Finite Group Databasebeta

← C2×#3179 #60684

Subgroups — C2×#3179 #60684

Order 256.

1017 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542C211yesmaximal, characteristic, complemented
2C2×#540C211yesmaximal, characteristic, complemented
3#3179C2116yesmaximal, direct product factor
4C2×#501C211yesmaximal, characteristic, complemented
5C2×#496C211yesmaximal, characteristic, complemented
6C2×#488C211yesmaximal, characteristic, complemented
7C2×#486C211yesmaximal, characteristic, complemented
8C2×#469C211yesmaximal, characteristic, complemented
9C2×#468C211yesmaximal, characteristic, complemented
10C2×#466C211yesmaximal, characteristic, complemented
11C2×#465C211yesmaximal, characteristic, complemented
12C2×#442C211yesmaximal, characteristic, complemented
13C2×#440C211yesmaximal, characteristic, complemented
14C2×C4×SD16C211yesmaximal, characteristic, complemented
15C2×C4×D8C211yesmaximal, characteristic, complemented
16C2×#405C211yesmaximal, characteristic, complemented
17C22×SD16C2211yescharacteristic
18C22×SD16C2211yescharacteristic
19C22×D8C2211yescharacteristic
20C22×D8C2211yescharacteristic
21C22×M16C2211yescharacteristic
22C23×C8C2211yescharacteristic
23#542—24no—
24#542C2218yescomplemented
25#540—24no—
26#540C2218yescomplemented
27C2×C4⋊Q8C2211yescharacteristic
28C2×#127C2211yescharacteristic
29C2×#126—21no—
30C2×#125C2211yescharacteristic
31C2×#124—21no—
32C2×#124C2211yescharacteristic
33C2×#123—21no—
34C2×#123—21no—
35C2×#123—21no—
36C2×C22⋊Q8—21no—
37C2×C22⋊Q8C2211yescharacteristic
38C2×#121—21no—
39C2×#121—21no—
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×C4×Q8C2211yescharacteristic
44C2×C4×D4C2211yescharacteristic
45C2×C4×D4C2211yescharacteristic
46C2×C4×D4C2211yescharacteristic
47C2×#117C2211yescharacteristic
48#501C2218yescomplemented
49#496C2218yescomplemented
50#488C2218yescomplemented
51#486C2218yescomplemented
52#469C2218yescomplemented
53#468C2218yescomplemented
54#466C2218yescomplemented
55#465C2218yescomplemented
56#442C2218yescomplemented
57#440C2218yescomplemented
58C4×SD16C2218yescomplemented
59C4×D8C2218yescomplemented
60C2×#107C2211yescharacteristic
61C2×#107C2211yescharacteristic
62C2×#106C2211yescharacteristic
63C2×#106C2211yescharacteristic
64C2×#103C2211yescharacteristic
65C2×#103C2211yescharacteristic
66C2×#102C2211yescharacteristic
67C2×#102C2211yescharacteristic
68C2×#102C2211yescharacteristic
69C2×#102C2211yescharacteristic
70C2×#102C2211yescharacteristic
71C2×#102C2211yescharacteristic
72#405C2218yescomplemented
73C2×#97C2211yescharacteristic
74C2×#97C2211yescharacteristic
75C2×C4×C8C2211yescharacteristic
76C2×C4×C8C2211yescharacteristic
77C22×Q8—21no—
78C22×Q8C2311yescharacteristic
79C22×D4—21no—
80C22×D4—21no—
81C22×D4—21no—
82C22×D4—21no—
83C22×D4—21no—
84C22×D4C2311yescharacteristic
85C22×D4C2311yescharacteristic
86C22×D4C2311yescharacteristic
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C2311yescharacteristic
91C2×SD16—24no—
92C2×SD16—24no—
93C2×SD16C2314yes—
94C2×SD16C2314yes—
95C2×D8—24no—
96C2×D8—24no—
97C2×D8C2314yes—
98C2×D8C2314yes—
99C2×M16—24no—
100C2×M16C2314yes—
101C22×C8—24no—
102C22×C8C2311yescharacteristic
103C22×C8C2314yes—
104C22×C8C2311yescharacteristic
105C22×C8C2311yescharacteristic
106C22×C8C2311yescharacteristic
107C4⋊Q8—22no—
108C4⋊Q8C2314yes—
109#127—22no—
110#127C2314yes—
111#126—28no—
112#125—22no—
113#125C2314yes—
114#124—28no—
115#124—22no—
116#124C2314yes—
117#123—28no—
118#123—28no—
119#123—28no—
120C22⋊Q8—22no—
121C22⋊Q8—28no—
122C22⋊Q8C2314yes—
123#121—22no—
124#121—22no—
125#121—22no—
126#121—28no—
127#121—28no—
128#121C2314yes—
129#121C2314yes—
130#121C2314yes—
131C4×Q8—22no—
132C4×Q8C2314yes—
133C4×D4—22no—
134C4×D4—22no—
135C4×D4—22no—
136C4×D4C2314yes—
137C4×D4C2314yes—
138C4×D4C2314yes—
139#117D414yes—
140#117C2314yes—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4D411yescharacteristic
147C2×C4⋊C4D411yescharacteristic
148C2×C4⋊C4C2311yescharacteristic
149C2×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4D411yescharacteristic
