Finite Group Databasebeta

← C2×#13113716 #15832484

Subgroups — C2×#13113716 #15832484

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×Dic26C211yesmaximal, characteristic, complemented
2C2×C4×#6095C211yesmaximal, characteristic
3C2×#11718349C211yesmaximal, characteristic
4#13113716C218yesmaximal, direct product factor
5C2×#11718050C211yesmaximal, characteristic, complemented
6C2×#11718048C211yesmaximal, characteristic, complemented
7C2×#11718051C211yesmaximal, characteristic
8C2×C13×#322C211yesmaximal, characteristic, complemented
9C22×#6095C411yescharacteristic
10C22×#6094—21no—
11C2×C4×D52C2211yescharacteristic
12C2×C4×Dic26C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88061C411yescharacteristic
17C2×#88060—21no—
18C2×#88057C411yescharacteristic
19C2×#88056C411yescharacteristic
20C2×#88054—21no—
21C2×C8×Dic13—21no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C4×#6095C414yes—
25C4×#6095C2214yes—
26#11718349—22no—
27#11718349C2214yes—
28C8×Dic26—22no—
29C8×Dic26C2214yescomplemented
30C13×#322C2214yescomplemented
31#11718051C2214yes—
32#11718050C2214yescomplemented
33#11718048C2214yescomplemented
34C22×D52C2×C411yescharacteristic
35C22×C4×D13—21no—
36C22×Dic26C2×C411yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C22×C8×C13D411yescharacteristic
42C2×C42×C13C2311yescharacteristic
43C2×#6103—21no—
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C2×#6095—24no—
51C2×#6095C2×C414yes—
52C2×#6094—24no—
53C2×#6094—44no—
54C4×D52—21no—
55C4×D52—21no—
56C4×D52C2×C412yes—
57C4×D52C2312yes—
58C4×Dic26—21no—
59C4×Dic26—21no—
60C4×Dic26C2×C412yes—
61C4×Dic26C2312yes—
62C4×C8×C13—21no—
63C4×C8×C13C2×C412yes—
64C4×C8×C13D412yes—
65C4×C8×C13C2312yes—
66C4×C8×C13C2312yes—
67C4×C8×C13C2312yes—
68#88061C2×C414yes—
69#88060—24no—
70#88057C2×C414yes—
71#88056C2×C414yes—
72#88054—24no—
73C8×Dic13—24no—
74C4⋊#1055—21no—
75C4⋊#1055—21no—
76C4⋊#1055C2312yes—
77C4⋊#1055C2312yes—
78C2×#1588—131nomaximal, Sylow
79C23×D13—21no—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C2×D52—22no—
87C2×D52—22no—
88C2×D52—21no—
89C2×D52C22×C412yes—
90C2×C4×D13—22no—
91C2×C4×D13—22no—
92C2×C4×D13—42no—
93C2×C4×D13—42no—
94C2×Dic26—21no—
95C2×Dic26—22no—
96C2×Dic26M1614yescomplemented
97C2×Dic26C22×C412yes—
98C2×C8×C13—24no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13C22×C412yes—
105C2×C8×C13C22×C412yes—
106C2×C8×C13C2×D412yes—
107C2×C8×C13C2×D412yes—
108C42×C13C22×C411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13#4111yescharacteristic
111C42×C13C2411yescharacteristic
112#6103—22no—
113#6103—22no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13C22×C412yes—
117C4⋊Dic13C22×C412yes—
118#6101—22no—
119#6101—22no—
120C4×Dic13—22no—
121C4×Dic13—22no—
122C2×#1055—22no—
123C2×#1055—22no—
124C2×#1055—42no—
125C2×#1055—42no—
126#6095—28no—
127#6094—48no—
128C2×C8×Q8—131no—
129C2×C4×SD16—131no—
