented
90#1959C2212yescomplemented
91#1944C2211yescharacteristic, complemented
92#1934C2212yescomplemented
93#1927C2212yescomplemented
94#1926C2212yescomplemented
95#1924C2212yescomplemented
96#1924C2212yescomplemented
97#1923C2212yescomplemented
98#1923C2212yescomplemented
99#1894C2212yescomplemented
100#1893C2212yescomplemented
101#1893C2212yescomplemented
102#1880C2212yescomplemented
103#1879C2212yescomplemented
104#1879C2212yescomplemented
105#1877C2212yescomplemented
106#1872C2212yescomplemented
107#1865C2212yescomplemented
108#1864C2212yescomplemented
109#1853C2212yescomplemented
110#1844C2211yescharacteristic, complemented
111#1809C2211yescharacteristic, complemented
112#1786C2212yescomplemented
113C4×#106C2211yescharacteristic, complemented
114#1762C2212yescomplemented
115#1729C2211yescharacteristic, complemented
116#1729C2211yescharacteristic, complemented
117C23×D4—22no—
118C23×D4C2312yes—
119C24×C4C2311yescharacteristic
120C22×Q16C2311yescharacteristic
121C22×SD16C2312yes—
122C22×SD16C2312yes—
123C22×D8C2311yescharacteristic
124C22×D8C2312yes—
125C22×D8C2311yescharacteristic
126C22×M16C2311yescharacteristic
127C22×M16C2311yescharacteristic
128C23×C8C2311yescharacteristic
129C23×C8C2311yescharacteristic
130#542—28no—
131#542—44no—
132C2×C4⋊Q8C2312yes—
133C2×#126—22no—
134C2×#124—22no—
135C2×#124—22no—
136C2×#124C2312yes—
137C2×#124C2312yes—
138C2×#123—22no—
139C2×#123—22no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×#121—22no—
146C2×#121—22no—
147C2×#121—28no—
148C2×#121—44no—
149C2×#121C2312yes—
150C2×#121C2312yes—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C22⋊C4—22no—
160C22×C22⋊C4—22no—
161#495—42no—
162#481—28no—
163#481—28no—
164#476—28no—
165#475—28no—
166#470—24no—
167#469—24no—
168#469—28no—
169#469D418yes—
170#465—28no—
171#465—44no—
172#464—28no—
173#463—28no—
174#450—44no—
175#447—28no—
176#447—28no—
177C4×D8—42no—
178C2×#107C2311yescharacteristic
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2311yescharacteristic
182C2×#106C2311yescharacteristic
183C2×#106C2312yes—
184C2×#106C2311yescharacteristic
185C2×#106C2311yescharacteristic
186#424—24no—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204#407—24no—
205C2×C22⋊C8—42no—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210#405—42no—
211C2×#97C2311yescharacteristic
212C2×#97C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#399—22no—
216#398—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#396—22no—
221#396—22no—
222#396—22no—
223#395—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#393—22no—
235#391C2312yes—
236#390—22no—
237#390—22no—
238#390C2312yes—
239#390C2312yes—
240#390C2312yes—
241#390C2312yes—
242#389—22no—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#384C2312yes—
262#381D411yescharacteristic
263#381D411yescharacteristic
264#380—22no—
265#380D412yes—
266#380D412yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#379—22no—
271#379—22no—
272#379—22no—
273#379—22no—
274#379D411yescharacteristic
275#379D411yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C22⋊C4—22no—
278C4×C22⋊C4C2312yes—
279C4×C22⋊C4C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C25—22no—
292C25C2×D411yescharacteristic
293C22×Q8—22no—
294C22×Q8C2412yes—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—42no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4—42no—
305C22×D4—42no—
306C22×D4—48no—
307C22×D4—84no—
308C22×D4—84no—
309C22×D4C2412yes—
310C22×D4C2412yes—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—41no—
317C23×C4—41no—
318C23×C4—41no—
319C23×C4—41no—
320C23×C4C2×D412yes—
321C23×C4C2×D411yescharacteristic
322C23×C4C2412yes—
323C23×C4C2411yescharacteristic
324C2×Q16—22no—
325C2×Q16—41no—
326C2×Q16—41no—
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—42no—
