Finite Group Databasebeta

← #6524922

Subgroups — #6524922

Order 512.

2004 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3207C211yesmaximal, characteristic
2C2×#3131C211yesmaximal, characteristic, complemented
3#35298C211yesmaximal, characteristic, complemented
4#34226C211yesmaximal, characteristic, complemented
5#28719C211yesmaximal, characteristic, complemented
6#28718C211yesmaximal, characteristic, complemented
7#28717C211yesmaximal, characteristic, complemented
8#28716C211yesmaximal, characteristic, complemented
9#28615C211yesmaximal, characteristic, complemented
10#28615C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#28614C211yesmaximal, characteristic, complemented
13#25327C214yesmaximal, complemented
14#25326C214yesmaximal, complemented
15#24537C214yesmaximal, complemented
16#24535C214yesmaximal, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21401C211yesmaximal, characteristic, complemented
19#21349C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3207—28no—
24C2×#493C2211yescharacteristic
25C2×#492C2211yescharacteristic
26#3131—28no—
27C2×#488C2214yes—
28C2×#487C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#486C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#463C2214yes—
35C2×#449C2214yes—
36C2×#431C2211yescharacteristic
37C2×#416C2214yes—
38C22×C4×C8C2211yescharacteristic
39#2868C2211yescharacteristic
40#2862C2211yescharacteristic
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2620—21no—
44#2620—21no—
45#2566C2212yes—
46#2566C2212yes—
47#2545—21no—
48#2545—21no—
49#2500C2212yes—
50#2500C2212yes—
51#2432—21no—
52#2432—21no—
53#2367C2212yes—
54#2367C2212yes—
55#2363—21no—
56#2363—21no—
57#2357—21no—
58#2349—21no—
59#2341C2212yes—
60#2339C2212yes—
61#2326—21no—
62#2326—21no—
63#2324—21no—
64#2324—21no—
65#2319—21no—
66C4×C4⋊Q8C2211yescharacteristic
67C4×C4⋊Q8C2211yescharacteristic
68C4×#127C2211yescharacteristic
69C4×#127C2211yescharacteristic
70#2285C2211yescharacteristic
71#2275—21no—
72C4×#117C2211yescharacteristic
73#2074C2214yes—
74#2073C2214yes—
75#2072C2214yes—
76#2071C2214yes—
77#2055C2214yes—
78#2055C2214yes—
79#2054C2214yes—
80#2054C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1989C2214yes—
88#1957C2211yescharacteristic
89#1957C2211yescharacteristic
90#1939C2212yes—
91#1939C2212yes—
92#1893C2214yes—
93#1880C2214yes—
94#1880C2214yes—
95#1879C2214yes—
96#1879C2214yes—
97#1850C2212yes—
98#1850C2212yes—
99#1825C2214yes—
100#1805C2214yes—
101#1804C2214yes—
102#1803C2214yes—
103#1802C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C4⋊C8C2211yescharacteristic
107C4×C4⋊C8C2211yescharacteristic
108C4×#102C2214yes—
109C22×#41—21no—
110C22×#41C2312yes—
111C22×SD16C2314yes—
112C22×D8C2314yes—
113C23×C8C2312yes—
114#533—24no—
115#533—24no—
116#532—24no—
117#532—24no—
118#532—24no—
119#532D418yes—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×#127C2311yescharacteristic
127C2×#127C2311yescharacteristic
128C2×#125C2312yes—
129C2×#124—21no—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×#124C2312yes—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×#117—21no—
156C2×#117D411yescharacteristic
157C2×#117D411yescharacteristic
158C2×#117C2312yes—
159C22×C42C2311yescharacteristic
160#493—24no—
161#492—24no—
162#488—216no—
163#487—24no—
164#487—24no—
165#487—24no—
166#486—24no—
167#486—24no—
168#486—24no—
169#463—216no—
170#449—216no—
171#431—24no—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177#416—216no—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×C22⋊C8C2312yes—
187C2×C4×C8—24no—
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193#396—22no—
194#396—22no—
195#396—22no—
196#396—22no—
197#394—22no—
198#394—22no—
199#394—22no—
200#394—22no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391C2312yes—
206#391C2312yes—
207#390—22no—
208#390—22no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#390C2312yes—
221#390C2312yes—
222#390C2312yes—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#386—22no—
236#386—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#385—22no—
242#385—22no—
243#384—21no—
244#384—21no—
245#384C2311yescharacteristic
246#384C2311yescharacteristic
247#384C2312yes—
248#384C2312yes—
249#382—21no—
250#382C2312yes—
251#382C2312yes—
252#381—22no—
253#380—21no—
254#380—22no—
255#380C2312yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C4⋊C4C2311yescharacteristic
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4D411yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C4×C22⋊C4C2311yescharacteristic
273#376D411yescharacteristic
274#376D411yescharacteristic
275C2×#95—22no—
276C43C2311yescharacteristic
277C43C2311yescharacteristic