130C2×#436—131no—
131#1588—138no—
132C2×#335—131no—
133C2×Q8⋊C8—131no—
134C2×D4⋊C8—131no—
135C2×#322D1311yescharacteristic, complemented
136C23×C13C4×D411yescharacteristic
137C22×D13—22no—
138C22×D13—42no—
139C22×D13—42no—
140C22×D13—42no—
141C2×C4×C13—22no—
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13C2×M1612yes—
146C2×C4×C13#13112yes—
147C2×C4×C13AGL(1,ℤ/8)12yes—
148C2×C4×C13#13712yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C2×#4111yescharacteristic
152C2×Dic13—22no—
153C2×Dic13—24no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158D52—22no—
159D52—22no—
160D52—42no—
161C4×D13—42no—
162C4×D13—42no—
163C4×D13—44no—
164Dic26—22no—
165Dic26—24no—
166Dic26C2×M1614yescomplemented
167C8×C13—24no—
168C8×C13—22no—
169C8×C13—22no—
170C8×C13—22no—
171C8×C13—22no—
172#1055—42no—
173#1055—42no—
174C22×SD16—131no—
175C22×M16—261no—
176C2×C4×Q8—131no—
177C2×C4×D4—131no—
178C8×Q8—134no—
179C8×Q8—262no—
180C4×SD16—134no—
181C4×SD16—134no—
182#436—134no—
183#436—262no—
184C2×#106—131no—
185C2×C4⋊C8—131no—
186C2×C4⋊C8—131no—
187C2×C4⋊C8—261no—
188C2×#103—131no—
189C2×#102—131no—
190C2×C22⋊C8—261no—
191C2×C4×C8—261no—
192C2×C4×C8C2×D1311yescharacteristic
193C2×C4×C8C2×D1311yescharacteristic
194C2×C4×C8C2×D1311yescharacteristic
195#335—134no—
196Q8⋊C8—134no—
197D4⋊C8—134no—
198#322C2×D1314yescomplemented
199C22×C13#43512yes—
200C22×C13#44012yes—
201C22×C13#44312yes—
202C22×C13C2×C4×D411yescharacteristic
203C2×D13—42no—
204C2×D13—42no—
205C2×D13—42no—
206C2×D13—84no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13#43512yes—
210C4×C13#44012yes—
211C4×C13C22×M1611yescharacteristic
212C4×C13C2×#13111yescharacteristic
213C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
214C4×C13C2×#13711yescharacteristic
215Dic13—24no—
216Dic13—42no—
217Dic13—42no—
218C22×Q8—131no—
219C22×D4—131no—
220C23×C4—261no—
221C2×SD16—134no—
222C2×SD16—264no—
223C2×M16—264no—
224C2×M16—524no—
225C22×C8—21no—
226C22×C8—261no—
227C22×C8—261no—
228C22×C8C4×D1311yescharacteristic
229C22×C8C4×D1311yescharacteristic
230C22×C8D5211yescharacteristic
231C22×C8D5211yescharacteristic
232C4×Q8—132no—
233C4×Q8—132no—
234C4×Q8—261no—
235C4×Q8—261no—
236C4×D4—132no—
237C4×D4—132no—
238C4×D4—261no—
239C4×D4—261no—
240C2×C4⋊C4—131no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—261no—
243C2×C22⋊C4—261no—
244C2×C42—261no—
245C2×C42C22×D1311yescharacteristic
246#106—134no—
247C4⋊C8—132no—
248C4⋊C8—132no—
249C4⋊C8—264no—
250C4⋊C8—261no—
251C4⋊C8—261no—
252#103—134no—
253#102—134no—
254C22⋊C8—264no—
255C4×C8—21no—
256C4×C8—264no—
257C4×C8C4×D1312yes—
258C4×C8D5212yes—
259C4×C8C22×D1312yes—
260C4×C8C22×D1312yes—
261C4×C8C22×D1312yes—
262C2×C13#158814yescomplemented
263C2×C13C2×#43511yescharacteristic
264C2×C13C2×#44011yescharacteristic
265C2×C13C2×#44311yescharacteristic
266D13—82no—
267C24—261no—
268C2×Q8—134no—
269C2×Q8—132no—
