Finite Group Databasebeta

← C2×#13113844 #15835148

Subgroups — C2×#13113844 #15835148

Order 3328.

1028 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718704C212yesmaximal
2C2×#11718644C211yesmaximal, characteristic
3#13113844C218yesmaximal, 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
17C22×#6101—21no—
18C2×#88075—22no—
19C2×#88071—21no—
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2212yes—
22#11718704—24no—
23#11718704C2218yes—
24#11718644—22no—
25#11718644C2214yes—
26C2×#88048—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—
64C2×#6101—24no—
65C2×#6101—44no—
66C22×#1055—22no—
67#88075—28no—
68#88071—24no—
69#88071—21no—
70#88071C2312yes—
71C22⋊#1055—22no—
72C22⋊#1055C2314yes—
73#88048—28no—
74C2×#1611—131nomaximal, Sylow
75C24×C13C2×D411yescharacteristic
76C2×Q8×C13—24no—
77C2×Q8×C13—22no—
78C2×Q8×C13—44no—
79C2×Q8×C13—82no—
80C2×Q8×C13C2×D414yes—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—22no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13SD1614yes—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2×D412yes—
93C22×C4×C13C2×D412yes—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D412yes—
96C22×C4×C13C2411yescharacteristic
97C22×Dic13—24no—
98C22×Dic13—22no—
99C22×Dic13—22no—
100C22×Dic13—42no—
101C22×Dic13—42no—
102C22×Dic13—41no—
103C22×Dic13—41no—
104C22×Dic13—42no—
105C22×Dic13—42no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—28no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4C2×D414yes—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—24no—
118C42×C13—28no—
119C4⋊Dic13—24no—
120C4⋊Dic13—42no—
121#6101—48no—
122C2×#1055—24no—
123C2×#1055—44no—
124C2×#544D1311yescharacteristic
125C2×#483—132no—
126C2×#398—131no—
127#1611—138no—
128C2×#328—132no—
129C2×#324—131no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13#12011yescharacteristic
133C23×C13#12011yescharacteristic
134C23×C13C2×SD1612yes—
135C23×C13#13712yes—
136C23×C13C22×D411yescharacteristic
137Q8×C13—44no—
138Q8×C13—82no—
139Q8×C13—84no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—24no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—22no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—44no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—42no—
155C2×C4×C13—81no—
156C2×C4×C13#12012yes—
157C2×C4×C13C2×SD1614yes—
158C2×C4×C13C22×D412yes—
159C2×Dic13—24no—
160C2×Dic13—48no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168#1055—44no—
169#544—24no—
170#544—22no—
171#544C2×D1314yes—
172C2×C4⋊Q8—22no—
173C2×#125—22no—
174C2×C22⋊Q8—21no—
175C2×C22⋊Q8C2×D1312yes—
176C2×#117—21no—
177C22×C4⋊C4—131no—
178C22×C4⋊C4—261no—
179C22×C4⋊C4C2×D1311yescharacteristic
180#483—138no—
181#483—264no—
182C2×#106—262no—
183C2×#103—262no—
184C2×C22⋊C8—132no—
185#398—134no—
186#398—262no—
187C2×#95—131no—
188C2×#95—261no—
189#328—138no—
190#324—134no—
191C22×C13—24no—
192C22×C13—24no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13#44812yes—
198C22×C13#44812yes—
199C22×C13#45612yes—
200C22×C13#45812yes—
201C22×C13C2×#12011yescharacteristic
202C22×C13C22×SD1611yescharacteristic
203C22×C13C2×#13711yescharacteristic
204C4×C13—24no—
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—44no—
208C4×C13—42no—
209C4×C13—44no—
210Dic13—44no—
211Dic13—82no—
212C22×Q8—21no—
213C22×Q8C22⋊D1312yes—
214C23×C4—261no—
215C23×C4—261no—
216C23×C4C22⋊D1311yescharacteristic
217C23×C4C22⋊D1311yescharacteristic
218C23×C4C22×D1311yescharacteristic
219C22×C8—262no—
220C4⋊Q8—28no—
221C4⋊Q8—28no—
222#125—28no—
223#125—28no—
224C22⋊Q8—24no—
225C22⋊Q8—24no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8C22⋊D1314yes—
229C22⋊Q8C22×D1314yes—
230#117—24no—
231#117—24no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—132no—
240C2×C4⋊C4—262no—
241C2×C4⋊C4—262no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—264no—
244C2×C4⋊C4—524no—
245C2×C4⋊C4C22⋊D1312yes—
246C2×C4⋊C4C22⋊D1312yes—
247C2×C4⋊C4C22×D1312yes—
248C2×C22⋊C4—22no—
249C2×C42—22no—
250#106—268no—
251#103—268no—
252C22⋊C8—134no—
253C22⋊C8—262no—
254#95—132no—
255#95—261no—
256#95—264no—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13—22no—
260C2×C13#161114yescomplemented
261C2×C13C2×#44811yescharacteristic
262C2×C13C2×#45611yescharacteristic
263C2×C13C2×#45811yescharacteristic
264C24C2×C22⋊D1311yescharacteristic
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×Q8—82no—
269C2×Q8C2×C22⋊D1314yes—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—264no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—522no—
283C22×C4—522no—
284C22×C4—522no—
285C22×C4—522no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4#610614yes—
289C22×C4C2×C22⋊D1312yes—
290C22×C4C2×C22⋊D1312yes—
291C22×C4C2×C22⋊D1312yes—
292C22×C4C2×C22⋊D1311yescharacteristic
293C22×C4C2×C22⋊D1312yes—
294C22×C4C23×D1311yescharacteristic
295C2×C8—264no—
296C2×C8—524no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—264no—
307C4⋊C4—528no—
308C4⋊C4—522no—
309C4⋊C4C2×C22⋊D1314yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C42—28no—
313C13C2×#161111yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23C2×#610612yes—
317C23#8819612yes—
318C23#8820711yescharacteristic
319C23#8820711yescharacteristic
320C23C22×C22⋊D1311yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—84no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—264no—
341C2×C4—522no—
342C2×C4—528no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—1042no—
348C2×C4—1042no—
349C2×C4C2×#610614yes—
350C2×C4#8820712yes—
351C2×C4C22×C22⋊D1312yes—
352C8—524no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—24no—
358C22—24no—
359C22#1171888812yes—
360C22#1171888812yes—
361C22#1171890412yes—
362C22#1171890712yes—
363C22C22×#610611yescharacteristic
364C22C2×#8819611yescharacteristic
365C22C2×#8820711yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—44no—
370C4—42no—
371C4—44no—
372C4—524no—
373C4—1042no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2#1311384414yesdirect product factor
378C2C2×#1171888811yescharacteristic
379C2C2×#1171890711yescharacteristic
380C2C2×#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×#1611
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. #13113844C2direct (N × H)
260. C2×C13#1611semidirect
313. C13C2×#1611semidirect
377. C2#13113844direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186442
#131138442
C2×#117181302
C2×#117181202
C2×C13×#5442
C2×#161113