330C2×SD16—42no—
331C2×SD16—42no—
332C2×SD16—42no—
333C2×D8—24no—
334C2×D8—22no—
335C2×D8—41no—
336C2×D8—41no—
337C2×D8—41no—
338C2×D8—42no—
339C2×D8—42no—
340C2×D8—41no—
341C2×D8C2×D414yes—
342C2×M16—22no—
343C2×M16—41no—
344C2×M16—41no—
345C2×M16—41no—
346C2×M16—41no—
347C2×M16C2×D414yes—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—41no—
352C22×C8—41no—
353C22×C8—41no—
354C22×C8C2412yes—
355C22×C8C2411yescharacteristic
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C4⋊Q8—24no—
361C4⋊Q8—42no—
362#126—48no—
363#124—24no—
364#124—42no—
365#124—42no—
366#124—42no—
367#124—48no—
368#124—84no—
369#123—48no—
370#123—84no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—48no—
374C22⋊Q8—42no—
375C22⋊Q8—42no—
376C22⋊Q8—42no—
377C22⋊Q8—42no—
378C22⋊Q8—84no—
379#121—24no—
380#121—24no—
381#121—24no—
382#121—24no—
383#121—24no—
384#121—48no—
385#121—42no—
386#121—42no—
387#121—48no—
388#121C2×D418yes—
389C4×Q8—24no—
390C4×Q8—42no—
391C4×D4—24no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—42no—
395#117—22no—
396#117—22no—
397#117—41no—
398#117—41no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
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⋊C4C2×D412yes—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
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⋊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—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—48no—
445C2×C22⋊C4—84no—
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D412yes—
449C2×C22⋊C4C2×D412yes—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D412yes—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42C2411yescharacteristic
457C2×C42C2412yes—
458C2×C42C2411yescharacteristic
459#107—41no—
460#106—22no—
461#106—22no—
462#106—24no—
463#106—24no—
464#106—41no—
465#106—42no—
466#106C2×D414yes—
467C4⋊C8—24no—
468C4⋊C8—24no—
469#103—24no—
470#103—24no—
471#103—42no—
472#103—42no—
473#103—42no—
474#102—24no—
475#102—24no—
476#102—24no—
477#102—24no—
478#102—24no—
479#102—42no—
480#102—42no—
481#102—42no—
482#102—42no—
483#102C2×D418yes—
484C22⋊C8—24no—
485C22⋊C8—24no—
486C22⋊C8—24no—
487C22⋊C8—42no—
488#97—41no—
489#97—41no—
490C4×C8—22no—
491C4×C8—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#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504#95C2×D412yes—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—22no—
509C24—41no—
510C24—42no—
511C24—41no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—82no—
517C24—82no—
518C24—82no—
519C24C22×D411yescharacteristic
520C24C22×D412yes—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—44no—
528C2×Q8—82no—
529C2×Q8—82no—
530C2×D4—28no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4—84no—
553C2×D4—84no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—832no—
561C2×D4C22×D414yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D412yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D412yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C4C2511yescharacteristic
608Q16—82no—
609SD16—84no—
610SD16—84no—
611D8—44no—
612D8—82no—
613D8—84no—
614M16—44no—
615M16—82no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—44no—
632C2×C8—82no—
633C2×C8C22×D412yes—
634C2×C8C22×D412yes—
635C2×C8H(5,𝔽2)12yes—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4C22×D414yes—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—28no—
665C22⋊C4—42no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
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—82no—
691C22⋊C4—82no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—44no—
699C42—82no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—48no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—82no—
727C23—84no—
728C23—88no—
729C23—88no—
730C23—82no—
