Finite Group Databasebeta

← C2×#13114480 #15850665

Subgroups — C2×#13114480 #15850665

Order 3328.

734 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×#11718739C211yesmaximal, characteristic
2C2×#11718754C211yesmaximal, characteristic
3C2×#11718342C211yesmaximal, characteristic
4C2×#11718742C211yesmaximal, characteristic
5C2×#11718742C211yesmaximal, characteristic
6#13114480C218yesmaximal, direct product factor
7C2×#11718046C211yesmaximal, characteristic
8C2×C13×#498C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×#88123C2211yescharacteristic
13C13×#498—22no—
14C13×#498C2214yes—
15C2×C13×#106—22no—
16C2×C4×C8×C13C2211yescharacteristic
17C2×#88075—22no—
18C2×#88075—22no—
19C2×#88056—22no—
20#11718754—22no—
21#11718754C2214yes—
22#11718742—22no—
23#11718742—22no—
24#11718742C2214yes—
25#11718742C2214yes—
26#11718739—22no—
27#11718739C2214yes—
28C2×#88050—22no—
29C2×#88047—22no—
30C2×C4×#1055C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718342—22no—
33#11718342C2214yes—
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—
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123—21no—
63#88123—21no—
64#88123—21no—
65#88123C2312yes—
66#88123C2312yes—
67C13×#106—28no—
68C4×C8×C13D412yes—
69C4×C8×C13C2312yes—
70#88075—28no—
71#88075—28no—
72#88056—28no—
73#88050—28no—
74#88047—28no—
75C4×#1055D412yes—
76C4×#1055D412yes—
77C4×#1055C2312yes—
78C4×#1055C2312yes—
79C2×#1718—131nomaximal, Sylow
80C2×Q8×C13—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—44no—
85C2×Q8×C13—44no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—41no—
92C22×Dic13—41no—
93C2×Dic26—22no—
94C2×Dic26—22no—
95C2×Dic26—44no—
96C2×Dic26—44no—
97C2×Dic26—41no—
98C2×Dic26—41no—
99C2×C8×C13—24no—
100C2×C8×C13C2×D414yes—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13C2411yescharacteristic
113C4⋊Dic13—22no—
114C4⋊Dic13—22no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C2×#1055—24no—
122C2×#1055—24no—
123C2×#1055C2×D414yes—
124C2×#1055C2×D414yes—
125C2×#500—131no—
126C2×#498D1311yescharacteristic
127C2×#487—131no—
128C2×#487—131no—
129C2×#487—131no—
130C2×#487—131no—
131#1718—138no—
132C2×#322—131no—
133C23×C13#12711yescharacteristic
134Q8×C13—44no—
135Q8×C13—44no—
136Q8×C13—82no—
137Q8×C13—82no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—82no—
141C2×C4×C13—82no—
142C2×C4×C13#12711yescharacteristic
143C2×C4×C13#12711yescharacteristic
144C2×C4×C13#12711yescharacteristic
145C2×C4×C13#13514yes—
146C2×C4×C13#13714yes—
147C2×C4×C13#13714yes—
148C2×C4×C13C22×D411yescharacteristic
149C2×C4×C13C22×D411yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155Dic26—44no—
156Dic26—44no—
157Dic26—82no—
158Dic26—82no—
159C8×C13—24no—
160#1055—24no—
161#1055—24no—
162C2×C4⋊Q8—131no—
163C2×C4⋊Q8—131no—
164C2×C4⋊Q8C2×D1311yescharacteristic
165C2×C4⋊Q8C2×D1311yescharacteristic
166#500—134no—
167#500—262no—
168#498—22no—
169#498C2×D1314yes—
170#487—134no—
171#487—134no—
172#487—134no—
173#487—134no—
174#487—262no—
175#487—262no—
176#487—262no—
177#487—262no—
178C2×#107—262no—
179C2×#106—22no—
180C2×#103—262no—
181C2×#103—262no—
182C2×#103—262no—
183C2×#103—262no—
