Finite Group Databasebeta

← C2×#13114515 #15850719

Subgroups — C2×#13114515 #15850719

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic
2C2×#11718739C211yesmaximal, characteristic
3C2×#11718740C211yesmaximal, characteristic
4C2×#11718360C211yesmaximal, characteristic
5C2×#11718742C211yesmaximal, characteristic
6#13114515C218yesmaximal, direct product factor
7C2×#11718046C211yesmaximal, characteristic
8C2×C13×#487C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C22×Dic52—22no—
12C2×#88123C2211yescharacteristic
13C2×#88123C2211yescharacteristic
14C13×#487—22no—
15C13×#487C2214yes—
16C2×C13×#103—22no—
17C2×C4×C8×C13C2211yescharacteristic
18C2×#88075—22no—
19#11718742—22no—
20#11718742C2214yes—
21#11718740—22no—
22#11718740C2214yes—
23#11718739—22no—
24#11718739—22no—
25#11718739C2214yes—
26#11718739C2214yes—
27C2×#88048—22no—
28C2×#88047—22no—
29C2×#88047—22no—
30C2×C4×#1055C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718360—22no—
33#11718360C2214yes—
34#11718046C2214yes—
35C22×Q8×C13—21no—
36C22×Q8×C13—21no—
37C22×Dic26—21no—
38C22×Dic26—21no—
39C22×C8×C13D412yes—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8C2312yes—
47C13×C4⋊Q8C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C42×C13C2311yescharacteristic
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C22×#1055D412yes—
58C22×#1055D412yes—
59C2×Dic52—28no—
60C2×Dic52—48no—
61#88123—21no—
62#88123—21no—
63#88123—21no—
64#88123—21no—
65#88123—21no—
66#88123—21no—
67#88123C2312yes—
68#88123C2312yes—
69C13×#103—28no—
70C4×C8×C13D412yes—
71C4×C8×C13C2312yes—
72#88075—28no—
73#88048—28no—
74#88047—28no—
75#88047—28no—
76C4×#1055D412yes—
77C4×#1055D412yes—
78C4×#1055C2312yes—
79C4×#1055C2312yes—
80C2×#1723—131nomaximal, Sylow
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—44no—
86C2×Q8×C13—44no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×Dic13—41no—
93C22×Dic13—41no—
94C2×Dic26—22no—
95C2×Dic26—22no—
96C2×Dic26—44no—
97C2×Dic26—44no—
98C2×Dic26—41no—
99C2×Dic26—41no—
100C2×C8×C13—24no—
101C2×C8×C13C2×D414yes—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2411yescharacteristic
114C4⋊Dic13—22no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C2×#1055—24no—
123C2×#1055Q1618yescomplemented
124C2×#1055C2×D414yes—
125C2×#1055C2×D414yes—
126Dic52—416no—
127C2×#500—131no—
128C2×#500—131no—
129C2×#498—131no—
130C2×#494—131no—
131C2×#487—131no—
132C2×#487D1311yescharacteristic
133#1723—138no—
134C2×#322—131no—
135C23×C13#12711yescharacteristic
136Q8×C13—44no—
137Q8×C13—44no—
138Q8×C13—82no—
139Q8×C13—82no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—82no—
143C2×C4×C13—82no—
144C2×C4×C13#12711yescharacteristic
145C2×C4×C13#12711yescharacteristic
146C2×C4×C13#12711yescharacteristic
147C2×C4×C13C2×Q1614yes—
148C2×C4×C13AGL(1,ℤ/8)14yes—
149C2×C4×C13#13714yes—
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C22×D411yescharacteristic
152C2×C4×C13C22×D411yescharacteristic
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—82no—
156C2×Dic13—82no—
157Dic26—44no—
158Dic26—44no—
159Dic26—82no—
160Dic26—82no—
161C8×C13—24no—
162#1055—24no—
163#1055C2×Q1618yescomplemented
164C22×Q16—262no—
165C2×C4⋊Q8—131no—
166C2×C4⋊Q8—131no—
167C2×C4⋊Q8C2×D1311yescharacteristic
168C2×C4⋊Q8C2×D1311yescharacteristic
169#500—134no—
170#500—134no—
171#500—262no—
172#500—262no—
173#498—134no—
174#498—262no—
175#494—134no—
176#494—262no—
177#487—22no—
178#487—134no—
179#487—262no—
