Finite Group Databasebeta

← C2×#13125367 #16732543

Subgroups — C2×#13125367 #16732543

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C212yesmaximal
2#13125367C2116yesmaximal, direct product factor
3C2×#11718363C214yesmaximal, complemented
4C2×#11718344C212yesmaximal, complemented
5C2×#11718341C212yesmaximal, complemented
6C2×#11718782C212yesmaximal
7C2×#11718767C211yesmaximal, characteristic
8C22×#88057C211yesmaximal, characteristic
9C2×C13×#405C211yesmaximal, characteristic
10C22×C13×M16C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2212yes—
14C22×C4⋊Dic13C2212yes—
15#11719224—28no—
16#11719224C22116yes—
17C2×#88144—22no—
18C2×#88142—22no—
19C2×#88132—24no—
20C2×#88124C2214yes—
21C2×#88123C2214yes—
22C13×#405C2218yes—
23C2×C13×#97C2212yes—
24C2×C4×C8×C13C2212yes—
25#11718782C22116yes—
26#11718767C2218yes—
27C2×#88058C2212yes—
28C2×#88058C2214yes—
29C2×#88057C2212yes—
30C2×#88057C2212yes—
31C2×#88057C2218yes—
32C2×#88057C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88057C2214yes—
35#11718363C22132yescomplemented
36#11718344C22116yescomplemented
37#11718341C22116yescomplemented
38C23×C4×C13C2311yescharacteristic
39C23×Dic13—22no—
40C22×Dic26—24no—
41C2×C13×M16Q818yescomplemented
42C2×C13×M16C2314yes—
43C22×C8×C13Q818yescomplemented
44C22×C8×C13C2311yescharacteristic
45C22×C8×C13C2312yes—
46C22×C8×C13C2311yescharacteristic
47C22×C8×C13C2314yes—
48C13×#117D414yes—
49C13×#117C2314yes—
50C2×C13×C4⋊C4D412yes—
51C2×C13×C22⋊C4D412yes—
52C2×C42×C13C2312yes—
53C2×C22⋊Dic13—22no—
54#88180—24no—
55#88180C2318yes—
56C2×C4⋊Dic13—24no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—24no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2314yes—
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2318yes—
63C2×#6101—24no—
64C2×#6101—24no—
65C2×C4×Dic13—22no—
66#88144—216no—
67#88142—216no—
68#88132—232no—
69#88124—28no—
70#88124C23116yes—
71#88123—28no—
72#88123C23116yes—
73C13×#97C2318yes—
74C4×C8×C13C2318yes—
75#88058C2318yes—
76#88058C23116yes—
77#88057C2318yes—
78#88057C2318yes—
79#88057C2314yes—
80#88057C2314yes—
81#88057C23116yes—
82C2×#3163—131nomaximal, Sylow
83C24×C13C2×D411yescharacteristic
84C22×C4×C13C2×D414yes—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D412yes—
87C22×C4×C13C2×Q814yes—
88C22×C4×C13C2×Q814yes—
89C22×C4×C13C2411yescharacteristic
90C22×C4×C13C2412yes—
91C22×Dic13—22no—
92C22×Dic13—22no—
93C22×Dic13—24no—
94C22×Dic13—28no—
95C22×Dic13—84no—
96C2×Dic26—216no—
97C2×Dic26—88no—
98C13×M16C2×Q8116yescomplemented
99C2×C8×C13C2×Q814yes—
100C2×C8×C13C2×Q814yes—
101C2×C8×C13C2×Q818yes—
102C2×C8×C13C2×Q8116yescomplemented
103C2×C8×C13C2412yes—
104C2×C8×C13C2414yes—
105C2×C8×C13C2412yes—
106C13×C4⋊C4C2×D418yes—
107C13×C22⋊C4C2×D418yes—
108C42×C13C2×D414yes—
109C42×C13C2414yes—