270C2×Q8—261no—
271C2×Q8—262no—
272C2×D4—132no—
273C2×D4—261no—
274C2×D4—262no—
275C2×D4—262no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—522no—
282C22×C4—522no—
283C22×C4C2×C4×D1311yescharacteristic
284C22×C4C2×D5211yescharacteristic
285C22×C4#612711yescharacteristic
286SD16—268no—
287M16—528no—
288C2×C8—24no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—262no—
295C2×C8—262no—
296C2×C8—522no—
297C2×C8—522no—
298C2×C8C2×C4×D1312yes—
299C2×C8C2×C4×D1312yes—
300C2×C8C2×D5212yes—
301C2×C8C2×D5212yes—
302C4⋊C4—132no—
303C4⋊C4—132no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4—262no—
307C4⋊C4—262no—
308C22⋊C4—262no—
309C22⋊C4—262no—
310C42—262no—
311C42—262no—
312C42C2×C4×D1311yescharacteristic
313C42C2×D5211yescharacteristic
314C42#612711yescharacteristic
315C42C23×D1311yescharacteristic
316C13C2×#158811yescharacteristic, complemented, Sylow
317C23—262no—
318C23—522no—
319C23—522no—
320C23—522no—
321C23C4×D5211yescharacteristic
322Q8—134no—
323Q8—262no—
324Q8—264no—
325D4—262no—
326D4—262no—
327D4—522no—
328C2×C4—22no—
329C2×C4—262no—
330C2×C4—264no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—524no—
338C2×C4C4×D5211yescharacteristic
339C2×C4C4×D5211yescharacteristic
340C2×C4C4×D5211yescharacteristic
341C2×C4M16×D1312yes—
342C2×C4#8816112yes—
343C2×C4#8816212yes—
344C2×C4#8816312yes—
345C2×C4C22×C4×D1311yescharacteristic
346C2×C4C22×D5211yescharacteristic
347C2×C4C2×#612711yescharacteristic
348C8—24no—
349C8—22no—
350C8—22no—
351C8—22no—
352C8—22no—
353C8—522no—
354C8—522no—
355C22—522no—
356C22—522no—
357C22—522no—
358C22—1044no—
359C22#1171836112yes—
360C22#1171836712yes—
361C22#1171837112yes—
362C22C2×C4×D5211yescharacteristic
363C4—21no—
364C4—21no—
365C4—264no—
366C4—522no—
367C4—522no—
368C4#1171836712yes—
369C4#1171837112yes—
370C4C2×M16×D1311yescharacteristic
371C4C2×#8816111yescharacteristic
372C4C2×#8816211yescharacteristic
373C4C2×#8816311yescharacteristic
374C2—1042no—
375C2#1311371614yesdirect product factor
376C2C2×#1171836711yescharacteristic
377C2C2×#1171837111yescharacteristic
378C2C2×#1171836111yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#322C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenterC2×#322D13
hypocenterC13C2×#1588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
1. C2×C8×Dic26C2semidirect
4. #13113716C2direct (N × H)
5. C2×#11718050C2semidirect
6. C2×#11718048C2semidirect
8. C2×C13×#322C2semidirect
29. C8×Dic26C22semidirect
30. C13×#322C22semidirect
32. #11718050C22semidirect
33. #11718048C22semidirect
96. C2×Dic26M16semidirect
135. C2×#322D13semidirect
166. Dic26C2×M16semidirect
198. #322C2×D13semidirect
262. C2×C13#1588semidirect
316. C13C2×#1588semidirect
375. C2#13113716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×Dic262
C2×C4×#60952
C2×#117183492
#131137162
C2×#117180502
C2×#117180482
C2×#117180512
C2×C13×#3222
C2×#158813