Finite Group Databasebeta

← C2×#13114552 #15860318

Subgroups — C2×#13114552 #15860318

Order 3328.

2398 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×#1055C211yesmaximal, characteristic
2C22×#88180C211yesmaximal, characteristic
3#13114552C218yesmaximal, direct product factor
4C2×#11718121C214yesmaximal, complemented
5C22×C13×#117C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C2×C13×#117—24no—
8C2×C13×#117—22no—
9C2×C13×#117C418yescomplemented
10C2×C13×#117C2214yes—
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C22⋊C4—21no—
13C22×C42×C13—21no—
14C22×C22⋊Dic13—21no—
15C2×#88180—24no—
16C2×#88180—22no—
17C2×#88180C418yescomplemented
18C2×#88180C2214yes—
19C22×C4⋊Dic13C2212yes—
20C22×C4×Dic13—21no—
21C23×#1055—24no—
22C23×#1055—24no—
23C23×#1055C418yescomplemented
24C23×#1055C2212yes—
25C23×#1055C2214yes—
26#11718121C22116yescomplemented
27C25×C13D411yescharacteristic
28C23×C4×C13—22no—
29C23×C4×C13C2×C414yes—
30C23×C4×C13C2×C414yes—
31C23×C4×C13C2×C414yes—
32C23×C4×C13D414yes—
33C23×C4×C13D412yes—
34C23×C4×C13D414yes—
35C23×C4×C13D411yescharacteristic
36C23×C4×C13Q814yes—
37C23×C4×C13C2311yescharacteristic
38C23×C4×C13C2312yes—
39C23×Dic13—22no—
40C13×#117—216no—
41C13×#117—28no—
42C13×#117C2×C4116yescomplemented
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4C2×C418yes—
46C2×C13×C4⋊C4C2314yes—
47C2×C13×C22⋊C4—28no—
48C2×C13×C22⋊C4—24no—
49C2×C42×C13—28no—
50C2×C42×C13—24no—
51C2×C22⋊Dic13—28no—
52C2×C22⋊Dic13—24no—
53#88180—216no—
54#88180—28no—
55#88180C2×C4116yescomplemented
56C2×C4⋊Dic13—24no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13C2×C418yes—
59C2×C4⋊Dic13C2314yes—
60C2×C4×Dic13—28no—
61C2×C4×Dic13—24no—
62C22×#1055—232no—
63C22×#1055—24no—
64C22×#1055—28no—
65C22×#1055—24no—
66C22×#1055—28no—
67C22×#1055C2×C418yes—
68C22×#1055C2×C4116yescomplemented
69C22×#1055C2314yes—
70C2×#1735—131nomaximal, Sylow
71C24×C13—28no—
72C24×C13C22⋊C414yes—
73C24×C13C22⋊C414yes—
74C24×C13C4⋊C414yes—
75C24×C13C2×D412yes—
76C24×C13C2×D411yescharacteristic
77C22×C4×C13—28no—
78C22×C4×C13—24no—
79C22×C4×C13—48no—
80C22×C4×C13C42116yes—
81C22×C4×C13C22⋊C414yes—
82C22×C4×C13C22⋊C418yes—
83C22×C4×C13C22⋊C4116yes—
84C22×C4×C13C22⋊C414yes—
85C22×C4×C13C22⋊C418yes—
86C22×C4×C13C4⋊C418yes—
87C22×C4×C13C4⋊C414yes—
88C22×C4×C13C4⋊C4116yes—
89C22×C4×C13C4⋊C4116yes—
90C22×C4×C13C22×C412yes—
91C22×C4×C13C22×C414yes—
92C22×C4×C13C22×C412yes—
93C22×C4×C13C22×C414yes—
94C22×C4×C13C22×C412yes—
95C22×C4×C13C22×C414yes—
96C22×C4×C13C2×D412yes—
97C22×C4×C13C2×D414yes—
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D414yes—
102C22×C4×C13C2×Q814yes—
103C22×C4×C13C2×Q812yes—
104C22×C4×C13C2411yescharacteristic
105C22×Dic13—28no—
106C22×Dic13—24no—
107C22×Dic13—48no—
108C13×C4⋊C4—28no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4C22×C418yes—
111C13×C22⋊C4—216no—
112C42×C13—216no—
113C22⋊Dic13—216no—
114C4⋊Dic13—28no—
115C4⋊Dic13—24no—
116C4⋊Dic13C22×C418yes—
117C4×Dic13—216no—
118C2×#1055—216no—
119C2×#1055—232no—
120C2×#1055—24no—
121C2×#1055—24no—
122C2×#1055C22×C418yes—
123C24×C8—131no—
124C22×#117—131no—
125C22×#117D1311yescharacteristic
126#1735—138no—
127C2×#340—134no—
128C23×C13—28no—
129C23×C13—216no—
130C23×C13—216no—
131C23×C13—216no—
132C23×C13#95116yes—
133C23×C13C2×C22⋊C414yes—
