Finite Group Databasebeta

← C2×#13120225 #16034156

Subgroups — C2×#13120225 #16034156

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic
2#13120225C2116yesmaximal, direct product factor
3C2×#11718644C212yesmaximal
4C2×#11718640C212yesmaximal
5C2×#11718634C212yesmaximal
6C2×#11718634C212yesmaximal
7C2×#11718633C214yesmaximal
8C2×C4×C4⋊Dic13C211yesmaximal, characteristic
9C22×C13×#125C211yesmaximal, characteristic
10C23×Dic26C2211yescharacteristic
11C2×C13×#125—28no—
12C2×C13×#125C2218yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2212yes—
20C22×#6101C2212yes—
21C22×#6101C2214yes—
22C22×#6101C2214yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2212yes—
25C2×C4×Dic26—28no—
26C2×C4×Dic26C2218yes—
27C2×#88071C2214yes—
28C2×#88071C2212yes—
29C2×#88071C2214yes—
30#11718644C22116yes—
31#11718640C22116yes—
32#11718634C22116yes—
33#11718634C22116yes—
34#11718633C22132yes—
35C4×C4⋊Dic13C2218yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2314yes—
43C23×Dic13C2312yes—
44C22×Dic26—24no—
45C22×Dic26—28no—
46C22×Dic26C2314yes—
47C13×#125—232no—
48C2×C13×C4⋊C4—28no—
49C2×C13×C4⋊C4—28no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4C2318yes—
53C2×C13×C4⋊C4C2314yes—
54C2×C13×C4⋊C4C2314yes—
55C2×C13×C4⋊C4C2318yes—
56C2×C42×C13D418yes—
57C2×C42×C13C2314yes—
58C2×C4⋊Dic13—24no—
59C2×C4⋊Dic13Q8116yescomplemented
60C2×C4⋊Dic13C2314yes—
61C2×C4⋊Dic13C2318yes—
62C2×#6101—28no—
63C2×#6101—216no—
64C2×#6101—48no—
65C2×#6101C2318yes—
66C2×#6101C23116yes—
67C2×#6101C23116yes—
68C2×C4×Dic13—28no—
69C2×C4×Dic13—44no—
70C2×C4×Dic13C2318yes—
71C2×C4×Dic13C2318yes—
72C4×Dic26—232no—
73#88071C2318yes—
74#88071C23116yes—
75#88071C23116yes—
76C2×#2584—131nomaximal, Sylow
77C24×C13C2411yescharacteristic
78C22×C4×C13—24no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—24no—
82C22×C4×C13—24no—
83C22×C4×C13—28no—
84C22×C4×C13—24no—
85C22×C4×C13—24no—
86C22×C4×C13C2×D414yes—
87C22×C4×C13C2×D414yes—
88C22×C4×C13C2×D414yes—
89C22×C4×C13C2×Q818yes—
90C22×C4×C13C2414yes—
91C22×C4×C13C2414yes—
92C22×C4×C13C2412yes—
93C22×C4×C13C2412yes—
94C22×C4×C13C2412yes—
95C22×Dic13—24no—
96C22×Dic13—28no—
97C22×Dic13—24no—
98C22×Dic13—28no—
99C22×Dic13—24no—
100C22×Dic13—24no—
101C22×Dic13—24no—
102C22×Dic13C2×Q8116yes—
103C22×Dic13#4118yes—
104C22×Dic13C2414yes—
105C22×Dic13C2418yes—
106C22×Dic13C2414yes—
107C2×Dic26—232no—
108C2×Dic26—28no—
109C2×Dic26—216no—
110C13×C4⋊C4—216no—
111C13×C4⋊C4—216no—
112C13×C4⋊C4—28no—
113C13×C4⋊C4—28no—
114C42×C13C2×D4116yes—
115C4⋊Dic13—28no—
116C4⋊Dic13C2×Q8132yescomplemented
117#6101—216no—
118#6101—232no—
119#6101—416no—
120C4×Dic13—216no—
121C4×Dic13—48no—
122C22×#125D1311yescharacteristic
