Finite Group Databasebeta

← #7613500

Subgroups — #7613500

Order 512.

2182 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3296C212yesmaximal, complemented
2#59807C212yesmaximal, complemented
3#31238C211yesmaximal, characteristic, complemented
4#31212C211yesmaximal, characteristic, complemented
5#31192C211yesmaximal, characteristic, complemented
6#31060C211yesmaximal, characteristic, complemented
7#28912C212yesmaximal, complemented
8#28120C212yesmaximal, complemented
9#28094C212yesmaximal, complemented
10#26821C212yesmaximal, complemented
11#26798C212yesmaximal, complemented
12#25163C212yesmaximal, complemented
13#25115C212yesmaximal, complemented
14#24094C212yesmaximal, complemented
15#23851C212yesmaximal, complemented
16#22877C212yesmaximal, complemented
17C4×#467C211yesmaximal, characteristic, complemented
18C8×#121C211yesmaximal, characteristic, complemented
19C2×#1970C211yesmaximal, characteristic, complemented
20C23×D8C2211yescharacteristic
21C2×#552C2212yes—
22C2×#546C2212yes—
23#3296—216no—
24C2×#488C2212yescomplemented
25C2×#482C2212yescomplemented
26C2×#483C2212yes—
27C2×#478C2212yescomplemented
28C2×#467C2211yescharacteristic
29C2×#465C2212yescomplemented
30C2×#464C2212yescomplemented
31C2×#452C2212yescomplemented
32C2×#449C2212yes—
33C2×#449C2212yes—
34C2×#450C2212yes—
35C2×C4×Q16C2211yescharacteristic, complemented
36C2×C4×SD16C2212yescomplemented
37C2×C8×D4C2212yes—
38C2×C8×D4C2211yescharacteristic, complemented
39C22×#107C2211yescharacteristic
40C2×#416C2212yescomplemented
41C22×#102C2212yes—
42C22×C4×C8C2211yescharacteristic
43#2714—22no—
44#2694—22no—
45#2554—22no—
46#2539—22no—
47#2490—22no—
48#2490C2212yescomplemented
49#2486C2212yes—
50#2454C2212yescomplemented
51#2448C2212yescomplemented
52#2426C2212yescomplemented
53#2414C2212yescomplemented
54#2412—22no—
55#2411—22no—
56#2408C2212yes—
57#2407C2212yescomplemented
58#2363C2212yescomplemented
59#2342—22no—
60#2341C2212yescomplemented
61C4×C22⋊Q8C2212yes—
62C4×#121C2211yescharacteristic
63C2×#390C2212yes—
64#2067C2212yescomplemented
65#2067C2212yescomplemented
66#2065C2212yescomplemented
67#2065C2212yescomplemented
68#2059C2212yescomplemented
69#2059C2212yescomplemented
70#2055C2212yescomplemented
71#2055C2212yescomplemented
72#2036C2212yescomplemented
73#2036C2212yescomplemented
74#2033C2212yescomplemented
75#2033C2212yescomplemented
76#2012C2212yes—
77#2012C2212yes—
78#1999C2212yes—
79#1999C2212yes—
80#1970C2211yescharacteristic
81#1970C2212yes—
82#1970C2212yes—
83#1970C2211yescharacteristic
84#1970C2211yescharacteristic
85#1970C2211yescharacteristic
86#1969C2211yescharacteristic, complemented
87#1954C2211yescharacteristic, complemented
88#1942C2211yescharacteristic, complemented
89#1939C2211yescharacteristic, complemented
90#1934C2212yescomplemented
91#1934C2212yescomplemented
92#1933C2212yescomplemented
93#1926C2212yescomplemented
94#1926C2212yescomplemented
95#1923C2212yescomplemented
96#1893C2212yescomplemented
97#1893C2212yescomplemented
98#1892C2212yes—
99#1880C2212yescomplemented
100#1880C2212yescomplemented
101#1879C2212yes—
102#1879C2212yes—
103#1869C2212yes—
104#1863C2212yescomplemented
105#1863C2212yescomplemented
106#1854C2212yescomplemented
107#1854C2212yescomplemented
108#1823C2212yes—
109#1808C2211yescharacteristic
110#1797C2211yescharacteristic
111#1786C2212yes—
112C4×#107C2211yescharacteristic, complemented
113C8×C4⋊C4C2211yescharacteristic, complemented
114C4×#103C2212yescomplemented
115C8×C22⋊C4C2212yescomplemented
