Finite Group Databasebeta

← C2×#13125364 #16732540

Subgroups — C2×#13125364 #16732540

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×#11719205C212yesmaximal
2#13125364C2116yesmaximal, direct product factor
3C2×#11718517C214yesmaximal, complemented
4C2×#11718519C212yesmaximal, complemented
5C2×#11718516C212yesmaximal, complemented
6C2×#11718625C212yesmaximal
7C2×#11718767C211yesmaximal, characteristic
8C2×#11718762C211yesmaximal, characteristic
9C22×C13×#106C211yesmaximal, characteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C2×#88180C2212yes—
13C2×#88180C2211yescharacteristic
14C2×#88178—24no—
15C22×#6099C2211yescharacteristic
16#11719205—28no—
17#11719205C22116yes—
18C2×#88144—22no—
19C2×#88144C2214yes—
20C2×#88142—22no—
21C2×#88142C2214yes—
22C2×C13×#106C2212yes—
23C2×C13×#106C2212yes—
24C2×C13×#106C2218yes—
25#11718767C2218yes—
26C2×#88058C2212yes—
27C2×#88057C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29#11718762C2218yes—
30C2×#88055C2212yes—
31C2×C8×Dic13C2212yes—
32#11718625C22116yes—
33C2×#88048C2214yes—
34C2×#88047C2214yes—
35#11718519C22116yescomplemented
36#11718517C22132yescomplemented
37#11718516C22116yescomplemented
38C23×C4×C13—22no—
39C23×C4×C13C2311yescharacteristic
40C22×Dic26—24no—
41C22×C8×C13Q818yescomplemented
42C22×C8×C13C2311yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C22×C8×C13C2314yes—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4C2314yes—
48C2×C13×C4⋊C4C2318yes—
49C2×C22⋊Dic13—22no—
50C2×C22⋊Dic13D412yes—
51#88180—24no—
52#88180D414yes—
53#88180C2318yes—
54#88180C2314yes—
55C2×C4⋊Dic13—24no—
56C2×C4⋊Dic13D412yes—
57C2×C4⋊Dic13C2312yes—
58C2×C4⋊Dic13C2312yes—
59#88178—232no—
60C2×#6101—24no—
61C2×#6101—24no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13C2312yes—
64C2×#6099Q818yescomplemented
65C2×#6099C2314yes—
66C22×#1055C2312yes—
67#88144—216no—
68#88144—28no—
69#88144C23116yes—
70#88142—216no—
71#88142—28no—
72#88142C23116yes—
73C13×#106C2318yes—
74C13×#106C2318yes—
75#88058C2318yes—
76#88057C2314yes—
77#88057C2314yes—
78#88055C2318yes—
79C8×Dic13C2318yes—
80#88048C23116yes—
81#88047C23116yes—
82C2×#3163—131nomaximal, Sylow
83C24×C13C2×D411yescharacteristic
84C22×C4×C13—24no—
85C22×C4×C13—28no—
86C22×C4×C13—84no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×Q814yes—
90C22×C4×C13C2×Q814yes—
91C22×C4×C13C2411yescharacteristic
92C22×C4×C13C2412yes—
93C22×Dic13—22no—
94C22×Dic13—22no—
95C22×Dic13C2×D414yes—
96C2×Dic26—216no—
97C2×Dic26—88no—
98C2×C8×C13C2×Q814yes—
99C2×C8×C13C2×Q814yes—
100C2×C8×C13C2×Q8116yescomplemented
101C2×C8×C13C2412yes—
102C2×C8×C13C2412yes—
103C13×C4⋊C4—28no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4C2418yes—
106C22⋊Dic13—28no—
