Finite Group Databasebeta

← C4×#2060 #359226

Subgroups — C4×#2060 #359226

Order 512.

1352 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#544C211yesmaximal, characteristic
2C2×#2060C211yesmaximal, characteristic
3C4×#428C212yesmaximal
4C4×#384C211yesmaximal, characteristic
5#11392C211yesmaximal, characteristic
6#11342C211yesmaximal, characteristic
7#11340C212yesmaximal
8#11217C212yesmaximal
9#11210C211yesmaximal, characteristic
10C4×#343C211yesmaximal, characteristic
11C4×#339C212yesmaximal
12C2×#544C2211yescharacteristic
13C2×#428C2212yes—
14C2×#428C2212yes—
15C2×C4×M16C2212yes—
16#2331—22no—
17#2330—22no—
18#2329—22no—
19#2317C2212yes—
20#2316C2211yescharacteristic
21C4×C4⋊Q8—22no—
22C4×#125—22no—
23C4×C22⋊Q8—22no—
24C2×#384C2211yescharacteristic
25C2×#384C2211yescharacteristic
26C4×#117C2212yes—
27C2×C4×C4⋊C4—22no—
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C43C2211yescharacteristic
31#2060C418yesdirect product factor
32#1776—22no—
33#1776—22no—
34C4×#107—22no—
35C4×#106—22no—
36C2×#343C2212yes—
37C2×#343C2211yescharacteristic
38C2×#343C2211yescharacteristic
39#1736C2212yes—
40#1736C2212yes—
41C2×#339C2212yes—
42C2×#339C2212yes—
43C2×#339C2212yes—
44C2×#339C2212yes—
45C4⋊#95—22no—
46C4⋊#95C2211yescharacteristic
47C4⋊#95C2211yescharacteristic
48C22×M16C2312yes—
49C22×M16C2312yes—
50#544—24no—
51#544—22no—
52#544C2×C414yes—
53C2×C4⋊Q8—22no—
54C2×#125—22no—
55C2×C22⋊Q8—22no—
56C2×C4×Q8—22no—
57C2×#117C2312yes—
58C2×#117C2312yes—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42—21no—
67C22×C42—21no—
68C22×C42D412yes—
69C22×C42C2311yescharacteristic
70C22×C42C2311yescharacteristic
71C22×C42C2311yescharacteristic
72#428—24no—
73#428—24no—
74#428—24no—
75#428C2×C418yes—
76C2×#107—22no—
77C2×#107—22no—
78C2×#106—22no—
79C2×#106—22no—
80C4×M16—24no—
81C4×M16Q818yescomplemented
82C2×#97—22no—
83C2×C4×C8—22no—
84#391—24no—
85#391—22no—
86#389—24no—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389—22no—
92#387—24no—
93#387—24no—
94#387—24no—
95#385—24no—
96#384—22no—
97#384—22no—
98#384—22no—
99#384—22no—
100#384C2×C414yes—
101#382—22no—
102#380—22no—
103C4×C4⋊C4—22no—
104C4×C4⋊C4—24no—
105C4×C4⋊C4—22no—
106C4×C4⋊C4—22no—
107C4×C4⋊C4—22no—
108C4×C4⋊C4—22no—
109C4×C4⋊C4—48no—
110C4×C4⋊C4D412yes—
111C4×C4⋊C4D412yes—
112C4×C4⋊C4D412yes—
113C4×C4⋊C4D412yes—
114C4×C22⋊C4—22no—
115C4×C22⋊C4—22no—
116#376—22no—
117C2×#95—21no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95D412yes—
121C43—22no—
122C43—22no—
123C43Q814yescomplemented
124#343—24no—
125#343—22no—
126#343C2×C414yes—
127#340—22no—
128#340—22no—
129#340—22no—
130#340—22no—
131#339—24no—
132#339—24no—
133#339—24no—
134#339C2×C418yes—
135C22×Q8—22no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D412yes—
142C23×C4C2×D412yes—
143C23×C4C2×D411yescharacteristic
144C23×C4C2411yescharacteristic
145C2×M16—22no—
146C2×M16—22no—
147C2×M16—22no—
148C2×M16—22no—
149C2×M16—22no—
150C2×M16—22no—
151C2×M16—22no—
152C2×M16—22no—
153C2×M16C22×C414yes—
154C2×M16C2×Q814yes—
155C2×M16C2×Q814yes—
156C2×M16#4114yes—
157C22×C8—22no—
158C22×C8—22no—
159C4⋊Q8—28no—
160C4⋊Q8—28no—
161#125—28no—
162#125—28no—
163C22⋊Q8—28no—
164C22⋊Q8—28no—
165C4×Q8—84no—
166#117—22no—
167#117—22no—
168#117—22no—
169#117—22no—
170#117—22no—
171#117—22no—
172#117C22×C414yes—
173#117#4114yes—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—44no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4C22×C412yes—
199C2×C4⋊C4C22×C412yes—
200C2×C4⋊C4C2×D412yes—
201C2×C4⋊C4C2×D412yes—
202C2×C4⋊C4C2×D412yes—
203C2×C4⋊C4C2×D412yes—
204C2×C4⋊C4#4112yes—
205C2×C4⋊C4#4112yes—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C42—24no—
209C2×C42—24no—
210C2×C42—24no—
211C2×C42—22no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—24no—
221C2×C42—22no—
222C2×C42—21no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—42no—
227C2×C42—42no—
228C2×C42—44no—
229C2×C42—44no—
230C2×C42—41no—
231C2×C42—41no—
232C2×C42C22×C412yes—
233C2×C42C2×D412yes—
234C2×C42C2×D412yes—
235C2×C42C2×Q812yes—
