Finite Group Databasebeta

← C2×#22550064 #30648115

Subgroups — C2×#22550064 #30648115

Order 16256.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16861254C211yesmaximal, characteristic, complemented
2C2×#16861179C212yesmaximal, complemented
3C2×#16861177C211yesmaximal, characteristic, complemented
4#22550064C218yesmaximal, direct product factor
5C2×#16861123C212yesmaximal, complemented
6C2×#99×C127C211yesmaximal, characteristic, complemented
7C24×D127C2211yescharacteristic, complemented
8#16861254—24no—
9#16861254—22no—
10#16861254C2214yescomplemented
11C2×#14523248—21no—
12C2×#14523247—22no—
13C22×D508—22no—
14C22×C22⋊D127—21no—
15C22×C22⋊D127—21no—
16C22×C22⋊D127C2212yes—
17C2×D4×D127—22no—
18#16861179—24no—
19#16861179C2218yescomplemented
20#16861177—22no—
21#16861177C2214yescomplemented
22C2×C22⋊Dic127C2211yescharacteristic, complemented
23C2×(C2×D127)⋊C4—22no—
24C2×(C2×D127)⋊C4—21no—
25#16861123C2218yescomplemented
26C22×D4×C127C2211yescharacteristic
27C2×C22⋊C4×C127C2212yescomplemented
28#99×C127C2214yescomplemented
29C23×D127—21no—
30C23×D127—21no—
31C23×D127—22no—
32C23×D127—21no—
33C23×D127—22no—
34C23×D127—44no—
35C23×D127D412yescomplemented
36C23×D127C2312yescomplemented
37#14523248—24no—
38#14523248—24no—
39#14523247—28no—
40#14523247—28no—
41C2×Dic254—21no—
42C2×D508—21no—
43C2×D508—28no—
44C2×D508—48no—
45C2×C22⋊D127—22no—
46C2×C22⋊D127—24no—
47C2×C22⋊D127—22no—
48C2×C22⋊D127—22no—
49C2×C22⋊D127—22no—
50C2×C22⋊D127—22no—
51C2×C22⋊D127—24no—
52C2×C22⋊D127—24no—
53C2×C22⋊D127—44no—
54C2×C22⋊D127D414yescomplemented
55C2×C22⋊D127C2314yes—
56D4×D127—28no—
57D4×D127—28no—
58C22×Dic127—21no—
59C22×Dic127—21no—
60C22×Dic127D412yescomplemented
61C2×C4×D127—22no—
62C22⋊Dic127—21no—
63C22⋊Dic127C2312yescomplemented
64(C2×D127)⋊C4—28no—
65(C2×D127)⋊C4—24no—
66C24×C127D411yescharacteristic, complemented
67C24×C127C2311yescharacteristic
68C2×D4×C127—22no—
69C2×D4×C127—22no—
70C2×D4×C127D412yescomplemented
71C2×D4×C127C2312yes—
72C22×C4×C127—22no—
73C22×C4×C127D411yescharacteristic, complemented
74C22⋊C4×C127—22no—
75C22⋊C4×C127C2314yescomplemented
76C22×D127—24no—
77C22×D127—28no—
78C22×D127—22no—
79C22×D127—22no—
80C22×D127—24no—
81C22×D127—24no—
82C22×D127—22no—
83C22×D127—44no—
84C22×D127—44no—
85C22×D127—48no—
86C22×D127—44no—
87C22×D127—42no—
88C22×D127—41no—
89C22×D127—42no—
90C22×D127—41no—
91C22×D127—44no—
92C22×D127—82no—
93C22×D127C2×D414yescomplemented
94Dic254—24no—
95D508—24no—
96D508—416no—
97C22⋊D127—28no—
98C22⋊D127—24no—
99C22⋊D127—24no—
100C22⋊D127—24no—
101C22⋊D127—24no—
102C22⋊D127—48no—
103C2×Dic127—24no—
104C2×Dic127—22no—
105C2×Dic127—22no—
106C2×Dic127—22no—
107C2×Dic127—42no—
108C2×Dic127C2×D414yescomplemented
109C4×D127—28no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127—42no—
