Finite Group Databasebeta

← #7533648

Subgroups — #7533648

Order 512.

2200 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3273C211yesmaximal, characteristic, complemented
2C2×#3168C211yesmaximal, characteristic, complemented
3#59044C212yesmaximal, complemented
4#30405C212yesmaximal, complemented
5#30396C212yesmaximal, complemented
6#28709C211yesmaximal, characteristic, complemented
7#28536C211yesmaximal, characteristic, complemented
8#28236C212yesmaximal, complemented
9#25890C212yesmaximal, complemented
10#25326C212yesmaximal, complemented
11#25037C212yesmaximal, complemented
12#24904C212yesmaximal, complemented
13#24897C212yesmaximal, complemented
14#24275C212yesmaximal, complemented
15#24159C212yesmaximal, complemented
16#23191C211yesmaximal, characteristic, complemented
17#22443C212yesmaximal, complemented
18C4×#466C211yesmaximal, characteristic, complemented
19#21487C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2212yes—
21C2×#546C2212yes—
22C2×#529C2212yescomplemented
23#3273—28no—
24#3168—28no—
25C2×#499C2211yescharacteristic, complemented
26C2×#495C2211yescharacteristic
27C2×#488C2212yescomplemented
28C2×#478C2212yescomplemented
29C2×#468C2212yes—
30C2×#467C2211yescharacteristic, complemented
31C2×#466C2211yescharacteristic
32C2×#466C2211yescharacteristic
33C2×#465C2212yescomplemented
34C2×#463C2212yes—
35C2×#452C2212yes—
36C2×#447C2212yes—
37C2×#440C2212yescomplemented
38C2×C4×Q16C2211yescharacteristic, complemented
39C2×C4×SD16C2212yescomplemented
40C2×C4×D8C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42C2×#436C2211yescharacteristic
43C2×#435C2212yescomplemented
44C22×C4×C8C2211yescharacteristic, complemented
45#2695—22no—
46#2685—22no—
47#2566C2212yescomplemented
48#2562C2212yes—
49#2537C2212yes—
50#2536C2212yescomplemented
51#2476—22no—
52#2464—22no—
53#2457—22no—
54#2424—22no—
55#2423C2212yescomplemented
56#2420C2212yes—
57#2418—22no—
58#2408C2212yescomplemented
59#2407C2212yes—
60#2367C2212yescomplemented
61#2342—22no—
62#2341C2212yes—
63D4×C22⋊C4C2212yescomplemented
64C4×#121C2211yescharacteristic
65C4×#121C2212yescomplemented
66#2093C2212yescomplemented
67#2092C2212yescomplemented
68#2076C2212yescomplemented
69#2075C2212yescomplemented
70#2074C2212yescomplemented
71#2071C2212yescomplemented
72#2055C2212yescomplemented
73#2054C2212yes—
74#2036C2212yescomplemented
75#2035C2212yescomplemented
76#2035C2212yescomplemented
77#2034C2212yes—
78#2033C2212yes—
79#2033C2212yescomplemented
80#2000C2212yescomplemented
81#1999C2212yes—
82#1989C2212yescomplemented
83#1983C2212yescomplemented
84#1973C2212yescomplemented
85#1972C2212yes—
86#1970C2211yescharacteristic
87#1954C2211yescharacteristic
88#1942C2211yescharacteristic, complemented
89#1939C2211yescharacteristic, complemented
90#1934C2212yescomplemented
91#1923C2212yescomplemented
92#1893C2212yescomplemented
93#1880C2212yescomplemented
94#1880C2212yescomplemented
95#1879C2212yes—
96#1879C2212yes—
97#1879C2212yes—
98#1878C2212yescomplemented
99#1869C2212yescomplemented
100#1864C2212yescomplemented
101#1863C2212yescomplemented
102#1847C2212yescomplemented
103#1809C2212yescomplemented
104#1809C2212yescomplemented
105#1808C2211yescharacteristic, complemented
106#1804C2212yescomplemented
107#1803C2212yescomplemented
108#1797C2211yescharacteristic, complemented
109#1788C2212yes—
110#1788C2212yes—
111#1786C2212yescomplemented
