Finite Group Databasebeta

← C2×#1904 #20996

Subgroups — C2×#1904 #20996

Order 256.

947 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×#518C211yesmaximal, characteristic, complemented
3C2×#421C211yesmaximal, characteristic, complemented
4C2×#418C211yesmaximal, characteristic, complemented
5C2×#410C211yesmaximal, characteristic, complemented
6#1904C218yesmaximal, direct product factor
7C2×#344C211yesmaximal, characteristic, complemented
8C2×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#41C2211yescharacteristic
10C23×D4C2211yescharacteristic
11C2×AGL(1,ℤ/8)—22no—
12C2×AGL(1,ℤ/8)—22no—
13C2×AGL(1,ℤ/8)—22no—
14C2×AGL(1,ℤ/8)—22no—
15C2×AGL(1,ℤ/8)C414yescomplemented
16C2×AGL(1,ℤ/8)C2214yes—
17C22×SD16C412yescomplemented
18C22×D8C412yescomplemented
19C22×M16C2211yescharacteristic
20C22×M16C2211yescharacteristic
21#518—22no—
22#518—22no—
23#518—22no—
24#518C2214yescomplemented
25C2×C4×D4—22no—
26C2×C4×D4—22no—
27C2×#117C2211yescharacteristic
28C2×#117C2211yescharacteristic
29C2×#117C2211yescharacteristic
30C22×C22⋊C4—22no—
31#421—22no—
32#421C2214yescomplemented
33C2×#104—22no—
34#418—22no—
35#418C2214yescomplemented
36C2×#102—22no—
37#410—22no—
38#410C2214yescomplemented
39C2×#99—22no—
40#344C2214yescomplemented
41H(3,ℤ/4)C2214yescomplemented
42C25—21no—
43C2×#41—21no—
44C2×#41—21no—
45C2×#41—21no—
46C2×#41—21no—
47C2×#41—21no—
48C2×#41—21no—
49C2×#41—21no—
50C2×#41—21no—
51C2×#41—21no—
52C2×#41—21no—
53C2×#41C2×C412yescomplemented
54C2×#41C2312yes—
55C22×Q8C2×C411yescharacteristic, complemented
56C22×D4—21no—
57C22×D4—21no—
58C22×D4—21no—
59C22×D4—21no—
60C22×D4—21no—
61C22×D4—21no—
62C22×D4—21no—
63C22×D4—21no—
64C22×D4C2×C412yes—
65C22×D4C2×C412yes—
66C22×D4C2×C411yescharacteristic, complemented
67C22×D4D412yes—
68C22×D4D412yes—
69C22×D4D412yes—
70C22×D4D412yes—
71C22×D4C2312yes—
72C23×C4—24no—
73C23×C4—21no—
74C23×C4C2311yescharacteristic
75AGL(1,ℤ/8)—28no—
76AGL(1,ℤ/8)—28no—
77AGL(1,ℤ/8)—28no—
78AGL(1,ℤ/8)—28no—
79C2×SD16—24no—
80C2×SD16—24no—
81C2×SD16C2×C418yescomplemented
82C2×D8—24no—
83C2×D8—24no—
84C2×D8C2×C418yescomplemented
85C2×M16—21no—
86C2×M16—21no—
87C2×M16—21no—
88C2×M16—21no—
89C2×M16—21no—
90C2×M16—21no—
91C2×M16—21no—
92C2×M16—21no—
93C2×M16—21no—
94C2×M16C2×C412yescomplemented
95C2×M16C2312yes—
96C2×M16C2312yes—
97C22×C8—21no—
98C22×C8C2×C412yescomplemented
99C4×D4—28no—
100C4×D4—28no—
101C4×D4—28no—
102C4×D4—28no—
103#117—21no—
104#117—21no—
105#117—21no—
106#117—21no—
107#117—21no—
108#117—21no—
109#117—21no—
110#117D412yes—
111#117D412yes—
112#117C2312yes—
113#117C2312yes—
114#117C2312yes—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C22⋊C4—24no—
119C2×C22⋊C4—28no—
120C2×C22⋊C4—21no—
121C2×C22⋊C4—28no—
122C2×C22⋊C4—21no—
123C2×C22⋊C4D412yes—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42D412yes—
127#104—28no—
128#102—28no—
129#99—28no—
130C24—22no—
131C24—22no—
132C24—22no—
133C24—22no—
134C24—22no—
135C24—22no—
136C24—22no—
137C24—21no—
138C24—84no—
139C24C2×D411yescharacteristic
140#41—22no—
141#41—22no—
142#41—22no—
143#41—22no—
144#41—22no—
145#41—22no—
146#41—22no—
147#41—22no—
148#41—41no—
149#41—41no—
150#41—41no—
151#41—41no—
152#41—41no—
153#41—41no—
154#41—41no—
155#41—41no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22×C412yescomplemented
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—22no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C22⋊C414yes—
195C2×D4C22⋊C414yes—
196C2×D4C22⋊C414yes—
197C2×D4C22⋊C414yes—
198C2×D4C22×C414yes—
199C2×D4C22×C412yescomplemented
200C2×D4C2×D414yes—
201C2×D4C2×D414yes—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—216no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—88no—
214C22×C4C22×C411yescharacteristic
215C22×C4C22×C411yescharacteristic
216C22×C4C2×D411yescharacteristic
217C22×C4C2×D411yescharacteristic
218C22×C4C2×D411yescharacteristic
219C22×C4C2×D411yescharacteristic
220C22×C4C2×D411yescharacteristic
221C22×C4C2×D411yescharacteristic
222C22×C4C2×D411yescharacteristic
223C22×C4#4111yescharacteristic
224C22×C4#4111yescharacteristic
225C22×C4#4111yescharacteristic
