Finite Group Databasebeta

← C4×#2061 #359227

Subgroups — C4×#2061 #359227

Order 512.

1264 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#544C211yesmaximal, characteristic
2C2×#2061C211yesmaximal, characteristic
3C4×#428C212yesmaximal
4C4×#382C211yesmaximal, characteristic
5#11392C211yesmaximal, characteristic
6#11342C211yesmaximal, characteristic
7#11339C212yesmaximal
8#11217C212yesmaximal
9#11211C211yesmaximal, 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×#382C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C4×#117C2212yes—
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C43C2211yescharacteristic
30#2061C418yesdirect product factor
31#1776—22no—
32#1776—22no—
33C4×#107—22no—
34C4×#106—22no—
35C2×#343C2212yes—
36C2×#343C2211yescharacteristic
37C2×#343C2211yescharacteristic
38#1736C2212yes—
39#1736C2212yes—
40C2×#339C2212yes—
41C2×#339C2212yes—
42C2×#339C2212yes—
43C2×#339C2212yes—
44C4⋊#95C2211yescharacteristic
45C4⋊#95C2211yescharacteristic
46#1434—22no—
47C4×#95—22no—
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⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C42—21no—
64C22×C42—21no—
65C22×C42—21no—
66C22×C42D412yes—
67C22×C42C2311yescharacteristic
68C22×C42C2311yescharacteristic
69C22×C42C2311yescharacteristic
70#428—24no—
71#428—24no—
72#428—24no—
73#428C2×C418yes—
74C2×#107—22no—
75C2×#107—22no—
76C2×#106—22no—
77C2×#106—22no—
78C4×M16—24no—
79C4×M16Q818yescomplemented
80C2×#97—22no—
81C2×C4×C8—22no—
82#391—24no—
83#391—22no—
84#389—24no—
85#389—22no—
86#389—22no—
87#389—22no—
88#389—22no—
89#389—22no—
90#387—24no—
91#387—24no—
92#387—24no—
93#385—24no—
94#384—22no—
95#382—22no—
96#382—22no—
97#382—22no—
98#382—22no—
99#382C2×C414yes—
100#380—22no—
101C4×C4⋊C4—22no—
102C4×C4⋊C4—24no—
103C4×C4⋊C4—22no—
104C4×C4⋊C4—22no—
105C4×C4⋊C4—22no—
106C4×C4⋊C4—22no—
107C4×C4⋊C4D412yes—
108C4×C4⋊C4D412yes—
109C4×C4⋊C4D412yes—
110C4×C4⋊C4D412yes—
111C4×C22⋊C4—22no—
112C4×C22⋊C4—22no—
113#376—22no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—21no—
119C2×#95D412yes—
120C43—22no—
121C43—22no—
122C43Q814yescomplemented
123#343—24no—
124#343—22no—
125#343C2×C414yes—
126#340—22no—
127#340—22no—
128#340—22no—
129#340—22no—
130#339—24no—
131#339—24no—
132#339—24no—
133#339C2×C418yes—
134C22×Q8—22no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D412yes—
141C23×C4C2×D412yes—
142C23×C4C2×D411yescharacteristic
143C23×C4C2411yescharacteristic
144C2×M16—22no—
145C2×M16—22no—
146C2×M16—22no—
147C2×M16—22no—
148C2×M16—22no—
149C2×M16—22no—
150C2×M16—22no—
151C2×M16—22no—
152C2×M16C22×C414yes—
153C2×M16C2×Q814yes—
154C2×M16C2×Q814yes—
155C2×M16#4114yes—
156C22×C8—22no—
157C22×C8—22no—
158C4⋊Q8—28no—
159C4⋊Q8—28no—
160#125—28no—
161#125—28no—
162C22⋊Q8—28no—
163C22⋊Q8—28no—
164C4×Q8—84no—
165#117—22no—
166#117—22no—
167#117—22no—
168#117—22no—
169#117—22no—
170#117—22no—
171#117C22×C414yes—
172#117#4114yes—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—22no—
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—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4C22×C412yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C2×D412yes—
194C2×C4⋊C4C2×D412yes—
195C2×C4⋊C4C2×D412yes—
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4#4112yes—
198C2×C4⋊C4#4112yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C42—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—24no—
211C2×C42—24no—
212C2×C42—22no—
213C2×C42—21no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—42no—
218C2×C42—42no—
219C2×C42—42no—
220C2×C42—42no—
221C2×C42—44no—
222C2×C42—44no—
223C2×C42—41no—
224C2×C42—41no—
225C2×C42C22×C412yes—
226C2×C42C2×D412yes—
227C2×C42C2×D412yes—
228C2×C42C2×Q812yes—
229C2×C42C2×Q812yes—
230C2×C42C2×Q814yes—
231C2×C42C2×Q812yes—
232C2×C42#4112yes—
233C2×C42#4112yes—
234#107—28no—
235#107—28no—
236#106—28no—
237#106—28no—
