Finite Group Databasebeta

← #6614901

Subgroups — #6614901

Order 512.

1842 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic, complemented
3#33278C211yesmaximal, characteristic, complemented
4#33170C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29177C211yesmaximal, characteristic, complemented
7#29077C214yesmaximal, complemented
8#28979C214yesmaximal, complemented
9#28613C211yesmaximal, characteristic, complemented
10#28555C214yesmaximal, complemented
11#27972C211yesmaximal, characteristic, complemented
12#27875C211yesmaximal, characteristic, complemented
13#25903C211yesmaximal, characteristic, complemented
14#25598C211yesmaximal, characteristic, complemented
15#23126C214yesmaximal, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21400C211yesmaximal, characteristic, complemented
18C2×#1990C211yesmaximal, characteristic, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#465C2214yes—
27C2×C8×D4C2212yes—
28C22×C4×C8C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30#2862C2211yescharacteristic
31#2859C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2566—21no—
37#2550—21no—
38#2512—21no—
39#2512C2212yes—
40#2504—21no—
41#2500—21no—
42#2492C2212yes—
43#2451C2212yes—
44#2446—21no—
45#2442—21no—
46#2439—21no—
47#2429—21no—
48#2422—21no—
49#2422C2212yes—
50#2417C2212yes—
51#2416—21no—
52#2416C2212yes—
53#2409—21no—
54#2361—21no—
55#2361C2212yes—
56#2360C2212yes—
57#2352—21no—
58Q8×C22⋊C4—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2088C2214yes—
65#2077C2214yes—
66#2072C2214yes—
67#2055C2214yes—
68#2023C2214yes—
69#2000C2214yes—
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1968C2214yes—
78#1957C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1934C2214yes—
83#1934C2214yes—
84#1933C2214yes—
85#1933C2214yes—
86#1920C2214yes—
87#1919C2214yes—
88#1893C2214yes—
89#1892C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1874C2214yes—
93#1872C2214yes—
94#1844C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97C8×C4⋊C4C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99C4×#103C2214yes—
100C4×#102C2214yes—
101C8×C22⋊C4C2212yes—
102C8×C22⋊C4C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C2×#340C2214yes—
106C42×C8C2211yescharacteristic
107C23×Q8—21no—
108C22×SD16C2314yes—
109C23×C8C2312yes—
110C23×C8C2312yes—
111#553—48no—
112#533—24no—
113#533—42no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2312yes—
121C2×C4⋊Q8C2311yescharacteristic
122C2×#127C2311yescharacteristic
123C2×#126—22no—
124C2×#125—21no—
125C2×#125—21no—
126C2×#123—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8C2312yes—
141C2×C4×D4—22no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2311yescharacteristic
148C2×#117—21no—
149C2×#117—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#492—42no—
158#486—24no—
159#486—42no—
160#465—216no—
161C8×D4—28no—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C4×C8—42no—
173C2×C4×C8—42no—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2312yes—
179C2×C4×C8C2312yes—
180C2×C4×C8C2312yes—
181C2×C4×C8C2312yes—
182#400—22no—
183#398—22no—
184#398—22no—
185#397—22no—
186#397—22no—
187#396—22no—
188#396—22no—
189#396—22no—
190#395—22no—
191#394—22no—
192#394—22no—
193#393—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—22no—
199#391—22no—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—22no—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#388—22no—
224#388—22no—
225#388—22no—
226#387—22no—
227#387—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#384—21no—
235#384—21no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2312yes—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#382—21no—
244#382—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—22no—
250#380C2312yes—
251#380C2312yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4D411yescharacteristic
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4—22no—
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8—22no—
281C22×Q8—44no—
282C22×Q8—44no—
283C22×Q8—82no—
284C22×Q8C2412yes—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C2×D411yescharacteristic
290C22×D4C2412yes—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×SD16—28no—
301C2×SD16—44no—
302C2×SD16—44no—
303C22×C8—24no—
