Finite Group Databasebeta

← C4×#16861241 #30647550

Subgroups — C4×#16861241 #30647550

Order 16256.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16861241C211yesmaximal, characteristic
2C4×#14523249C211yesmaximal, characteristic
3C4×Q8×D127C211yesmaximal, characteristic, complemented
4#22549983C211yesmaximal, characteristic, complemented
5#22549980C211yesmaximal, characteristic, complemented
6#22549979C211yesmaximal, characteristic, complemented
7#22549975C211yesmaximal, characteristic, complemented
8C4×#14523238C211yesmaximal, characteristic, complemented
9C4×#14523237C211yesmaximal, characteristic, complemented
10C4×#14523235C211yesmaximal, characteristic, complemented
11#22549917C211yesmaximal, characteristic, complemented
12#22549883C211yesmaximal, characteristic, complemented
13#22549876C211yesmaximal, characteristic
14C4×#14523231C211yesmaximal, characteristic, complemented
15C4×Q16×C127C211yesmaximal, characteristic, complemented
16C2×#14523249C2211yescharacteristic
17C2×Q8×D127C2211yescharacteristic
18#16861241C418yesdirect product factor
19C2×#14523238C2211yescharacteristic
20C2×#14523237C2211yescharacteristic
21C2×#14523235C2211yescharacteristic
22C2×#14523231C2211yescharacteristic
23C2×#14523231C2211yescharacteristic
24Q8×Dic127C2211yescharacteristic
25Q8×Dic127C2211yescharacteristic
26C4×Dic254—21no—
27C4×Dic254C2211yescharacteristic
28#16861174—21no—
29#16861174C2211yescharacteristic
30C4×D508—21no—
31C4×D508C2211yescharacteristic
32#16861171—21no—
33#16861171C2211yescharacteristic
34#16861167—21no—
35#16861167C2211yescharacteristic
36C4⋊C4×D127—21no—
37C4⋊C4×D127C2211yescharacteristic
38C42×D127—21no—
39C42×D127—21no—
40C42×D127C2211yescharacteristic
41#16861142C2211yescharacteristic
42#16861141C2211yescharacteristic
43#16861140C2211yescharacteristic
44#16861134C2211yescharacteristic
45#16861133C2211yescharacteristic
46#16861133C2211yescharacteristic
47#16861132C2211yescharacteristic
48#16861131C2211yescharacteristic
49#16861129C2211yescharacteristic
50#16861119C2211yescharacteristic
51#16861119C2211yescharacteristic
52C4×C127⋊C8C2211yescharacteristic
53C2×Q16×C127C2211yescharacteristic
54C4×Q8×C127C2211yescharacteristic
55C4×Q8×C127C2211yescharacteristic
56#107×C127C2211yescharacteristic
57#103×C127C2211yescharacteristic
58#103×C127C2211yescharacteristic
59C4×C8×C127C2211yescharacteristic
60#14523249—22no—
61#14523249C2×C414yes—
62C2×Dic254—21no—
63C2×Dic254C2311yescharacteristic
64Q8×D127—22no—
65Q8×D127C2×C414yescomplemented
66C2×D508—21no—
67C2×D508C2311yescharacteristic
68C2×C4×D127—21no—
69C2×C4×D127—21no—
70C2×C4×D127—21no—
71C2×C4×D127—21no—
72C2×C4×D127—21no—
73C2×C4×D127D411yescharacteristic
74C2×C4×D127D411yescharacteristic
75C2×C4×D127C2311yescharacteristic
76#14523238C2×C414yescomplemented
77#14523237C2×C414yescomplemented
78#14523235C2×C414yescomplemented
79#14523231—22no—
80#14523231C2×C414yescomplemented
81C2×C127⋊C8C2311yescharacteristic
82C2×C127⋊C8C2311yescharacteristic
83C4⋊Dic127—21no—
84C4⋊Dic127—21no—
85C4⋊Dic127C2311yescharacteristic
86C4⋊Dic127C2311yescharacteristic
87Dic127⋊C4—21no—
88Dic127⋊C4—21no—
89Dic127⋊C4—21no—
90(C2×D127)⋊C4—21no—
91(C2×D127)⋊C4—21no—
92(C2×D127)⋊C4—21no—
93C4×Dic127—21no—
94C4×Dic127—21no—
