Finite Group Databasebeta

← C2×#13114513 #15850717

Subgroups — C2×#13114513 #15850717

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×#11718343C211yesmaximal, characteristic
2C2×#11718343C211yesmaximal, characteristic
3C2×#11718341C211yesmaximal, characteristic
4C2×#11718360C211yesmaximal, characteristic
5C2×#11718342C211yesmaximal, characteristic
6C2×#11718342C211yesmaximal, characteristic
7#13114513C218yesmaximal, direct product factor
8C2×C13×#322C211yesmaximal, characteristic
9C22×Dic52—22no—
10C2×#88123C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×#88123C2211yescharacteristic
13C2×#88123C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C2×C4×C8×C13C2211yescharacteristic
16C2×C4×C8×C13C2211yescharacteristic
17C2×#88058—22no—
18C2×#88058—22no—
19C2×#88057—22no—
20C2×#88056—22no—
21C2×#88056—22no—
22#11718360—22no—
23#11718360C2214yes—
24#11718343—22no—
25#11718343—22no—
26#11718343C2214yes—
27#11718343C2214yes—
28#11718342—22no—
29#11718342—22no—
30#11718342C2214yes—
31#11718342C2214yes—
32#11718341—22no—
33#11718341C2214yes—
34C13×#322C2214yes—
35C22×Dic26—21no—
36C22×Dic26—21no—
37C22×Dic26—21no—
38C22×Dic26—21no—
39C22×C8×C13D412yes—
40C22×C8×C13D412yes—
41C22×C8×C13D412yes—
42C2×C42×C13C2311yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—21no—
51C2×Dic52—28no—
52C2×Dic52—48no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123—21no—
63#88123—21no—
64#88123—21no—
65#88123C2312yes—
66#88123C2312yes—
67#88123C2312yes—
68#88123C2312yes—
69C4×C8×C13D412yes—
70C4×C8×C13D412yes—
71C4×C8×C13D412yes—
72C4×C8×C13C2312yes—
73C4×C8×C13C2312yes—
74C4×C8×C13C2312yes—
75#88058—28no—
76#88058—28no—
77#88057—28no—
78#88056—28no—
79#88056—28no—
80C2×#1723—131nomaximal, Sylow
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C2×Dic26—22no—
89C2×Dic26—22no—
90C2×Dic26—22no—
91C2×Dic26—22no—
92C2×Dic26—44no—
93C2×Dic26—44no—
94C2×Dic26—44no—
95C2×Dic26—44no—
96C2×Dic26—41no—
97C2×Dic26—41no—
98C2×Dic26—41no—
99C2×Dic26—41no—
100C2×C8×C13—24no—
101C2×C8×C13—24no—
102C2×C8×C13Q1618yescomplemented
103C2×C8×C13C2×D414yes—
104C2×C8×C13C2×D414yes—
105C2×C8×C13C2×D414yes—
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2411yescharacteristic
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113C4⋊Dic13—22no—
114C4⋊Dic13—22no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125C4⋊Dic13—41no—
126Dic52—416no—
127C2×#500—131no—
128C2×#500—131no—
129C2×#498—131no—
130C2×#494—131no—
131C2×#487—131no—
132C2×#487—131no—
133#1723—138no—
134C2×#322D1311yescharacteristic
135C23×C13#12711yescharacteristic
136C2×C4×C13#12711yescharacteristic
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13#12711yescharacteristic
139C2×C4×C13C2×Q1614yes—
140C2×C4×C13AGL(1,ℤ/8)14yes—
141C2×C4×C13#13714yes—
142C2×C4×C13C22×D411yescharacteristic
143C2×C4×C13C22×D411yescharacteristic
144C2×C4×C13C22×D411yescharacteristic
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—82no—
150C2×Dic13—82no—
151C2×Dic13—82no—
152C2×Dic13—82no—
153Dic26—44no—
154Dic26—44no—
155Dic26—44no—
156Dic26—44no—
157Dic26—82no—
158Dic26—82no—
159Dic26—82no—
160Dic26—82no—
161C8×C13—24no—
162C8×C13—24no—
163C8×C13C2×Q1618yescomplemented
164C22×Q16—262no—
165C2×C4⋊Q8—131no—
166C2×C4⋊Q8—131no—
167C2×C4⋊Q8—131no—
168C2×C4⋊Q8—131no—
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—134no—
178#487—134no—
179#487—262no—
180#487—262no—
181C2×#107—262no—
182C2×#107—262no—
183C2×#106—262no—
184C2×#103—262no—
185C2×#103—262no—
186C2×C4×C8C2×D1311yescharacteristic