304C22×C8—42no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8#4118yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—42no—
320C4⋊Q8—44no—
321C4⋊Q8—44no—
322C4⋊Q8#4114yes—
323#127—22no—
324#127—22no—
325#126—48no—
326#125—44no—
327#125—44no—
328#123—48no—
329C22⋊Q8—28no—
330C22⋊Q8—24no—
331C22⋊Q8—42no—
332C22⋊Q8—44no—
333C22⋊Q8—82no—
334#121—28no—
335#121—48no—
336#121—44no—
337#121—44no—
338#121—44no—
339#121—44no—
340#121—82no—
341C4×Q8—24no—
342C4×Q8—42no—
343C4×Q8—44no—
344C4×Q8—82no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—44no—
348C4×D4—48no—
349C4×D4—44no—
350C4×D4—82no—
351C4×D4SD1618yescomplemented
352#117—44no—
353#117—44no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—82no—
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#106—28no—
433C4⋊C8—24no—
434#103—28no—
435#103—44no—
436#103—44no—
437#102—28no—
438#102—28no—
439#102—44no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442C4×C8—24no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—42no—
448C4×C8—42no—
449C4×C8—42no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470C24—22no—
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—24no—
478C2×Q8—44no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—82no—
486C2×Q8—816no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—82no—
504C2×D4—82no—
505C2×D4C2×SD1614yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4C2×SD1614yes—
539C22×C4C2×SD1614yes—
540C22×C4#13514yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2×#4114yes—
554C22×C4C2511yescharacteristic
555SD16—88no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—48no—
567C2×C8—48no—
568C2×C8C2×#4114yes—
569C2×C8C2×#4114yes—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C2×SD1614yes—
604C4⋊C4C2×#4114yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4C2×SD1614yes—
623C22⋊C4C2×SD1614yes—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—44no—
638C42—44no—
639C42—82no—
640C42C2×SD1614yes—
641C42C2×#4112yes—
642C42H(5,𝔽2)12yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23#53212yes—
661C23C22×SD1612yes—
662C23C22×SD1612yes—
663C23C2×#13512yes—
664C23C23×D411yescharacteristic
665Q8—48no—
666Q8—44no—
667Q8—44no—
668Q8—88no—
669Q8—84no—
670D4—28no—
671D4—44no—
672D4—44no—
673D4—88no—
674D4—84no—
675D4—84no—
676D4—164no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—24no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—88no—
731C2×C4—164no—
732C2×C4—164no—
733C2×C4#53212yes—
734C2×C4#54612yes—
735C2×C4#54612yes—
736C2×C4C22×SD1612yes—
737C2×C4C22×SD1612yes—
738C2×C4C22×SD1612yes—
739C2×C4C22×SD1612yes—
740C2×C4C22×SD1612yes—
741C2×C4C2×#13512yes—
742C2×C4C2×#13512yes—
743C2×C4#57612yes—
744C2×C4#57812yes—
745C2×C4C22×#4111yescharacteristic
746C2×C4C22×#4112yes—
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C2×C4#58512yes—
749C8—24no—
750C8—24no—
751C8—42no—
752C8—42no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22#316714yes—
774C22C2×#53211yescharacteristic
775C22C2×#54611yescharacteristic
776C22#350011yescharacteristic
777C22C23×SD1611yescharacteristic
778C22C22×#13511yescharacteristic
779C22C2×#57611yescharacteristic
780C22C2×#57811yescharacteristic
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—44no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4#329714yes—
799C4#329814yes—
800C4#348012yes—
801C4#350512yes—
802C2—24no—
803C2—42no—
804C2—162no—
805C2#3639611yescharacteristic
806C2C2×#316711yescharacteristic
807C2#6071811yescharacteristic
808C2C2×#329711yescharacteristic
809C2C2×#329811yescharacteristic
810C2#6252511yescharacteristic
811C2#6252811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36182C2
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
2. #36129C2semidirect
3. #33278C2semidirect
4. #33170C2semidirect
5. #33042C2semidirect
6. #29177C2semidirect
7. #29077C2semidirect
8. #28979C2semidirect
9. #28613C2semidirect
10. #28555C2semidirect
11. #27972C2semidirect
12. #27875C2semidirect
13. #25903C2semidirect
14. #25598C2semidirect
15. #23126C2semidirect
16. C4×#486C2semidirect
17. #21400C2semidirect
18. C2×#1990C2semidirect
19. C4×C8×D4C2semidirect
351. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
#361822
#361292
#332782
#331702
#330422
#291772
#290772
#289792
#286132
#285552
#279722
#278752
#259032
#255982
#231262
C4×#4862
#214002
C2×#19902
C4×C8×D42