Finite Group Databasebeta

← C2×#13113878 #15835154

Subgroups — C2×#13113878 #15835154

Order 3328.

984 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C212yesmaximal
2C2×#11718647C211yesmaximal, characteristic
3#13113878C218yesmaximal, direct product factor
4C2×#11718130C212yesmaximal
5C2×#11718120C211yesmaximal, characteristic
6C2×C13×#544C211yesmaximal, characteristic
7C13×#544—24no—
8C13×#544—22no—
9C13×#544C2214yes—
10C2×C13×C4⋊Q8—22no—
11C2×C13×#125—22no—
12C2×C13×C22⋊Q8—21no—
13C2×C13×C22⋊Q8C2212yes—
14C2×C13×#117—21no—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C2×#88075—22no—
18C2×#88071—21no—
19C2×#88071—21no—
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2212yes—
22#11718705—24no—
23#11718705C2218yes—
24#11718647—22no—
25#11718647C2214yes—
26C2×#88047—22no—
27#11718130C2218yes—
28#11718120C2214yes—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C23×Dic13—21no—
36C13×C4⋊Q8—28no—
37C13×C4⋊Q8—28no—
38C13×#125—28no—
39C13×#125—28no—
40C13×C22⋊Q8—24no—
41C13×C22⋊Q8—24no—
42C13×C22⋊Q8—22no—
43C13×C22⋊Q8—22no—
44C13×C22⋊Q8D414yes—
45C13×C22⋊Q8C2314yes—
46C13×#117—24no—
47C13×#117—24no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4D412yes—
56C2×C13×C4⋊C4D412yes—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C42×C13—22no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13C2312yes—
64C22×#1055—22no—
65#88075—28no—
66#88071—24no—
67#88071—24no—
68#88071—21no—
69#88071C2312yes—
70C22⋊#1055—22no—
71C22⋊#1055C2314yes—
72#88047—28no—
73C2×#1617—131nomaximal, Sylow
74C24×C13C2×D411yescharacteristic
75C2×Q8×C13—24no—
76C2×Q8×C13—22no—
77C2×Q8×C13—44no—
78C2×Q8×C13—82no—
79C2×Q8×C13C2×D414yes—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13Q1614yes—
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2×D412yes—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D412yes—
95C22×C4×C13C2411yescharacteristic
96C22×Dic13—22no—
97C22×Dic13—22no—
98C22×Dic13—42no—
99C22×Dic13—42no—
100C22×Dic13—44no—
101C22×Dic13—41no—
102C22×Dic13—41no—
103C22×Dic13—42no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—28no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4C2×D414yes—
114C13×C22⋊C4—24no—
115C13×C22⋊C4—24no—
116C42×C13—28no—
117C4⋊Dic13—24no—
118C4⋊Dic13—42no—
119C2×#1055—24no—
120C2×#1055—44no—
121C2×#544D1311yescharacteristic
122C2×#484—132no—
123C2×#400—131no—
124#1617—138no—
125C2×#328—132no—
126C2×#324—131no—
127C23×C13—22no—
128C23×C13—22no—
129C23×C13#12011yescharacteristic
130C23×C13#12011yescharacteristic
131C23×C13C2×Q1612yes—
132C23×C13#13712yes—
133C23×C13C22×D411yescharacteristic
134Q8×C13—44no—
135Q8×C13—82no—
136Q8×C13—84no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—24no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—22no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—44no—
149C2×C4×C13—42no—
150C2×C4×C13—44no—
151C2×C4×C13—42no—
152C2×C4×C13—81no—
153C2×C4×C13#12012yes—
154C2×C4×C13C2×Q1614yes—
155C2×C4×C13C22×D412yes—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—44no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—84no—
162C2×Dic13—82no—
163C2×Dic13—82no—
164#1055—44no—
165#544—24no—
166#544—22no—
167#544C2×D1314yes—
168C2×C4⋊Q8—22no—
169C2×#125—22no—
170C2×C22⋊Q8—21no—
171C2×C22⋊Q8C2×D1312yes—
172C2×#117—21no—
173C22×C4⋊C4—131no—
174C22×C4⋊C4C2×D1311yescharacteristic
175#484—138no—
176#484—264no—
177C2×#107—262no—
178C2×#103—262no—
179C2×C22⋊C8—132no—
180#400—134no—
181#400—262no—
182C2×#95—131no—
183C2×#95—261no—
184C2×#95—261no—
