Finite Group Databasebeta

← #6467829

Subgroups — #6467829

Order 512.

2092 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic, complemented
2C2×#3169C211yesmaximal, characteristic
3#35298C211yesmaximal, characteristic, complemented
4#34226C211yesmaximal, characteristic, complemented
5#28750C211yesmaximal, characteristic, complemented
6#28716C211yesmaximal, characteristic, complemented
7#28689C211yesmaximal, characteristic, complemented
8#28656C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#28615C211yesmaximal, characteristic, complemented
11#28613C211yesmaximal, characteristic, complemented
12#28586C214yesmaximal, complemented
13#28443C211yesmaximal, characteristic, complemented
14#24763C214yesmaximal, complemented
15#23692C214yesmaximal, complemented
16#21509C214yesmaximal, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21400C211yesmaximal, characteristic, complemented
19C4×#424C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3182—28no—
24#3169—28no—
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#493C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#486C2211yescharacteristic
31C2×#486C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#468C2214yes—
34C2×#466C2214yes—
35C2×#463C2214yes—
36C2×#440C2214yes—
37C2×C4×D8C2214yes—
38C2×#424C2212yes—
39C2×C4×M16C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2858C2211yescharacteristic
45#2620C2212yes—
46#2620C2212yes—
47#2566—21no—
48#2566—21no—
49#2545—21no—
50#2545—21no—
51#2500—21no—
52#2500—21no—
53#2432—21no—
54#2432—21no—
55#2367—21no—
56#2367—21no—
57#2363—21no—
58#2363—21no—
59#2357—21no—
60#2349—21no—
61#2341—21no—
62#2339—21no—
63#2326C2212yes—
64#2326C2212yes—
65#2324C2212yes—
66#2324C2212yes—
67#2319C2212yes—
68C4×C4⋊Q8C2211yescharacteristic
69C4×C4⋊Q8C2211yescharacteristic
70C4×#127C2211yescharacteristic
71C4×#127C2211yescharacteristic
72#2285C2211yescharacteristic
73#2275C2212yes—
74C4×#117C2211yescharacteristic
75#2083C2214yes—
76#2071C2214yes—
77#2068C2214yes—
78#2067C2214yes—
79#2055C2214yes—
80#2054C2214yes—
81#2042C2214yes—
82#2012C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1983C2214yes—
88#1957C2211yescharacteristic
89#1957C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1947C2214yes—
93#1928C2214yes—
94#1925C2214yes—
95#1895C2214yes—
96#1892C2214yes—
97#1879C2214yes—
98#1877C2214yes—
99#1802C2214yes—
100#1768C2212yes—
101#1768C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×C4⋊C8C2211yescharacteristic
104C4×C4⋊C8C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106#1762C2214yes—
107C4×#103C2214yes—
108#1729C2212yes—
109C22×#41—21no—
110C22×#41—21no—
111C22×SD16C2314yes—
112C22×D8C2314yes—
113C22×M16C2312yes—
114C23×C8C2312yes—
115#533—24no—
116#533—24no—
117#532—24no—
118#532—24no—
119#532—24no—
120#532D418yes—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×#127C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125—21no—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×#124C2312yes—
135C2×#124C2312yes—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8C2312yes—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2312yes—
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×C4×D4C2312yes—
156C2×#117—21no—
157C2×#117—21no—
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#500—24no—
162#500—24no—
163#493—24no—
164#492—24no—
165#487—24no—
166#486—24no—
167#486—24no—
168#486—24no—
169#468—216no—
170#466—216no—
171#463—216no—
172#440—216no—
173C4×D8—216no—
174C2×#107C2314yes—
175C2×#107C2314yes—
176#424—28no—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C4×M16—24no—
190C2×#97C2312yes—
191C2×C4×C8—24no—
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2312yes—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197#396—22no—
198#396—22no—
199#396—22no—
200#396—22no—
201#394—22no—
202#394—22no—
203#394—22no—
204#394—22no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391C2312yes—
210#391C2312yes—
211#390—22no—
212#390—22no—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390—21no—
218#390—21no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390—21no—
223#390C2312yes—
224#390C2312yes—
225#390C2312yes—
226#390C2312yes—
227#389—21no—
228#389—21no—
229#389C2312yes—
230#389C2312yes—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#386—22no—
240#386—22no—
241#385—22no—
242#385—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#385—22no—
247#384—21no—
248#384—21no—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2312yes—
252#384C2312yes—
253#382—21no—
254#382—21no—
255#382—21no—
256#381—22no—
257#380—21no—
258#380—22no—
259#380C2312yes—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4D411yescharacteristic
264C4×C4⋊C4D411yescharacteristic
265C4×C4⋊C4D411yescharacteristic
266C4×C4⋊C4D411yescharacteristic
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277#376C2311yescharacteristic
278#376C2311yescharacteristic
279C2×#95—22no—
280C43C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290C2×#41—28no—
291C2×#41—44no—
292C2×#41—82no—
293C2×#41—82no—
294C2×#41—82no—