116C22×#41C2312yes—
117C23×D4C2312yes—
118C22×Q16C2311yescharacteristic
119C22×SD16C2312yes—
120C22×SD16C2312yes—
121C22×D8—24no—
122C22×D8—42no—
123C22×D8—42no—
124C22×D8C2312yes—
125C22×D8C2311yescharacteristic
126C22×D8C2311yescharacteristic
127C23×C8C2311yescharacteristic
128C23×C8C2312yes—
129C23×C8C2311yescharacteristic
130#552—28no—
131#552—44no—
132#546—28no—
133#546—44no—
134C2×#126—22no—
135C2×#125—22no—
136C2×#125C2312yes—
137C2×#124C2312yes—
138C2×#123—22no—
139C2×#123—22no—
140C2×#123—22no—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
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×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2311yescharacteristic
155C2×#117—22no—
156C2×#117C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—22no—
159C22×C22⋊C4—22no—
160C22×C22⋊C4—22no—
161C22×C42C2311yescharacteristic
162#488—28no—
163#483—28no—
164#482—28no—
165#478—28no—
166#467D418yescomplemented
167#465—28no—
168#464—28no—
169#452—28no—
170#450—28no—
171#449—28no—
172#449—44no—
173C4×Q16—42no—
174C4×SD16—28no—
175C8×D4—28no—
176C8×D4—42no—
177C2×#107—42no—
178C2×#107C2311yescharacteristic
179C2×#107C2312yes—
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2311yescharacteristic
189#416—28no—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#102—28no—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C4×C8—42no—
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2312yes—
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2311yescharacteristic
216#399—22no—
217#399—22no—
218#398—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#396—22no—
223#396—22no—
224#394—22no—
225#394—22no—
226#394—22no—
227#394—22no—
228#394—22no—
229#392—22no—
230#392—22no—
231#392—22no—
232#391C2312yes—
233#390—22no—
234#390—22no—
235#390—22no—
236#390—22no—
237#390—22no—
238#390—22no—
239#390—22no—
240#390—22no—
241#390D411yescharacteristic
242#390C2312yes—
243#390C2312yes—
244#390C2312yes—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#389D411yescharacteristic
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#388D412yes—
259#387—22no—
260#386—22no—
261#386—22no—
262#386D412yes—
263#385—22no—
264#385—22no—
265#385—22no—
266#381—22no—
267#380—22no—
268#380—22no—
269#380D411yescharacteristic
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#379—22no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C25—22no—
292C2×#41—24no—
293C2×#41—24no—
294C2×#41—42no—
295C2×#41—42no—
296C2×#41—42no—
297C2×#41—42no—
298C22×Q8C2412yes—
299C22×D4—24no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—24no—
307C22×D4—42no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4C2×D412yes—
311C22×D4C2×D411yescharacteristic
312C22×D4C2412yes—
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321C2×Q16—41no—
322C2×Q16—41no—
323C2×Q16C2×D414yes—
324C2×SD16—24no—
325C2×SD16—24no—
326C2×SD16—24no—
327C2×SD16—42no—
328C2×SD16—42no—
329C2×SD16—42no—
330C2×D8—24no—
331C2×D8—22no—
332C2×D8—24no—
333C2×D8—41no—
334C2×D8—41no—
335C2×D8—41no—
336C2×D8—42no—
337C2×D8—41no—
338C2×D8—416no—
339C2×D8#4114yes—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—24no—
344C22×C8—41no—
345C22×C8—41no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8C2×D414yes—
349C22×C8C2412yes—
350C22×C8C2412yes—
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355#126—48no—
356#125—24no—
357#125—42no—
358#125—48no—
359#124—24no—
360#124—42no—
361#123—48no—
362#123—48no—
363#123—84no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—42no—
