Finite Group Databasebeta

← C2×#13130628 #16797118

Subgroups — C2×#13130628 #16797118

Order 3328.

1438 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88112C211yesmaximal, characteristic
2C22×C4×#1057C212yesmaximal
3C22×C4×#1057C211yesmaximal, characteristic
4#13130628C218yesmaximal, direct product factor
5C2×#11718290C212yesmaximal
6C2×#11718310C211yesmaximal, characteristic
7C23×#1057C2211yescharacteristic
8C23×#1057C2212yes—
9C23×#1057C2211yescharacteristic
10C22×#6101C412yes—
11C22×C4×Dic13C2212yes—
12C22×C4×Dic13C2211yescharacteristic
13C2×#88112C418yescomplemented
14C2×#88112C2214yes—
15C2×C4×#1057—28no—
16C2×C4×#1057C418yescomplemented
17C2×C4×#1057C2218yes—
18C2×C4×#1057C2214yes—
19C2×C13×#95C411yescharacteristic
20C2×#88071C411yescharacteristic
21#11718310C414yes—
22#11718310C2214yes—
23#11718290C2218yes—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C412yes—
26C23×Dic13C2×C412yes—
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2311yescharacteristic
29C22×#1057—24no—
30C22×#1057—22no—
31C22×#1057—22no—
32C22×#1057—24no—
33C22×#1057C2×C414yes—
34C22×#1057C2×C418yes—
35C22×#1057C2×C414yes—
36C22×#1057D414yes—
37C22×#1057Q814yes—
38C22×#1057C2312yes—
39C22×#1057C2314yes—
40C22×#1057C2312yes—
41C2×#6101C8116yescomplemented
42C2×#6101C2×C418yes—
43C2×C4×Dic13—24no—
44C2×C4×Dic13—24no—
45C2×C4×Dic13C2×C414yes—
46C2×C4×Dic13C2×C412yes—
47C2×C4×Dic13C2×C414yes—
48C2×C4×Dic13C2×C414yes—
49C2×C4×Dic13C2314yes—
50C2×C4×Dic13C2312yes—
51#88112C2×C4116yescomplemented
52C4×#1057—216no—
53C4×#1057C2×C4116yescomplemented
54C13×#95C2×C414yes—
55#88071C2×C414yes—
56C2×C8×C4⋊C4—131nomaximal, Sylow
57C24×C13C22×C411yescharacteristic
58C22×C4×C13—24no—
59C22×C4×C13—24no—
60C22×C4×C13—24no—
61C22×C4×C13C4214yes—
62C22×C4×C13C2×C818yes—
63C22×C4×C13C22×C412yes—
64C22×C4×C13C22×C414yes—
65C22×Dic13—24no—
66C22×Dic13—24no—
67C22×Dic13C4214yes—
68C22×Dic13C2×C818yes—
69C22×Dic13C2×C818yes—
70C22×Dic13C22×C414yes—
71C22×Dic13C22×C411yescharacteristic
72C22×Dic13C22×C412yes—
73C22×Dic13C22×C412yes—
74C22×Dic13C22×C412yes—
75C22×Dic13C2×D412yes—
76C22×Dic13C2×Q812yes—
77C22×Dic13#4112yes—
78C22×Dic13#4112yes—
79C22×Dic13C2411yescharacteristic
80C2×#1057—28no—
81C2×#1057—216no—
82C2×#1057—24no—
83C2×#1057—22no—
84C2×#1057—22no—
85C2×#1057—24no—
86C2×#1057C4⋊C4116yescomplemented
87C2×#1057C22×C414yes—
88C2×#1057C22×C418yes—
89C2×#1057C22×C414yes—
90C2×#1057C2×D414yes—
91C2×#1057C2×Q814yes—
92#6101C2×C8132yescomplemented
93C4×Dic13—28no—
94C4×Dic13—24no—
95C4×Dic13—24no—
96C4×Dic13C4218yes—
97C4×Dic13C22×C414yes—
98C4×Dic13C22×C414yes—
99C22×C4⋊C8—131no—
100C22×C4×C8—131no—
101C22×C4×C8—132no—
102C2×C4×C4⋊C4—131no—