95C4×Dic127—21no—
96C4×Dic127—21no—
97C4×Dic127—21no—
98C4×Dic127D411yescharacteristic
99C4×Dic127D411yescharacteristic
100C4×Dic127C2311yescharacteristic
101C2×Q8×C127C2311yescharacteristic
102C2×Q8×C127C2311yescharacteristic
103Q16×C127C2×C414yescomplemented
104C2×C8×C127C2311yescharacteristic
105C2×C8×C127C2311yescharacteristic
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127C2311yescharacteristic
109C4⋊C4×C127C2311yescharacteristic
110C42×C127—21no—
111C42×C127—21no—
112C42×C127C2311yescharacteristic
113C22×D127—21no—
114C22×D127C2×D411yescharacteristic
115Dic254—21no—
116Dic254—24no—
117Dic254C22×C412yes—
118D508—24no—
119D508—21no—
120D508C22×C412yes—
121C2×Dic127—21no—
122C2×Dic127—21no—
123C2×Dic127—21no—
124C2×Dic127C2×D411yescharacteristic
125C2×Dic127C2×D411yescharacteristic
126C2×Dic127C2×D411yescharacteristic
127C4×D127—24no—
128C4×D127—22no—
129C4×D127—24no—
130C4×D127—41no—
131C4×D127—42no—
132C4×D127—42no—
133C4×D127—42no—
134C4×D127C22×C412yes—
135C4×D127#4112yes—
136C127⋊C8—21no—
137C127⋊C8C22×C412yes—
138Q8×C127—21no—
139Q8×C127—21no—
140Q8×C127C22×C412yes—
141Q8×C127C22×C412yes—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127C2×D411yescharacteristic
147C2×C4×C127C2×D411yescharacteristic
148C2×C4×C127C2411yescharacteristic
149C8×C127—21no—
150C8×C127C22×C412yes—
151C22×C127C22×D411yescharacteristic
152C2×D127—21no—
153C2×D127—21no—
154C2×D127—22no—
155C2×D127—41no—
156C2×D127—41no—
157C2×D127C4×D412yes—
158C4×C127—22no—
159C4×C127—22no—
160C4×C127—21no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127#13712yescomplemented
164C4×C127C23×C411yescharacteristic
165C4×C127C2×#4111yescharacteristic
166Dic127—22no—
167Dic127—21no—
168Dic127—21no—
169Dic127—41no—
170Dic127—41no—
171Dic127C4×D412yes—
172C2×C127C2×C4×D411yescharacteristic
173C2×C127C2×#13711yescharacteristic
174C2×C127#57511yescharacteristic
175D127—22no—
176D127—42no—
177C4×#137—1271nomaximal, Sylow
178C127C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1271no—
180C4×#41—1271no—
181C2×C4×Q8—1271no—
182#441—1271no—
183#441—1271no—
184#440—1271no—
185#440—1271no—
186C4×Q16—1271no—
187C4×Q16D12711yescharacteristic, complemented
188C4×SD16—1271no—
189C4×SD16—1271no—
190#428—1271no—
191#419—1271no—
192#417—1271no—
193C4×M16—1271no—
194C2×#41—1271no—
195C22×Q8—1271no—
196#137—1278no—
197C2×Q16—1271no—
198C2×Q16C2×D12711yescharacteristic
199C2×SD16—1271no—
200C2×SD16—1271no—
201C2×M16—1271no—
202C2×M16—1271no—
203C4×Q8—1271no—
204C4×Q8—1271no—
205C4×Q8—1271no—
206C4×Q8—1271no—
207C4×Q8—2541no—
208C4×Q8—2541no—
209C4×Q8C2×D12711yescharacteristic
210C4×Q8C2×D12711yescharacteristic
211C4×D4—1271no—
212C4×D4—1271no—
213C4×D4—2541no—
214C4×D4—2541no—
215#117—1271no—
216#117—2541no—
217C2×C4⋊C4—1271no—
218C2×C4⋊C4—2541no—
219C2×C42—1271no—
220C2×C42—2541no—
221C2×C42—2541no—
222#107—1271no—
223#107C2×D12711yescharacteristic
224#106—1271no—
225#106—1271no—
226#103—1271no—
227#103—1271no—
228#103—1271no—
229#103—1271no—
230#103C2×D12711yescharacteristic
231#103C2×D12711yescharacteristic
232#102—1271no—
233#102—1271no—
234#97—1271no—
235#97—1271no—
236C4×C8—1271no—
237C4×C8C2×D12711yescharacteristic
238#41—1274no—
239#41—2542no—
240C2×Q8—1274no—
241C2×Q8—1271no—