367C22⋊Q8C2×D418yes—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—48no—
372#121—42no—
373#121—42no—
374#121—42no—
375#121—42no—
376#120—48no—
377#120—84no—
378C4×Q8—24no—
379C4×Q8—42no—
380C4×Q8—42no—
381C4×Q8—42no—
382C4×D4—24no—
383C4×D4—24no—
384C4×D4—24no—
385C4×D4—42no—
386C4×D4—41no—
387C4×D4—41no—
388#117—24no—
389#117—48no—
390#117—42no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
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—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4C2×D412yes—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
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—48no—
437C2×C22⋊C4—48no—
438C2×C22⋊C4—84no—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D412yes—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C22⋊C4C2×D412yes—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—41no—
449C2×C42—41no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2412yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—41no—
456#107—42no—
457#107—41no—
458#107—41no—
459#107—41no—
460#107C2×D414yes—
461#106—24no—
462#106—24no—
463C4⋊C8—24no—
464C4⋊C8—41no—
465C4⋊C8—41no—
466#103—24no—
467#103—24no—
468#103—24no—
469#103—24no—
470#103C2×D418yes—
471#102—24no—
472#102—24no—
473#102—24no—
474#102—24no—
475#102—24no—
476#102—24no—
477#102—24no—
478#102—42no—
479#102—42no—
480#102—42no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C4×C8—24no—
486C4×C8—22no—
487C4×C8—22no—
488C4×C8—41no—
489C4×C8—41no—
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#95C2×D412yes—
500#95C2×D412yes—
501#95C2×D412yes—
502C24—22no—
503C24—22no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—82no—
509C24—82no—
510C24—82no—
511C24C22×D412yes—
512C24C22×D411yescharacteristic
513#41—48no—
514#41—84no—
515#41—84no—
516#41—84no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8C22×D414yes—
523C2×D4—24no—
524C2×D4—24no—
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—22no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—84no—
549C2×D4—84no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4C2×#4114yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
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—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4#13514yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4H(5,𝔽2)12yes—
601C22×C4C2511yescharacteristic
602Q16—44no—
603SD16—48no—
604SD16—84no—
605D8—44no—
606D8—48no—
607D8—44no—
608C2×C8—28no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—44no—
624C2×C8—84no—
625C2×C8C22×D412yes—
626C2×C8C22×D412yes—
627C2×C8C2×#4112yes—
628C2×C8H(5,𝔽2)12yes—
629C4⋊C4—28no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—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—41no—
642C4⋊C4—41no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4—82no—
651C4⋊C4—82no—
652C4⋊C4C22×D414yes—
653C22⋊C4—28no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—82no—
678C22⋊C4—82no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C42—22no—
683C42—21no—
684C42—21no—
685C42—22no—
686C42—21no—
687C42—21no—
688C42—41no—
689C42—41no—
690C42—44no—
691C42—44no—
692C42—82no—
693C42—82no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—88no—
720C23—88no—
721C23—88no—
722C23—88no—
723C23—164no—
724C23—164no—
725C23—164no—
726C23D4212yes—
727C23C2×#13512yes—
728C23#57612yes—
729C23C23×D411yescharacteristic
730Q8—24no—
731Q8—24no—
732Q8—42no—
733Q8—42no—
734D4—24no—
735D4—24no—