134C23×C13C2×C22⋊C414yes—
135C23×C13C2×C22⋊C412yes—
136C23×C13C2×C22⋊C412yes—
137C23×C13C2×C4⋊C414yes—
138C23×C13C2×C4⋊C412yes—
139C23×C13#13518yes—
140C23×C13C22×D411yescharacteristic
141C2×C4×C13—28no—
142C2×C4×C13—48no—
143C2×C4×C13—416no—
144C2×C4×C13#95132yes—
145C2×C4×C13#95116yes—
146C2×C4×C13C2×C4218yes—
147C2×C4×C13C2×C4214yes—
148C2×C4×C13C2×C22⋊C418yes—
149C2×C4×C13C2×C22⋊C414yes—
150C2×C4×C13C2×C22⋊C414yes—
151C2×C4×C13C2×C22⋊C412yes—
152C2×C4×C13C2×C22⋊C414yes—
153C2×C4×C13C2×C22⋊C412yes—
154C2×C4×C13C2×C4⋊C418yes—
155C2×C4×C13C2×C4⋊C414yes—
156C2×C4×C13C2×C4⋊C418yes—
157C2×C4×C13C2×C4⋊C414yes—
158C2×C4×C13C2×C4⋊C412yes—
159C2×C4×C13C2×C4⋊C414yes—
160C2×C4×C13C23×C411yescharacteristic
161C2×C4×C13C23×C411yescharacteristic
162C2×C4×C13C23×C411yescharacteristic
163C2×C4×C13C22×D411yescharacteristic
164C2×C4×C13C22×D411yescharacteristic
165C2×C4×C13C22×Q811yescharacteristic
166C2×Dic13—28no—
167C2×Dic13—48no—
168C2×Dic13—416no—
169#1055—28no—
170C24×C4C2×D1311yescharacteristic
171C23×C8—138no—
172C23×C8—132no—
173C23×C8—134no—
174C23×C8—264no—
175C23×C8—264no—
176C2×#117—24no—
177C2×#117—22no—
178C2×#117—138no—
179C2×#117—134no—
180C2×#117—264no—
181C2×#117—262no—
182C2×#117Dic1318yescomplemented
183C2×#117C2×D1314yes—
184C22×C4⋊C4—132no—
185C22×C4⋊C4C2×D1312yes—
186C22×C22⋊C4—21no—
187C22×C22⋊C4—261no—
188C22×C42—21no—
189C22×C42—261no—
190#340—1316no—
191C22×C13—28no—
192C22×C13—28no—
193C22×C13—28no—
194C22×C13—232no—
195C22×C13C2×#9518yes—
196C22×C13C2×#9514yes—
197C22×C13#41618yes—
198C22×C13#41618yes—
199C22×C13#42718yes—
200C22×C13C22×C22⋊C411yescharacteristic
201C22×C13C22×C22⋊C411yescharacteristic
202C22×C13C22×C4⋊C411yescharacteristic
203C22×C13C2×#13514yes—
204C4×C13—48no—
205C4×C13C2×#9518yes—
206C4×C13C2×#9514yes—
207C4×C13C22×C4211yescharacteristic
208C4×C13C22×C22⋊C411yescharacteristic
209C4×C13C22×C4⋊C411yescharacteristic
210C4×C13C22×C4⋊C411yescharacteristic
211Dic13—48no—
212C25C22⋊D1311yescharacteristic
213C23×C4—22no—
214C23×C4—262no—
215C23×C4Dic2614yes—
216C23×C4C4×D1314yes—
217C23×C4C4×D1314yes—
218C23×C4D5214yes—
219C23×C4C2×Dic1314yes—
220C23×C4C22⋊D1312yes—
221C23×C4C22⋊D1314yes—
222C23×C4C22⋊D1311yescharacteristic
223C23×C4C22×D1311yescharacteristic
224C23×C4C22×D1312yes—
225C22×C8—138no—
226C22×C8—1316no—
227C22×C8—134no—
228C22×C8—2632no—
229C22×C8—264no—
230C22×C8—268no—
231C22×C8—264no—
232C22×C8—268no—
233#117—216no—
234#117—28no—
235#117—1316no—
236#117—2616no—
237#117—268no—
238#117C2×Dic13116yescomplemented
239C2×C4⋊C4—22no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—138no—
242C2×C4⋊C4—134no—
243C2×C4⋊C4—264no—
244C2×C4⋊C4—262no—
245C2×C4⋊C4C2×Dic1318yes—
246C2×C4⋊C4C22×D1314yes—
247C2×C22⋊C4—28no—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—268no—
250C2×C22⋊C4—264no—
251C2×C42—28no—
252C2×C42—24no—
253C2×C42—268no—
254C2×C42—264no—
255C2×C13—28no—
256C2×C13#173518yescomplemented
257C2×C13C22×#9511yescharacteristic
258C2×C13C2×#41612yes—
259C2×C13C2×#41612yes—
260C2×C13C2×#42712yes—
261C24—28no—
262C24#610114yes—
263C24#610314yes—
264C24C22⋊Dic1314yes—
265C24C2×C22⋊D1312yes—
266C24C2×C22⋊D1311yescharacteristic
267C22×C4—28no—
268C22×C4—24no—
269C22×C4—48no—
270C22×C4—268no—
271C22×C4—264no—
272C22×C4—528no—
273C22×C4C4×Dic13116yes—
274C22×C4#610118yes—
