Finite Group Databasebeta

← #6683566

Subgroups — #6683566

Order 512.

2348 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3209C211yesmaximal, characteristic, complemented
2C22×#494C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic
5#33043C211yesmaximal, characteristic, complemented
6#30744C214yesmaximal, complemented
7#30449C214yesmaximal, complemented
8#30262C211yesmaximal, characteristic, complemented
9#29808C211yesmaximal, characteristic, complemented
10#28616C211yesmaximal, characteristic, complemented
11#28440C211yesmaximal, characteristic, complemented
12#25856C211yesmaximal, characteristic, complemented
13#25722C211yesmaximal, characteristic, complemented
14#25722C211yesmaximal, characteristic, complemented
15#25600C211yesmaximal, characteristic, complemented
16#24360C214yesmaximal, complemented
17#23856C214yesmaximal
18#22270C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic
20C23×Q16C2214yes—
21C2×D4×Q8C2212yes—
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26#3209—28no—
27C2×#494—28no—
28C2×#494C2211yescharacteristic
29C2×#494C2211yescharacteristic
30C2×#494C2214yes—
31C2×#494C2211yescharacteristic
32C2×#494C2211yescharacteristic
33C2×#494C2211yescharacteristic
34C2×#494C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#462C2214yes—
39C2×#462C2214yes—
40C2×#451C2214yes—
41C2×#451C2214yes—
42C2×#451C2214yes—
43C2×#431C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2868C2211yescharacteristic
46#2862C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2551—21no—
52#2551—21no—
53#2550—21no—
54#2546C2212yes—
55#2492—21no—
56#2451—21no—
57#2446C2212yes—
58#2442—21no—
59#2440—21no—
60#2440—21no—
61#2440—21no—
62#2440—21no—
63#2439—21no—
64#2434C2212yes—
65#2434C2212yes—
66#2429C2212yes—
67#2417—21no—
68#2409C2212yes—
69#2360—21no—
70#2352—21no—
71D4×C4⋊C4—21no—
72D4×C4⋊C4—21no—
73Q8×C22⋊C4C2212yes—
74C4×C4⋊Q8C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic
76C42×D4C2211yescharacteristic
77#2056C2214yes—
78#2056C2214yes—
79#2043C2214yes—
80#2016C2214yes—
81#2016C2214yes—
82#2016C2214yes—
83#2016C2214yes—
84#2016C2214yes—
85#2001C2214yes—
86#2001C2214yes—
87#1990C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1956C2211yescharacteristic
93#1933C2214yes—
94#1923C2212yes—
95#1916C2212yes—
96#1892C2214yes—
97#1878C2214yes—
98#1878C2214yes—
99#1878C2214yes—
100#1878C2214yes—
101#1869C2212yes—
102#1850C2212yes—
103#1834C2211yescharacteristic
104#1787C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C23×Q8C2312yes—
110C23×Q8C2312yes—
111C23×Q8C2312yes—
112C22×Q16—216no—
113C22×Q16—48no—
114C22×Q16—48no—
115C22×Q16C2314yes—
116C22×Q16C2314yes—
117C22×Q16C2314yes—
118C22×Q16C2314yes—
119C22×Q16C2314yes—
120C22×Q16C2314yes—
121C23×C8C2312yes—
122D4×Q8—48no—
123#533—24no—
124#533—42no—
125C2×C4⋊Q8—22no—
126C2×C4⋊Q8—24no—
127C2×C4⋊Q8—24no—
128C2×C4⋊Q8—24no—
129C2×C4⋊Q8—21no—
130C2×C4⋊Q8—21no—
131C2×C4⋊Q8—21no—
132C2×C4⋊Q8—21no—
133C2×C4⋊Q8—21no—
134C2×C4⋊Q8—21no—
135C2×C4⋊Q8—42no—
136C2×C4⋊Q8—42no—
137C2×C4⋊Q8—42no—
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2312yes—
142C2×C4⋊Q8C2312yes—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2311yescharacteristic
149C2×#125—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—22no—
154C2×C22⋊Q8C2312yes—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C4×Q8—21no—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×D4—22no—
163C2×C4×D4D411yescharacteristic
164C2×C4×D4D411yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×#117—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#494—216no—
176#494—24no—
177#494—24no—
178#494—24no—
179#494—24no—
180#494—42no—
181#494D418yescomplemented
182#487—24no—
183#487—24no—
184#487—42no—
185#462—216no—
186#462—48no—
187#451—216no—
188#451—48no—
189#451—48no—