184C2×C4×C8—131no—
185C2×C4×C8—131no—
186C2×C4×C8C2×D1311yescharacteristic
187#322—134no—
188C22×C13#49512yes—
189C22×C13#49712yes—
190C22×C13#49712yes—
191C22×C13C2×#12711yescharacteristic
192C4×C13—82no—
193C4×C13—82no—
194C4×C13#49512yes—
195C4×C13#49712yes—
196C4×C13#49712yes—
197C4×C13C2×#13512yes—
198C4×C13C2×#13712yes—
199C4×C13C2×#13712yes—
200Dic13—82no—
201Dic13—82no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—261no—
205C22×Q8—261no—
206C22×C8—132no—
207C22×C8—132no—
208C22×C8C22⋊D1312yes—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
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⋊Q8C22×D1312yes—
224C4⋊Q8C22×D1312yes—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C42C22×D1311yescharacteristic
234#107—268no—
235#106—28no—
236#103—268no—
237#103—268no—
238#103—268no—
239#103—268no—
240C4×C8—132no—
241C4×C8—132no—
242C4×C8—132no—
243C4×C8—132no—
244C4×C8C22⋊D1312yes—
245C4×C8C22×D1312yes—
246C2×C13#171814yescomplemented
247C2×C13C2×#49511yescharacteristic
248C2×C13C2×#49711yescharacteristic
249C2×C13C2×#49711yescharacteristic
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—44no—
255C2×Q8—44no—
256C2×Q8—262no—
257C2×Q8—262no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8—524no—
261C2×Q8—524no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4D4×D1311yescharacteristic
267C22×C4D4×D1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269C2×C8—24no—
270C2×C8—134no—
271C2×C8—134no—
272C2×C8—264no—
273C2×C8—264no—
274C2×C8C2×C22⋊D1314yes—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C42D4×D1311yescharacteristic
292C42D4×D1311yescharacteristic
293C42C2×C22⋊D1311yescharacteristic
294C42C23×D1311yescharacteristic
295C13C2×#171811yescharacteristic, complemented, Sylow
296C23#8819411yescharacteristic
297Q8—44no—
298Q8—44no—
299Q8—82no—
300Q8—82no—
301Q8—524no—
302Q8—524no—
303Q8—1042no—
304Q8—1042no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—1042no—
312C2×C4—1042no—
313C2×C4#8816914yes—
314C2×C4#8817014yes—
315C2×C4#8819411yescharacteristic
316C2×C4#8819411yescharacteristic
317C2×C4#8819411yescharacteristic
318C2×C4#8819614yes—
319C2×C4C2×D4×D1311yescharacteristic
320C2×C4C2×D4×D1311yescharacteristic
321C2×C4C22×C22⋊D1311yescharacteristic
322C8—24no—
323C8—264no—
324C8—264no—
325C22#1171874712yes—
326C22#1171882812yes—
327C22#1171882912yes—
328C22C2×#8819411yescharacteristic
329C4—82no—
330C4—82no—
331C4—1042no—
332C4—1042no—
333C4#1171874712yes—
334C4#1171882812yes—
335C4#1171882912yes—
336C4C2×#8816912yes—
337C4C2×#8817012yes—
338C4C2×#8819612yes—
339C2#1311448014yesdirect product factor
340C2C2×#1171882911yescharacteristic
341C2C2×#1171882811yescharacteristic
342C2C2×#1171874711yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#498C2
socle, prime radicalC23×C13#127
hypercenterC2×#498D13
hypocenterC13C2×#1718
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
6. #13114480C2direct (N × H)
246. C2×C13#1718semidirect
295. C13C2×#1718semidirect
339. C2#13114480direct (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×#117187542
C2×#117183422
C2×#117187422
#131144802
C2×#117180462
C2×C13×#4982
C2×#171813