Finite Group Databasebeta

← C2×#3119 #60548

Subgroups — C2×#3119 #60548

Order 256.

1099 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540C211yesmaximal, characteristic, complemented
2C2×#520C211yesmaximal, characteristic, complemented
3#3119C2116yesmaximal, direct product factor
4C2×#481C211yesmaximal, characteristic, complemented
5C2×#480C211yesmaximal, characteristic, complemented
6C2×#479C211yesmaximal, characteristic, complemented
7C2×#478C211yesmaximal, characteristic, complemented
8C2×#460C211yesmaximal, characteristic, complemented
9C2×#459C211yesmaximal, characteristic, complemented
10C2×#449C211yesmaximal, characteristic, complemented
11C2×#449C211yesmaximal, characteristic, complemented
12C2×#442C211yesmaximal, characteristic, complemented
13C2×#440C211yesmaximal, characteristic, complemented
14C2×C4×SD16C211yesmaximal, characteristic, complemented
15C2×C4×D8C211yesmaximal, characteristic, complemented
16C2×#433C211yesmaximal, characteristic, complemented
17C22×#41C2211yescharacteristic
18C22×SD16C2211yescharacteristic
19C22×SD16C2211yescharacteristic
20C22×D8C2211yescharacteristic
21C22×D8C2211yescharacteristic
22#540—24no—
23#540C2218yescomplemented
24C2×#127C2211yescharacteristic
25C2×#125C2211yescharacteristic
26C2×#123—21no—
27C2×#123—21no—
28C2×#121—21no—
29C2×#121—21no—
30C2×#121C2211yescharacteristic
31C2×#121C2211yescharacteristic
32#520—24no—
33#520C2218yescomplemented
34C2×C4×Q8C2211yescharacteristic
35C2×C4×Q8C2211yescharacteristic
36C2×C4×D4—21no—
37C2×C4×D4—21no—
38C2×C4×D4C2211yescharacteristic
39C2×C4×D4C2211yescharacteristic
40C2×C4×D4C2211yescharacteristic
41C2×C4×D4C2211yescharacteristic
42C2×#117—21no—
43C2×#117C2211yescharacteristic
44C22×C4⋊C4—21no—
45C22×C4⋊C4C2211yescharacteristic
46#481C2218yescomplemented
47#480C2218yescomplemented
48#479C2218yescomplemented
49#478C2218yescomplemented
50#460C2218yescomplemented
51#459C2218yescomplemented
52#449C2218yescomplemented
53#449C2218yescomplemented
54#442C2218yescomplemented
55#440C2218yescomplemented
56C4×SD16C2218yescomplemented
57C4×D8C2218yescomplemented
58#433C2218yescomplemented
59C2×#107C2211yescharacteristic
60C2×#107C2211yescharacteristic
61C2×#106C2211yescharacteristic
62C2×#106C2211yescharacteristic
63C2×C4⋊C8C2211yescharacteristic
64C2×C4⋊C8C2211yescharacteristic
65C2×#103C2211yescharacteristic
66C2×#103C2211yescharacteristic
67C2×#102C2211yescharacteristic
68C2×#102C2211yescharacteristic
69C2×#102C2211yescharacteristic
70C2×#102C2211yescharacteristic
71C2×#102C2211yescharacteristic
72C2×#102C2211yescharacteristic
73C2×C22⋊C8C2211yescharacteristic
74C2×C22⋊C8C2211yescharacteristic
75C2×#97C2211yescharacteristic
76C2×C4×C8C2211yescharacteristic
77C2×#41—24no—
78C2×#41—24no—
79C2×#41—22no—
80C2×#41C2314yes—
81C22×Q8C2311yescharacteristic
82C22×D4—21no—
83C22×D4—21no—
84C22×D4—21no—
85C22×D4—21no—
86C22×D4—21no—
87C22×D4C2311yescharacteristic
88C22×D4C2311yescharacteristic
89C22×D4C2311yescharacteristic
90C23×C4—21no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C2311yescharacteristic
97C2×SD16—24no—
98C2×SD16—24no—
99C2×SD16C2314yes—
100C2×SD16C2314yes—
101C2×D8—24no—
102C2×D8—24no—
103C2×D8C2314yes—
104C2×D8C2314yes—
105C22×C8C2311yescharacteristic
106C22×C8C2311yescharacteristic
107C22×C8C2311yescharacteristic
108C22×C8C2311yescharacteristic
109#127—22no—
110#127C2314yes—
111#125—22no—
112#125C2314yes—
113#123—28no—
114#123—28no—
115#121—22no—
116#121—22no—
117#121—28no—
118#121—28no—
119#121C2314yes—
120#121C2314yes—
121C4×Q8—22no—
122C4×Q8—22no—
123C4×Q8C2314yes—
124C4×Q8C2314yes—
125C4×D4—28no—
126C4×D4—28no—
127C4×D4—22no—
128C4×D4—22no—
129C4×D4—22no—
130C4×D4—22no—
131C4×D4C2314yes—
132C4×D4C2314yes—
133C4×D4C2314yes—
134C4×D4C2314yes—
135#117—28no—
136#117D414yes—
137#117C2314yes—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—28no—
145C2×C4⋊C4D411yescharacteristic
146C2×C4⋊C4D411yescharacteristic
147C2×C4⋊C4C2311yescharacteristic
148C2×C4⋊C4C2311yescharacteristic
149C2×C4⋊C4C2314yes—
150C2×C4⋊C4C2311yescharacteristic
151C2×C4⋊C4C2311yescharacteristic
152C2×C22⋊C4—21no—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—21no—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4D411yescharacteristic
