Finite Group Databasebeta

← #6684410

Subgroups — #6684410

Order 512.

1858 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3229C211yesmaximal, characteristic, complemented
2C2×#3139C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33210C211yesmaximal, characteristic, complemented
6#30828C214yesmaximal, complemented
7#30649C214yesmaximal, complemented
8#30281C211yesmaximal, characteristic, complemented
9#29844C211yesmaximal, characteristic, complemented
10#28719C211yesmaximal, characteristic, complemented
11#28653C211yesmaximal, characteristic, complemented
12#25971C214yesmaximal, complemented
13#25902C211yesmaximal, characteristic, complemented
14#25856C211yesmaximal, characteristic, complemented
15#25812C211yesmaximal, characteristic, complemented
16#25674C211yesmaximal, characteristic, complemented
17#24884C214yesmaximal
18#22221C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3229—28no—
25C2×#500C2211yescharacteristic
26C2×#498C2211yescharacteristic
27C2×#498C2211yescharacteristic
28#3139—28no—
29C2×#491C2214yes—
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#483C2214yes—
37C2×#475C2214yes—
38C2×#431C2211yescharacteristic
39C2×#419C2214yes—
40C2×C4×M16C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550—21no—
48#2550C2212yes—
49#2492—21no—
50#2492—21no—
51#2451—21no—
52#2451—21no—
53#2446—21no—
54#2446C2212yes—
55#2442—21no—
56#2442C2212yes—
57#2439—21no—
58#2439C2212yes—
59#2429—21no—
60#2429C2212yes—
61#2417—21no—
62#2417—21no—
63#2409—21no—
64#2409C2212yes—
65#2360—21no—
66#2360—21no—
67#2352—21no—
68#2352C2212yes—
69Q8×C22⋊C4—21no—
70Q8×C22⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2097C2214yes—
75#2097C2214yes—
76#2074C2214yes—
77#2068C2214yes—
78#2066C2214yes—
79#2059C2214yes—
80#2043C2214yes—
81#2036C2214yes—
82#2036C2214yes—
83#2024C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1943C2214yes—
91#1928C2214yes—
92#1927C2214yes—
93#1924C2212yes—
94#1917C2212yes—
95#1872C2214yes—
96#1870C2212yes—
97#1863C2214yes—
98#1863C2214yes—
99#1854C2214yes—
100#1851C2212yes—
101#1845C2211yescharacteristic
102#1809C2214yes—
103#1805C2214yes—
104#1787C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C23×Q8—21no—
110C23×Q8C2312yes—
111C22×M16C2312yes—
112#533—24no—
113#533—24no—
114#533—42no—
115#533—42no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2312yes—
131C2×C4⋊Q8C2311yescharacteristic
132C2×#125—21no—
133C2×#125C2312yes—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×#117—21no—
152C2×#117C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#500—42no—
160#498—24no—
161#498—24no—
162#491—216no—
163#487—24no—
164#487—24no—
165#487—24no—
166#487—24no—
167#487—42no—
168#487D418yescomplemented
169#483—216no—
170#475—216no—
171#431—24no—
172C2×#107C2314yes—
173C2×#107C2314yes—
174C2×#106C2314yes—
175C2×#106C2314yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178#419—216no—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C4×M16—24no—
191C2×#97C2312yes—
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196#400—22no—
197#400—22no—
198#398—22no—
199#398—22no—
200#398—22no—
201#398—22no—
202#396—22no—
203#396—22no—
204#395—22no—
205#395—22no—
206#393—22no—
207#393—22no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—22no—
219#391—22no—
220#391—22no—
221#391—22no—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—22no—
235#389—22no—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#386—22no—
247#386—22no—
248#385—22no—
249#385—22no—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#382—21no—
253#382—21no—
254#382C2312yes—
255#382C2312yes—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—22no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4D411yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C22⋊C4—22no—
274C4×C22⋊C4—22no—
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—24no—
298C22×Q8—28no—
299C22×Q8—42no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—44no—
303C22×Q8—82no—
304C22×Q8C2412yes—
305C22×Q8C2412yes—
306C22×D4C2×D411yescharacteristic
307C23×C4—22no—
308C23×C4—22no—
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—42no—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—24no—