103C8×C4⋊C4—138no—
104C2×#336—132no—
105C23×C13C2×C4212yes—
106C23×C13C4×D412yes—
107C23×C13C4×Q812yes—
108C23×C13C22×C814yes—
109C23×C13#13114yes—
110C23×C13C23×C411yescharacteristic
111C2×C4×C13—24no—
112C2×C4×C13—24no—
113C2×C4×C13—24no—
114C2×C4×C13—28no—
115C2×C4×C13—216no—
116C2×C4×C13C2×C4214yes—
117C2×C4×C13C22×C818yes—
118C2×Dic13—24no—
119C2×Dic13—24no—
120C2×Dic13—216no—
121C2×Dic13C4×C8116yescomplemented
122C2×Dic13C2×C4212yes—
123C2×Dic13C2×C4214yes—
124C2×Dic13C2×C4⋊C414yes—
125C2×Dic13#11714yes—
126C2×Dic13C4×D414yes—
127C2×Dic13C4×D412yes—
128C2×Dic13C4×Q814yes—
129C2×Dic13C4×Q812yes—
130C2×Dic13C22×C818yes—
131C2×Dic13C22×C818yes—
132C2×Dic13C23×C411yescharacteristic
133C2×Dic13C23×C411yescharacteristic
134C2×Dic13C22×D411yescharacteristic
135C2×Dic13C22×Q811yescharacteristic
136C2×Dic13C2×#4111yescharacteristic
137C2×Dic13C2×#4111yescharacteristic
138#1057—24no—
139#1057—28no—
140#1057C2×C4⋊C418yescomplemented
141C23×C8—131no—
142C23×C8—132no—
143C23×C8—131no—
144C22×C4⋊C4—132no—
145C22×C42—131no—
146C22×C42—132no—
147C2×C4⋊C8—138no—
148C2×C4⋊C8—134no—
149C2×C4×C8—138no—
150C2×C4×C8—134no—
151C2×C4×C8—138no—
152C2×C4×C8—268no—
153C4×C4⋊C4—134no—
154C4×C4⋊C4—134no—
155C2×#95—131no—
156C2×#95#26111yescharacteristic
157#336—138no—
158C22×C13C4×C4⋊C414yes—
159C22×C13C2×C4×C814yes—
160C22×C13#40514yes—
161C22×C13C8×D418yes—
162C22×C13C8×Q818yes—
163C22×C13C22×C4211yescharacteristic
164C22×C13C2×C4×D411yescharacteristic
165C22×C13C2×C4×Q811yescharacteristic
166C22×C13C23×C812yes—
167C22×C13C2×#13112yes—
168C4×C13—24no—
169C4×C13—28no—
170Dic13—28no—
171Dic13C4×C4⋊C414yes—
172Dic13C2×C4×C818yescomplemented
173Dic13C22×C4⋊C411yescharacteristic
174Dic13C2×#11711yescharacteristic
175Dic13C2×C4×D411yescharacteristic
176Dic13C2×C4×Q811yescharacteristic
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—132no—
180C23×C4C2×#26112yes—
181C23×C4C2×#26111yescharacteristic
182C22×C8—132no—
183C22×C8—134no—
184C22×C8—134no—
185C22×C8—134no—
186C22×C8—132no—
187C22×C8—134no—
188C22×C8—134no—
189C22×C8—138no—
190C22×C8—264no—
191C22×C8—262no—
192C22×C8—264no—
193C22×C8—262no—
194C2×C4⋊C4—1316no—
195C2×C4⋊C4—138no—
196C2×C42—134no—
197C2×C42—134no—
198C2×C42—132no—
199C2×C42—132no—
200C2×C42—134no—
201C2×C42—134no—
202C2×C42—264no—
203C2×C42—264no—
204C4⋊C8—1316no—
205C4×C8—1316no—
206C4×C8—2616no—
207#95—134no—
208#95C2×#26114yes—
209C2×C13C8×C4⋊C418yescomplemented
210C2×C13C2×C4×C4⋊C411yescharacteristic
211C2×C13C22×C4×C811yescharacteristic
212C2×C13C2×#40511yescharacteristic
213C2×C13C2×C8×D412yes—
214C2×C13C2×C8×Q812yes—
215C24C22×#26111yescharacteristic
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—138no—
