Finite Group Databasebeta

← #6579392

Subgroups — #6579392

Order 512.

2298 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×#3141C211yesmaximal, characteristic, complemented
2C22×#487C211yesmaximal, characteristic, complemented
3#36122C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33238C211yesmaximal, characteristic, complemented
6#33049C211yesmaximal, characteristic, complemented
7#33042C211yesmaximal, characteristic, complemented
8#28750C211yesmaximal, characteristic, complemented
9#28717C211yesmaximal, characteristic, complemented
10#27785C214yesmaximal, complemented
11#27274C214yesmaximal, complemented
12#27266C214yesmaximal, complemented
13#25903C211yesmaximal, characteristic, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25857C211yesmaximal, characteristic, complemented
16#25856C211yesmaximal, characteristic, complemented
17#22421C214yesmaximal, complemented
18#21647C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×D4×Q8—21no—
21C2×#548C2212yes—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26#3141—28no—
27C2×#489C2214yes—
28C2×#487—28no—
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2214yes—
34C2×#487C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#486C2211yescharacteristic
39C2×#435C2212yes—
40C2×#417C2214yes—
41C22×#103C2214yes—
42C2×C4×M16C2211yescharacteristic
43C22×C4×C8C2211yescharacteristic
44#2868C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2551—21no—
51#2551C2212yes—
52#2546—21no—
53#2545C2212yes—
54#2491—21no—
55#2491—21no—
56#2452—21no—
57#2452—21no—
58#2440—21no—
59#2440—21no—
60#2440C2212yes—
61#2440C2212yes—
62#2436C2212yes—
63#2434—21no—
64#2434—21no—
65#2432C2212yes—
66#2416—21no—
67#2416—21no—
68#2361—21no—
69#2361—21no—
70D4×C4⋊C4—21no—
71D4×C4⋊C4C2212yes—
72C4×C4⋊Q8C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic
74C42×D4C2211yescharacteristic
75#2072C2214yes—
76#2043C2214yes—
77#2042C2214yes—
78#2042C2214yes—
79#2024C2214yes—
80#2023C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1983C2214yes—
85#1959C2214yes—
86#1959C2214yes—
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1935C2214yes—
91#1935C2214yes—
92#1934C2214yes—
93#1894C2214yes—
94#1893C2214yes—
95#1874C2214yes—
96#1872C2214yes—
97#1834C2211yescharacteristic
98#1803C2214yes—
99#1788C2214yes—
100#1787C2214yes—
101#1771C2212yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104#1753C2212yes—
105#1752C2212yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41C2312yes—
110C23×Q8—21no—
111C23×Q8—21no—
112C23×Q8C2312yes—
113C22×M16C2312yes—
114C23×C8C2312yes—
115D4×Q8—48no—
116#548—216no—
117#532—24no—
118#532—42no—
119C2×C4⋊Q8—22no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—21no—
128C2×C4⋊Q8—21no—
129C2×C4⋊Q8—21no—
130C2×C4⋊Q8—21no—
131C2×C4⋊Q8—42no—
132C2×C4⋊Q8—42no—
133C2×C4⋊Q8—42no—
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2312yes—
136C2×C4⋊Q8C2311yescharacteristic
137C2×C4⋊Q8C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2312yes—
140C2×C4⋊Q8C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#127C2311yescharacteristic
143C2×#124—22no—
144C2×#124C2312yes—
145C2×#124C2312yes—
146C2×#124C2312yes—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8C2312yes—
153C2×#121—22no—
154C2×#121—21no—
155C2×#121—21no—
156C2×#121—21no—
157C2×#121—21no—
158C2×#121C2312yes—
159C2×C4×Q8—21no—
160C2×C4×Q8C2312yes—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4D411yescharacteristic
166C2×C4×D4D411yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#489—216no—
177#487—24no—
178#487—24no—
179#487—24no—
180#487—216no—
181#487—24no—
182#487—42no—
183#487D418yescomplemented
184#486—24no—
185#486—24no—
186#486—42no—
187#435—28no—
188C2×C4⋊C8C2312yes—
189#417—216no—
