Finite Group Databasebeta

← C4×#1326 #128342

Subgroups — C4×#1326 #128342

Order 512.

868 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#385C211yesmaximal, characteristic
2C2×#1326C212yesmaximal
3C4×#323C211yesmaximal, characteristic
4C4×#323C211yesmaximal, characteristic
5#7187C212yesmaximal
6C23×C42C411yescharacteristic
7C2×#385C411yescharacteristic
8C2×#385C2211yescharacteristic
9C2×C4×C4⋊C4—21no—
10C2×C4×C22⋊C4C411yescharacteristic
11C2×C4×C22⋊C4C2211yescharacteristic
12C4×C22⋊C8—21no—
13C4×C22⋊C8—21no—
14C2×#323C2212yes—
15C2×#323C2212yes—
16#1436—21no—
17#1436—21no—
18C22⋊#95C411yescharacteristic
19C22⋊#95C2211yescharacteristic
20C4×#95—21no—
21#1326C418yesdirect product factor
22#1280—21no—
23#1280—21no—
24C24×C4C2×C411yescharacteristic
25C24×C4C2×C411yescharacteristic
26C24×C4C2×C411yescharacteristic
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C22⋊C4C2×C411yescharacteristic
30C22×C22⋊C4C2×C411yescharacteristic
31C22×C22⋊C4C2×C411yescharacteristic
32C22×C22⋊C4C2311yescharacteristic
33C22×C42—21no—
34C22×C42—21no—
35C22×C42—21no—
36C22×C42—44no—
37C22×C42—41no—
38C22×C42—41no—
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C2×C22⋊C8—22no—
42C2×C22⋊C8—22no—
43C2×C4×C8—41no—
44C2×C4×C8—41no—
45#385—22no—
46#385—22no—
47#385C814yescomplemented
48#385C2×C414yes—
49C4×C4⋊C4—44no—
50C4×C22⋊C4—22no—
51C4×C22⋊C4—41no—
52C4×C22⋊C4—41no—
53C4×C22⋊C4C814yescomplemented
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95D411yescharacteristic
62C2×#95D411yescharacteristic
63#336—41no—
64#336—41no—
65#323—22no—
66#323—22no—
67#323C2×C414yes—
68#323C2×C414yes—
69C25C22×C411yescharacteristic
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4—22no—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—42no—
80C23×C4—42no—
81C23×C4—42no—
82C23×C4—42no—
83C23×C4—42no—
84C23×C4—42no—
85C23×C4—41no—
86C23×C4—41no—
87C23×C4—41no—
88C23×C4—41no—
89C23×C4C4212yes—
90C23×C4C22⋊C411yescharacteristic
91C23×C4C22⋊C411yescharacteristic
92C23×C4C22⋊C411yescharacteristic
93C23×C4C22⋊C411yescharacteristic
94C23×C4C2×C812yes—
95C23×C4C2×C812yes—
96C23×C4M1612yes—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C22×C8—42no—
100C22×C8—42no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—42no—
107C2×C22⋊C4—21no—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—41no—
112C2×C22⋊C4—41no—
113C2×C22⋊C4—41no—
114C2×C22⋊C4—41no—
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C22⋊C4C4212yes—
118C2×C22⋊C4C2×C812yes—
119C2×C22⋊C4C2×C812yes—
120C2×C22⋊C4C2×C812yes—
121C2×C22⋊C4C2×C812yes—
122C2×C22⋊C4M1612yes—
123C2×C22⋊C4C22×C412yes—
124C2×C22⋊C4#4112yes—
125C2×C42—24no—
126C2×C42—24no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42—42no—
134C2×C42—42no—
135C2×C42—42no—
136C2×C42—42no—
137C2×C42—44no—
138C2×C42—44no—
139C2×C42—44no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—44no—
143C2×C42—42no—
144C2×C42—42no—
145C22⋊C8—24no—
146C22⋊C8—24no—
147C22⋊C8—42no—
148C22⋊C8—42no—
149C4×C8—82no—
150C4×C8—82no—
151#95—24no—
152#95—24no—
153#95—24no—
154#95—41no—
155#95—41no—
156#95—42no—
157#95—42no—
158#95—42no—
159#95—42no—
160C24—21no—
161C24—21no—
162C24—21no—
163C24—21no—
164C24—41no—
165C24—41no—
166C24—41no—
167C24—41no—
168C24C2×C4211yescharacteristic
169C24C2×C22⋊C411yescharacteristic
170C24#11711yescharacteristic
171C24C22×C811yescharacteristic
172C24C22×C811yescharacteristic
173C24C2×M1611yescharacteristic
174C24C2×M1611yescharacteristic
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—48no—
204C22×C4—44no—
205C22×C4—44no—
206C22×C4—44no—
207C22×C4—44no—
208C22×C4—44no—
209C22×C4—44no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—48no—
223C22×C4—48no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C22⋊C812yes—
255C22×C4C22⋊C812yes—
256C22×C4C22⋊C812yes—
257C22×C4C22⋊C812yes—
258C22×C4#9911yescharacteristic
259C22×C4#9911yescharacteristic
260C22×C4#10112yes—
261C22×C4C4×D412yes—
262C22×C4C4×D412yes—
263C2×C8—44no—
264C2×C8—44no—
265C2×C8—82no—
266C2×C8—82no—
267C2×C8—82no—
268C2×C8—82no—
269C4⋊C4—48no—
270C4⋊C4—48no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4C4×C814yescomplemented
281C42—48no—
282C42—44no—
283C42—48no—
284C42—42no—
285C42—44no—
286C42—42no—
287C42—81no—
288C42—81no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23C4×C22⋊C411yescharacteristic
328C23C2×C4×C811yescharacteristic
329C23C4×M1611yescharacteristic
330C23C2×C22⋊C811yescharacteristic
331C23C2×C22⋊C811yescharacteristic
332C23C2×#9911yescharacteristic
333C23#41011yescharacteristic
334C23C2×#10111yescharacteristic
335C23#41311yescharacteristic
336C23#43111yescharacteristic
337C23#43111yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4#32412yes—
408C2×C4#32412yes—
409C2×C4AΣL(1,𝔽16)12yes—
410C2×C4#35212yes—
411C8—84no—
412C8—84no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22C2×#32411yescharacteristic
452C22#145811yescharacteristic
453C22#145911yescharacteristic
454C22#146111yescharacteristic
455C22C4×C22⋊C811yescharacteristic
456C22C4×#9911yescharacteristic
457C22C4×#10111yescharacteristic
458C22C2×AΣL(1,𝔽16)11yescharacteristic
459C22C2×#35211yescharacteristic
460C22#212011yescharacteristic
461C22#212011yescharacteristic
462C4—22no—
463C4—44no—
464C4—42no—
465C4—44no—
466C4—42no—
467C4—42no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4#132614yesdirect product factor
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—41no—
478C2—41no—
479C2—41no—
480C2—41no—
481C2C4×#32411yescharacteristic
482C2C2×#132611yescharacteristic
483C2#1145211yescharacteristic
484C2#1147111yescharacteristic
485C2#1147211yescharacteristic
486C2C4×AΣL(1,𝔽16)11yescharacteristic
487C2C4×#35211yescharacteristic
subgroupG/H
centerC22×C4#99
commutatorC23C2×C4×C8
Frattini, cosocleC22×C22⋊C4C23
socleC23C2×#99
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
21. #1326C4direct (N × H)
47. #385C8semidirect
53. C4×C22⋊C4C8semidirect
280. C22⋊C4C4×C8semidirect
472. C4#1326direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#3852
C2×#13262
C4×#3232
#71872