242C2×Q8—2541no—
243C2×Q8—2542no—
244C2×Q8C22×D12711yescharacteristic
245C2×Q8C22×D12711yescharacteristic
246C2×D4—1271no—
247C2×D4—2541no—
248C22×C4—1271no—
249C22×C4—1271no—
250C22×C4—1271no—
251C22×C4—2541no—
252C22×C4—2541no—
253C22×C4—2541no—
254C22×C4—2541no—
255C22×C4—2541no—
256Q16—1274no—
257Q16C4×D12714yescomplemented
258SD16—1274no—
259SD16—1274no—
260M16—1274no—
261M16—2542no—
262C2×C8—1271no—
263C2×C8—1271no—
264C2×C8C22×D12711yescharacteristic
265C2×C8C22×D12711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1271no—
269C4⋊C4—1271no—
270C4⋊C4—2541no—
271C4⋊C4—2541no—
272C4⋊C4—2541no—
273C4⋊C4—2541no—
274C4⋊C4—2541no—
275C4⋊C4C22×D12711yescharacteristic
276C4⋊C4C22×D12711yescharacteristic
277C22⋊C4—2541no—
278C22⋊C4—2541no—
279C22⋊C4—2541no—
280C42—21no—
281C42—21no—
282C42—1271no—
283C42—1271no—
284C42—1271no—
285C42—2541no—
286C42—2541no—
287C42—2541no—
288C42—2541no—
289C42—2541no—
290C42C22×D12711yescharacteristic
291C23—1271no—
292C23—2541no—
293Q8—21no—
294Q8—21no—
295Q8—1272no—
296Q8—2544no—
297Q8—2541no—
298Q8C2×C4×D12712yes—
299Q8C2×C4×D12712yes—
300D4—1272no—
301D4—2544no—
302D4—2541no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1271no—
308C2×C4—1272no—
309C2×C4—1272no—
310C2×C4—1271no—
311C2×C4—1271no—
312C2×C4—5081no—
313C2×C4—5082no—
314C2×C4—5082no—
315C2×C4—5082no—
316C2×C4—2544no—
317C2×C4—2544no—
318C2×C4—2541no—
319C2×C4—2541no—
320C2×C4—2541no—
321C2×C4—2542no—
322C2×C4D4×D12711yescharacteristic
323C2×C4D4×D12711yescharacteristic
324C2×C4C23×D12711yescharacteristic
325C8—21no—
326C8—1272no—
327C8—2541no—
328C8C2×C4×D12712yes—
329C22—1272no—
330C22—5081no—
331C22—5081no—
332C22—2542no—
333C22—2541no—
334C22—2541no—
335C22C2×D4×D12711yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—1272no—
342C4—5081no—
343C4—5081no—
344C4—2542no—
345C4—2541no—
346C4—2541no—
347C4#1686124112yesdirect product factor
348C4C22×C4×D12711yescharacteristic
349C4#41×D12711yescharacteristic
350C2—5082no—
351C2—2542no—
352C2C4×D4×D12711yescharacteristic
353C2C2×#1686124111yescharacteristic
354C2#2255067311yescharacteristic
subgroupG/H
centerC2×C4D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC4×Q16×C127C2
socleC22×C127C22×D4
prime radicalC2×#14523249C22
cosocleC2×C4×C127C24
hypercenterC4×Q16D127
hypocenterC127C4×#137
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D127C2semidirect
4. #22549983C2semidirect
5. #22549980C2semidirect
6. #22549979C2semidirect
7. #22549975C2semidirect
8. C4×#14523238C2semidirect
9. C4×#14523237C2semidirect
10. C4×#14523235C2semidirect
11. #22549917C2semidirect
12. #22549883C2semidirect
14. C4×#14523231C2semidirect
15. C4×Q16×C127C2semidirect
18. #16861241C4direct (N × H)
65. Q8×D127C2×C4semidirect
76. #14523238C2×C4semidirect
77. #14523237C2×C4semidirect
78. #14523235C2×C4semidirect
80. #14523231C2×C4semidirect
103. Q16×C127C2×C4semidirect
163. C4×C127#137semidirect
178. C127C4×#137semidirect
187. C4×Q16D127semidirect
257. Q16C4×D127semidirect
347. C4#16861241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168612412
C4×#145232492
C4×Q8×D1272
#225499832
#225499802
#225499792
#225499752
C4×#145232382
C4×#145232372
C4×#145232352
#225499172
#225498832
#225498762
C4×#145232312
C4×Q16×C1272
C4×#137127