Finite Group Databasebeta

← C2×#13125348 #16732522

Subgroups — C2×#13125348 #16732522

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719222C212yesmaximal
2#13125348C2116yesmaximal, direct product factor
3C2×#11718535C212yesmaximal, complemented
4C2×#11718539C212yesmaximal, complemented
5C2×#11718519C212yesmaximal, complemented
6C2×#11718516C212yesmaximal, complemented
7C2×#11718767C211yesmaximal, characteristic
8C2×#11718659C212yesmaximal
9C22×C8×Dic13C211yesmaximal, characteristic
10C2×C13×#427C211yesmaximal, characteristic
11C23×C8×C13C2211yescharacteristic
12C2×C13×#117C2212yes—
13C2×#88180C2212yes—
14C22×C4×Dic13C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16#11719222—28no—
17#11719222C22116yes—
18C2×#88144C2214yes—
19C2×#88142C2214yes—
20C2×#88132—24no—
21C2×C4×Dic26—24no—
22C13×#427C2218yes—
23C2×C13×#107C2212yes—
24C2×C13×#106C2212yes—
25#11718767C2218yes—
26C2×#88058C2212yes—
27C2×#88057C2212yes—
28C2×C8×Dic13C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30C2×C8×Dic13C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32C2×C8×Dic13C2218yes—
33#11718659C22116yes—
34C2×#88048C2214yes—
35C2×#88047C2214yes—
36#11718539C22116yescomplemented
37#11718535C22116yescomplemented
38#11718519C22116yescomplemented
39#11718516C22116yescomplemented
40C23×C4×C13C2311yescharacteristic
41C23×Dic13D412yes—
42C22×Dic26—24no—
43C22×C8×C13Q818yescomplemented
44C22×C8×C13C2311yescharacteristic
45C22×C8×C13C2311yescharacteristic
46C22×C8×C13C2314yes—
47C13×#117—24no—
48C13×#117C2318yes—
49C2×C13×C4⋊C4C2314yes—
50C2×C13×C22⋊C4—22no—
51C2×C42×C13—22no—
52C2×C22⋊Dic13—22no—
53#88180—24no—
54#88180C2318yes—
55C2×C4⋊Dic13—24no—
56C2×C4⋊Dic13C2314yes—
57C2×#6101—24no—
58C2×#6101—24no—
59C2×C4×Dic13—22no—
60C2×C4×Dic13D412yes—
61C2×C4×Dic13D414yes—
62C2×C4×Dic13C2311yescharacteristic
63C2×C4×Dic13C2311yescharacteristic
64C2×C4×Dic13C2314yes—
65C22×#1055Q818yescomplemented
66C22×#1055C2311yescharacteristic
67C22×#1055C2311yescharacteristic
68C22×#1055C2314yes—
69#88144—28no—
70#88144C23116yes—
71#88142—28no—
72#88142C23116yes—
73#88132—232no—
74C4×Dic26—232no—
75C13×#107C2318yes—
76C13×#106C2318yes—
77#88058C2318yes—
78#88057C2318yes—
79C8×Dic13C2314yes—
80C8×Dic13C2314yes—
81C8×Dic13C2314yes—
82C8×Dic13C2314yes—
83#88048C23116yes—
84#88047C23116yes—
85C2×#3160—131nomaximal, Sylow
86C24×C13C2×D411yescharacteristic
87C22×C4×C13—24no—
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×Q814yes—
91C22×C4×C13C2×Q814yes—
92C22×C4×C13C2411yescharacteristic
93C22×C4×C13C2412yes—
94C22×Dic13—28no—
95C22×Dic13—24no—
96C22×Dic13C2×D418yes—
97C22×Dic13C2×D412yes—
98C22×Dic13C2×D412yes—
99C2×Dic26—216no—
100C2×Dic26—416no—
101C2×C8×C13C2×Q814yes—
102C2×C8×C13C2×Q814yes—
103C2×C8×C13C2×Q8116yescomplemented
104C2×C8×C13C2412yes—
105C2×C8×C13C2412yes—
106C13×C4⋊C4—24no—
107C13×C4⋊C4C2418yes—
108C13×C22⋊C4—28no—
109C42×C13—28no—