123C22×C4×Q8—131no—
124#2584—1316no—
125C2×#398—132no—
126C2×#395—132no—
127C2×#389—134no—
128C2×#389—132no—
129C2×#389—132no—
130C2×C4×C4⋊C4—131no—
131C23×C13C22×D412yes—
132C23×C13C22×Q814yes—
133C23×C13C2×#4114yes—
134C23×C13H(5,𝔽2)12yes—
135C23×C132−1+412yes—
136C23×C13C2511yescharacteristic
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13—24no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—28no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—48no—
148C2×C4×C13—48no—
149C2×C4×C13C4⋊Q8116yes—
150C2×C4×C13C22×D414yes—
151C2×C4×C13C22×D414yes—
152C2×C4×C13C22×D414yes—
153C2×C4×C13C22×Q818yes—
154C2×Dic13—216no—
155C2×Dic13—232no—
156C2×Dic13—24no—
157C2×Dic13—28no—
158C2×Dic13—24no—
159C2×Dic13—28no—
160C2×Dic13—24no—
161C2×Dic13—24no—
162C2×Dic13—24no—
163C2×Dic13—48no—
164C2×Dic13C22×Q8116yes—
165C2×Dic13C2×#4118yes—
166Dic26—232no—
167C23×Q8—131no—
168C2×#125—28no—
169C2×#125C2×D1318yes—
170C2×C4×Q8—138no—
171C2×C4×Q8—268no—
172C22×C4⋊C4—132no—
173C22×C4⋊C4—134no—
174C22×C4⋊C4—132no—
175C22×C4⋊C4—131no—
176C22×C4⋊C4—134no—
177C22×C4⋊C4C2×D1312yes—
178C22×C4⋊C4C2×D1312yes—
179C22×C4⋊C4C2×D1311yescharacteristic
180C22×C4⋊C4C2×D1311yescharacteristic
181C22×C42—132no—
182C22×C42—132no—
183C22×C42C2×D1311yescharacteristic
184#398—1316no—
185#395—1316no—
186#389—1332no—
187#389—1316no—
188#389—1316no—
189C4×C4⋊C4—138no—
190C2×#95—132no—
191C2×#95—134no—
192C2×#95—134no—
193C22×C13#52514yes—
194C22×C13C2×C4⋊Q814yes—
195C22×C13#53714yes—
196C22×C13#55418yes—
197C22×C13#55718yes—
198C22×C13C23×D411yescharacteristic
199C22×C13C23×Q812yes—
200C22×C13C22×#4112yes—
201C22×C13C2×H(5,𝔽2)11yescharacteristic
202C22×C13C2×2−1+411yescharacteristic
203C4×C13—24no—
204C4×C13—24no—
205C4×C13—44no—
206C4×C13—44no—
207C4×C13C2×C4⋊Q818yes—
208Dic13—28no—
209Dic13—216no—
210Dic13—44no—
211C22×Q8—134no—
212C22×Q8—268no—
213C22×Q8—264no—
214C23×C4—132no—
215C23×C4—134no—
216C23×C4—132no—
217C23×C4C22×D1312yes—
218C23×C4C22×D1312yes—
219C23×C4C22×D1311yescharacteristic
220C23×C4C22×D1311yescharacteristic
221C23×C4C22×D1311yescharacteristic
222#125—232no—
223C4×Q8—2632no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—1316no—
229C2×C4⋊C4—138no—
230C2×C4⋊C4—138no—
231C2×C4⋊C4—134no—
232C2×C4⋊C4—1316no—
233C2×C4⋊C4—1316no—
234C2×C4⋊C4—2616no—
235C2×C4⋊C4—268no—
236C2×C4⋊C4—264no—
237C2×C4⋊C4—528no—
238C2×C4⋊C4C22×D1318yes—
239C2×C4⋊C4C22×D1314yes—
240C2×C4⋊C4C22×D1314yes—
241C2×C4⋊C4C22×D1318yes—
242C2×C42—138no—
243C2×C42—138no—
244C2×C42—268no—
245C2×C42—524no—
246C2×C42C22⋊D1318yes—
247C2×C42C22×D1314yes—
248#95—138no—
249#95—1316no—
250#95—1316no—
251C2×C13#258418yescomplemented
252C2×C13C2×#52511yescharacteristic