113C23×C127—42no—
114C23×C127C2×D412yes—
115C23×C127C2×D412yes—
116C23×C127C2×D411yescharacteristic
117C23×C127C2×D411yescharacteristic
118C23×C127C2×D412yescomplemented
119C23×C127C2411yescharacteristic
120D4×C127—24no—
121D4×C127—24no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—24no—
125C2×C4×C127—44no—
126C2×C4×C127C2×D412yescomplemented
127C22×C127—24no—
128C22×C127—22no—
129C22×C127—22no—
130C22×C127—42no—
131C22×C127—41no—
132C22×C127—41no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—81no—
136C22×C127#12011yescharacteristic
137C22×C127#12012yes—
138C22×C127#12011yescharacteristic
139C22×C127C22×D412yes—
140C22×C127C22×D411yescharacteristic
141C2×D127—24no—
142C2×D127—28no—
143C2×D127—24no—
144C2×D127—42no—
145C2×D127—44no—
146C2×D127—48no—
147C2×D127—44no—
148C2×D127—42no—
149C2×D127—44no—
150C2×D127—44no—
151C2×D127—44no—
152C2×D127—82no—
153C2×D127—84no—
154C4×C127—22no—
155C4×C127—44no—
156Dic127—24no—
157Dic127—42no—
158C2×C127—21no—
159C2×C127—22no—
160C2×C127—22no—
161C2×C127—21no—
162C2×C127—42no—
163C2×C127B(4,𝔽2)12yescomplemented
164C2×C127C2×#12011yescharacteristic
165D127—44no—
166D127—44no—
167C2×B(4,𝔽2)—1271nomaximal, Sylow
168C127C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
169C2×H(5,𝔽2)—1271no—
170C2×#120—1271no—
171C2×#120—1272no—
172B(4,𝔽2)—1278no—
173C2×#99—1272no—
174C2×#99D12711yescharacteristic, complemented
175C25—1271no—
176H(5,𝔽2)—1274no—
177H(5,𝔽2)—2544no—
178H(5,𝔽2)—2542no—
179C2×#41—2542no—
180C2×#41—2541no—
181C22×D4—1272no—
182C22×D4—2542no—
183C22×D4—2542no—
184C22×D4—2541no—
185C22×D4—2541no—
186C22×D4C2×D12711yescharacteristic
187#120—1274no—
188#120—1278no—
189#120—2544no—
190#120—2542no—
191C2×C22⋊C4—1271no—
192C2×C22⋊C4—2542no—
193C2×C22⋊C4—2541no—
194C2×C22⋊C4C2×D12712yescomplemented
195#99—1278no—
196#99C2×D12714yescomplemented
197C24—1272no—
198C24—1272no—
199C24—5084no—
200C24—2541no—
201C24—2542no—
202C24—2541no—
203C24—2542no—
204C24—2541no—
205C24D50811yescharacteristic, complemented
206C24C22×D12711yescharacteristic
207#41—2544no—
208#41—2548no—
209#41—2548no—
210#41—2544no—
211C2×Q8—2541no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—1274no—
215C2×D4—1274no—
216C2×D4—5088no—
217C2×D4—5084no—
218C2×D4—2548no—
219C2×D4—2541no—
220C2×D4—2548no—
221C2×D4—2548no—
222C2×D4—2544no—
223C2×D4—2542no—
224C2×D4—2544no—
225C2×D4—2542no—
226C2×D4—2542no—
227C2×D4—2542no—
228C2×D4—2542no—
229C2×D4—2544no—
230C2×D4D50812yescomplemented
231C2×D4C22×D12712yes—
232C22×C4—22no—
233C22×C4—1272no—
234C22×C4—2542no—
235C22×C4—2541no—
236C22×C4—2541no—
237C22×C4D50811yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—1272no—
240C22⋊C4—2548no—
241C22⋊C4—2541no—
242C22⋊C4—2544no—
243C22⋊C4C22×D12714yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—1274no—
