Finite Group Databasebeta

← C2×#3111 #60543

Subgroups — C2×#3111 #60543

Order 256.

1091 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529C211yesmaximal, characteristic, complemented
2C2×C4×#41C211yesmaximal, characteristic, complemented
3#3111C2116yesmaximal, direct product factor
4C2×#485C211yesmaximal, characteristic, complemented
5C2×#482C211yesmaximal, characteristic, complemented
6C2×#479C211yesmaximal, characteristic, complemented
7C2×#478C211yesmaximal, characteristic, complemented
8C2×#464C211yesmaximal, characteristic, complemented
9C2×#463C211yesmaximal, characteristic, complemented
10C2×#452C211yesmaximal, characteristic, complemented
11C2×#449C211yesmaximal, characteristic
12C2×#442C211yesmaximal, characteristic, complemented
13C2×#441C211yesmaximal, characteristic, complemented
14C2×#440C211yesmaximal, characteristic, complemented
15C2×#440C211yesmaximal, characteristic, complemented
16C2×#432C211yesmaximal, characteristic, complemented
17C22×#41C2211yescharacteristic
18C22×Q16C2211yescharacteristic
19C22×SD16C2211yescharacteristic
20C22×SD16C2211yescharacteristic
21C22×D8C2211yescharacteristic
22#529—24no—
23#529C2218yescomplemented
24C2×#126—21no—
25C2×#125C2211yescharacteristic
26C2×#124C2211yescharacteristic
27C2×#123—21no—
28C2×C22⋊Q8C2211yescharacteristic
29C2×#121C2211yescharacteristic
30C4×#41—24no—
31C4×#41C2218yescomplemented
32C2×C4×Q8C2211yescharacteristic
33C2×C4×Q8C2211yescharacteristic
34C2×C4×Q8C2211yescharacteristic
35C2×C4×D4—21no—
36C2×C4×D4—21no—
37C2×C4×D4—21no—
38C2×C4×D4C2211yescharacteristic
39C2×C4×D4C2211yescharacteristic
40C2×C4×D4C2211yescharacteristic
41C2×#117—21no—
42C2×#117—21no—
43C2×#117C2211yescharacteristic
44C22×C42—21no—
45C22×C42C2211yescharacteristic
46#485C2218yescomplemented
47#482C2218yescomplemented
48#479C2218yescomplemented
49#478C2218yescomplemented
50#464C2218yescomplemented
51#463C2218yescomplemented
52#452C2218yescomplemented
53#449C2218yes—
54#442C2218yescomplemented
55#441C2218yescomplemented
56#440C2218yescomplemented
57#440C2218yescomplemented
58#432C2218yescomplemented
59C2×#107C2211yescharacteristic
60C2×#107C2211yescharacteristic
61C2×#106C2211yescharacteristic
62C2×#106C2211yescharacteristic
63C2×C4⋊C8C2211yescharacteristic
64C2×C4⋊C8C2211yescharacteristic
65C2×#103C2211yescharacteristic
66C2×#103C2211yescharacteristic
67C2×#103C2211yescharacteristic
68C2×#103C2211yescharacteristic
69C2×#102C2211yescharacteristic
70C2×#102C2211yescharacteristic
71C2×#102C2211yescharacteristic
72C2×#102C2211yescharacteristic
73C2×C22⋊C8C2211yescharacteristic
74C2×C22⋊C8C2211yescharacteristic
75C2×#97C2211yescharacteristic
76C2×#97C2211yescharacteristic
77C2×#41—24no—
78C2×#41—24no—
79C2×#41—22no—
80C2×#41C2314yes—
81C22×Q8C2311yescharacteristic
82C22×Q8C2311yescharacteristic
83C22×D4—21no—
84C22×D4—21no—
85C22×D4C2311yescharacteristic
86C22×D4C2311yescharacteristic
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—21no—
91C23×C4D411yescharacteristic
92C23×C4D411yescharacteristic
93C23×C4C2311yescharacteristic
94C2×Q16—24no—
95C2×Q16C2314yes—
96C2×SD16—24no—
97C2×SD16—24no—
98C2×SD16C2314yes—
99C2×SD16C2314yes—
100C2×D8—24no—
101C2×D8C2314yes—
102C22×C8C2311yescharacteristic
103C22×C8C2311yescharacteristic
104C22×C8C2311yescharacteristic
105C22×C8C2311yescharacteristic
106#126—28no—
107#125—22no—
108#125C2314yes—
109#124—22no—
110#124C2314yes—
111#123—28no—
112C22⋊Q8—22no—
113C22⋊Q8C2314yes—
114#121—22no—
115#121C2314yes—
116C4×Q8—22no—
117C4×Q8—22no—
118C4×Q8—22no—
119C4×Q8C2314yes—
120C4×Q8C2314yes—
121C4×Q8C2314yes—
122C4×D4—28no—
123C4×D4—28no—
124C4×D4—28no—
125C4×D4—22no—
126C4×D4—22no—
127C4×D4—22no—
128C4×D4C2314yes—
129C4×D4C2314yes—
130C4×D4C2314yes—
131#117—22no—
132#117—28no—
133#117—28no—
134#117C2314yes—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C2311yescharacteristic
142C2×C4⋊C4C2311yescharacteristic
143C2×C4⋊C4C2311yescharacteristic
144C2×C4⋊C4C2311yescharacteristic