190#431—24no—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#103C2314yes—
200C2×#103C2314yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C4×C8—24no—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210#400—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#398—22no—
215#396—22no—
216#395—22no—
217#395—22no—
218#395—22no—
219#395—22no—
220#395—22no—
221#393—22no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—22no—
226#391—22no—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#391C2312yes—
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#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—22no—
248#389C2312yes—
249#388—22no—
250#387—22no—
251#387—22no—
252#386—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#384—21no—
259#384—21no—
260#384—21no—
261#384—21no—
262#384C2311yescharacteristic
263#384C2311yescharacteristic
264#382—21no—
265#382—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380—22no—
274#380C2312yes—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4D411yescharacteristic
280C4×C4⋊C4D411yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C22⋊C4—22no—
283C4×C22⋊C4D411yescharacteristic
284C4×C22⋊C4D411yescharacteristic
285C4×C22⋊C4D411yescharacteristic
286C4×C22⋊C4D411yescharacteristic
287C4×C22⋊C4C2311yescharacteristic
288C4×C22⋊C4C2311yescharacteristic
289C43C2311yescharacteristic
290#340C2314yes—
291#340C2314yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—24no—
302C22×Q8—24no—
303C22×Q8—24no—
304C22×Q8—28no—
305C22×Q8—28no—
306C22×Q8—42no—
307C22×Q8—42no—
308C22×Q8—42no—
309C22×Q8—44no—
310C22×Q8—44no—
311C22×Q8—44no—
312C22×Q8—44no—
313C22×Q8C2412yes—
314C22×Q8C2412yes—
315C22×Q8C2412yes—
316C22×Q8C2412yes—
317C22×Q8C2412yes—
318C22×D4C2×D411yescharacteristic
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×Q16—28no—
329C2×Q16—28no—
330C2×Q16—28no—
331C2×Q16—28no—
332C2×Q16—28no—
333C2×Q16—28no—
334C2×Q16—44no—
335C2×Q16—44no—
336C2×Q16—44no—
337C2×Q16—44no—
338C2×Q16—44no—
339C2×Q16—44no—
340C2×Q16—464no—
341C2×Q16—44no—
342C2×Q16—44no—
343C2×Q16—44no—
344C2×Q16—44no—
345C2×Q16—44no—
346C2×Q16C2×D4116yes—
347C22×C8—24no—
348C22×C8—24no—
349C22×C8—24no—
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2412yes—
354C4⋊Q8—24no—
355C4⋊Q8—24no—
356C4⋊Q8—24no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—44no—
368C4⋊Q8—44no—
369C4⋊Q8—44no—
370C4⋊Q8—44no—
371C4⋊Q8—44no—
372C4⋊Q8—44no—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—44no—
377C4⋊Q8—44no—
378C4⋊Q8—48no—
379C4⋊Q8C2×D414yes—
380C4⋊Q8C2×D414yes—
381#125—44no—
382C22⋊Q8—24no—
383C22⋊Q8—28no—
384C22⋊Q8—48no—
385C22⋊Q8—48no—
386C22⋊Q8—42no—
387C22⋊Q8—44no—
388C22⋊Q8—44no—
389C22⋊Q8—44no—
390C22⋊Q8—44no—
391C4×Q8—24no—
392C4×Q8—42no—
393C4×Q8—44no—
394C4×Q8—44no—
395C4×Q8—44no—
396C4×D4—24no—
397C4×D4—24no—
398C4×D4—48no—
399C4×D4Q1618yescomplemented
400#117—44no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D411yescharacteristic
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477C4⋊C8—24no—
478C4⋊C8—24no—
479#103—28no—
480#103—28no—
481#103—28no—
482#103—44no—
483#103—44no—
484#103—44no—
485#103—44no—
486#103—44no—
487C22⋊C8—24no—
488C22⋊C8—24no—
489C22⋊C8—24no—
490C4×C8—24no—
491C4×C8—22no—
492C4×C8—22no—
493C4×C8—22no—
494C4×C8C2×D414yes—
495#95—22no—
496#95—22no—
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#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95C2×D411yescharacteristic
512#95C2×D411yescharacteristic
513#95C2×D411yescharacteristic
514#95C2×D411yescharacteristic
515#95C2×D411yescharacteristic
516#95C2×D411yescharacteristic
517C24C22×D411yescharacteristic
518C24C22×D411yescharacteristic
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—24no—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8—22no—
530C2×Q8—24no—