249C23—10162no—
250C23—5084no—
251C23—5084no—
252C23—5082no—
253C23—5088no—
254C23—5084no—
255C23—5084no—
256C23—5081no—
257C23—5082no—
258C23—5081no—
259C23—2544no—
260C23—2548no—
261C23—2544no—
262C23—2542no—
263C23—2544no—
264C23—2542no—
265C23—2542no—
266C23D4×D12712yes—
267C23D4×D12712yes—
268C23C2×D50811yescharacteristic
269C23C2×D50811yescharacteristic
270C23C2×D50812yescomplemented
271C23C23×D12711yescharacteristic
272Q8—2544no—
273D4—24no—
274D4—24no—
275D4—50816no—
276D4—5088no—
277D4—2544no—
278D4—2548no—
279D4—2544no—
280D4—2544no—
281D4—2544no—
282D4—2544no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—1274no—
288C2×C4—5082no—
289C2×C4—2548no—
290C2×C4—2542no—
291C2×C4—2544no—
292C2×C4—2542no—
293C2×C4—2542no—
294C2×C4C2×D50812yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—10162no—
305C22—10164no—
306C22—5084no—
307C22—5084no—
308C22—5082no—
309C22—5084no—
310C22—5088no—
311C22—5084no—
312C22—5084no—
313C22—5082no—
314C22—2548no—
315C22—2544no—
316C22—2544no—
317C22#1686117911yescharacteristic
318C22#1686117912yes—
319C22#1686117911yescharacteristic
320C22C2×D4×D12712yes—
321C22C22×D50811yescharacteristic
322C4—22no—
323C4—44no—
324C4—5082no—
325C4—2544no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—5084no—
332C2—5084no—
333C2#2255006412yesdirect product factor
334C2C2×#1686117911yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC23×C127C24
FrattiniC23C23×D127
FittingC2×#99×C127C2
socleC22×C127#120
hypercenterC2×#99D127
hypocenterC127C2×B(4,𝔽2)
LCSG ▷ C23×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#16861254C2semidirect
2. C2×#16861179C2semidirect
3. C2×#16861177C2semidirect
4. #22550064C2direct (N × H)
5. C2×#16861123C2semidirect
6. C2×#99×C127C2semidirect
7. C24×D127C22semidirect
10. #16861254C22semidirect
19. #16861179C22semidirect
21. #16861177C22semidirect
22. C2×C22⋊Dic127C22semidirect
25. #16861123C22semidirect
27. C2×C22⋊C4×C127C22semidirect
28. #99×C127C22semidirect
35. C23×D127D4semidirect
36. C23×D127C23semidirect
54. C2×C22⋊D127D4semidirect
60. C22×Dic127D4semidirect
63. C22⋊Dic127C23semidirect
66. C24×C127D4semidirect
70. C2×D4×C127D4semidirect
73. C22×C4×C127D4semidirect
75. C22⋊C4×C127C23semidirect
93. C22×D127C2×D4semidirect
108. C2×Dic127C2×D4semidirect
118. C23×C127C2×D4semidirect
126. C2×C4×C127C2×D4semidirect
163. C2×C127B(4,𝔽2)semidirect
168. C127C2×B(4,𝔽2)semidirect
174. C2×#99D127semidirect
194. C2×C22⋊C4C2×D127semidirect
196. #99C2×D127semidirect
205. C24D508semidirect
230. C2×D4D508semidirect
237. C22×C4D508semidirect
243. C22⋊C4C22×D127semidirect
270. C23C2×D508semidirect
294. C2×C4C2×D508semidirect
333. C2#22550064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168612542
C2×#168611792
C2×#168611772
#225500642
C2×#168611232
C2×#99×C1272
C2×B(4,𝔽2)127