Finite Group Databasebeta

← #6684411

Subgroups — #6684411

Order 512.

2066 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic, complemented
2C2×#3141C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#33212C211yesmaximal, characteristic, complemented
6#30832C214yesmaximal, complemented
7#30659C214yesmaximal, complemented
8#30276C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic, complemented
10#28717C211yesmaximal, characteristic, complemented
11#28655C211yesmaximal, characteristic, complemented
12#25975C214yesmaximal, complemented
13#25903C211yesmaximal, characteristic, complemented
14#25857C211yesmaximal, characteristic, complemented
15#25813C211yesmaximal, characteristic, complemented
16#25674C211yesmaximal, characteristic, complemented
17#24883C214yesmaximal, complemented
18#22218C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×D4×Q8—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3230—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29#3141—28no—
30C2×#489C2214yes—
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#484C2214yes—
38C2×#477C2214yes—
39C2×#431C2211yescharacteristic
40C2×#417C2214yes—
41C2×C4×M16C2211yescharacteristic
42#2868C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2551—21no—
49#2551C2212yes—
50#2546—21no—
51#2540—21no—
52#2490—21no—
53#2454—21no—
54#2448C2212yes—
55#2440—21no—
56#2440—21no—
57#2440C2212yes—
58#2440C2212yes—
59#2434—21no—
60#2434—21no—
61#2427—21no—
62#2426—21no—
63#2426C2212yes—
64#2414—21no—
65#2407C2212yes—
66#2367—21no—
67#2363—21no—
68D4×C4⋊C4—21no—
69D4×C4⋊C4C2212yes—
70#2341C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2093C2214yes—
75#2093C2214yes—
76#2072C2214yes—
77#2067C2214yes—
78#2065C2214yes—
79#2057C2214yes—
80#2042C2214yes—
81#2036C2214yes—
82#2034C2214yes—
83#2023C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1944C2214yes—
91#1927C2214yes—
92#1925C2214yes—
93#1924C2212yes—
94#1917C2212yes—
95#1874C2214yes—
96#1870C2212yes—
97#1865C2214yes—
98#1863C2214yes—
99#1852C2214yes—
100#1851C2212yes—
101#1844C2211yescharacteristic
102#1809C2214yes—
103#1803C2214yes—
104#1788C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41C2312yes—
110C23×Q8—21no—
111C23×Q8—21no—
112C22×M16C2312yes—
113D4×Q8—48no—
114#533—24no—
115#533—42no—
116#532—24no—
117#532—42no—
118C2×C4⋊Q8—22no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—42no—
128C2×C4⋊Q8—42no—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×C4⋊Q8C2312yes—
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×#127C2311yescharacteristic
137C2×#125—21no—
138C2×#124—21no—
139C2×#124—21no—
140C2×#124C2312yes—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8C2312yes—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121—21no—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×D4—22no—
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C2×C4×D4D411yescharacteristic
161C2×C4×D4D411yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×#117—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#500—24no—
171#500—24no—
172#500—42no—
173#489—216no—
174#487—24no—
175#487—24no—
176#487D418yescomplemented
177#486—24no—
178#486—24no—
179#486—42no—
180#484—216no—
181#477—216no—
182#431—24no—
183C2×#107C2314yes—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×#106C2314yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189#417—216no—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C4×M16—24no—
202C2×#97C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207#399—22no—
208#398—22no—
209#398—22no—
210#397—22no—
211#396—22no—
212#395—22no—
213#395—22no—
214#395—22no—
215#395—22no—
216#394—22no—
217#394—22no—
218#392—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2312yes—
224#390—22no—
225#390—22no—
226#390—22no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390C2312yes—
232#390C2312yes—
233#390C2312yes—
234#389—22no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#388—22no—
247#388—22no—
248#388—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#385—22no—
255#384—21no—
256#384—21no—
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#384C2312yes—
260#384C2312yes—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—22no—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C2×#41—24no—
293C2×#41—28no—
294C2×#41—42no—
295C2×#41—44no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—44no—
303C22×Q8—44no—
304C22×Q8—44no—
305C22×Q8—44no—
306C22×Q8—82no—
307C22×Q8—82no—
308C22×Q8C2412yes—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4C2×D411yescharacteristic
314C22×D4C2412yes—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—42no—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C4⋊Q8—24no—
332C4⋊Q8—24no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—42no—
342C4⋊Q8—42no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8—44no—
346C4⋊Q8—44no—
347C4⋊Q8—48no—