159C2×C22⋊C4D411yescharacteristic
160C2×C42—21no—
161C2×C42—21no—
162C2×C42C2311yescharacteristic
163C2×C42C2311yescharacteristic
164#107C2314yes—
165#107C2314yes—
166#106C2314yes—
167#106C2314yes—
168C4⋊C8C2314yes—
169C4⋊C8C2314yes—
170#103C2314yes—
171#103C2314yes—
172#102C2314yes—
173#102C2314yes—
174#102C2314yes—
175#102C2314yes—
176#102C2314yes—
177#102C2314yes—
178C22⋊C8C2314yes—
179C22⋊C8C2314yes—
180#97C2314yes—
181C4×C8C2314yes—
182C24—21no—
183C24—21no—
184C24—21no—
185C24C2×D411yescharacteristic
186#41—216no—
187#41—28no—
188#41—28no—
189C2×Q8—21no—
190C2×Q8—22no—
191C2×Q8#4114yes—
192C2×Q8C2412yes—
193C2×D4—28no—
194C2×D4—24no—
195C2×D4—24no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—24no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—82no—
208C2×D4—82no—
209C2×D4—82no—
210C2×D4—82no—
211C2×D4#4114yes—
212C2×D4C2412yes—
213C2×D4C2412yes—
214C2×D4C2412yes—
215C22×C4—28no—
216C22×C4—21no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—82no—
230C22×C4—82no—
231C22×C4—82no—
232C22×C4—82no—
233C22×C4—82no—
234C22×C4C2×D412yes—
235C22×C4C2×D411yescharacteristic
236C22×C4C2×D411yescharacteristic
237C22×C4C2×D411yescharacteristic
238C22×C4C2×D411yescharacteristic
239C22×C4C2×D411yescharacteristic
240C22×C4C2412yes—
241C22×C4C2411yescharacteristic
242SD16—28no—
243SD16—28no—
244D8—28no—
245D8—28no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8C2412yes—
251C2×C8C2412yes—
252C2×C8C2412yes—
253C2×C8C2412yes—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C2×D414yes—
264C4⋊C4C2×D414yes—
265C4⋊C4C2412yes—
266C4⋊C4C2412yes—
267C4⋊C4C2412yes—
268C4⋊C4C2412yes—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—24no—
275C22⋊C4C2×D414yes—
276C22⋊C4C2×D414yes—
277C42—24no—
278C42—24no—
279C42C2×D412yes—
280C42C2×D412yes—
281C42C2412yes—
282C42C2412yes—
283C23—22no—
284C23—24no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23C22×D412yes—
299C23C22×D411yescharacteristic
300Q8—24no—
301Q8—22no—
302Q8C2×#4114yes—
303D4—216no—
304D4—24no—
305D4—22no—
306D4—22no—
307D4—22no—
308D4—22no—
309D4—22no—
310D4—42no—
311D4—42no—
312D4—84no—
313D4—84no—
314D4—84no—
315D4—84no—
316D4C2×#4114yes—
317C2×C4—216no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—84no—
337C2×C4—84no—
338C2×C4—84no—
339C2×C4—84no—
340C2×C4—84no—
341C2×C4C22×D412yes—
342C2×C4C22×D412yes—
343C2×C4C22×D412yes—
344C2×C4C22×D412yes—
345C2×C4C22×D412yes—
346C2×C4C22×D411yescharacteristic
347C2×C4C2×#4112yes—
348C2×C4C2×#4112yes—
349C2×C4C2511yescharacteristic
350C8—22no—
351C8—22no—
352C8—22no—
353C8—22no—
354C22—22no—
355C22—24no—
356C22—22no—
357C22—22no—
358C22—44no—
359C22—48no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—84no—
369C22—84no—
370C22#52512yes—
371C22#57612yes—
372C22#57712yes—
373C22C23×D411yescharacteristic
374C4—22no—
375C4—24no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—42no—
383C4—42no—
384C4#52512yes—
385C4C22×#4111yescharacteristic
386C4C22×#4111yescharacteristic
387C2—42no—
388C2—44no—
389C2—82no—
390C2—82no—
391C2#311914yesdirect product factor
392C2C2×#52511yescharacteristic
393C2C2×#57611yescharacteristic
394C2C2×#57711yescharacteristic
subgroupG/H
center, socleC23C22×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#117 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#540C2semidirect
2. C2×#520C2semidirect
3. #3119C2direct (N × H)
4. C2×#481C2semidirect
5. C2×#480C2semidirect
6. C2×#479C2semidirect
7. C2×#478C2semidirect
8. C2×#460C2semidirect
9. C2×#459C2semidirect
10. C2×#449C2semidirect
11. C2×#449C2semidirect
12. C2×#442C2semidirect
13. C2×#440C2semidirect
14. C2×C4×SD16C2semidirect
15. C2×C4×D8C2semidirect
16. C2×#433C2semidirect
23. #540C22semidirect
33. #520C22semidirect
46. #481C22semidirect
47. #480C22semidirect
48. #479C22semidirect
49. #478C22semidirect
50. #460C22semidirect
51. #459C22semidirect
52. #449C22semidirect
53. #449C22semidirect
54. #442C22semidirect
55. #440C22semidirect
56. C4×SD16C22semidirect
57. C4×D8C22semidirect
58. #433C22semidirect
391. C2#3119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5402
C2×#5202
#31192
C2×#4812
C2×#4802
C2×#4792
C2×#4782
C2×#4602
C2×#4592
C2×#4492
C2×#4422
C2×#4402
C2×C4×SD162
C2×C4×D82
C2×#4332