Finite Group Databasebeta

← #6687222

Subgroups — #6687222

Order 512.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3209C211yesmaximal, characteristic, complemented
2C2×#3170C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33043C211yesmaximal, characteristic, complemented
6#30600C214yesmaximal, complemented
7#30407C214yesmaximal
8#30279C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#28717C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#26171C214yesmaximal, complemented
13#25856C211yesmaximal, characteristic, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25600C211yesmaximal, characteristic, complemented
17#24906C214yesmaximal, complemented
18#22270C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3209—28no—
25#3170—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#494C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#467C2214yes—
36C2×#462C2214yes—
37C2×#451C2214yes—
38C2×C4×Q16C2214yes—
39C2×#431C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2552—21no—
48#2550—21no—
49#2542—21no—
50#2538C2212yes—
51#2492—21no—
52#2451—21no—
53#2446C2212yes—
54#2442—21no—
55#2441—21no—
56#2441—21no—
57#2439—21no—
58#2429—21no—
59#2429—21no—
60#2429C2212yes—
61#2423C2212yes—
62#2423C2212yes—
63#2417—21no—
64#2409C2212yes—
65#2365—21no—
66#2360—21no—
67#2354—21no—
68#2352—21no—
69Q8×C4⋊C4C2212yes—
70Q8×C22⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2095C2214yes—
75#2095C2214yes—
76#2087C2214yes—
77#2076C2214yes—
78#2072C2214yes—
79#2056C2214yes—
80#2043C2214yes—
81#2036C2214yes—
82#2036C2214yes—
83#2001C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1956C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1933C2214yes—
91#1923C2212yes—
92#1916C2212yes—
93#1892C2214yes—
94#1878C2214yes—
95#1878C2214yes—
96#1878C2214yes—
97#1878C2214yes—
98#1869C2212yes—
99#1863C2214yes—
100#1863C2214yes—
101#1850C2212yes—
102#1834C2211yescharacteristic
103#1803C2214yes—
104#1787C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C23×Q8C2312yes—
110C22×Q16C2314yes—
111C22×Q16C2314yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#533—42no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2312yes—
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×#125—21no—
133C2×#125—21no—
134C2×#125—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2312yes—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C2×#117—21no—
158C2×#117—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#500—24no—
164#500—42no—
165#494—24no—
166#494D418yescomplemented
167#487—24no—
168#487—24no—
169#487—24no—
170#487—24no—
171#487—42no—
172#467—216no—
173#462—216no—
174#451—216no—
175C4×Q16—216no—
176#431—24no—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C4×C8—24no—
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2312yes—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198#400—22no—
199#399—22no—
200#399—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#396—22no—
206#396—22no—
207#396—22no—
208#395—22no—
209#393—22no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—22no—
216#391—22no—
217#391C2312yes—
218#391C2312yes—
219#391C2312yes—
220#391C2312yes—
221#391C2312yes—
222#390—22no—
223#389—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—22no—
234#389—22no—
235#389—22no—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#386—22no—
247#385—22no—
248#384—22no—
249#384—21no—
250#384—21no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2312yes—
254#384C2312yes—
255#382—21no—
256#382—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
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—22no—
295C22×Q8—24no—
296C22×Q8—42no—
297C22×Q8—44no—
298C22×Q8—44no—
299C22×Q8C2412yes—
300C22×Q8C2412yes—
301C22×Q8C2412yes—
302C22×D4C2×D411yescharacteristic
303C23×C4—22no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C2×Q16—28no—
311C2×Q16—44no—
312C2×Q16—44no—
313C2×Q16—44no—
314C2×Q16—44no—
315C2×Q16C2×D4116yes—
316C22×C8—24no—
317C22×C8—42no—
318C22×C8—42no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
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—44no—
335C4⋊Q8—44no—
336C4⋊Q8—42no—
337C4⋊Q8—44no—
338C4⋊Q8—82no—
339C4⋊Q8C2×D414yes—
340C4⋊Q8C2×D414yes—
341#125—44no—
342#125—44no—
343#125—44no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—42no—
348C22⋊Q8—42no—
349C22⋊Q8—42no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—82no—
