Finite Group Databasebeta

← C2×#3343 #61235

Subgroups — C2×#3343 #61235

Order 256.

1047 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552C211yesmaximal, characteristic, complemented
2C2×#547C211yesmaximal, characteristic
3#3343C2116yesmaximal, direct product factor
4C2×#501C211yesmaximal, characteristic, complemented
5C2×#484C211yesmaximal, characteristic, complemented
6C2×#482C211yesmaximal, characteristic, complemented
7C2×#483C211yesmaximal, characteristic, complemented
8C2×#480C211yesmaximal, characteristic, complemented
9C2×#477C211yesmaximal, characteristic, complemented
10C2×#478C211yesmaximal, characteristic, complemented
11C2×#468C211yesmaximal, characteristic, complemented
12C2×#465C211yesmaximal, characteristic, complemented
13C2×#440C211yesmaximal, characteristic, complemented
14C2×#435C211yesmaximal, characteristic, complemented
15C2×#428C211yesmaximal, characteristic, complemented
16C22×#107C211yesmaximal, characteristic, complemented
17C22×#41—21no—
18C22×SD16C2211yescharacteristic
19C22×M16C2211yescharacteristic
20C23×C8C2211yescharacteristic
21#552—24no—
22#552C2218yescomplemented
23#547—24no—
24#547C2218yes—
25C2×C4⋊Q8C2211yescharacteristic
26C2×#126—21no—
27C2×#125—21no—
28C2×#125C2211yescharacteristic
29C2×#123—21no—
30C2×#123—21no—
31C2×#123—21no—
32C2×C22⋊Q8—21no—
33C2×C22⋊Q8C2211yescharacteristic
34C2×C22⋊Q8C2211yescharacteristic
35C2×#121C2211yescharacteristic
36C2×#121C2211yescharacteristic
37C2×C4×Q8C2211yescharacteristic
38C2×C4×D4C2211yescharacteristic
39C2×C4×D4C2211yescharacteristic
40C2×#117—21no—
41C2×#117C2211yescharacteristic
42C22×C4⋊C4C2211yescharacteristic
43C22×C4⋊C4C2211yescharacteristic
44C22×C4⋊C4C2211yescharacteristic
45#501C2218yescomplemented
46#484C2218yescomplemented
47#483C2218yescomplemented
48#482C2218yescomplemented
49#480C2218yescomplemented
50#478C2218yescomplemented
51#477C2218yescomplemented
52#468C2218yescomplemented
53#465C2218yescomplemented
54#440C2218yescomplemented
55#435C2218yescomplemented
56#428C2218yescomplemented
57C2×#107C2211yescharacteristic
58C2×#107C2211yescharacteristic
59C2×#107C2211yescharacteristic
60C2×#107C2211yescharacteristic
61C2×#107C2211yescharacteristic
62C2×#107C2211yescharacteristic
63C2×#107C2218yescomplemented
64C2×#106C2211yescharacteristic
65C2×#106C2211yescharacteristic
66C2×#106C2211yescharacteristic
67C2×C4⋊C8C2211yescharacteristic
68C2×#103C2211yescharacteristic
69C2×#103C2211yescharacteristic
70C2×#103C2211yescharacteristic
71C2×#102C2211yescharacteristic
72C2×#102C2211yescharacteristic
73C2×#102C2211yescharacteristic
74C2×C22⋊C8C2211yescharacteristic
75C2×C22⋊C8C2211yescharacteristic
76C2×#97C2211yescharacteristic
77C2×#41—28no—
78C2×#41—48no—
79C22×Q8—21no—
80C22×Q8C2311yescharacteristic
81C22×D4—21no—
82C22×D4—21no—
83C22×D4D411yescharacteristic
84C22×D4C2311yescharacteristic
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4C2311yescharacteristic
90C23×C4C2311yescharacteristic
91C2×SD16—24no—
92C2×SD16C2314yes—
93C2×M16—24no—
94C2×M16C2314yes—
95C22×C8—24no—
96C22×C8C2311yescharacteristic
97C22×C8C2314yes—
98C22×C8C2311yescharacteristic
99C22×C8C2311yescharacteristic
100C22×C8C2311yescharacteristic
101C4⋊Q8—22no—
102C4⋊Q8C2314yes—
103#126—28no—
104#125—28no—
105#125—22no—
106#125C2314yes—
107#123—28no—
108#123—28no—
109#123—28no—
110C22⋊Q8—22no—
111C22⋊Q8—22no—
112C22⋊Q8—28no—
113C22⋊Q8C2314yes—
114C22⋊Q8C2314yes—
115#121—22no—
116#121—22no—
117#121C2314yes—
118#121C2314yes—
119C4×Q8—22no—
120C4×Q8C2314yes—
121C4×D4—22no—
122C4×D4D414yes—
123C4×D4C2314yes—
124C4×D4C2314yes—
125#117—22no—
126#117—28no—
127#117C2314yes—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4D411yescharacteristic
141C2×C4⋊C4C2311yescharacteristic
142C2×C4⋊C4C2311yescharacteristic
143C2×C4⋊C4C2311yescharacteristic
144C2×C4⋊C4C2311yescharacteristic
145C2×C4⋊C4C2311yescharacteristic
146C2×C4⋊C4C2314yes—
147C2×C4⋊C4C2314yes—
148C2×C4⋊C4C2314yes—
149C2×C4⋊C4C2311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—21no—
155C2×C22⋊C4—21no—
156C2×C22⋊C4D411yescharacteristic
157C2×C22⋊C4D411yescharacteristic
158C2×C42—21no—
159C2×C42—21no—
160C2×C42C2311yescharacteristic
161#107C2314yes—