220C22×C4—132no—
221C22×C4—132no—
222C22×C4—134no—
223C22×C4—132no—
224C22×C4—132no—
225C22×C4—132no—
226C22×C4—132no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—132no—
230C22×C4—138no—
231C22×C4—134no—
232C22×C4—264no—
233C22×C4—264no—
234C22×C4D13⋊C818yes—
235C22×C4C4×#26114yes—
236C22×C4C22×#26114yes—
237C22×C4C22×#26112yes—
238C2×C8—134no—
239C2×C8—134no—
240C2×C8—1316no—
241C2×C8—134no—
242C2×C8—134no—
243C2×C8—138no—
244C2×C8—264no—
245C2×C8—2616no—
246C2×C8—268no—
247C2×C8—262no—
248C2×C8—262no—
249C2×C8—264no—
250C4⋊C4—1332no—
251C42—134no—
252C42—134no—
253C42—138no—
254C42—264no—
255C42—264no—
256C42—268no—
257C13C2×C8×C4⋊C411yescharacteristic, complemented, Sylow
258C23C2×D13⋊C814yes—
259C23C2×C4×#26112yes—
260C23#8823814yes—
261C23D4×#26112yes—
262C23Q8×#26112yes—
263C23C23×#26111yescharacteristic
264C2×C4—28no—
265C2×C4—216no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—1316no—
270C2×C4—134no—
271C2×C4—134no—
272C2×C4—134no—
273C2×C4—134no—
274C2×C4—138no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—132no—
278C2×C4—134no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—132no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—132no—
285C2×C4—138no—
286C2×C4—2616no—
287C2×C4—264no—
288C2×C4—264no—
289C2×C4C2×D13⋊C818yes—
290C2×C4C2×C4×#26114yes—
291C8—138no—
292C8—264no—
293C8—268no—
294C22C4×D13⋊C814yes—
295C22#1171906214yes—
296C22#1171906318yes—
297C22#1171907418yes—
298C22C4⋊C4×#26114yes—
299C22C22×D13⋊C812yes—
300C22C22×C4×#26111yescharacteristic
301C22C2×#8823812yes—
302C22C2×D4×#26111yescharacteristic
303C22C2×Q8×#26111yescharacteristic
304C4—28no—
305C4—24no—
306C4—131no—
307C4—131no—
308C4—131no—
309C4—131no—
310C4—134no—
311C4—138no—
312C4—268no—
313C2#1313062818yesdirect product factor
314C2C2×C4⋊C4×#26111yescharacteristic
315C2C2×C4×D13⋊C811yescharacteristic
316C2C2×#1171906211yescharacteristic
317C2C2×#1171906312yes—
318C2C2×#1171907412yes—
subgroupG/H
centerC24C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC2×C13×#95C4
socle, prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#95#261
hypocenterC13C2×C8×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. #13130628C2direct (N × H)
13. C2×#88112C4semidirect
16. C2×C4×#1057C4semidirect
41. C2×#6101C8semidirect
51. #88112C2×C4semidirect
53. C4×#1057C2×C4semidirect
86. C2×#1057C4⋊C4semidirect
92. #6101C2×C8semidirect
121. C2×Dic13C4×C8semidirect
140. #1057C2×C4⋊C4semidirect
172. Dic13C2×C4×C8semidirect
209. C2×C13C8×C4⋊C4semidirect
257. C13C2×C8×C4⋊C4semidirect
313. C2#13130628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881122
C22×C4×#10572
#131306282
C2×#117182902
C2×#117183102
C2×C8×C4⋊C413