236C2×C42C2×Q812yes—
237C2×C42C2×Q814yes—
238C2×C42C2×Q812yes—
239C2×C42#4112yes—
240C2×C42#4112yes—
241#107—28no—
242#107—28no—
243#106—28no—
244#106—28no—
245#97—28no—
246C4×C8—28no—
247#95—24no—
248#95—24no—
249#95—24no—
250#95—24no—
251#95—22no—
252#95—22no—
253#95—22no—
254#95—22no—
255#95—44no—
256#95—44no—
257#95—42no—
258C24C22×D411yescharacteristic
259C2×Q8—28no—
260C2×Q8—82no—
261C2×Q8—82no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C4×D414yes—
304C22×C4#12012yes—
305C22×C4#12011yescharacteristic
306C22×C4#12011yescharacteristic
307C22×C4C22⋊Q812yes—
308C22×C4C22⋊Q812yes—
309C22×C4C4⋊Q812yes—
310C22×C4C4⋊Q812yes—
311C22×C4C23×C411yescharacteristic
312C22×C4C22×D412yes—
313C22×C4C22×Q812yes—
314C22×C4C22×Q811yescharacteristic
315C22×C4C2×#4112yes—
316C22×C4C2×#4112yes—
317C22×C4C2×#4111yescharacteristic
318C22×C4C2×#4111yescharacteristic
319C22×C4C2×#4111yescharacteristic
320C22×C4C2×#4111yescharacteristic
321M16—24no—
322M16—24no—
323M16—24no—
324M16—24no—
325M16—24no—
326M16—42no—
327M16—42no—
328M16C4×Q818yescomplemented
329C2×C8—24no—
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—24no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—28no—
336C4⋊C4—216no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—24no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—416no—
348C4⋊C4—416no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—84no—
354C4⋊C4—82no—
355C4⋊C4—82no—
356C4⋊C4—84no—
357C4⋊C4C4×D414yes—
358C4⋊C4C4×D414yes—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—216no—
364C42—24no—
365C42—22no—
366C42—24no—
367C42—22no—
368C42—22no—
369C42—24no—
370C42—48no—
371C42—42no—
372C42—42no—
373C42—42no—
374C42—44no—
375C42—44no—
376C42—44no—
377C42—82no—
378C42—82no—
379C42—82no—
380C42—82no—
381C42—82no—
382C42C4×Q814yescomplemented
383C42C22⋊Q814yes—
384C42C22⋊Q814yes—
385C42C4⋊Q814yes—
386C42C4⋊Q814yes—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23C2×C4×D411yescharacteristic
392C23C2×#12011yescharacteristic
393C23C2×C22⋊Q811yescharacteristic
394C23#52511yescharacteristic
395C23#52511yescharacteristic
396C23C2×C4⋊Q811yescharacteristic
397C23#53211yescharacteristic
398Q8—88no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4#39512yes—
454C2×C4#39514yes—
455C2×C4#39512yes—
456C2×C4#45312yes—
457C2×C4#45612yes—
458C2×C4C2×C4×D412yes—
459C2×C4C2×C4×Q811yescharacteristic
460C2×C4C2×C4×Q812yes—
461C2×C4C4×#4111yescharacteristic
462C2×C4C2×C22⋊Q812yes—
463C2×C4#52512yes—
464C2×C4#52512yes—
465C2×C4#52911yescharacteristic
466C2×C4#52912yes—
467C2×C4C2×C4⋊Q812yes—
468C2×C4#53212yes—
469C2×C4#53312yes—
470C2×C4#53312yes—
471C2×C4#53312yes—
472C2×C4#53311yescharacteristic
473C2×C4#53312yes—
474C8—28no—
475C8—44no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22C4×#12011yescharacteristic
489C22C4×C22⋊Q811yescharacteristic
490C22C4×C4⋊Q811yescharacteristic
491C22C2×#39511yescharacteristic
492C22#238811yescharacteristic
493C22#239611yescharacteristic
494C22#239911yescharacteristic
495C22C2×#45311yescharacteristic
496C22C2×#45611yescharacteristic
497C22#301811yescharacteristic
498C22#301811yescharacteristic
499C4—28no—
500C4—22no—
501C4—24no—
502C4—44no—
503C4—44no—
504C4—44no—
505C4—44no—
506C4—82no—
507C4—82no—
508C4—82no—
509C4—82no—
510C4—82no—
511C4#206014yesdirect product factor
512C4C4×C22⋊Q812yes—
513C4C4×C4⋊Q812yes—
514C4#239612yes—
515C4#239912yes—
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2C4×#39511yescharacteristic
521C2C4×#45311yescharacteristic
522C2C4×#45611yescharacteristic
523C2C2×#206011yescharacteristic
524C2#2356011yescharacteristic
525C2#2358711yescharacteristic
526C2#2359011yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×#120
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
31. #2060C4direct (N × H)
81. C4×M16Q8semidirect
123. C43Q8semidirect
328. M16C4×Q8semidirect
382. C42C4×Q8semidirect
511. C4#2060direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#5442
C2×#20602
C4×#4282
C4×#3842
#113922
#113422
#113402
#112172
#112102
C4×#3432
C4×#3392