162#107C2314yes—
163#107C2314yes—
164#107C2314yes—
165#107C2314yes—
166#107C2314yes—
167#106C2314yes—
168#106C2314yes—
169#106C2314yes—
170C4⋊C8C2314yes—
171#103C2314yes—
172#103C2314yes—
173#103C2314yes—
174#102C2314yes—
175#102C2314yes—
176#102C2314yes—
177C22⋊C8C2314yes—
178C22⋊C8C2314yes—
179#97C2314yes—
180C24—21no—
181C24C2×D411yescharacteristic
182C24C2×D411yescharacteristic
183#41—432no—
184C2×Q8—21no—
185C2×Q8—24no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8—44no—
189C2×Q8C2412yes—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—24no—
193C2×D4—21no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—44no—
197C2×D4—44no—
198C2×D4C2×D414yes—
199C2×D4C2412yes—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—24no—
205C22×C4—24no—
206C22×C4—24no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—24no—
215C22×C4—44no—
216C22×C4—44no—
217C22×C4—44no—
218C22×C4—44no—
219C22×C4C2×D412yes—
220C22×C4C2×D412yes—
221C22×C4C2×D411yescharacteristic
222C22×C4C2×D411yescharacteristic
223C22×C4C2×D411yescharacteristic
224C22×C4C2×D411yescharacteristic
225C22×C4C2412yes—
226C22×C4C2412yes—
227C22×C4C2411yescharacteristic
228SD16—28no—
229M16—28no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—28no—
234C2×C8#4114yescomplemented
235C2×C8C2412yes—
236C2×C8C2412yes—
237C2×C8C2412yes—
238C2×C8C2412yes—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—21no—
246C4⋊C4—24no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—21no—
254C4⋊C4C2×D414yes—
255C4⋊C4C2412yes—
256C4⋊C4C2412yes—
257C4⋊C4C2412yes—
258C4⋊C4C2412yes—
259C4⋊C4C2412yes—
260C4⋊C4C2412yes—
261C22⋊C4—24no—
262C22⋊C4—24no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4C2×D414yes—
268C22⋊C4C2×D414yes—
269C42—24no—
270C42—24no—
271C42C2×D412yes—
272C42C2412yes—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23AGL(1,ℤ/8)14yes—
283C23C22×D412yes—
284C23C22×D412yes—
285C23C22×D411yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—48no—
289Q8—42no—
290D4—28no—
291D4—22no—
292D4—22no—
293D4—48no—
294D4—48no—
295D4—42no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—48no—
314C2×C4—48no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—48no—
323C2×C4—42no—
324C2×C4C22×D412yes—
325C2×C4C22×D412yes—
326C2×C4C22×D412yes—
327C2×C4C22×D412yes—
328C2×C4C22×D411yescharacteristic
329C2×C4C2×#4112yes—
330C2×C42−1+412yes—
331C2×C4C2511yescharacteristic
332C8—22no—
333C8—22no—
334C8—22no—
335C8C2×#4114yescomplemented
336C22—28no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—44no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22—84no—
347C22#54712yes—
348C22C2×AGL(1,ℤ/8)14yes—
349C22C2×AGL(1,ℤ/8)12yes—
350C22#57812yes—
351C22C23×D411yescharacteristic
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—42no—
357C4—42no—
358C4—42no—
359C4—42no—
360C4—42no—
361C4—42no—
362C4—42no—
363C4#54712yes—
364C4C22×#4111yescharacteristic
365C4C2×2−1+411yescharacteristic
366C2—24no—
367C2—42no—
368C2—82no—
369C2#334314yesdirect product factor
370C2C2×#54711yescharacteristic
371C2C22×AGL(1,ℤ/8)11yescharacteristic
372C2C2×#57811yescharacteristic
subgroupG/H
center, socleC23C22×D4
commutator, Frattini, cosocleC2×C4C25
prime radicalC2×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#552C2semidirect
3. #3343C2direct (N × H)
4. C2×#501C2semidirect
5. C2×#484C2semidirect
6. C2×#482C2semidirect
7. C2×#483C2semidirect
8. C2×#480C2semidirect
9. C2×#477C2semidirect
10. C2×#478C2semidirect
11. C2×#468C2semidirect
12. C2×#465C2semidirect
13. C2×#440C2semidirect
14. C2×#435C2semidirect
15. C2×#428C2semidirect
16. C22×#107C2semidirect
22. #552C22semidirect
45. #501C22semidirect
46. #484C22semidirect
47. #483C22semidirect
48. #482C22semidirect
49. #480C22semidirect
50. #478C22semidirect
51. #477C22semidirect
52. #468C22semidirect
53. #465C22semidirect
54. #440C22semidirect
55. #435C22semidirect
56. #428C22semidirect
63. C2×#107C22semidirect
234. C2×C8#41semidirect
335. C8C2×#41semidirect
369. C2#3343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5522
C2×#5472
#33432
C2×#5012
C2×#4842
C2×#4822
C2×#4832
C2×#4802
C2×#4772
C2×#4782
C2×#4682
C2×#4652
C2×#4402
C2×#4352
C2×#4282
C22×#1072