107C22⋊Dic13C2×D418yes—
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—216no—
111C4⋊Dic13C2×D418yes—
112C4⋊Dic13C2414yes—
113C4⋊Dic13C2414yes—
114#6101—216no—
115#6101—216no—
116C4×Dic13—28no—
117C4×Dic13C2×D414yes—
118C4×Dic13C2414yes—
119#6099C2×Q8116yescomplemented
120C2×#1055C2×Q818yes—
121C2×#1055C2414yes—
122C2×#544—132no—
123#3163—1316no—
124C2×#501—134no—
125C2×#499—132no—
126C2×#498—132no—
127C2×#428—132no—
128C2×#427—131no—
129C22×#106D1311yescharacteristic
130C2×#405—131no—
131C23×C13—24no—
132C23×C13C4⋊Q814yes—
133C23×C13C22×D412yes—
134C23×C13C22×D411yescharacteristic
135C2×C4×C13—28no—
136C2×C4×C13—48no—
137C2×C4×C13—88no—
138C2×C4×C13C4⋊Q818yes—
139C2×C4×C13C4⋊Q814yes—
140C2×C4×C13C22×D412yes—
141C2×C4×C13C22×D411yescharacteristic
142C2×C4×C13C22×Q812yes—
143C2×C4×C13C22×Q814yes—
144C2×C4×C13C22×Q812yes—
145C2×C4×C13C22×Q814yes—
146C2×C4×C13C2511yescharacteristic
147C2×Dic13—28no—
148C2×Dic13—24no—
149C2×Dic13—24no—
150C2×Dic13—44no—
151C2×Dic13—44no—
152C2×Dic13C22×D418yes—
153Dic26—816no—
154C8×C13C22×Q814yes—
155C8×C13C22×Q814yes—
156#1055C22×Q818yes—
157C22×M16—131no—
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—131no—
167C2×#117—132no—
168C22×C4⋊C4C2×D1312yes—
169#501—1332no—
170#499—1316no—
171#498—1316no—
172#428—1316no—
173#427—138no—
174C2×#107—132no—
175C2×#107—134no—
176C2×#106—131no—
177C2×#106—131no—
178C2×#106—134no—
179C2×#106C2×D1312yes—
180C2×#106C2×D1312yes—
181C2×#106C2×D1318yes—
182#405—138no—
183C2×#97—132no—
184C2×C4×C8—132no—
185C22×C13—28no—
186C22×C13—24no—
187C22×C13C2×C4⋊Q814yes—
188C22×C13C2×C4⋊Q812yes—
189C22×C13#57714yes—
190C22×C13C23×D411yescharacteristic
191C4×C13—48no—
192C4×C13C2×C4⋊Q814yes—
193C4×C13C2×C4⋊Q812yes—
194C4×C13C23×Q811yescharacteristic
195C4×C13C23×Q811yescharacteristic
196Dic13—28no—
197Dic13—44no—
198Dic13—44no—
199C22×Q8—264no—
200C23×C4—22no—
201C23×C4C22×D1311yescharacteristic
202C2×M16—138no—
203C2×M16—134no—
204C22×C8—132no—
205C22×C8Dic2618yescomplemented
206C22×C8C22×D1311yescharacteristic
207C22×C8C22×D1311yescharacteristic
208C22×C8C22×D1314yes—
209C4⋊Q8—1316no—
210C4⋊Q8—268no—
211C4⋊Q8—2616no—
212#125—1316no—
213#125—268no—
214#125—2616no—
215C22⋊Q8—2632no—
216#117—134no—
217#117—134no—
218#117—138no—
219#117—264no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—132no—
223C2×C4⋊C4—132no—
224C2×C4⋊C4—132no—
225C2×C4⋊C4—264no—
226C2×C4⋊C4—264no—
227C2×C4⋊C4—264no—
228C2×C4⋊C4C22×D1314yes—
229C2×C4⋊C4C22×D1318yes—
230C2×C22⋊C4—132no—
231C2×C22⋊C4—262no—
232C2×C42—132no—
233C2×C42—262no—
234#107—138no—
235#107—1316no—
236#106—134no—
237#106—134no—
238#106—1316no—
239#106C22×D1318yes—
240#106C22×D1318yes—
241#97—138no—
242C4×C8—138no—