110C22⋊Dic13—28no—
111C4⋊Dic13—22no—
112C4⋊Dic13—24no—
113C4⋊Dic13—216no—
114C4⋊Dic13—22no—
115C4⋊Dic13—28no—
116C4⋊Dic13C2414yes—
117C4⋊Dic13C2418yes—
118C4⋊Dic13C2414yes—
119#6101—216no—
120#6101—216no—
121C4×Dic13—28no—
122C2×#544—132no—
123#3163—1316no—
124C2×#501—134no—
125C2×#499—132no—
126C2×#498—132no—
127C2×#428—132no—
128C2×#427—131no—
129C22×#106—131no—
130C2×#405D1311yescharacteristic
131C23×C13—24no—
132C23×C13C4⋊Q814yes—
133C23×C13C22×D412yes—
134C23×C13C22×D411yescharacteristic
135C2×C4×C13—28no—
136C2×C4×C13C4⋊Q818yes—
137C2×C4×C13C4⋊Q814yes—
138C2×C4×C13C22×D418yes—
139C2×C4×C13C22×D412yes—
140C2×C4×C13C22×D411yescharacteristic
141C2×C4×C13C22×Q812yes—
142C2×C4×C13C22×Q812yes—
143C2×C4×C13C22×Q814yes—
144C2×C4×C13C22×Q814yes—
145C2×C4×C13C2511yescharacteristic
146C2×Dic13—24no—
147C2×Dic13—24no—
148C2×Dic13—28no—
149C2×Dic13—44no—
150C2×Dic13—48no—
151C2×Dic13—44no—
152C2×Dic13—88no—
153Dic26—816no—
154C8×C13C22×Q814yes—
155C8×C13C22×Q814yes—
156C8×C13C22×Q818yes—
157C22×M16C2×D1311yescharacteristic
158C23×C8C2×D1311yescharacteristic
159#544—1316no—
160#544—268no—
161C2×C4⋊Q8—134no—
162C2×C4⋊Q8—262no—
163C2×#125—134no—
164C2×#125—262no—
165C2×C22⋊Q8—264no—
166C2×#117—132no—
167C2×#117C2×D1311yescharacteristic
168C22×C4⋊C4—132no—
169#501—1332no—
170#499—1316no—
171#498—1316no—
172#428—1316no—
173#427—138no—
174C2×#107—134no—
175C2×#107—132no—
176C2×#106—131no—
177C2×#106—132no—
178C2×#106—134no—
179C2×#106—131no—
180C2×#106—132no—
181C2×#106—138no—
182#405C2×D1318yes—
183C2×#97C2×D1312yes—
184C2×C4×C8C2×D1312yes—
185C22×C13—28no—
186C22×C13—24no—
187C22×C13C2×C4⋊Q814yes—
188C22×C13C2×C4⋊Q812yes—
189C22×C13#57714yes—
190C22×C13C23×D411yescharacteristic
191C4×C13—28no—
192C4×C13C2×C4⋊Q814yes—
193C4×C13C2×C4⋊Q812yes—
194C4×C13C23×Q811yescharacteristic
195C4×C13C23×Q811yescharacteristic
196Dic13—44no—
197Dic13—48no—
198Dic13—44no—
199C22×Q8—264no—
200C23×C4—262no—
201C23×C4C22×D1311yescharacteristic
202C2×M16Dic2618yescomplemented
203C2×M16C22×D1314yes—
204C22×C8Dic2618yescomplemented
205C22×C8C22×D1311yescharacteristic
206C22×C8C22×D1311yescharacteristic
207C22×C8C22×D1312yes—
208C22×C8C22×D1314yes—
209C4⋊Q8—1316no—
210C4⋊Q8—2616no—
211C4⋊Q8—268no—
212#125—1316no—
213#125—2616no—
214#125—268no—
215C22⋊Q8—2632no—
216#117—138no—
217#117—264no—
218#117D5214yes—
219#117C22×D1314yes—
220C2×C4⋊C4—134no—
221C2×C4⋊C4—138no—
222C2×C4⋊C4—132no—
223C2×C4⋊C4—132no—
224C2×C4⋊C4—262no—
225C2×C4⋊C4—264no—
226C2×C4⋊C4—264no—
227C2×C4⋊C4—264no—
228C2×C4⋊C4—264no—
229C2×C4⋊C4D5212yes—
230C2×C22⋊C4—262no—
231C2×C22⋊C4D5212yes—
232C2×C42—262no—
233C2×C42C22×D1312yes—
234#107—138no—
235#107—1316no—
236#106—138no—
237#106—138no—
238#106—134no—
239#106—134no—
240#106—1316no—
241#97C22×D1318yes—
242C4×C8C22×D1318yes—
243C2×C13—24no—