275C22×C4#610114yes—
276C22×C4#6101116yes—
277C22×C4C4⋊Dic13116yes—
278C22×C4#610314yes—
279C22×C4#610318yes—
280C22×C4#6103116yes—
281C22×C4C22⋊Dic1314yes—
282C22×C4C22⋊Dic1318yes—
283C22×C4C2×Dic2614yes—
284C22×C4C2×Dic2612yes—
285C22×C4C2×C4×D1312yes—
286C22×C4C2×C4×D1314yes—
287C22×C4C2×C4×D1314yes—
288C22×C4C2×C4×D1312yes—
289C22×C4C2×D5212yes—
290C22×C4C2×D5214yes—
291C22×C4C22×Dic1312yes—
292C22×C4C22×Dic1314yes—
293C22×C4C2×C22⋊D1312yes—
294C22×C4C2×C22⋊D1311yescharacteristic
295C22×C4C2×C22⋊D1312yes—
296C22×C4C2×C22⋊D1314yes—
297C22×C4C23×D1311yescharacteristic
298C2×C8—138no—
299C2×C8—2616no—
300C2×C8—2632no—
301C2×C8—264no—
302C2×C8—264no—
303C4⋊C4—28no—
304C4⋊C4—24no—
305C4⋊C4—138no—
306C4⋊C4—268no—
307C4⋊C4—264no—
308C4⋊C4C22×Dic1318yes—
309C22⋊C4—216no—
310C22⋊C4—2616no—
311C42—216no—
312C42—2616no—
313C13C2×#173511yescharacteristic, complemented, Sylow
314C23—216no—
315C23—216no—
316C23—28no—
317C23—216no—
318C23#88071116yes—
319C23C2×#610114yes—
320C23C2×#610112yes—
321C23C2×#610314yes—
322C23C2×#610312yes—
323C23#8820418yes—
324C23C2×C22⋊Dic1314yes—
325C23C2×C22⋊Dic1312yes—
326C23C22×C22⋊D1311yescharacteristic
327C2×C4—28no—
328C2×C4—48no—
329C2×C4—416no—
330C2×C4—268no—
331C2×C4—5216no—
332C2×C4—528no—
333C2×C4#88071132yes—
334C2×C4#88071116yes—
335C2×C4C2×C4×Dic1318yes—
336C2×C4C2×C4×Dic1314yes—
337C2×C4C2×#610118yes—
338C2×C4C2×#610114yes—
339C2×C4C2×#610112yes—
340C2×C4C2×#610114yes—
341C2×C4C2×C4⋊Dic1318yes—
342C2×C4C2×C4⋊Dic1314yes—
343C2×C4C2×#610318yes—
344C2×C4C2×#610314yes—
345C2×C4C2×#610314yes—
346C2×C4C2×#610312yes—
347C2×C4C2×C22⋊Dic1314yes—
348C2×C4C2×C22⋊Dic1312yes—
349C2×C4C22×Dic2611yescharacteristic
350C2×C4C22×C4×D1311yescharacteristic
351C2×C4C22×C4×D1311yescharacteristic
352C2×C4C22×D5211yescharacteristic
353C2×C4C23×Dic1311yescharacteristic
354C2×C4C22×C22⋊D1311yescharacteristic
355C8—268no—
356C22—28no—
357C22—28no—
358C22—28no—
359C22—232no—
360C22#1171865918yes—
361C22#1171866318yes—
362C22C2×#8807118yes—
363C22C2×#8807114yes—
364C22#1171889418yes—
365C22C22×#610111yescharacteristic
366C22C22×#610311yescharacteristic
367C22C2×#8820414yes—
368C22C22×C22⋊Dic1311yescharacteristic
369C4—48no—
370C4—528no—
371C4C2×#8807118yes—
372C4C2×#8807114yes—
373C4C22×C4×Dic1311yescharacteristic
374C4C22×#610111yescharacteristic
375C4C22×C4⋊Dic1311yescharacteristic
376C4C22×#610311yescharacteristic
377C2—28no—
378C2#1311455218yesdirect product factor
379C2C22×#8807111yescharacteristic
380C2C2×#1171866312yes—
381C2C2×#1171889412yes—
382C2C2×#1171865912yes—
subgroupG/H
centerC23×C4C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C13×#117C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC22×C4×C13C24
hypercenterC22×#117D13
hypocenterC13C2×#1735
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #13114552C2direct (N × H)
4. C2×#11718121C2semidirect
9. C2×C13×#117C4semidirect
17. C2×#88180C4semidirect
23. C23×#1055C4semidirect
26. #11718121C22semidirect
42. C13×#117C2×C4semidirect
55. #88180C2×C4semidirect
68. C22×#1055C2×C4semidirect
182. C2×#117Dic13semidirect
238. #117C2×Dic13semidirect
256. C2×C13#1735semidirect
313. C13C2×#1735semidirect
378. C2#13114552direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#10552
C22×#881802
#131145522
C2×#117181212
C22×C13×#1172
C2×#173513