356C22⋊Q8—82no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8—44no—
361C4×Q8—42no—
362C4×Q8—42no—
363C4×Q8—42no—
364C4×Q8—44no—
365C4×Q8—44no—
366C4×Q8—44no—
367C4×Q8—44no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4Q1618yescomplemented
371#117—44no—
372#117—44no—
373#117—44no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—28no—
451#107—44no—
452C4⋊C8—24no—
453C4⋊C8—42no—
454#103—28no—
455#103—28no—
456#103—28no—
457#103—28no—
458#103—44no—
459#103—44no—
460#103—44no—
461#103—44no—
462C22⋊C8—24no—
463C22⋊C8—42no—
464C22⋊C8—42no—
465C4×C8—24no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8C2×D414yes—
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#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95C2×D411yescharacteristic
487#95C2×D411yescharacteristic
488#95C2×D411yescharacteristic
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—82no—
516C2×Q8—88no—
517C2×Q8—88no—
518C2×Q8C22×D414yes—
519C2×Q8C22×D414yes—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4C2×Q1614yes—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
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—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
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—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—82no—
552C22×C4C2×Q1614yes—
553C22×C4C2×Q1614yes—
554C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
567Q16—416no—
568Q16—88no—
569C2×C8—22no—
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—48no—
581C2×C8C22×D414yes—
582C4⋊C4—24no—
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—24no—
593C4⋊C4—24no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—44no—
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—44no—
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—42no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4—82no—
622C4⋊C4—82no—
623C4⋊C4C2×Q1614yes—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C22⋊C4C2×Q1614yes—
636C22⋊C4C2×Q1614yes—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—22no—
649C42—22no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—82no—
655C42C2×Q1614yes—
656C42C22×D412yes—
657C42H(5,𝔽2)12yes—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23C22×Q1612yes—
671C23C22×Q1612yes—
672C23C23×D411yescharacteristic
673Q8—28no—
674Q8—28no—
675Q8—44no—
676Q8—44no—
677Q8—44no—
678Q8—44no—
679Q8—88no—
680Q8—84no—
681Q8—84no—
682Q8—84no—
683D4—44no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—24no—
702C2×C4—24no—
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—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
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—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—88no—
743C2×C4D4212yes—
744C2×C4D4212yes—
745C2×C4C22×Q1612yes—
746C2×C4C22×Q1612yes—
747C2×C4C22×Q1612yes—
748C2×C4C22×Q1612yes—
749C2×C4C22×Q1612yes—
750C2×C4#57512yes—
751C2×C4#57712yes—
752C2×C4#57812yes—
753C2×C4C23×D411yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4#58512yes—
756C2×C4#58512yes—
757C8—24no—
758C8—42no—
759C8—42no—
760C8—42no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22#344911yescharacteristic
776C22C2×D4211yescharacteristic
777C22#350011yescharacteristic
778C22C23×Q1611yescharacteristic
779C22C2×#57511yescharacteristic
780C22C2×#57711yescharacteristic
781C22C2×#57811yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—44no—
789C4—44no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#327114yes—
801C4D4×Q1614yes—
802C4#348512yes—
803C4#356212yes—
804C2—42no—
805C2—42no—
806C2#3768211yescharacteristic
807C2#6094311yescharacteristic
808C2#6100811yescharacteristic
809C2C2×#327111yescharacteristic
810C2C2×D4×Q1611yescharacteristic
811C2#6253011yescharacteristic
812C2#6254511yescharacteristic
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×#3209C2semidirect
2. C2×#3170C2semidirect
5. #33043C2semidirect
6. #30600C2semidirect
8. #30279C2semidirect
9. #29878C2semidirect
10. #28717C2semidirect
11. #28616C2semidirect
12. #26171C2semidirect
13. #25856C2semidirect
14. #25674C2semidirect
15. #25674C2semidirect
16. #25600C2semidirect
17. #24906C2semidirect
18. #22270C2semidirect
166. #494D4semidirect
370. C4×D4Q16semidirect

Maximal subgroups

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

subgroupindex
C2×#32092
C2×#31702
#361342
#361292
#330432
#306002
#304072
#302792
#298782
#287172
#286162
#261712
#258562
#256742
#256002
#249062
#222702
#211012