226C22×C4#4111yescharacteristic
227C22×C4C2411yescharacteristic
228SD16—216no—
229D8—216no—
230M16—22no—
231M16—22no—
232M16—22no—
233M16—22no—
234M16—22no—
235M16—22no—
236M16—41no—
237M16—41no—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8C22×C414yescomplemented
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C22⋊C4—216no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—41no—
256C22⋊C4C2×D414yes—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42C2×D414yes—
263C23—24no—
264C23—24no—
265C23—24no—
266C23—24no—
267C23—24no—
268C23—24no—
269C23—24no—
270C23—22no—
271C23—42no—
272C23—48no—
273C23—41no—
274C23—41no—
275C23—84no—
276C23—84no—
277C23—82no—
278C23—84no—
279C23—84no—
280C23—84no—
281C23—84no—
282C23C4×D411yescharacteristic
283C23C4×D411yescharacteristic
284C23#12011yescharacteristic
285C23#12011yescharacteristic
286C23#12111yescharacteristic
287C23#12111yescharacteristic
288C23C22×D411yescharacteristic
289Q8—22no—
290Q8—22no—
291Q8—41no—
292Q8—41no—
293D4—22no—
294D4—24no—
295D4—22no—
296D4—24no—
297D4—24no—
298D4—24no—
299D4—24no—
300D4—24no—
301D4—24no—
302D4—42no—
303D4—42no—
304D4—42no—
305D4—42no—
306D4—41no—
307D4—41no—
308D4C2×C22⋊C418yes—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—816no—
322C2×C4—82no—
323C2×C4C2×C22⋊C411yescharacteristic
324C2×C4C2×C22⋊C411yescharacteristic
325C2×C4C2×C22⋊C411yescharacteristic
326C2×C4C2×C22⋊C411yescharacteristic
327C2×C4C4×D411yescharacteristic
328C2×C4C4×D411yescharacteristic
329C2×C4C4×D411yescharacteristic
330C2×C4C4×D411yescharacteristic
331C2×C4C4×D411yescharacteristic
332C2×C4C4×D411yescharacteristic
333C2×C4#12011yescharacteristic
334C2×C4#12011yescharacteristic
335C2×C4#12111yescharacteristic
336C2×C4#12111yescharacteristic
337C2×C4#12111yescharacteristic
338C2×C4#12111yescharacteristic
339C2×C4#12111yescharacteristic
340C2×C4#12111yescharacteristic
341C2×C4#12311yescharacteristic
342C2×C4#12311yescharacteristic
343C2×C4#12311yescharacteristic
344C2×C4#12311yescharacteristic
345C2×C4C23×C411yescharacteristic
346C2×C4C22×D411yescharacteristic
347C2×C4C22×D411yescharacteristic
348C2×C4C22×D411yescharacteristic
349C2×C4C2×#4111yescharacteristic
350C2×C4C2×#4111yescharacteristic
351C8—24no—
352C8—42no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—28no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—48no—
362C22—48no—
363C22—48no—
364C22—42no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22—84no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22#38611yescharacteristic
373C22#38611yescharacteristic
374C22#38611yescharacteristic
375C22#38611yescharacteristic
376C22C2×C4×D411yescharacteristic
377C22C2×#12011yescharacteristic
378C22C2×#12111yescharacteristic
379C4—44no—
380C4—44no—
381C4—42no—
382C4—82no—
383C4#38611yescharacteristic
384C4#38611yescharacteristic
385C4#38611yescharacteristic
386C4#38611yescharacteristic
387C4C22×C22⋊C411yescharacteristic
388C4C2×C4×D411yescharacteristic
389C4C2×#12111yescharacteristic
390C4C2×#12311yescharacteristic
391C2—21no—
392C2—21no—
393C2—21no—
394C2—21no—
395C2—21no—
396C2—21no—
397C2—48no—
398C2—82no—
399C2#190412yesdirect product factor
400C2C2×#38611yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC2×C4C23×C4
Frattini, cosocleC22×C4C24
prime radicalC22×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#518C2semidirect
3. C2×#421C2semidirect
4. C2×#418C2semidirect
5. C2×#410C2semidirect
6. #1904C2direct (N × H)
7. C2×#344C2semidirect
8. C2×H(3,ℤ/4)C2semidirect
15. C2×AGL(1,ℤ/8)C4semidirect
17. C22×SD16C4semidirect
18. C22×D8C4semidirect
24. #518C22semidirect
32. #421C22semidirect
35. #418C22semidirect
38. #410C22semidirect
40. #344C22semidirect
41. H(3,ℤ/4)C22semidirect
53. C2×#41C2×C4semidirect
55. C22×Q8C2×C4semidirect
66. C22×D4C2×C4semidirect
81. C2×SD16C2×C4semidirect
84. C2×D8C2×C4semidirect
94. C2×M16C2×C4semidirect
98. C22×C8C2×C4semidirect
161. C2×Q8C22×C4semidirect
199. C2×D4C22×C4semidirect
243. C2×C8C22×C4semidirect
399. C2#1904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)2
C2×#5182
C2×#4212
C2×#4182
C2×#4102
#19042
C2×#3442
C2×H(3,ℤ/4)2