731C23—88no—
732C23—88no—
733C23—164no—
734C23—164no—
735C23—164no—
736C23D4212yes—
737C23#57714yes—
738C23C23×D411yescharacteristic
739Q8—42no—
740Q8—42no—
741Q8—42no—
742Q8—42no—
743Q8—164no—
744D4—24no—
745D4—24no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—88no—
753D4—88no—
754D4—88no—
755D4—88no—
756D4—88no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
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—84no—
803C2×C4—82no—
804C2×C4—88no—
805C2×C4—164no—
806C2×C4—164no—
807C2×C4D4212yes—
808C2×C4C23×D411yescharacteristic
809C2×C4C2×H(5,𝔽2)11yescharacteristic
810C2×C4C2×H(5,𝔽2)11yescharacteristic
811C2×C4#58511yescharacteristic
812C2×C4#58511yescharacteristic
813C2×C4#58511yescharacteristic
814C8—22no—
815C8—22no—
816C8—22no—
817C8—42no—
818C8—42no—
819C8—41no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—22no—
825C22—42no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—88no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—1616no—
848C22#344911yescharacteristic
849C22C2×D4211yescharacteristic
850C22#349611yescharacteristic
851C22C2×#57712yes—
852C22#358512yes—
853C4—22no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4#349611yescharacteristic
868C4#350011yescharacteristic
869C4#353411yescharacteristic
870C4#356011yescharacteristic
871C2—42no—
872C2—44no—
873C2—84no—
874C2—162no—
875C2#3935411yescharacteristic
876C2#6098012yes—
877C2#6107112yes—
878C2#6226911yescharacteristic
879C2#6228311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3192C2
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
1. C2×#3263C2semidirect
3. #37664C2semidirect
4. #33181C2semidirect
5. #31134C2semidirect
6. #31086C2semidirect
7. #31008C2semidirect
8. #30448C2semidirect
9. #29785C2semidirect
10. #29743C2semidirect
11. #28585C2semidirect
12. #27243C2semidirect
13. #26946C2semidirect
14. #26788C2semidirect
15. #25513C2semidirect
16. #25160C2semidirect
17. #24379C2semidirect
18. #21536C2semidirect
19. #21050C2semidirect
20. C2×#542C22semidirect
24. C2×#495C22semidirect
27. C2×#475C22semidirect
28. C2×#476C22semidirect
29. C2×#470C22semidirect
33. C2×#465C22semidirect
34. C2×#465C22semidirect
35. C2×#464C22semidirect
36. C2×#463C22semidirect
37. C2×#450C22semidirect
40. C2×C4×D8C22semidirect
41. C2×#424C22semidirect
44. C2×#405C22semidirect
50. #2624C22semidirect
51. #2620C22semidirect
54. #2440C22semidirect
57. #2435C22semidirect
62. #2360C22semidirect
63. D4×C22⋊C4C22semidirect
64. #2324C22semidirect
66. #2088C22semidirect
67. #2084C22semidirect
68. #2077C22semidirect
69. #2071C22semidirect
70. #2067C22semidirect
71. #2065C22semidirect
72. #2058C22semidirect
73. #2054C22semidirect
74. #2042C22semidirect
75. #2042C22semidirect
76. #2036C22semidirect
77. #2035C22semidirect
80. #2023C22semidirect
81. #2012C22semidirect
82. #2012C22semidirect
83. #2001C22semidirect
86. #1972C22semidirect
87. #1972C22semidirect
88. #1971C22semidirect
89. #1968C22semidirect
90. #1959C22semidirect
91. #1944C22semidirect
92. #1934C22semidirect
93. #1927C22semidirect
94. #1926C22semidirect
95. #1924C22semidirect
96. #1924C22semidirect
97. #1923C22semidirect
98. #1923C22semidirect
99. #1894C22semidirect
100. #1893C22semidirect
101. #1893C22semidirect
102. #1880C22semidirect
103. #1879C22semidirect
104. #1879C22semidirect
105. #1877C22semidirect
106. #1872C22semidirect
107. #1865C22semidirect
108. #1864C22semidirect
109. #1853C22semidirect
110. #1844C22semidirect
111. #1809C22semidirect
112. #1786C22semidirect
113. C4×#106C22semidirect
114. #1762C22semidirect
115. #1729C22semidirect
116. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32632
C2×#31922
#376642
#331812
#311342
#310862
#310082
#304482
#297852
#297432
#285852
#272432
#269462
#267882
#255132
#251602
#243792
#215362
#210502