190C2×#103—216no—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×#102C2314yes—
202C2×#102C2314yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C4×M16—24no—
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×#97C2312yes—
209C2×C4×C8—24no—
210C2×C4×C8C2312yes—
211C2×C4×C8C2311yescharacteristic
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215#398—22no—
216#398—22no—
217#396—22no—
218#396—22no—
219#395—22no—
220#395—22no—
221#395—22no—
222#395—22no—
223#394—22no—
224#394—22no—
225#393—22no—
226#393—22no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391C2312yes—
231#391C2312yes—
232#390—21no—
233#390—21no—
234#390—21no—
235#390—21no—
236#390—21no—
237#390—21no—
238#390C2312yes—
239#389—22no—
240#389—22no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#388—22no—
252#388—22no—
253#386—22no—
254#386—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#384—21no—
262#384—21no—
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#384C2312yes—
266#384C2312yes—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380C2312yes—
272#380C2312yes—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4D411yescharacteristic
277C4×C4⋊C4D411yescharacteristic
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2311yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4D411yescharacteristic
283C4×C22⋊C4D411yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285C4×C22⋊C4C2311yescharacteristic
286C43C2311yescharacteristic
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#340C2314yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294C2×#41—24no—
295C2×#41—28no—
296C2×#41—42no—
297C2×#41—44no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—24no—
305C22×Q8—28no—
306C22×Q8—42no—
307C22×Q8—44no—
308C22×Q8—44no—
309C22×Q8—44no—
310C22×Q8—44no—
311C22×Q8—44no—
312C22×Q8—82no—
313C22×Q8—82no—
314C22×Q8C2412yes—
315C22×Q8C2412yes—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C2×D411yescharacteristic
321C22×D4C2412yes—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—42no—
335C22×C8—24no—
336C22×C8—24no—
337C22×C8—42no—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C4⋊Q8—24no—
343C4⋊Q8—24no—
344C4⋊Q8—24no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—42no—
354C4⋊Q8—42no—
355C4⋊Q8—44no—
356C4⋊Q8—44no—
357C4⋊Q8—44no—
358C4⋊Q8—44no—
359C4⋊Q8—42no—
360C4⋊Q8—44no—
361C4⋊Q8—44no—
362C4⋊Q8—44no—
363C4⋊Q8—48no—
364C4⋊Q8—82no—
365C4⋊Q8C2×D414yes—
366C4⋊Q8C2×D414yes—
367#127—22no—
368#127—22no—
369#124—24no—
370#124—28no—
371#124—42no—
372#124—44no—
373#124—48no—
374C22⋊Q8—28no—
375C22⋊Q8—48no—
376C22⋊Q8—48no—
377C22⋊Q8—44no—
378C22⋊Q8—44no—
379C22⋊Q8—48no—
380#121—28no—
381#121—44no—
382#121—44no—
383#121—48no—
384#121—44no—
385#121—44no—
386C4×Q8—28no—
387C4×Q8—44no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—44no—
391C4×D4—44no—
392C4×D4—48no—
393C4×D4—48no—
394C4×D4#4118yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4—44no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4C2×D411yescharacteristic
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D411yescharacteristic
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C4⋊C8—24no—
475#103—28no—
476#103—28no—
477#103—28no—
478#103—28no—
479#103—44no—
480#103—44no—
481#103—44no—
482#103C2×D4116yes—
483#102—28no—
484#102—28no—
485#102—44no—
486#102—44no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489#97—24no—
490#97—24no—
491#97—42no—
492C4×C8—24no—
493C4×C8—22no—
494C4×C8—22no—
495C4×C8—22no—
496C4×C8C2×D414yes—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95C2×D411yescharacteristic
508#95C2×D411yescharacteristic
509#95C2×D411yescharacteristic
510#95C2×D411yescharacteristic
511#95C2×D411yescharacteristic
512#95C2×D411yescharacteristic
513C24—22no—