238#97—28no—
239C4×C8—28no—
240#95—28no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—28no—
245#95—24no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95—22no—
250#95—44no—
251#95—44no—
252#95—42no—
253C24C22×D411yescharacteristic
254C2×Q8—28no—
255C2×Q8—82no—
256C2×Q8—82no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
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—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C4×D414yes—
299C22×C4#12012yes—
300C22×C4#12011yescharacteristic
301C22×C4#12011yescharacteristic
302C22×C4C22⋊Q812yes—
303C22×C4C22⋊Q812yes—
304C22×C4C4⋊Q812yes—
305C22×C4C4⋊Q812yes—
306C22×C4C23×C411yescharacteristic
307C22×C4C22×D412yes—
308C22×C4C22×Q812yes—
309C22×C4C22×Q811yescharacteristic
310C22×C4C2×#4112yes—
311C22×C4C2×#4112yes—
312C22×C4C2×#4111yescharacteristic
313C22×C4C2×#4111yescharacteristic
314C22×C4C2×#4111yescharacteristic
315C22×C4C2×#4111yescharacteristic
316M16—24no—
317M16—24no—
318M16—24no—
319M16—24no—
320M16—24no—
321M16—42no—
322M16—42no—
323M16C4×Q818yescomplemented
324C2×C8—24no—
325C2×C8—24no—
326C2×C8—24no—
327C2×C8—24no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—28no—
331C4⋊C4—216no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—84no—
347C4⋊C4—82no—
348C4⋊C4—82no—
349C4⋊C4—84no—
350C4⋊C4C4×D414yes—
351C4⋊C4C4×D414yes—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C42—24no—
357C42—22no—
358C42—24no—
359C42—22no—
360C42—22no—
361C42—24no—
362C42—48no—
363C42—48no—
364C42—42no—
365C42—42no—
366C42—42no—
367C42—44no—
368C42—44no—
369C42—44no—
370C42—82no—
371C42—82no—
372C42—82no—
373C42—82no—
374C42—82no—
375C42C4×Q814yescomplemented
376C42C22⋊Q814yes—
377C42C22⋊Q814yes—
378C42C4⋊Q814yes—
379C42C4⋊Q814yes—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23C2×C4×D411yescharacteristic
385C23C2×#12011yescharacteristic
386C23C2×C22⋊Q811yescharacteristic
387C23#52511yescharacteristic
388C23#52511yescharacteristic
389C23C2×C4⋊Q811yescharacteristic
390C23#53211yescharacteristic
391Q8—88no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—82no—
446C2×C4#39512yes—
447C2×C4#39514yes—
448C2×C4#39512yes—
449C2×C4#45412yes—
450C2×C4#45512yes—
451C2×C4C2×C4×D412yes—
452C2×C4C2×C4×Q811yescharacteristic
453C2×C4C2×C4×Q812yes—
454C2×C4C4×#4111yescharacteristic
455C2×C4C2×C22⋊Q812yes—
456C2×C4#52512yes—
457C2×C4#52512yes—
458C2×C4#52911yescharacteristic
459C2×C4#52912yes—
460C2×C4C2×C4⋊Q812yes—
461C2×C4#53212yes—
462C2×C4#53312yes—
463C2×C4#53312yes—
464C2×C4#53312yes—
465C2×C4#53311yescharacteristic
466C2×C4#53312yes—
467C8—28no—
468C8—44no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22C4×#12011yescharacteristic
482C22C4×C22⋊Q811yescharacteristic
483C22C4×C4⋊Q811yescharacteristic
484C22C2×#39511yescharacteristic
485C22#238811yescharacteristic
486C22#239611yescharacteristic
487C22#239911yescharacteristic
488C22C2×#45511yescharacteristic
489C22C2×#45411yescharacteristic
490C22#301811yescharacteristic
491C22#301811yescharacteristic
492C4—22no—
493C4—24no—
494C4—44no—
495C4—44no—
496C4—44no—
497C4—44no—
498C4—44no—
499C4—82no—
500C4—82no—
501C4—82no—
502C4—82no—
503C4—82no—
504C4#206114yesdirect product factor
505C4C4×C22⋊Q812yes—
506C4C4×C4⋊Q812yes—
507C4#239612yes—
508C4#239912yes—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2C4×#39511yescharacteristic
514C2C4×#45511yescharacteristic
515C2C4×#45411yescharacteristic
516C2C2×#206111yescharacteristic
517C2#2356011yescharacteristic
518C2#2358811yescharacteristic
519C2#2358911yescharacteristic
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
30. #2061C4direct (N × H)
79. C4×M16Q8semidirect
122. C43Q8semidirect
323. M16C4×Q8semidirect
375. C42C4×Q8semidirect
504. C4#2061direct (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×#20612
C4×#4282
C4×#3822
#113922
#113422
#113392
#112172
#112112
C4×#3432
C4×#3392