Finite Group Databasebeta

← #6579398

Subgroups — #6579398

Order 512.

2150 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3141C211yesmaximal, characteristic, complemented
2C2×#3131C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic, complemented
4#36127C211yesmaximal, characteristic
5#33236C211yesmaximal, characteristic, complemented
6#33049C211yesmaximal, characteristic, complemented
7#33043C211yesmaximal, characteristic, complemented
8#28748C211yesmaximal, characteristic, complemented
9#28718C211yesmaximal, characteristic, complemented
10#27784C214yesmaximal, complemented
11#27272C214yesmaximal, complemented
12#27265C214yesmaximal, complemented
13#25904C211yesmaximal, characteristic, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25857C211yesmaximal, characteristic, complemented
16#25857C211yesmaximal, characteristic, complemented
17#22420C214yesmaximal, complemented
18#21646C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#547C2212yes—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3141—28no—
26C2×#489C2214yes—
27#3131—28no—
28C2×#488C2214yes—
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#435C2212yes—
39C2×#417C2214yes—
40C2×#416C2214yes—
41C2×C4×M16C2211yescharacteristic
42C22×C4×C8C2211yescharacteristic
43#2868C2211yescharacteristic
44#2862C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2550C2212yes—
50#2547C2212yes—
51#2537—21no—
52#2537—21no—
53#2492—21no—
54#2451—21no—
55#2446—21no—
56#2442C2212yes—
57#2439C2212yes—
58#2432C2212yes—
59#2432C2212yes—
60#2429—21no—
61#2422—21no—
62#2422—21no—
63#2422—21no—
64#2422—21no—
65#2417—21no—
66#2409—21no—
67#2360—21no—
68#2352C2212yes—
69D4×C4⋊C4—21no—
70D4×C4⋊C4—21no—
71Q8×C22⋊C4—21no—
72C4×C4⋊Q8C2211yescharacteristic
73C4×#127C2211yescharacteristic
74C42×D4C2211yescharacteristic
75#2073C2214yes—
76#2043C2214yes—
77#2042C2214yes—
78#2042C2214yes—
79#2026C2214yes—
80#2024C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1981C2214yes—
85#1960C2214yes—
86#1960C2214yes—
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1936C2214yes—
91#1935C2214yes—
92#1933C2214yes—
93#1894C2214yes—
94#1892C2214yes—
95#1873C2214yes—
96#1872C2214yes—
97#1834C2211yescharacteristic
98#1804C2214yes—
99#1788C2214yes—
100#1788C2214yes—
101#1771C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103#1762C2214yes—
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41C2312yes—
110C22×#41C2312yes—
111C23×Q8—21no—
112C22×M16C2312yes—
113C23×C8C2312yes—
114#547—216no—
115#533—24no—
116#533—42no—
117#532—24no—
118#532—24no—
119#532—42no—
120#532—42no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2312yes—
132C2×C4⋊Q8C2311yescharacteristic
133C2×#127C2311yescharacteristic
134C2×#125C2312yes—
135C2×#124C2312yes—
136C2×#124C2312yes—
137C2×#123—22no—
138C2×#123—22no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×#121—22no—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4D411yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4C2312yes—
162C2×C4×D4C2311yescharacteristic
163C2×#117C2312yes—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#489—216no—
170#488—216no—
171#487—24no—
172#487—24no—
173#487—24no—
174#487—24no—
175#487—42no—
176#487—42no—
177#486—24no—
178#486—24no—
179#486D418yescomplemented
180#435—28no—
181C2×C4⋊C8C2312yes—
182#417—216no—
183#416—216no—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C4×M16—24no—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×#97C2312yes—
202C2×C4×C8—24no—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208#400—22no—
209#398—22no—
210#398—22no—
211#397—22no—
212#397—22no—
213#396—22no—
214#395—22no—
215#394—22no—
216#394—22no—
217#394—22no—
218#394—22no—
219#393—22no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#391—22no—
228#391—22no—
229#391C2312yes—
230#391C2312yes—
231#390—21no—
232#390—21no—
233#390C2312yes—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#387—22no—
247#387—22no—
248#386—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#384—21no—
255#384—21no—
256#384—21no—
257#384—21no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#382C2312yes—
261#382C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—22no—
269#380—22no—
270#380—22no—
271#380C2312yes—
272#380C2312yes—
273C4×C4⋊C4—21no—
274C4×C4⋊C4D411yescharacteristic
275C4×C4⋊C4D411yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4—22no—
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C43C2311yescharacteristic
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293C2×#41—24no—
294C2×#41—24no—
295C2×#41—28no—
296C2×#41—28no—
297C2×#41—42no—
298C2×#41—42no—
299C2×#41—44no—
300C2×#41—44no—
301C22×Q8—21no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×Q8—22no—
305C22×Q8—44no—
306C22×Q8—44no—
307C22×Q8—82no—
308C22×Q8C2412yes—
309C22×Q8C2412yes—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4C2×D411yescharacteristic
315C22×D4C2412yes—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—42no—