253C2×C13C22×C4⋊Q811yescharacteristic
254C2×C13C2×#53711yescharacteristic
255C2×C13C2×#55412yes—
256C2×C13C2×#55712yes—
257C24C23×D1311yescharacteristic
258C2×Q8—2616no—
259C2×Q8—2632no—
260C2×Q8—268no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—28no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—1316no—
270C22×C4—138no—
271C22×C4—138no—
272C22×C4—134no—
273C22×C4—134no—
274C22×C4—268no—
275C22×C4—264no—
276C22×C4—268no—
277C22×C4—264no—
278C22×C4—264no—
279C22×C4—264no—
280C22×C4—264no—
281C22×C4Q8×D1318yes—
282C22×C4C2×C22⋊D1314yes—
283C22×C4C2×C22⋊D1314yes—
284C22×C4C2×C22⋊D1314yes—
285C22×C4C23×D1314yes—
286C22×C4C23×D1314yes—
287C22×C4C23×D1312yes—
288C22×C4C23×D1312yes—
289C22×C4C23×D1312yes—
290C4⋊C4—216no—
291C4⋊C4—216no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—1332no—
295C4⋊C4—2632no—
296C4⋊C4—2616no—
297C4⋊C4—268no—
298C4⋊C4—5216no—
299C42—2616no—
300C42—528no—
301C42C2×C22⋊D13116yes—
302C13C2×#258411yescharacteristic, complemented, Sylow
303C23C2×Q8×D1314yes—
304C23#41×D1314yes—
305C23#8825612yes—
306C23#8825712yes—
307C23C22×C22⋊D1312yes—
308C23C24×D1311yescharacteristic
309Q8—2632no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—28no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—48no—
321C2×C4—48no—
322C2×C4—1316no—
323C2×C4—138no—
324C2×C4—2616no—
325C2×C4—268no—
326C2×C4—264no—
327C2×C4—268no—
328C2×C4—2632no—
329C2×C4—264no—
330C2×C4—264no—
331C2×C4—264no—
332C2×C4—264no—
333C2×C4—528no—
334C2×C4#88198116yes—
335C2×C4C2×Q8×D1318yes—
336C2×C4C22×C22⋊D1314yes—
337C2×C4C22×C22⋊D1314yes—
338C2×C4C22×C22⋊D1314yes—
339C22#1171939018yes—
340C22#1171939518yes—
341C22C2×#8819814yes—
342C22#1171953314yes—
343C22#1171953814yes—
344C22C22×Q8×D1312yes—
345C22C2×#41×D1312yes—
346C22C2×#8825611yescharacteristic
347C22C2×#8825711yescharacteristic
348C22C23×C22⋊D1311yescharacteristic
349C4—24no—
350C4—24no—
351C4—44no—
352C4—44no—
353C4—268no—
354C4—2616no—
355C4—524no—
356C4C2×#8819818yes—
357C2#1312022518yesdirect product factor
358C2C2×#1171953311yescharacteristic
359C2C22×#8819811yescharacteristic
360C2C2×#1171953811yescharacteristic
361C2C2×#1171939512yes—
362C2C2×#1171939012yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#125C2
socle, prime radicalC24×C13C24
hypercenterC22×#125D13
hypocenterC13C2×#2584
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13120225C2direct (N × H)
59. C2×C4⋊Dic13Q8semidirect
116. C4⋊Dic13C2×Q8semidirect
251. C2×C13#2584semidirect
302. C13C2×#2584semidirect
357. C2#13120225direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
#131202252
C2×#117186442
C2×#117186402
C2×#117186342
C2×#117186332
C2×C4×C4⋊Dic132
C22×C13×#1252
C2×#258413