736D4—44no—
737D4—48no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—88no—
745D4—88no—
746D4—164no—
747D4—164no—
748D4—164no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
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—88no—
799C2×C4—88no—
800C2×C4—164no—
801C2×C4D4212yes—
802C2×C4C2×#13512yes—
803C2×C4C2×#13512yes—
804C2×C4C23×D411yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C2×C4C2×H(5,𝔽2)11yescharacteristic
807C2×C4C2×H(5,𝔽2)11yescharacteristic
808C2×C4#58511yescharacteristic
809C2×C4#58511yescharacteristic
810C8—22no—
811C8—22no—
812C8—22no—
813C8—22no—
814C8—42no—
815C8—42no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—42no—
831C22—44no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—1616no—
844C22#328714yes—
845C22C2×D4211yescharacteristic
846C22D4×#4111yescharacteristic
847C22#349611yescharacteristic
848C22C22×#13511yescharacteristic
849C22C2×#57611yescharacteristic
850C22#358411yescharacteristic
851C22#358411yescharacteristic
852C4—22no—
853C4—22no—
854C4—22no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—42no—
861C4—44no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4D4×#4111yescharacteristic
867C4#349011yescharacteristic
868C4#349611yescharacteristic
869C4#354511yescharacteristic
870C2—24no—
871C2—82no—
872C2—84no—
873C2—162no—
874C2#5981411yescharacteristic
875C2C2×#328711yescharacteristic
876C2#6108811yescharacteristic
877C2#6142711yescharacteristic
878C2#6148911yescharacteristic
879C2#6224711yescharacteristic
880C2#6227811yescharacteristic
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×#3296C2semidirect
2. #59807C2semidirect
3. #31238C2semidirect
4. #31212C2semidirect
5. #31192C2semidirect
6. #31060C2semidirect
7. #28912C2semidirect
8. #28120C2semidirect
9. #28094C2semidirect
10. #26821C2semidirect
11. #26798C2semidirect
12. #25163C2semidirect
13. #25115C2semidirect
14. #24094C2semidirect
15. #23851C2semidirect
16. #22877C2semidirect
17. C4×#467C2semidirect
18. C8×#121C2semidirect
19. C2×#1970C2semidirect
24. C2×#488C22semidirect
25. C2×#482C22semidirect
27. C2×#478C22semidirect
29. C2×#465C22semidirect
30. C2×#464C22semidirect
31. C2×#452C22semidirect
35. C2×C4×Q16C22semidirect
36. C2×C4×SD16C22semidirect
38. C2×C8×D4C22semidirect
40. C2×#416C22semidirect
48. #2490C22semidirect
50. #2454C22semidirect
51. #2448C22semidirect
52. #2426C22semidirect
53. #2414C22semidirect
57. #2407C22semidirect
58. #2363C22semidirect
60. #2341C22semidirect
64. #2067C22semidirect
65. #2067C22semidirect
66. #2065C22semidirect
67. #2065C22semidirect
68. #2059C22semidirect
69. #2059C22semidirect
70. #2055C22semidirect
71. #2055C22semidirect
72. #2036C22semidirect
73. #2036C22semidirect
74. #2033C22semidirect
75. #2033C22semidirect
86. #1969C22semidirect
87. #1954C22semidirect
88. #1942C22semidirect
89. #1939C22semidirect
90. #1934C22semidirect
91. #1934C22semidirect
92. #1933C22semidirect
93. #1926C22semidirect
94. #1926C22semidirect
95. #1923C22semidirect
96. #1893C22semidirect
97. #1893C22semidirect
99. #1880C22semidirect
100. #1880C22semidirect
104. #1863C22semidirect
105. #1863C22semidirect
106. #1854C22semidirect
107. #1854C22semidirect
112. C4×#107C22semidirect
113. C8×C4⋊C4C22semidirect
114. C4×#103C22semidirect
115. C8×C22⋊C4C22semidirect
166. #467D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32962
#598072
#312382
#312122
#311922
#310602
#289122
#281202
#280942
#268212
#267982
#251632
#251152
#240942
#238512
#228772
C4×#4672
C8×#1212
C2×#19702