162C2×C22⋊C4D411yescharacteristic
163C2×C42—21no—
164C2×C42C2311yescharacteristic
165C2×C42C2311yescharacteristic
166#107C2314yes—
167#107C2314yes—
168#106C2314yes—
169#106C2314yes—
170#103C2314yes—
171#103C2314yes—
172#102C2314yes—
173#102C2314yes—
174#102C2314yes—
175#102C2314yes—
176#102C2314yes—
177#102C2314yes—
178#97C2314yes—
179#97C2314yes—
180C4×C8C2314yes—
181C4×C8C2314yes—
182C24—21no—
183C24—21no—
184C24—21no—
185C24C2×D411yescharacteristic
186C2×Q8—21no—
187C2×Q8—24no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—82no—
191C2×Q8C2412yes—
192C2×D4—24no—
193C2×D4—24no—
194C2×D4—24no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—24no—
199C2×D4—24no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—82no—
207C2×D4—82no—
208C2×D4—82no—
209C2×D4—82no—
210C2×D4—82no—
211C2×D4C2412yes—
212C2×D4C2412yes—
213C2×D4C2412yes—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—82no—
225C22×C4—82no—
226C22×C4—82no—
227C22×C4C2×D412yes—
228C22×C4C2×D411yescharacteristic
229C22×C4C2×D411yescharacteristic
230C22×C4C2×D411yescharacteristic
231C22×C4C2×D411yescharacteristic
232C22×C4C2×D411yescharacteristic
233C22×C4C2412yes—
234C22×C4C2411yescharacteristic
235SD16—28no—
236SD16—28no—
237D8—28no—
238D8—28no—
239M16—28no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—28no—
243C2×C8#4114yes—
244C2×C8#4114yes—
245C2×C8C2412yes—
246C2×C8C2412yes—
247C2×C8C2412yes—
248C2×C8C2412yes—
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⋊C4C2×D414yes—
259C4⋊C4C2×D414yes—
260C4⋊C4C2412yes—
261C4⋊C4C2412yes—
262C4⋊C4C2412yes—
263C4⋊C4C2412yes—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4C2×D414yes—
274C22⋊C4C2×D414yes—
275C42—24no—
276C42C2×D412yes—
277C42C2×D412yes—
278C42C2412yes—
279C42C2412yes—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23C22×D412yes—
296C23C22×D411yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—84no—
301D4—22no—
302D4—22no—
303D4—22no—
304D4—22no—
305D4—22no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—42no—
310D4—84no—
311D4—84no—
312D4—84no—
313D4—84no—
314D4—84no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—84no—
334C2×C4—84no—
335C2×C4—84no—
336C2×C4C22×D412yes—
337C2×C4C22×D412yes—
338C2×C4C22×D412yes—
339C2×C4C22×D412yes—
340C2×C4C22×D412yes—
341C2×C4C22×D411yescharacteristic
342C2×C4C2×#4112yes—
343C2×C4C2×#4112yes—
344C2×C4C2511yescharacteristic
345C8—22no—
346C8—22no—
347C8C2×#4114yes—
348C8C2×#4114yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—44no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22—84no—
364C22—84no—
365C22#53212yes—
366C22#57612yes—
367C22#57712yes—
368C22C23×D411yescharacteristic
369C4—22no—
370C4—22no—
371C4—22no—
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—42no—
379C4#53212yes—
380C4C22×#4111yescharacteristic
381C4C22×#4111yescharacteristic
382C2—42no—
383C2—82no—
384C2—82no—
385C2—82no—
386C2#317914yesdirect product factor
387C2C2×#53211yescharacteristic
388C2C2×#57611yescharacteristic
389C2C2×#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×#542C2semidirect
2. C2×#540C2semidirect
3. #3179C2direct (N × H)
4. C2×#501C2semidirect
5. C2×#496C2semidirect
6. C2×#488C2semidirect
7. C2×#486C2semidirect
8. C2×#469C2semidirect
9. C2×#468C2semidirect
10. C2×#466C2semidirect
11. C2×#465C2semidirect
12. C2×#442C2semidirect
13. C2×#440C2semidirect
14. C2×C4×SD16C2semidirect
15. C2×C4×D8C2semidirect
16. C2×#405C2semidirect
24. #542C22semidirect
26. #540C22semidirect
48. #501C22semidirect
49. #496C22semidirect
50. #488C22semidirect
51. #486C22semidirect
52. #469C22semidirect
53. #468C22semidirect
54. #466C22semidirect
55. #465C22semidirect
56. #442C22semidirect
57. #440C22semidirect
58. C4×SD16C22semidirect
59. C4×D8C22semidirect
72. #405C22semidirect
386. C2#3179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5422
C2×#5402
#31792
C2×#5012
C2×#4962
C2×#4882
C2×#4862
C2×#4692
C2×#4682
C2×#4662
C2×#4652
C2×#4422
C2×#4402
C2×C4×SD162
C2×C4×D82
C2×#4052