110C22⋊Dic13—28no—
111C4⋊Dic13—24no—
112C4⋊Dic13—216no—
113C4⋊Dic13C2418yes—
114#6101—216no—
115#6101—216no—
116C4×Dic13—28no—
117C4×Dic13C2×D418yes—
118C4×Dic13C2×D412yes—
119C4×Dic13C2×D412yes—
120C4×Dic13C2412yes—
121C4×Dic13C2412yes—
122C2×#1055C2×Q814yes—
123C2×#1055C2×Q814yes—
124C2×#1055C2×Q8116yescomplemented
125C2×#1055C2412yes—
126C2×#1055C2412yes—
127C2×#533—132no—
128#3160—1316no—
129C2×#500—132no—
130C2×#499—132no—
131C2×#499—132no—
132C2×#498—132no—
133C2×#427—131no—
134C2×#427—132no—
135C2×#427D1311yescharacteristic
136C22×C4×C8—131no—
137C23×C13—24no—
138C23×C13C4⋊Q814yes—
139C23×C13C22×D412yes—
140C23×C13C22×D411yescharacteristic
141C2×C4×C13—28no—
142C2×C4×C13—48no—
143C2×C4×C13C4⋊Q818yes—
144C2×C4×C13C4⋊Q814yes—
145C2×C4×C13C22×D412yes—
146C2×C4×C13C22×D411yescharacteristic
147C2×C4×C13C22×Q812yes—
148C2×C4×C13C22×Q814yes—
149C2×C4×C13C22×Q812yes—
150C2×C4×C13C22×Q814yes—
151C2×C4×C13C2511yescharacteristic
152C2×Dic13—24no—
153C2×Dic13—216no—
154C2×Dic13—28no—
155C2×Dic13—48no—
156C2×Dic13#13518yes—
157C2×Dic13C22×D414yes—
158C2×Dic13C22×D414yes—
159Dic26—432no—
160C8×C13C22×Q814yes—
161C8×C13C22×Q814yes—
162#1055C22×Q814yes—
163#1055C22×Q814yes—
164C23×C8—131no—
165C23×C8C2×D1311yescharacteristic
166#533—1316no—
167#533—268no—
168C2×C4⋊Q8—134no—
169C2×#125—134no—
170C2×C22⋊Q8—264no—
171C2×C4×Q8—264no—
172C2×#117—132no—
173C2×#117C2×D1312yes—
174C22×C42—131no—
175#500—1316no—
176#499—1316no—
177#499—1316no—
178#498—1316no—
179#427—138no—
180#427—1316no—
181#427C2×D1318yes—
182C2×#107—132no—
183C2×#107—134no—
184C2×#107C2×D1312yes—
185C2×#106—132no—
186C2×#106—134no—
187C2×#106C2×D1312yes—
188C2×C4×C8—131no—
189C2×C4×C8—131no—
190C2×C4×C8—131no—
191C2×C4×C8—131no—
192C2×C4×C8—138no—
193C22×C13—28no—
194C22×C13—24no—
195C22×C13C2×C4⋊Q814yes—
196C22×C13C2×C4⋊Q812yes—
197C22×C13C2×#13514yes—
198C22×C13C23×D411yescharacteristic
199C4×C13—48no—
200C4×C13C2×C4⋊Q814yes—
201C4×C13C2×C4⋊Q812yes—
202C4×C13C23×Q811yescharacteristic
203C4×C13C23×Q811yescharacteristic
204Dic13—24no—
205Dic13—48no—
206Dic13C2×#13518yes—
207C22×Q8—264no—
208C23×C4—132no—
209C23×C4C22×D1311yescharacteristic
210C22×C8—138no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—134no—
214C22×C8Dic2618yescomplemented
215C22×C8C22×D1311yescharacteristic
216C22×C8C22×D1311yescharacteristic
217C22×C8C22×D1314yes—
218C4⋊Q8—1316no—
219C4⋊Q8—268no—
220#125—1316no—
221#125—268no—
222C22⋊Q8—2632no—
223C4×Q8—2632no—
224#117—24no—
225#117—138no—
226#117—264no—
227#117C22×D1318yes—
228C2×C4⋊C4—134no—
229C2×C4⋊C4—264no—
230C2×C4⋊C4—264no—
231C2×C4⋊C4—264no—
232C2×C4⋊C4C22×D1314yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—262no—
235C2×C42—22no—
236C2×C42—134no—
237C2×C42—132no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—134no—
241C2×C42—262no—
242#107—138no—
243#107—1316no—
244#107C22×D1318yes—
245#106—138no—