531C2×Q8—24no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—24no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—416no—
542C2×Q8—416no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8—42no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—82no—
549C2×Q8—82no—
550C2×Q8—82no—
551C2×Q8—88no—
552C2×Q8—88no—
553C2×Q8—88no—
554C2×Q8—88no—
555C2×Q8C22×D414yes—
556C2×Q8C22×D414yes—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4C2×Q1614yes—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4C2×Q1614yes—
594C22×C4C2×Q1614yescomplemented
595C22×C4#13714yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4H(5,𝔽2)14yes—
609C22×C4C2511yescharacteristic
610Q16—416no—
611Q16—416no—
612Q16—416no—
613Q16—416no—
614Q16—88no—
615Q16—88no—
616C2×C8—216no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8C22×D414yes—
628C2×C8H(5,𝔽2)14yes—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4C2×Q1614yescomplemented
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—82no—
678C22⋊C4C2×Q1614yes—
679C22⋊C4C2×Q1614yescomplemented
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—21no—
688C42—21no—
689C42—22no—
690C42—21no—
691C42—21no—
692C42—22no—
693C42—44no—
694C42—44no—
695C42—82no—
696C42C2×Q1614yescomplemented
697C42C22×D412yes—
698C42H(5,𝔽2)12yes—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23#53512yes—
710C23C22×Q1612yes—
711C23C22×Q1612yes—
712C23C2×#13712yes—
713C23C23×D411yescharacteristic
714Q8—28no—
715Q8—28no—
716Q8—44no—
717Q8—44no—
718Q8—44no—
719Q8—44no—
720Q8—44no—
721Q8—44no—
722Q8—44no—
723Q8—44no—
724Q8—88no—
725Q8—88no—
726Q8—88no—
727Q8—84no—
728D4—28no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
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—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—88no—
786C2×C4—88no—
787C2×C4—88no—
788C2×C4#53512yes—
789C2×C4D4212yes—
790C2×C4D4212yes—
791C2×C4C22×Q1612yes—
792C2×C4C22×Q1612yes—
793C2×C4C22×Q1612yes—
794C2×C4C22×Q1612yes—
795C2×C4C22×Q1612yes—
796C2×C4C2×#13712yes—
797C2×C4C2×#13712yes—
798C2×C4#57812yes—
799C2×C4#57812yes—
800C2×C4C23×D411yescharacteristic
801C2×C4C2×H(5,𝔽2)12yes—
802C2×C4C2×H(5,𝔽2)12yes—
803C2×C4C2×H(5,𝔽2)11yescharacteristic
804C8—24no—
805C8—24no—
806C8—42no—
807C8—42no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22#320914yescomplemented
822C22C2×#53511yescharacteristic
823C22C2×D4211yescharacteristic
824C22#349811yescharacteristic
825C22C23×Q1611yescharacteristic
826C22C22×#13711yescharacteristic
827C22C2×#57811yescharacteristic
828C22C2×#57811yescharacteristic
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—41no—
836C4—44no—
837C4—44no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#327014yes—
848C4D4×Q1614yes—
849C4#348412yes—
850C4#354312yes—
851C2—24no—
852C2—42no—
853C2#3767411yescharacteristic
854C2C2×#320911yescharacteristic
855C2#6082111yescharacteristic
856C2C2×#327011yescharacteristic
857C2C2×D4×Q1611yescharacteristic
858C2#6241611yescharacteristic
859C2#6242411yescharacteristic
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. C22×#494C2semidirect
5. #33043C2semidirect
6. #30744C2semidirect
7. #30449C2semidirect
8. #30262C2semidirect
9. #29808C2semidirect
10. #28616C2semidirect
11. #28440C2semidirect
12. #25856C2semidirect
13. #25722C2semidirect
14. #25722C2semidirect
15. #25600C2semidirect
16. #24360C2semidirect
18. #22270C2semidirect
181. #494D4semidirect
399. C4×D4Q16semidirect
594. C22×C4C2×Q16semidirect
668. C4⋊C4C2×Q16semidirect
679. C22⋊C4C2×Q16semidirect
696. C42C2×Q16semidirect
821. C22#3209semidirect

Maximal subgroups

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

subgroupindex
C2×#32092
C22×#4942
#361292
D4×C4⋊Q82
#330432
#307442
#304492
#302622
#298082
#286162
#284402
#258562
#257222
#256002
#243602
#238562
#222702
#211012