295C2×#41—82no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8C2412yes—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2412yes—
307C22×D4C2412yes—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×SD16—28no—
316C2×SD16—28no—
317C2×SD16—44no—
318C2×D8—28no—
319C2×D8—28no—
320C2×D8—44no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—42no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—42no—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—82no—
339C4⋊Q8—82no—
340C4⋊Q8C2×D414yes—
341#127—22no—
342#127—22no—
343#127—22no—
344#127C2×D414yes—
345#125—44no—
346#124—28no—
347#124—28no—
348#124—44no—
349#124—44no—
350#124—82no—
351#124—82no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—44no—
355#121—28no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—44no—
360#121C2×D418yes—
361C4×Q8—24no—
362C4×Q8—24no—
363C4×Q8—44no—
364C4×Q8—82no—
365C4×Q8—82no—
366C4×D4—28no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—28no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—82no—
374C4×D4—82no—
375C4×D4—82no—
376C4×D4—82no—
377C4×D4C2×D418yes—
378#117—24no—
379#117—42no—
380#117—44no—
381#117—82no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
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⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D414yes—
447C2×C42#4114yes—
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—28no—
455#107—28no—
456C4⋊C8—24no—
457C4⋊C8—24no—
458C4⋊C8—24no—
459C4⋊C8#4118yescomplemented
460#103—28no—
461#103—28no—
462#103—44no—
463#102—28no—
464#102—28no—
465#102—28no—
466#102—28no—
467#102—44no—
468#97—24no—
469C4×C8—24no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492C24—22no—
493C24—22no—
494C24C22×D411yescharacteristic
495#41—816no—
496#41—816no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×D4—28no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—22no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—44no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—82no—
532C2×D4—82no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4C22×D414yes—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4#12114yes—
561C22×C4#12114yes—
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C2×#4112yes—
577C22×C4C2511yescharacteristic
578SD16—416no—
579D8—416no—
580M16—48no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—48no—
592C2×C8C2×#4114yes—
593C2×C8C2×#4114yes—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4—82no—
622C4⋊C4C22×D414yes—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—82no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—44no—
659C42—82no—
660C42—82no—
661C42—82no—
662C42#12114yes—
663C42#12114yes—
664C42C22×D412yes—
665C42C22×D412yes—
666C42C2×#4112yes—
667C42C2×#4112yes—
668C42C2×#4114yes—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—24no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23C2×#12112yes—
690C23C23×D411yescharacteristic
691Q8—48no—
692Q8—44no—
693Q8—44no—
694Q8—84no—
695Q8—84no—
696D4—28no—
697D4—44no—
698D4—44no—
699D4—44no—
700D4—48no—
701D4—48no—
702D4—88no—
703D4—88no—
704D4—84no—
705D4—84no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—24no—
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—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
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—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—88no—
757C2×C4—88no—
758C2×C4—164no—
759C2×C4—164no—
760C2×C4C2×#12112yes—
761C2×C4C2×#12112yes—
762C2×C4C2×#12112yes—
763C2×C4C2×#12112yes—
764C2×C4C2×#12112yes—
765C2×C4#53212yes—
766C2×C4#53212yes—
767C2×C4#57612yes—
768C2×C4#57612yes—
769C2×C4#57712yes—
770C2×C4#57812yes—
771C2×C4C23×D411yescharacteristic
772C2×C4C22×#4112yes—
773C2×C4C22×#4111yescharacteristic
774C2×C4#58512yes—
775C8—24no—
776C8—24no—
777C8—42no—
778C8—42no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22C22×#12111yescharacteristic
801C22C2×#53211yescharacteristic
802C22#344911yescharacteristic
803C22C2×#57611yescharacteristic
804C22C2×#57611yescharacteristic
805C22C2×#57711yescharacteristic
806C22C2×#57811yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#304114yes—
825C4#304614yes—
826C4D4×#4112yes—
827C4#348012yes—
828C2—42no—
829C2—84no—
830C2—162no—
831C2#3493711yescharacteristic
832C2C2×#304111yescharacteristic
833C2C2×#304611yescharacteristic
834C2#6071811yescharacteristic
835C2#6072211yescharacteristic
836C2#6100611yescharacteristic
837C2#6101411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3169C2
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
1. C2×#3182C2semidirect
3. #35298C2semidirect
4. #34226C2semidirect
5. #28750C2semidirect
6. #28716C2semidirect
7. #28689C2semidirect
8. #28656C2semidirect
9. #28655C2semidirect
10. #28615C2semidirect
11. #28613C2semidirect
12. #28586C2semidirect
13. #28443C2semidirect
14. #24763C2semidirect
15. #23692C2semidirect
16. #21509C2semidirect
17. #21410C2semidirect
18. #21400C2semidirect
19. C4×#424C2semidirect
459. C4⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#31822
C2×#31692
#352982
#342262
#287502
#287162
#286892
#286562
#286552
#286152
#286132
#285862
#284432
#247632
#236922
#215092
#214102
#214002
C4×#4242