243C2×C13—24no—
244C2×C13#316314yescomplemented
245C2×C13C22×C4⋊Q811yescharacteristic
246C2×C13C2×#57712yes—
247C24D4×D1311yescharacteristic
248C2×Q8—2616no—
249C2×Q8—1048no—
250C22×C4—24no—
251C22×C4—28no—
252C22×C4—84no—
253C22×C4—134no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4C2×Dic2614yes—
257C22×C4D4×D1312yes—
258C22×C4D4×D1311yescharacteristic
259C22×C4Q8×D1314yes—
260C22×C4C23×D1312yes—
261C22×C4C23×D1311yescharacteristic
262M16—1316no—
263C2×C8—138no—
264C2×C8—134no—
265C2×C8C2×Dic2614yes—
266C2×C8C2×Dic2614yes—
267C2×C8C2×Dic26116yescomplemented
268C2×C8C23×D1312yes—
269C2×C8C23×D1312yes—
270C4⋊C4—24no—
271C4⋊C4—28no—
272C4⋊C4—138no—
273C4⋊C4—134no—
274C4⋊C4—134no—
275C4⋊C4—2616no—
276C4⋊C4—2616no—
277C4⋊C4—2616no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4C23×D1318yes—
281C22⋊C4—138no—
282C22⋊C4—268no—
283C42—134no—
284C42—134no—
285C42—268no—
286C13C2×#316311yescharacteristic, complemented, Sylow
287C23—24no—
288C23#8814214yes—
289C23C2×D4×D1312yes—
290C23C2×D4×D1311yescharacteristic
291Q8—10416no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4—88no—
295C2×C4—138no—
296C2×C4—268no—
297C2×C4—264no—
298C2×C4—264no—
299C2×C4—524no—
300C2×C4—524no—
301C2×C4#8814218yes—
302C2×C4#8814214yes—
303C2×C4C22×Dic2612yes—
304C2×C4C22×Dic2614yes—
305C2×C4C2×D4×D1311yescharacteristic
306C2×C4C2×D4×D1312yes—
307C2×C4C2×Q8×D1312yes—
308C2×C4C2×Q8×D1314yes—
309C2×C4C24×D1311yescharacteristic
310C8—138no—
311C8C22×Dic2614yes—
312C8C22×Dic2614yes—
313C22—24no—
314C22—28no—
315C22C2×#8814214yes—
316C22C2×#8814212yes—
317C22#1171946714yes—
318C22C22×D4×D1311yescharacteristic
319C4—48no—
320C4—268no—
321C4—524no—
322C4—524no—
323C4C2×#8814212yes—
324C4C2×#8814214yes—
325C4C23×Dic2611yescharacteristic
326C4C22×Q8×D1311yescharacteristic
327C2—24no—
328C2#1312536414yesdirect product factor
329C2C22×#8814211yescharacteristic
330C2C2×#1171946712yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#106C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#106D13
hypocenterC13C2×#3163
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. #13125364C2direct (N × H)
3. C2×#11718517C2semidirect
4. C2×#11718519C2semidirect
5. C2×#11718516C2semidirect
35. #11718519C22semidirect
36. #11718517C22semidirect
37. #11718516C22semidirect
41. C22×C8×C13Q8semidirect
64. C2×#6099Q8semidirect
100. C2×C8×C13C2×Q8semidirect
119. #6099C2×Q8semidirect
205. C22×C8Dic26semidirect
244. C2×C13#3163semidirect
267. C2×C8C2×Dic26semidirect
286. C13C2×#3163semidirect
328. C2#13125364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192052
#131253642
C2×#117185172
C2×#117185192
C2×#117185162
C2×#117186252
C2×#117187672
C2×#117187622
C22×C13×#1062
C2×#316313