112#1786C2212yescomplemented
113C4×#107C2211yescharacteristic, complemented
114#1770C2211yescharacteristic, complemented
115C4×#102C2212yescomplemented
116#1753C2212yescomplemented
117C22×#41C2312yes—
118C23×D4C2312yes—
119C2×AGL(1,ℤ/8)—28no—
120C2×AGL(1,ℤ/8)—28no—
121C2×AGL(1,ℤ/8)—44no—
122C22×Q16C2311yescharacteristic
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125C22×D8C2312yes—
126C22×D8C2311yescharacteristic
127C22×D8C2311yescharacteristic
128C22×M16C2312yes—
129C23×C8C2311yescharacteristic
130C23×C8C2311yescharacteristic
131#546—28no—
132#546—44no—
133#529—28no—
134#529—44no—
135C2×#126—22no—
136C2×#125C2312yes—
137C2×#124C2312yes—
138C2×#123—22no—
139C2×#123—22no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121—22no—
143C2×#121—22no—
144C2×#121D411yescharacteristic
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×#120—22no—
149C2×#120—22no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×D4—22no—
153C2×C4×D4—22no—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2312yes—
159C2×#117—22no—
160C22×C22⋊C4—22no—
161C22×C22⋊C4—22no—
162C22×C42C2311yescharacteristic
163#499—24no—
164#495D418yescomplemented
165#488—28no—
166#478—44no—
167#468—28no—
168#467—24no—
169#466—24no—
170#466—24no—
171#465—28no—
172#463—28no—
173#452—28no—
174#447—28no—
175#440—44no—
176C4×Q16—24no—
177C4×SD16—28no—
178C4×D8—24no—
179C4×D8—24no—
180#436—24no—
181#435—44no—
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#107C2311yescharacteristic
185C2×#107C2311yescharacteristic
186C2×#107C2311yescharacteristic
187C2×#107C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×#97C2312yes—
213C2×C4×C8—24no—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#400—22no—
219#399—22no—
220#398—22no—
221#398—22no—
222#397—22no—
223#396—22no—
224#396—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#394—22no—
232#392—22no—
233#392—22no—
234#391C2312yes—
235#390—22no—
236#390—22no—
237#390D411yescharacteristic
238#390C2312yes—
239#390C2312yes—
240#390C2312yes—
241#390C2312yes—
242#389D411yescharacteristic
243#389C2312yes—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388D412yes—
253#387—22no—
254#386—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386D412yes—
260#385—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#384C2312yes—
265#382C2312yes—
266#381—22no—
267#380—22no—
268#380—22no—
269#380D411yescharacteristic
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#379—22no—
276#379—22no—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C22⋊C4—22no—
280C4×C22⋊C4—22no—
281C4×C22⋊C4—22no—
282C4×C22⋊C4C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C25—22no—
294C2×#41—24no—
295C2×#41—24no—
296C2×#41—42no—
297C2×#41—42no—
298C2×#41—42no—
299C2×#41—42no—
300C22×Q8C2412yes—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4—42no—
311C22×D4—42no—
312C22×D4C2×D411yescharacteristic
313C22×D4C2×D412yes—
314C22×D4C2412yes—
315C22×D4C2412yes—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2412yes—
324AGL(1,ℤ/8)—432no—
325C2×Q16—41no—
326C2×Q16—41no—
327C2×Q16C2×D414yes—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—42no—
333C2×SD16C2×D418yes—
334C2×D8—24no—
335C2×D8—24no—
336C2×D8—22no—
337C2×D8—22no—
338C2×D8—41no—
339C2×D8—41no—
340C2×D8—42no—
341C2×D8C2×D414yes—
342C2×D8#4114yes—
343C2×M16—24no—
344C2×M16—24no—
345C2×M16—24no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—41no—