187C2×C4×C8C2×D1311yescharacteristic
188C2×C4×C8C2×D1311yescharacteristic
189#322C2×D1314yes—
190C22×C13#49412yes—
191C22×C13#49612yes—
192C22×C13#49712yes—
193C22×C13C2×#12711yescharacteristic
194C4×C13#49412yes—
195C4×C13#49612yes—
196C4×C13#49712yes—
197C4×C13C22×Q1612yes—
198C4×C13C2×AGL(1,ℤ/8)12yes—
199C4×C13C2×#13712yes—
200Dic13—82no—
201Dic13—82no—
202Dic13—82no—
203Dic13—82no—
204C22×Q8—261no—
205C22×Q8—261no—
206C22×Q8—261no—
207C22×Q8—261no—
208C2×Q16—268no—
209C2×Q16—528no—
210C22×C8D5212yes—
211C22×C8D5212yes—
212C22×C8D5212yes—
213C4⋊Q8—132no—
214C4⋊Q8—132no—
215C4⋊Q8—132no—
216C4⋊Q8—132no—
217C4⋊Q8—261no—
218C4⋊Q8—261no—
219C4⋊Q8—261no—
220C4⋊Q8—261no—
221C4⋊Q8—261no—
222C4⋊Q8—261no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225C4⋊Q8—261no—
226C4⋊Q8—261no—
227C4⋊Q8—261no—
228C4⋊Q8—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
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—268no—
242#103—268no—
243C4×C8D5212yes—
244C4×C8D5212yes—
245C4×C8D5212yes—
246C4×C8C22×D1312yes—
247C4×C8C22×D1312yes—
248C4×C8C22×D1312yes—
249C2×C13#172314yescomplemented
250C2×C13C2×#49411yescharacteristic
251C2×C13C2×#49611yescharacteristic
252C2×C13C2×#49711yescharacteristic
253C2×Q8—262no—
254C2×Q8—262no—
255C2×Q8—262no—
256C2×Q8—262no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8—521no—
261C2×Q8—524no—
262C2×Q8—524no—
263C2×Q8—524no—
264C2×Q8—524no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4C2×D5211yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4C2×D5211yescharacteristic
272Q16—5216no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8Dic5218yescomplemented
276C2×C8C2×D5214yes—
277C2×C8C2×D5214yes—
278C2×C8C2×D5214yes—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4—521no—
295C42C2×D5211yescharacteristic
296C42C2×D5211yescharacteristic
297C42C2×D5211yescharacteristic
298C42C23×D1311yescharacteristic
299C13C2×#172311yescharacteristic, complemented, Sylow
300C23#8812811yescharacteristic
301Q8—524no—
302Q8—524no—
303Q8—524no—
304Q8—524no—
305Q8—1042no—
306Q8—1042no—
307Q8—1042no—
308Q8—1042no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—1042no—
314C2×C4—1042no—
315C2×C4—1042no—
316C2×C4—1042no—
317C2×C4#8812811yescharacteristic
318C2×C4#8812811yescharacteristic
319C2×C4#8812811yescharacteristic
320C2×C4C2×Dic5214yes—
321C2×C4#8816214yes—
322C2×C4#8816314yes—
323C2×C4C22×D5211yescharacteristic
324C2×C4C22×D5211yescharacteristic
325C2×C4C22×D5211yescharacteristic
326C8—24no—
327C8—24no—
328C8C2×Dic5218yescomplemented
329C22#1171836012yes—
330C22#1171837312yes—
331C22#1171837612yes—
332C22C2×#8812811yescharacteristic
333C4—1042no—
334C4—1042no—
335C4—1042no—
336C4—1042no—
337C4#1171836012yes—
338C4#1171837312yes—
339C4#1171837612yes—
340C4C22×Dic5212yes—
341C4C2×#8816212yes—
342C4C2×#8816312yes—
343C2#1311451314yesdirect product factor
344C2C2×#1171836011yescharacteristic
345C2C2×#1171837311yescharacteristic
346C2C2×#1171837611yescharacteristic
subgroupG/H
centerC23#88128
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#322C2
socle, prime radicalC23×C13#127
hypercenterC2×#322D13
hypocenterC13C2×#1723
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
7. #13114513C2direct (N × H)
102. C2×C8×C13Q16semidirect
163. C8×C13C2×Q16semidirect
249. C2×C13#1723semidirect
275. C2×C8Dic52semidirect
299. C13C2×#1723semidirect
328. C8C2×Dic52semidirect
343. C2#13114513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183432
C2×#117183412
C2×#117183602
C2×#117183422
#131145132
C2×C13×#3222
C2×#172313