514C24C22×D411yescharacteristic
515C24C22×D411yescharacteristic
516#41—416no—
517#41—88no—
518C2×Q8—24no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8—416no—
531C2×Q8—44no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—44no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8—82no—
542C2×Q8—82no—
543C2×Q8—82no—
544C2×Q8—88no—
545C2×Q8—816no—
546C2×Q8—816no—
547C2×Q8C22×D414yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—24no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—82no—
566C2×D4#12414yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4AGL(1,ℤ/8)14yes—
603C22×C4#13714yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2×#4114yes—
617C22×C4C2×#4114yes—
618C22×C4C2511yescharacteristic
619M16—48no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—48no—
632C2×C8C22×D414yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4#12414yes—
669C4⋊C4C22×D414yes—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4#12414yes—
687C22⋊C4#12414yes—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—22no—
701C42—44no—
702C42—44no—
703C42C22×D412yes—
704C42C2×#4114yes—
705C42H(5,𝔽2)12yes—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23C2×#12412yes—
724C23C2×#12412yes—
725C23C2×AGL(1,ℤ/8)12yes—
726C23C2×#13712yes—
727C23C23×D411yescharacteristic
728Q8—28no—
729Q8—44no—
730Q8—48no—
731Q8—44no—
732Q8—44no—
733Q8—88no—
734Q8—88no—
735Q8—88no—
736Q8—84no—
737Q8—84no—
738D4—28no—
739D4—44no—
740D4—44no—
741D4—88no—
742D4—88no—
743D4—84no—
744D4—84no—
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—21no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
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—88no—
801C2×C4—88no—
802C2×C4C2×#12412yes—
803C2×C4C2×#12412yes—
804C2×C4C2×#12412yes—
805C2×C4C2×#12412yes—
806C2×C4D4212yes—
807C2×C4D4212yes—
808C2×C4C2×AGL(1,ℤ/8)12yes—
809C2×C4C2×AGL(1,ℤ/8)12yes—
810C2×C4C2×#13712yes—
811C2×C4C2×#13712yes—
812C2×C4#57712yes—
813C2×C4#57812yes—
814C2×C4C23×D411yescharacteristic
815C2×C4C22×#4112yes—
816C2×C4C2×H(5,𝔽2)11yescharacteristic
817C2×C4#58512yes—
818C8—24no—
819C8—42no—
820C8—42no—
821C8—42no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22#314114yescomplemented
843C22C22×#12411yescharacteristic
844C22C2×D4211yescharacteristic
845C22#350011yescharacteristic
846C22C22×AGL(1,ℤ/8)11yescharacteristic
847C22C22×#13711yescharacteristic
848C22C2×#57711yescharacteristic
849C22C2×#57811yescharacteristic
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—44no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—44no—
861C4—41no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4#326514yes—
868C4#327014yes—
869C4D4×#4112yes—
870C4#351412yes—
871C2—24no—
872C2—42no—
873C2—162no—
874C2D4×#12411yescharacteristic
875C2C2×#314111yescharacteristic
876C2#6062311yescharacteristic
877C2C2×#326511yescharacteristic
878C2C2×#327011yescharacteristic
879C2#6253811yescharacteristic
880C2#6254211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
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. C22×#487C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33238C2semidirect
6. #33049C2semidirect
7. #33042C2semidirect
8. #28750C2semidirect
9. #28717C2semidirect
10. #27785C2semidirect
11. #27274C2semidirect
12. #27266C2semidirect
13. #25903C2semidirect
14. #25902C2semidirect
15. #25857C2semidirect
16. #25856C2semidirect
17. #22421C2semidirect
18. #21647C2semidirect
19. C4×#435C2semidirect
183. #487D4semidirect
842. C22#3141semidirect

Maximal subgroups

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

subgroupindex
C2×#31412
C22×#4872
#361222
D4×C4⋊Q82
#332382
#330492
#330422
#287502
#287172
#277852
#272742
#272662
#259032
#259022
#258572
#258562
#224212
#216472
C4×#4352