351C22×C8—41no—
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358#126—48no—
359#125—24no—
360#125—24no—
361#124—24no—
362#124C2×D418yes—
363#123—48no—
364#123—48no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—42no—
368C22⋊Q8—42no—
369#121—24no—
370#121—24no—
371#121—24no—
372#121—42no—
373#121—48no—
374#121—42no—
375#121—42no—
376#121—42no—
377#121—84no—
378#120—48no—
379#120—84no—
380C4×Q8—24no—
381C4×Q8—42no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×D4—24no—
385C4×D4—22no—
386C4×D4—24no—
387C4×D4—22no—
388C4×D4—24no—
389C4×D4—42no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—48no—
395C4×D4—84no—
396#117—48no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D412yes—
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C22⋊C4—22no—
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⋊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—48no—
439C2×C22⋊C4—48no—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2412yes—
454C2×C42C2411yescharacteristic
455#107—22no—
456#107—22no—
457#107—22no—
458#107—22no—
459#107—22no—
460#107—42no—
461#106—24no—
462#106—42no—
463C4⋊C8—22no—
464C4⋊C8—22no—
465C4⋊C8—42no—
466#103—24no—
467#103—24no—
468#103—24no—
469#103—42no—
470#103—42no—
471#102—24no—
472#102—24no—
473#102—24no—
474#102—24no—
475#102—24no—
476#102—42no—
477#102—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481C22⋊C8—24no—
482C22⋊C8—42no—
483C22⋊C8—42no—
484C22⋊C8—42no—
485#97—24no—
486C4×C8—22no—
487C4×C8—22no—
488C4×C8—22no—
489C4×C8C2×D414yes—
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#95C2×D412yes—
502#95C2×D412yes—
503#95C2×D412yes—
504C24—22no—
505C24—22no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—82no—
510C24—82no—
511C24—82no—
512C24—82no—
513C24C22×D412yes—
514C24C22×D411yescharacteristic
515#41—48no—
516#41—84no—
517#41—84no—
518#41—84no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8C22×D414yes—
525C2×D4—24no—
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—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—42no—
538C2×D4—41no—
539C2×D4—42no—
540C2×D4—41no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—82no—
552C2×D4—84no—
553C2×D4—84no—
554C2×D4—84no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C22×D414yes—
561C2×D4C2×#4114yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C2511yescharacteristic
607Q16—44no—
608SD16—216no—
609SD16—48no—
610D8—28no—
611D8—44no—
612D8—48no—
613M16—48no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—21no—
628C2×C8—44no—
629C2×C8—44no—
630C2×C8C22×D412yes—
631C2×C8C22×D412yes—
632C2×C8C2×#4112yes—
633C2×C8H(5,𝔽2)12yes—
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—22no—
644C4⋊C4—22no—
645C4⋊C4—41no—
646C4⋊C4—42no—
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—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C42—22no—
686C42—22no—
687C42—21no—
688C42—22no—
689C42—21no—
690C42—22no—
691C42—44no—
692C42—82no—
693C42—82no—
694C42C22×D412yes—
695C42H(5,𝔽2)12yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—88no—
724C23—88no—
725C23—88no—
726C23—164no—
727C23—164no—
728C23—164no—
729C23—164no—
730C23#57612yes—
731C23C23×D411yescharacteristic
732Q8—24no—
733Q8—24no—
734Q8—42no—
735Q8—42no—
736D4—24no—
737D4—24no—
738D4—24no—
739D4—24no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—82no—
745D4—84no—
746D4—88no—
747D4—88no—
748D4—88no—
749D4—88no—