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—28no—
158C2×C42D411yescharacteristic
159C2×C42D414yes—
160C2×C42D411yescharacteristic
161C2×C42C2311yescharacteristic
162C2×C42C2311yescharacteristic
163C2×C42C2314yes—
164#107C2314yes—
165#107C2314yes—
166#106C2314yes—
167#106C2314yes—
168C4⋊C8C2314yes—
169C4⋊C8C2314yes—
170#103C2314yes—
171#103C2314yes—
172#103C2314yes—
173#103C2314yes—
174#102C2314yes—
175#102C2314yes—
176#102C2314yes—
177#102C2314yes—
178C22⋊C8C2314yes—
179C22⋊C8C2314yes—
180#97C2314yes—
181#97C2314yes—
182C24—21no—
183C24—21no—
184C24C2×D411yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8#4114yes—
194C2×Q8C2412yes—
195C2×Q8C2412yes—
196C2×D4—28no—
197C2×D4—24no—
198C2×D4—24no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—44no—
205C2×D4#4114yes—
206C2×D4C2412yes—
207C2×D4C2412yes—
208C22×C4—28no—
209C22×C4—21no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4C2×D412yes—
227C22×C4C2×D411yescharacteristic
228C22×C4C2×D411yescharacteristic
229C22×C4C2×D411yescharacteristic
230C22×C4C2×D411yescharacteristic
231C22×C4C2×D411yescharacteristic
232C22×C4C2×D414yes—
233C22×C4C2×D414yes—
234C22×C4C2412yes—
235C22×C4C2411yescharacteristic
236Q16—28no—
237SD16—28no—
238SD16—28no—
239D8—28no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8C2412yes—
245C2×C8C2412yes—
246C2×C8C2412yes—
247C2×C8C2412yes—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4C2412yes—
259C4⋊C4C2412yes—
260C4⋊C4C2412yes—
261C4⋊C4C2412yes—
262C22⋊C4—24no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C42—24no—
271C42—24no—
272C42—24no—
273C42—24no—
274C42C2×D414yes—
275C42C2×D414yes—
276C42C2×D412yes—
277C42C2×D412yes—
278C42C2412yes—
279C42C2412yes—
280C23—22no—
281C23—24no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23C22×D412yes—
292C23C22×D411yescharacteristic
293Q8—24no—
294Q8—22no—
295Q8—22no—
296Q8—22no—
297Q8—42no—
298Q8C2×#4114yes—
299D4—216no—
300D4—24no—
301D4—22no—
302D4—22no—
303D4—22no—
304D4—48no—
305D4—42no—
306D4C2×#4114yes—
307C2×C4—216no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—48no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4C22×D412yes—
334C2×C4C22×D412yes—
335C2×C4C22×D412yes—
336C2×C4C22×D412yes—
337C2×C4C22×D412yes—
338C2×C4C22×D411yescharacteristic
339C2×C4C2×#4112yes—
340C2×C4C2×#4112yes—
341C2×C4C2511yescharacteristic
342C8—22no—
343C8—22no—
344C8—22no—
345C8—22no—
346C22—22no—
347C22—24no—
348C22—22no—
349C22—22no—
350C22—44no—
351C22—48no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—84no—
358C22#52512yes—
359C22#57512yes—
360C22#57512yes—
361C22C23×D411yescharacteristic
362C4—22no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—42no—
369C4—42no—
370C4—42no—
371C4—42no—
372C4—42no—
373C4#52512yes—
374C4C22×#4111yescharacteristic
375C4C22×#4111yescharacteristic
376C2—42no—
377C2—44no—
378C2—82no—
379C2#311114yesdirect product factor
380C2C2×#52511yescharacteristic
381C2C2×#57511yescharacteristic
382C2C2×#57511yescharacteristic
subgroupG/H
center, socleC23C22×D4
commutator, Frattini, cosocleC2×C4C25
prime radicalC2×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#529C2semidirect
2. C2×C4×#41C2semidirect
3. #3111C2direct (N × H)
4. C2×#485C2semidirect
5. C2×#482C2semidirect
6. C2×#479C2semidirect
7. C2×#478C2semidirect
8. C2×#464C2semidirect
9. C2×#463C2semidirect
10. C2×#452C2semidirect
12. C2×#442C2semidirect
13. C2×#441C2semidirect
14. C2×#440C2semidirect
15. C2×#440C2semidirect
16. C2×#432C2semidirect
23. #529C22semidirect
31. C4×#41C22semidirect
46. #485C22semidirect
47. #482C22semidirect
48. #479C22semidirect
49. #478C22semidirect
50. #464C22semidirect
51. #463C22semidirect
52. #452C22semidirect
54. #442C22semidirect
55. #441C22semidirect
56. #440C22semidirect
57. #440C22semidirect
58. #432C22semidirect
379. C2#3111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5292
C2×C4×#412
#31112
C2×#4852
C2×#4822
C2×#4792
C2×#4782
C2×#4642
C2×#4632
C2×#4522
C2×#4492
C2×#4422
C2×#4412
C2×#4402
C2×#4322