246#106—1316no—
247#106C22×D1318yes—
248C4×C8—134no—
249C4×C8—134no—
250C4×C8—134no—
251C4×C8—134no—
252C2×C13—24no—
253C2×C13#316014yescomplemented
254C2×C13C22×C4⋊Q811yescharacteristic
255C2×C13C22×#13512yes—
256C24D4×D1311yescharacteristic
257C2×Q8—2616no—
258C2×Q8—5216no—
259C22×C4—24no—
260C22×C4—132no—
261C22×C4—132no—
262C22×C4—138no—
263C22×C4—268no—
264C22×C4—264no—
265C22×C4C2×Dic2614yes—
266C22×C4D4×D1312yes—
267C22×C4D4×D1311yescharacteristic
268C22×C4Q8×D1314yes—
269C22×C4C23×D1311yescharacteristic
270C22×C4C23×D1312yes—
271C2×C8—134no—
272C2×C8—134no—
273C2×C8—1316no—
274C2×C8—132no—
275C2×C8—132no—
276C2×C8C2×Dic2614yes—
277C2×C8C2×Dic2614yes—
278C2×C8C2×Dic26116yescomplemented
279C2×C8C23×D1312yes—
280C2×C8C23×D1312yes—
281C4⋊C4—24no—
282C4⋊C4—138no—
283C4⋊C4—2616no—
284C4⋊C4—2616no—
285C4⋊C4—2616no—
286C4⋊C4—264no—
287C4⋊C4C23×D1318yes—
288C22⋊C4—28no—
289C22⋊C4—268no—
290C42—28no—
291C42—138no—
292C42—132no—
293C42—132no—
294C42—132no—
295C42—132no—
296C42—268no—
297C13C2×#316011yescharacteristic, complemented, Sylow
298C23—24no—
299C23#8814214yes—
300C23C2×D4×D1312yes—
301C23C2×D4×D1311yescharacteristic
302Q8—5232no—
303C2×C4—28no—
304C2×C4—48no—
305C2×C4—138no—
306C2×C4—134no—
307C2×C4—134no—
308C2×C4—2616no—
309C2×C4—264no—
310C2×C4—268no—
311C2×C4—528no—
312C2×C4#8814218yes—
313C2×C4#8814214yes—
314C2×C4C22×Dic2612yes—
315C2×C4C22×Dic2614yes—
316C2×C4C2×D4×D1312yes—
317C2×C4C2×D4×D1311yescharacteristic
318C2×C4C2×Q8×D1314yes—
319C2×C4C2×Q8×D1312yes—
320C2×C4C24×D1311yescharacteristic
321C8—134no—
322C8—134no—
323C8C22×Dic2614yes—
324C8C22×Dic2614yes—
325C22—24no—
326C22—28no—
327C22C2×#8814214yes—
328C22C2×#8814212yes—
329C22D13×#13514yes—
330C22C22×D4×D1311yescharacteristic
331C4—48no—
332C4—138no—
333C4—264no—
334C4—528no—
335C4C2×#8814212yes—
336C4C2×#8814214yes—
337C4C23×Dic2611yescharacteristic
338C4C22×Q8×D1311yescharacteristic
339C2—24no—
340C2#1312534814yesdirect product factor
341C2C22×#8814211yescharacteristic
342C2C2×D13×#13512yes—
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#427C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#427D13
hypocenterC13C2×#3160
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #13125348C2direct (N × H)
3. C2×#11718535C2semidirect
4. C2×#11718539C2semidirect
5. C2×#11718519C2semidirect
6. C2×#11718516C2semidirect
36. #11718539C22semidirect
37. #11718535C22semidirect
38. #11718519C22semidirect
39. #11718516C22semidirect
43. C22×C8×C13Q8semidirect
65. C22×#1055Q8semidirect
103. C2×C8×C13C2×Q8semidirect
124. C2×#1055C2×Q8semidirect
214. C22×C8Dic26semidirect
253. C2×C13#3160semidirect
278. C2×C8C2×Dic26semidirect
297. C13C2×#3160semidirect
340. C2#13125348direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
#131253482
C2×#117185352
C2×#117185392
C2×#117185192
C2×#117185162
C2×#117187672
C2×#117186592
C22×C8×Dic132
C2×C13×#4272
C2×#316013