750D4—164no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
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—88no—
801C2×C4—88no—
802C2×C4—164no—
803C2×C4—164no—
804C2×C4D4212yes—
805C2×C4D4212yes—
806C2×C4#57512yes—
807C2×C4C23×D411yescharacteristic
808C2×C4C22×#4111yescharacteristic
809C2×C4C2×H(5,𝔽2)11yescharacteristic
810C2×C4C2×H(5,𝔽2)11yescharacteristic
811C2×C4#58511yescharacteristic
812C2×C4#58511yescharacteristic
813C8—22no—
814C8—41no—
815C8—42no—
816C8—41no—
817C8—42no—
818C8#54614yes—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—1616no—
848C22C2×D4211yescharacteristic
849C22D4×#4111yescharacteristic
850C22#349611yescharacteristic
851C22C2×#57511yescharacteristic
852C22C2×#57611yescharacteristic
853C22#358411yescharacteristic
854C22#358411yescharacteristic
855C4—22no—
856C4—22no—
857C4—22no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—44no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4C2×#54611yescharacteristic
870C4#348511yescharacteristic
871C4#351411yescharacteristic
872C4#354611yescharacteristic
873C2—42no—
874C2—82no—
875C2—84no—
876C2—84no—
877C2#5903511yescharacteristic
878C2#6103011yescharacteristic
879C2#6105611yescharacteristic
880C2#6144211yescharacteristic
881C2#6148911yescharacteristic
882C2#6226311yescharacteristic
883C2#6234411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3273C2semidirect
2. C2×#3168C2semidirect
3. #59044C2semidirect
4. #30405C2semidirect
5. #30396C2semidirect
6. #28709C2semidirect
7. #28536C2semidirect
8. #28236C2semidirect
9. #25890C2semidirect
10. #25326C2semidirect
11. #25037C2semidirect
12. #24904C2semidirect
13. #24897C2semidirect
14. #24275C2semidirect
15. #24159C2semidirect
16. #23191C2semidirect
17. #22443C2semidirect
18. C4×#466C2semidirect
19. #21487C2semidirect
22. C2×#529C22semidirect
25. C2×#499C22semidirect
27. C2×#488C22semidirect
28. C2×#478C22semidirect
30. C2×#467C22semidirect
33. C2×#465C22semidirect
37. C2×#440C22semidirect
38. C2×C4×Q16C22semidirect
39. C2×C4×SD16C22semidirect
43. C2×#435C22semidirect
44. C22×C4×C8C22semidirect
47. #2566C22semidirect
50. #2536C22semidirect
55. #2423C22semidirect
58. #2408C22semidirect
60. #2367C22semidirect
63. D4×C22⋊C4C22semidirect
65. C4×#121C22semidirect
66. #2093C22semidirect
67. #2092C22semidirect
68. #2076C22semidirect
69. #2075C22semidirect
70. #2074C22semidirect
71. #2071C22semidirect
72. #2055C22semidirect
74. #2036C22semidirect
75. #2035C22semidirect
76. #2035C22semidirect
79. #2033C22semidirect
80. #2000C22semidirect
82. #1989C22semidirect
83. #1983C22semidirect
84. #1973C22semidirect
88. #1942C22semidirect
89. #1939C22semidirect
90. #1934C22semidirect
91. #1923C22semidirect
92. #1893C22semidirect
93. #1880C22semidirect
94. #1880C22semidirect
98. #1878C22semidirect
99. #1869C22semidirect
100. #1864C22semidirect
101. #1863C22semidirect
102. #1847C22semidirect
103. #1809C22semidirect
104. #1809C22semidirect
105. #1808C22semidirect
106. #1804C22semidirect
107. #1803C22semidirect
108. #1797C22semidirect
111. #1786C22semidirect
112. #1786C22semidirect
113. C4×#107C22semidirect
114. #1770C22semidirect
115. C4×#102C22semidirect
116. #1753C22semidirect
164. #495D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32732
C2×#31682
#590442
#304052
#303962
#287092
#285362
#282362
#258902
#253262
#250372
#249042
#248972
#242752
#241592
#231912
#224432
C4×#4662
#214872