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#336C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288C2×#41—24no—
289C2×#41—44no—
290C2×#41—44no—
291C2×#41—44no—
292C2×#41—82no—
293C2×#41—82no—
294C2×#41C2×D418yes—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8C2412yes—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4C2412yes—
306C22×D4C2412yes—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×SD16—28no—
315C2×SD16—44no—
316C2×SD16—44no—
317C2×D8—28no—
318C2×D8—44no—
319C2×D8—44no—
320C22×C8—24no—
321C22×C8—42no—
322C22×C8—42no—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—82no—
335C4⋊Q8—82no—
336C4⋊Q8C2×D414yes—
337#127—22no—
338#127—22no—
339#127—22no—
340#127C2×D414yes—
341#125—24no—
342#125—24no—
343#124—24no—
344#124—44no—
345#124—44no—
346#124—44no—
347#124—82no—
348#124—82no—
349#124C2×D418yes—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352#121—28no—
353#121—28no—
354#121—24no—
355#121—24no—
356#121—44no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×D4—28no—
362C4×D4—28no—
363C4×D4—24no—
364C4×D4—24no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—44no—
368C4×D4—44no—
369C4×D4—44no—
370C4×D4—82no—
371C4×D4—82no—
372#117—24no—
373#117—24no—
374#117—24no—
375#117—42no—
376#117—82no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D414yes—
441C2×C42C2×D411yescharacteristic
442C2×C42#4114yes—
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C4⋊C8—24no—
450C4⋊C8—42no—
451C4⋊C8—42no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454#103—28no—
455#103—28no—
456#103—28no—
457#102—28no—
458#102—28no—
459#102—28no—
460#102—44no—
461#102—44no—
462C22⋊C8—24no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8—24no—
466C4×C8—22no—
467C4×C8—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486C24—22no—
487C24—22no—
488C24C22×D411yescharacteristic
489#41—416no—
490#41—88no—
491#41—816no—
492C2×Q8—22no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8C22×D414yes—
505C2×D4—28no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—44no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4C22×D414yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4#12114yes—
556C22×C4#12114yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4112yes—
572C22×C4C2511yescharacteristic
573SD16—88no—
574D8—88no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—48no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C22⋊C4—82no—
636C22⋊C4—82no—
637C22⋊C4—82no—
638C22⋊C4—82no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—44no—
653C42—82no—
654C42—82no—
655C42—82no—
656C42#12114yes—
657C42#12114yes—
658C42#13514yes—
659C42C22×D412yes—
660C42C22×D412yes—
661C42C2×#4112yes—
662C42C2×#4112yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23C2×#12112yes—
684C23C23×D411yescharacteristic
685Q8—28no—
686Q8—44no—
687Q8—84no—
688Q8—84no—
689Q8—84no—
690D4—28no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—48no—
695D4—48no—
696D4—88no—
697D4—88no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4—164no—
753C2×C4—164no—
754C2×C4C2×#12112yes—
755C2×C4C2×#12112yes—
756C2×C4C2×#12112yes—
757C2×C4C2×#12112yes—
758C2×C4C2×#12112yes—
759C2×C4C2×#13512yes—
760C2×C4C2×#13512yes—
761C2×C4C2×#13512yes—
762C2×C4#57512yes—
763C2×C4#57612yes—
764C2×C4#57712yes—
765C2×C4C23×D411yescharacteristic
766C2×C4C22×#4111yescharacteristic
767C2×C4#58512yes—
768C2×C4#58512yes—
769C8—42no—
770C8—42no—
771C8—42no—
772C8—42no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C22×#12111yescharacteristic
795C22#350011yescharacteristic
796C22#350011yescharacteristic
797C22C22×#13511yescharacteristic
798C22C2×#57511yescharacteristic
799C22C2×#57611yescharacteristic
800C22C2×#57711yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#303514yes—
819C4#304514yes—
820C4#348512yes—
821C4#351012yes—
822C2—42no—
823C2—84no—
824C2—162no—
825C2#3561711yescharacteristic
826C2C2×#303511yescharacteristic
827C2C2×#304511yescharacteristic
828C2#6252711yescharacteristic
829C2#6253211yescharacteristic
830C2#6254311yescharacteristic
831C2#6254611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3207C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3131C2semidirect
3. #35298C2semidirect
4. #34226C2semidirect
5. #28719C2semidirect
6. #28718C2semidirect
7. #28717C2semidirect
8. #28716C2semidirect
9. #28615C2semidirect
10. #28615C2semidirect
11. #28614C2semidirect
12. #28614C2semidirect
13. #25327C2semidirect
14. #25326C2semidirect
15. #24537C2semidirect
16. #24535C2semidirect
17. #21835C2semidirect
18. #21401C2semidirect
19. #21349C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32072
C2×#31312
#352982
#342262
#287192
#287182
#287172
#287162
#286152
#286142
#253272
#253262
#245372
#245352
#218352
#214012
#213492