329C22×C8—24no—
330C22×C8—24no—
331C22×C8—42no—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—24no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—28no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—42no—
348C4⋊Q8—44no—
349C4⋊Q8—44no—
350C4⋊Q8—44no—
351C4⋊Q8C2×D414yes—
352#127—22no—
353#127C2×D414yes—
354#125—24no—
355#125—42no—
356#124—24no—
357#124—24no—
358#124—42no—
359#124—42no—
360#123—48no—
361#123—48no—
362C22⋊Q8—28no—
363C22⋊Q8—28no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366C22⋊Q8—44no—
367C22⋊Q8—82no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—44no—
372#121—48no—
373C4×Q8—44no—
374C4×Q8—44no—
375C4×Q8—82no—
376C4×D4—28no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—44no—
380C4×D4—44no—
381C4×D4—44no—
382C4×D4—44no—
383C4×D4—44no—
384C4×D4—44no—
385C4×D4#4118yes—
386#117—24no—
387#117—42no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—48no—
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C4⋊C8—24no—
462#103—28no—
463#103—28no—
464#103—28no—
465#103—28no—
466#103—44no—
467#103—44no—
468#103—44no—
469#103—44no—
470#102—28no—
471#102—28no—
472#102—44no—
473#102C2×D4116yes—
474C22⋊C8—24no—
475C22⋊C8—24no—
476#97—24no—
477#97—24no—
478#97—42no—
479C4×C8—24no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8—22no—
483C4×C8C2×D414yes—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
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#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502#95C2×D411yescharacteristic
503#95C2×D411yescharacteristic
504C24—22no—
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507#41—416no—
508#41—416no—
509#41—88no—
510#41—88no—
511C2×Q8—24no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—24no—
519C2×Q8—24no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—82no—
531C2×Q8—816no—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—22no—
536C2×D4—24no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4#12414yes—
550C2×D4C22×D414yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
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—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2511yescharacteristic
603M16—48no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—48no—
616C2×C8C22×D414yes—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—24no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4#12414yes—
651C4⋊C4C22×D414yes—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
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—82no—
668C22⋊C4#12414yes—
669C22⋊C4#12414yes—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—22no—
683C42—44no—
684C42—82no—
685C42C22×D412yes—
686C42C2×#4114yes—
687C42H(5,𝔽2)12yes—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—24no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23C2×#12412yes—
708C23C2×#12412yes—
709C23C23×D411yescharacteristic
710Q8—48no—
711Q8—44no—
712Q8—44no—
713Q8—44no—
714Q8—44no—
715Q8—88no—
716Q8—84no—
717Q8—84no—
718D4—28no—
719D4—44no—
720D4—44no—
721D4—48no—
722D4—48no—
723D4—88no—
724D4—88no—
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—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4—88no—
783C2×C4—88no—
784C2×C4C2×#12412yes—
785C2×C4C2×#12412yes—
786C2×C4C2×#12412yes—
787C2×C4C2×#12412yes—
788C2×C4D4212yes—
789C2×C4D4212yes—
790C2×C4#57512yes—
791C2×C4#57512yes—
792C2×C4#57712yes—
793C2×C4#57812yes—
794C2×C4C23×D411yescharacteristic
795C2×C4C22×#4112yes—
796C2×C4C2×H(5,𝔽2)11yescharacteristic
797C2×C4#58512yes—
798C8—24no—
799C8—42no—
800C8—42no—
801C8—42no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22C22×#12411yescharacteristic
824C22C2×D4211yescharacteristic
825C22#350011yescharacteristic
826C22C2×#57511yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57711yescharacteristic
829C22C2×#57811yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—44no—
839C4—41no—
840C4—41no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#326714yes—
848C4#326914yes—
849C4D4×#4112yes—
850C4#351412yes—
851C2—42no—
852C2—42no—
853C2—84no—
854C2D4×#12411yescharacteristic
855C2#6061811yescharacteristic
856C2#6062311yescharacteristic
857C2C2×#326711yescharacteristic
858C2C2×#326911yescharacteristic
859C2#6254311yescharacteristic
860C2#6254511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3141C2semidirect
2. C2×#3131C2semidirect
3. #36129C2semidirect
5. #33236C2semidirect
6. #33049C2semidirect
7. #33043C2semidirect
8. #28748C2semidirect
9. #28718C2semidirect
10. #27784C2semidirect
11. #27272C2semidirect
12. #27265C2semidirect
13. #25904C2semidirect
14. #25902C2semidirect
15. #25857C2semidirect
16. #25857C2semidirect
17. #22420C2semidirect
18. #21646C2semidirect
19. C4×#435C2semidirect
179. #486D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31412
C2×#31312
#361292
#361272
#332362
#330492
#330432
#287482
#287182
#277842
#272722
#272652
#259042
#259022
#258572
#224202
#216462
C4×#4352