348C4⋊Q8—44no—
349C4⋊Q8—82no—
350C4⋊Q8C2×D414yes—
351C4⋊Q8C2×D414yes—
352#127—22no—
353#127—22no—
354#125—44no—
355#124—24no—
356#124—42no—
357#124—44no—
358#124—82no—
359C22⋊Q8—24no—
360C22⋊Q8—48no—
361C22⋊Q8—48no—
362C22⋊Q8—42no—
363C22⋊Q8—44no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366C22⋊Q8—82no—
367#121—44no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—82no—
372C4×Q8—24no—
373C4×Q8—42no—
374C4×Q8—44no—
375C4×Q8—44no—
376C4×Q8—44no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—44no—
381C4×D4—44no—
382C4×D4—48no—
383#117—44no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
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—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2412yes—
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⋊C4—22no—
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463#107—28no—
464#107—28no—
465#107—44no—
466#106—44no—
467C4⋊C8—24no—
468C4⋊C8—42no—
469#103—28no—
470#103—28no—
471#103—44no—
472#103C2×D4116yes—
473#102—28no—
474#102—28no—
475#102—44no—
476#102—44no—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C22⋊C8—42no—
480#97—24no—
481C4×C8—22no—
482C4×C8—22no—
483C4×C8—22no—
484C4×C8C2×D414yes—
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#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501C24—22no—
502C24C22×D411yescharacteristic
503C24C22×D411yescharacteristic
504#41—416no—
505#41—88no—
506C2×Q8—24no—
507C2×Q8—22no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—82no—
526C2×Q8—82no—
527C2×Q8—816no—
528C2×Q8—816no—
529C2×Q8C22×D414yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—82no—
547C2×D4—82no—
548C2×D4—82no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
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—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4#13714yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
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×C42−1+414yes—
597C22×C4C2511yescharacteristic
598M16—48no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C22×D414yes—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—44no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4C22×D414yes—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—22no—
680C42—22no—
681C42—44no—
682C42—44no—
683C42—82no—
684C42AGL(1,ℤ/8)14yes—
685C42C22×D412yes—
686C42H(5,𝔽2)12yes—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23#53612yes—
707C23C2×#13712yes—
708C23C23×D411yescharacteristic
709Q8—28no—
710Q8—48no—
711Q8—44no—
712Q8—88no—
713Q8—88no—
714Q8—84no—
715Q8—84no—
716Q8—84no—
717D4—28no—
718D4—44no—
719D4—44no—
720D4—88no—
721D4—84no—
722D4—84no—
723D4—164no—
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—24no—
733C2×C4—28no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—24no—
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—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
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—88no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4#53612yes—
783C2×C4D4212yes—
784C2×C4D4212yes—
785C2×C4C2×AGL(1,ℤ/8)12yes—
786C2×C4C2×AGL(1,ℤ/8)12yes—
787C2×C4C2×AGL(1,ℤ/8)12yes—
788C2×C4C2×#13712yes—
789C2×C4C2×#13712yes—
790C2×C4#57612yes—
791C2×C4#57812yes—
792C2×C4C23×D411yescharacteristic
793C2×C4C2×H(5,𝔽2)11yescharacteristic
794C2×C4C2×2−1+412yes—
795C2×C4#58512yes—
796C8—24no—
797C8—42no—
798C8—42no—
799C8—42no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22C2×#53611yescharacteristic
822C22C2×D4211yescharacteristic
823C22#350011yescharacteristic
824C22C22×AGL(1,ℤ/8)11yescharacteristic
825C22C22×#13711yescharacteristic
826C22C2×#57611yescharacteristic
827C22C2×#57811yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—41no—
833C4—44no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—44no—
839C4—41no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4#327014yes—
846C4#327414yes—
847C4#348912yes—
848C4#356112yes—
849C2—42no—
850C2—42no—
851C2—162no—
852C2#3767611yescharacteristic
853C2#6086011yescharacteristic
854C2#6088011yescharacteristic
855C2C2×#327011yescharacteristic
856C2C2×#327411yescharacteristic
857C2#6253711yescharacteristic
858C2#6253811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
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×#3230C2semidirect
2. C2×#3141C2semidirect
4. D4×C4⋊Q8C2semidirect
5. #33212C2semidirect
6. #30832C2semidirect
7. #30659C2semidirect
8. #30276C2semidirect
9. #29843C2semidirect
10. #28717C2semidirect
11. #28655C2semidirect
12. #25975C2semidirect
13. #25903C2semidirect
14. #25857C2semidirect
15. #25813C2semidirect
16. #25674C2semidirect
17. #24883C2semidirect
18. #22218C2semidirect
19. #21102C2semidirect
176. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#31412
#361502
D4×C4⋊Q82
#332122
#308322
#306592
#302762
#298432
#287172
#286552
#259752
#259032
#258572
#258132
#256742
#248832
#222182
#211022