185#328—138no—
186#324—134no—
187C22×C13—24no—
188C22×C13—24no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#45112yes—
194C22×C13#45112yes—
195C22×C13#45412yes—
196C22×C13#45812yes—
197C22×C13C2×#12011yescharacteristic
198C22×C13C22×Q1611yescharacteristic
199C22×C13C2×#13711yescharacteristic
200C4×C13—24no—
201C4×C13—22no—
202C4×C13—22no—
203C4×C13—44no—
204C4×C13—42no—
205C4×C13—44no—
206Dic13—82no—
207Dic13—82no—
208C22×Q8—21no—
209C22×Q8C22⋊D1312yes—
210C23×C4—261no—
211C23×C4—261no—
212C23×C4C22⋊D1311yescharacteristic
213C23×C4C22⋊D1311yescharacteristic
214C23×C4C22×D1311yescharacteristic
215C22×C8—262no—
216C4⋊Q8—28no—
217C4⋊Q8—28no—
218#125—28no—
219#125—28no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C22⋊Q8C22⋊D1314yes—
225C22⋊Q8C22×D1314yes—
226#117—24no—
227#117—24no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—132no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—262no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4C22⋊D1312yes—
240C2×C4⋊C4C22⋊D1312yes—
241C2×C4⋊C4C22×D1312yes—
242C2×C22⋊C4—22no—
243C2×C42—22no—
244#107—268no—
245#103—268no—
246C22⋊C8—134no—
247C22⋊C8—262no—
248#95—132no—
249#95—261no—
250#95—264no—
251#95—264no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—22no—
255C2×C13#161714yescomplemented
256C2×C13C2×#45111yescharacteristic
257C2×C13C2×#45411yescharacteristic
258C2×C13C2×#45811yescharacteristic
259C24C2×C22⋊D1311yescharacteristic
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—44no—
263C2×Q8—82no—
264C2×Q8C2×C22⋊D1314yes—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—522no—
277C22×C4—522no—
278C22×C4—524no—
279C22×C4—522no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4#610714yes—
283C22×C4C2×C22⋊D1312yes—
284C22×C4C2×C22⋊D1312yes—
285C22×C4C2×C22⋊D1312yes—
286C22×C4C2×C22⋊D1311yescharacteristic
287C22×C4C2×C22⋊D1312yes—
288C22×C4C23×D1311yescharacteristic
289C2×C8—264no—
290C2×C8—524no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—28no—
295C4⋊C4—24no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—264no—
301C4⋊C4—522no—
302C4⋊C4C2×C22⋊D1314yes—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C42—28no—
306C13C2×#161711yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23#8819612yes—
310C23C2×#610712yes—
311C23#8820711yescharacteristic
312C23#8820711yescharacteristic
313C23C22×C22⋊D1311yescharacteristic
314Q8—44no—
315Q8—82no—
316Q8—84no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—524no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4—1044no—
339C2×C4—1042no—
340C2×C4—1042no—
341C2×C4C2×#610714yes—
342C2×C4#8820712yes—
343C2×C4C22×C22⋊D1312yes—
344C8—524no—
345C22—24no—
346C22—24no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22#1171888912yes—
352C22#1171888912yes—
353C22#1171890412yes—
354C22#1171890612yes—
355C22C2×#8819611yescharacteristic
356C22C22×#610711yescharacteristic
357C22C2×#8820711yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—44no—
362C4—42no—
363C4—44no—
364C4—1042no—
365C4—1042no—
366C2—21no—
367C2—21no—
368C2—22no—
369C2#1311387814yesdirect product factor
370C2C2×#1171888911yescharacteristic
371C2C2×#1171890611yescharacteristic
372C2C2×#1171890411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13C2×#1617
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13113878C2direct (N × H)
255. C2×C13#1617semidirect
306. C13C2×#1617semidirect
369. C2#13113878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187052
C2×#117186472
#131138782
C2×#117181302
C2×#117181202
C2×C13×#5442
C2×#161713