180#487C2×D1314yes—
181C2×#107—262no—
182C2×#107—262no—
183C2×#106—262no—
184C2×#103—22no—
185C2×#103—262no—
186C2×C4×C8—131no—
187C2×C4×C8—131no—
188C2×C4×C8C2×D1311yescharacteristic
189#322—134no—
190C22×C13#49412yes—
191C22×C13#49612yes—
192C22×C13#49712yes—
193C22×C13C2×#12711yescharacteristic
194C4×C13—82no—
195C4×C13—82no—
196C4×C13#49412yes—
197C4×C13#49612yes—
198C4×C13#49712yes—
199C4×C13C22×Q1612yes—
200C4×C13C2×AGL(1,ℤ/8)12yes—
201C4×C13C2×#13712yes—
202Dic13—82no—
203Dic13—82no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—261no—
207C22×Q8—261no—
208C2×Q16—268no—
209C2×Q16—528no—
210C22×C8—132no—
211C22×C8—132no—
212C22×C8C22⋊D1312yes—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—132no—
220C4⋊Q8—132no—
221C4⋊Q8—261no—
222C4⋊Q8—261no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225C4⋊Q8—261no—
226C4⋊Q8—261no—
227C4⋊Q8C22×D1312yes—
228C4⋊Q8C22×D1312yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C42C22×D1311yescharacteristic
238#107—268no—
239#107—268no—
240#106—268no—
241#103—28no—
242#103—268no—
243C4×C8—132no—
244C4×C8—132no—
245C4×C8—132no—
246C4×C8—132no—
247C4×C8C22⋊D1312yes—
248C4×C8C22×D1312yes—
249C2×C13#172314yescomplemented
250C2×C13C2×#49411yescharacteristic
251C2×C13C2×#49611yescharacteristic
252C2×C13C2×#49711yescharacteristic
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—44no—
258C2×Q8—44no—
259C2×Q8—262no—
260C2×Q8—262no—
261C2×Q8—521no—
262C2×Q8—521no—
263C2×Q8—524no—
264C2×Q8—524no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4D4×D1311yescharacteristic
270C22×C4D4×D1311yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272Q16—5216no—
273C2×C8—24no—
274C2×C8—138no—
275C2×C8—134no—
276C2×C8—134no—
277C2×C8—264no—
278C2×C8C2×C22⋊D1314yes—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4—521no—
295C42D4×D1311yescharacteristic
296C42D4×D1311yescharacteristic
297C42C2×C22⋊D1311yescharacteristic
298C42C23×D1311yescharacteristic
299C13C2×#172311yescharacteristic, complemented, Sylow
300C23#8819411yescharacteristic
301Q8—44no—
302Q8—44no—
303Q8—82no—
304Q8—82no—
305Q8—524no—
306Q8—524no—
307Q8—1042no—
308Q8—1042no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—1042no—
316C2×C4—1042no—
317C2×C4#8816914yes—
318C2×C4Q16×D1314yes—
319C2×C4#8819411yescharacteristic
320C2×C4#8819411yescharacteristic
321C2×C4#8819411yescharacteristic
322C2×C4#8820314yes—
323C2×C4C2×D4×D1311yescharacteristic
324C2×C4C2×D4×D1311yescharacteristic
325C2×C4C22×C22⋊D1311yescharacteristic
326C8—24no—
327C8—138no—
328C8—264no—
329C22#1171871912yes—
330C22#1171882812yes—
331C22#1171884212yes—
332C22C2×#8819411yescharacteristic
333C4—82no—
334C4—82no—
335C4—1042no—
336C4—1042no—
337C4#1171871912yes—
338C4#1171882812yes—
339C4#1171884212yes—
340C4C2×#8816912yes—
341C4C2×Q16×D1312yes—
342C4C2×#8820312yes—
343C2#1311451514yesdirect product factor
344C2C2×#1171884211yescharacteristic
345C2C2×#1171871911yescharacteristic
346C2C2×#1171882811yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#487C2
socle, prime radicalC23×C13#127
hypercenterC2×#487D13
hypocenterC13C2×#1723
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
6. #13114515C2direct (N × H)
123. C2×#1055Q16semidirect
163. #1055C2×Q16semidirect
249. C2×C13#1723semidirect
299. C13C2×#1723semidirect
343. C2#13114515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117187402
C2×#117183602
C2×#117187422
#131145152
C2×#117180462
C2×C13×#4872
C2×#172313