244C2×C13#316314yescomplemented
245C2×C13C22×C4⋊Q811yescharacteristic
246C2×C13C2×#57712yes—
247C24C2×D5211yescharacteristic
248C2×Q8—2616no—
249C2×Q8—1048no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—264no—
253C22×C4—268no—
254C22×C4—1044no—
255C22×C4C2×Dic2614yes—
256C22×C4C2×Dic2614yes—
257C22×C4C2×D5214yes—
258C22×C4C2×D5212yes—
259C22×C4C2×D5211yescharacteristic
260C22×C4C23×D1312yes—
261C22×C4C23×D1311yescharacteristic
262M16C2×Dic26116yescomplemented
263C2×C8C2×Dic2614yes—
264C2×C8C2×Dic2614yes—
265C2×C8C2×Dic2618yes—
266C2×C8C2×Dic26116yescomplemented
267C2×C8C23×D1312yes—
268C2×C8C23×D1314yes—
269C2×C8C23×D1312yes—
270C4⋊C4—138no—
271C4⋊C4—134no—
272C4⋊C4—134no—
273C4⋊C4—268no—
274C4⋊C4—264no—
275C4⋊C4—262no—
276C4⋊C4—262no—
277C4⋊C4—2616no—
278C4⋊C4—2616no—
279C4⋊C4—2616no—
280C4⋊C4C2×D5218yes—
281C22⋊C4—268no—
282C22⋊C4C2×D5218yes—
283C42—268no—
284C42C2×D5214yes—
285C42C23×D1314yes—
286C13C2×#316311yescharacteristic, complemented, Sylow
287C23—24no—
288C23#8812314yes—
289C23C22×D5212yes—
290C23C22×D5211yescharacteristic
291Q8—10416no—
292C2×C4—28no—
293C2×C4—264no—
294C2×C4—264no—
295C2×C4—268no—
296C2×C4—524no—
297C2×C4—528no—
298C2×C4—524no—
299C2×C4—1048no—
300C2×C4#8812318yes—
301C2×C4#8812314yes—
302C2×C4C22×Dic2612yes—
303C2×C4C22×Dic2612yes—
304C2×C4C22×Dic2614yes—
305C2×C4C22×Dic2614yes—
306C2×C4C22×D5218yes—
307C2×C4C22×D5212yes—
308C2×C4C22×D5211yescharacteristic
309C2×C4C24×D1311yescharacteristic
310C8C22×Dic2614yes—
311C8C22×Dic2614yes—
312C8C22×Dic2618yes—
313C22—24no—
314C22—28no—
315C22C2×#8812314yes—
316C22C2×#8812312yes—
317C22#1171945614yes—
318C22C23×D5211yescharacteristic
319C4—28no—
320C4—524no—
321C4—528no—
322C4—524no—
323C4C2×#8812312yes—
324C4C2×#8812314yes—
325C4C23×Dic2611yescharacteristic
326C4C23×Dic2611yescharacteristic
327C2—24no—
328C2#1312536714yesdirect product factor
329C2C22×#8812311yescharacteristic
330C2C2×#1171945612yes—
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#405C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#405D13
hypocenterC13C2×#3163
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #13125367C2direct (N × H)
3. C2×#11718363C2semidirect
4. C2×#11718344C2semidirect
5. C2×#11718341C2semidirect
35. #11718363C22semidirect
36. #11718344C22semidirect
37. #11718341C22semidirect
41. C2×C13×M16Q8semidirect
43. C22×C8×C13Q8semidirect
98. C13×M16C2×Q8semidirect
102. C2×C8×C13C2×Q8semidirect
202. C2×M16Dic26semidirect
204. C22×C8Dic26semidirect
244. C2×C13#3163semidirect
262. M16C2×Dic26semidirect
266. C2×C8C2×Dic26semidirect
286. C13C2×#3163semidirect
328. C2#13125367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192242
#131253672
C2×#117183632
C2×#117183442
C2×#117183412
C2×#117187822
C2×#117187672
C22×#880572
C2×C13×#4052
C2×#316313