323C4⋊Q8—24no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—42no—
335C4⋊Q8—44no—
336C4⋊Q8—44no—
337C4⋊Q8—44no—
338C4⋊Q8—42no—
339C4⋊Q8—44no—
340C4⋊Q8C2×D414yes—
341C4⋊Q8C2×D414yes—
342#125—24no—
343#125—42no—
344#125—44no—
345C22⋊Q8—24no—
346C22⋊Q8—42no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—82no—
354C4×Q8—24no—
355C4×Q8—42no—
356C4×Q8—44no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×Q8—44no—
360C4×Q8—82no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—42no—
364#117—24no—
365#117—42no—
366#117—44no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440#107—44no—
441#107—44no—
442#106—28no—
443#106—28no—
444C4⋊C8—24no—
445C4⋊C8—42no—
446#103—28no—
447#103—28no—
448#103—28no—
449#103—28no—
450#103—44no—
451#103—44no—
452#103—44no—
453#103C2×D4116yes—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—42no—
457#97—24no—
458C4×C8—22no—
459C4×C8—22no—
460C4×C8—22no—
461C4×C8C2×D414yes—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—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#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C2×Q8—24no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—416no—
501C2×Q8—44no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—44no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—82no—
515C2×Q8—82no—
516C2×Q8—88no—
517C2×Q8—816no—
518C2×Q8C22×D414yes—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—41no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4#13714yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C42−1+414yes—
568C22×C4C2511yescharacteristic
569M16—48no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8C22×D414yes—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—41no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
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⋊C4C22×D414yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—22no—
646C42—22no—
647C42—44no—
648C42—44no—
649C42—82no—
650C42—82no—
651C42C22×D412yes—
652C42H(5,𝔽2)12yes—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23#53612yes—
666C23C2×#13712yes—
667C23C23×D411yescharacteristic
668Q8—28no—
669Q8—48no—
670Q8—44no—
671Q8—44no—
672Q8—44no—
673Q8—88no—
674Q8—88no—
675Q8—84no—
676Q8—84no—
677Q8—84no—
678D4—44no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
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—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
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—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—88no—
740C2×C4—88no—
741C2×C4#53612yes—
742C2×C4D4212yes—
743C2×C4D4212yes—
744C2×C4C2×#13712yes—
745C2×C4C2×#13712yes—
746C2×C4#57512yes—
747C2×C4#57712yes—
748C2×C4#57812yes—
749C2×C4C23×D411yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×2−1+412yes—
752C2×C4#58512yes—
753C8—24no—
754C8—42no—
755C8—42no—
756C8—42no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C2×#53611yescharacteristic
772C22C2×D4211yescharacteristic
773C22#350011yescharacteristic
774C22C22×#13711yescharacteristic
775C22C2×#57511yescharacteristic
776C22C2×#57711yescharacteristic
777C22C2×#57811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—44no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—44no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4#326614yes—
797C4#327714yes—
798C4#348912yes—
799C4#356112yes—
800C2—42no—
801C2—42no—
802C2#3767611yescharacteristic
803C2#6086511yescharacteristic
804C2#6087811yescharacteristic
805C2C2×#326611yescharacteristic
806C2C2×#327711yescharacteristic
807C2#6253611yescharacteristic
808C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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×#3229C2semidirect
2. C2×#3139C2semidirect
5. #33210C2semidirect
6. #30828C2semidirect
7. #30649C2semidirect
8. #30281C2semidirect
9. #29844C2semidirect
10. #28719C2semidirect
11. #28653C2semidirect
12. #25971C2semidirect
13. #25902C2semidirect
14. #25856C2semidirect
15. #25812C2semidirect
16. #25674C2semidirect
18. #22221C2semidirect
168. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32292
C2×#31392
#361292
#332102
#308282
#306492
#302812
#298442
#287192
#286532
#259712
#259022
#258562
#258122
#256742
#248842
#222212
#211022