Finite Group Databasebeta

← C2×#13131565 #16808277

Subgroups — C2×#13131565 #16808277

Order 3328.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88238C212yesmaximal, complemented
2#13131565C2116yesmaximal, direct product factor
3C2×#11719144C218yesmaximal, complemented
4C2×#11719053C211yesmaximal, characteristic, complemented
5C2×#11719147C212yesmaximal, complemented
6C2×#11719047C211yesmaximal, characteristic, complemented
7C2×#11719421C211yesmaximal, characteristic
8C22×#6129C2212yes—
9C22×#6122C2214yes—
10C23×#1057C2214yes—
11C2×#88238—216no—
12C2×#88238C22116yescomplemented
13C22×#6118C2212yes—
14C22×D13⋊C8C2211yescharacteristic
15C22×D13⋊C8C2211yescharacteristic
16C2×C13×#127C411yescharacteristic
17C2×#88192C414yes—
18C2×#88190C412yes—
19C2×D4×Dic13C2214yes—
20#11719421C418yes—
21#11719421C2218yes—
22C2×C42×D13C2211yescharacteristic
23C2×#88123C411yescharacteristic
24C2×C22⋊#1057C2218yes—
25#11719147C22116yescomplemented
26#11719144C22164yescomplemented
27C2×#88112C2214yes—
28C2×#88110C2214yes—
29#11719053C2218yescomplemented
30#11719047C2218yescomplemented
31C22×D4×C13C2×C412yes—
32C22×D4×C13C2×C414yes—
33C22×C22⋊D13C2×C414yes—
34C23×Dic13C2314yes—
35C2×#6129—28no—
36C2×#6129—28no—
37C2×#6129C2×C418yes—
38C2×#6129C2318yes—
39C22×C4×D13C2×C412yes—
40C22×C4×D13C2311yescharacteristic
41C22×Dic26C2×C412yes—
42C2×#6122—216no—
43C2×#6122C23116yes—
44C22×#1057—216no—
45C22×#1057C2312yes—
46C22×#1057C2314yes—
47C22×#1057C23116yes—
48C22×#1057C2312yes—
49#88238—264no—
50C2×#6118—28no—
51C2×#6118C2318yes—
52C2×D13⋊C8—24no—
53C2×D13⋊C8D418yescomplemented
54C2×D13⋊C8C2314yes—
55C2×D13⋊C8C2314yes—
56C13×#127C2×C418yes—
57C2×C42×C13C2×C411yescharacteristic
58C2×C22⋊Dic13C2×C418yes—
59#88192C2×C4132yes—
60#88190C2×C4116yes—
61D4×Dic13C2×C4116yes—
62D4×Dic13C23116yes—
63C2×C4⋊Dic13C2×C414yes—
64C2×C4×Dic13C2×C411yescharacteristic
65C2×C4×Dic13C2312yes—
66C42×D13C2×C414yes—
67C42×D13C2314yes—
68#88123C2×C418yes—
69C22⋊#1057C23132yes—
70#88112C23116yes—
71#88110C23116yes—
72C2×#2932—131nomaximal, Sylow
73C24×C13C22×C414yes—
74C23×D13C22×C411yescharacteristic
75C2×D4×C13—28no—
76C2×D4×C13—48no—
77C2×D4×C13C22×C418yes—
78C2×D4×C13C22×C4116yes—
79C22×C4×C13C22×C412yes—
80C22×C4×C13C22×C411yescharacteristic
81C2×C22⋊D13—216no—
82C2×C22⋊D13C22×C4116yes—
83C22×Dic13—28no—
84C22×Dic13—28no—
85C22×Dic13C22×C412yes—
86C22×Dic13C22×C414yes—
87C22×Dic13C22×C418yes—
88C22×Dic13C2418yes—
89C22×Dic13C2411yescharacteristic
90#6129—232no—
91#6129—216no—
92#6129—216no—
93C2×C4×D13—44no—
94C2×C4×D13C22×C418yes—
95C2×C4×D13C22×C412yes—
96C2×C4×D13C2×D414yes—
97C2×C4×D13#4114yes—
98C2×C4×D13C2412yes—
99C2×Dic26—28no—
100C2×Dic26C22×C418yes—
101#6122—232no—
102C2×#1057—28no—
103C2×#1057—24no—
104C2×#1057—232no—
105C2×#1057C2×D418yes—
106C2×#1057C2414yes—
107C2×#1057C2418yes—
108C2×#1057C2414yes—
109#6118—216no—
110D13⋊C8—28no—
111D13⋊C8C2×D4116yescomplemented
112C42×C13C22×C414yes—
113C22⋊Dic13C22×C4132yes—
114C4⋊Dic13C22×C4116yes—
115C4×Dic13C22×C414yes—
116C4×Dic13C22×C414yes—
117C4×Dic13C2414yes—
118C22×#131—132no—
119C2×#532—131no—
120#2932—1316no—
121C2×#435—138no—
122C2×#423—131no—
123C2×#408—132no—
124C22×#97—131no—
125C23×C13—28no—
126C23×C13—216no—
127C23×C13C23×C418yes—
128C23×C13C23×C411yescharacteristic
129C22×D13—24no—
130C22×D13C4×D414yes—
131C22×D13C23×C412yes—
132D4×C13—216no—
133D4×C13—416no—
134C2×C4×C13—24no—
135C2×C4×C13C4×D414yes—
136C2×C4×C13C23×C414yes—
137C2×C4×C13C23×C412yes—
138C22⋊D13—232no—
139C2×Dic13—28no—
140C2×Dic13—24no—
141C2×Dic13—216no—
142C2×Dic13—28no—
143C2×Dic13—28no—
144C2×Dic13C23×C414yes—
145C2×Dic13C23×C418yes—
146C2×Dic13C23×C411yescharacteristic
147C2×Dic13C22×D412yes—
148C2×Dic13C2×#4112yes—
149C2×Dic13C2511yescharacteristic
150C4×D13—48no—
151C4×D13C4×D418yes—
152C4×D13C22×D414yes—
153C4×D13C2×#4114yes—
154Dic26—216no—
155#1057—28no—
156#1057—24no—
157#1057C22×D418yes—
158C22×#41—132no—
159C2×#131—1316no—
160C2×#131—2616no—
161C22×M16—132no—
162C22×M16—134no—
163C23×C8—131no—
164C23×C8—131no—
165C23×C8—134no—
166#532—138no—
167#532—138no—
168C2×C4⋊Q8—131no—
169C2×#127#26111yescharacteristic
170C2×#124—132no—
171C2×#121—134no—
172C2×C4×D4—134no—
173C22×C42—131no—
174#435—1364no—
175#423—138no—
176C2×C4⋊C8—134no—
177#408—1316no—
178C2×C22⋊C8—138no—
179C2×#97—134no—
180C2×#97—138no—
181C22×C13—28no—
182C22×C13—216no—
183C22×C13—416no—
184C22×C13C2×C4×D412yes—
185C22×C13#56814yes—
186C22×C13C24×C411yescharacteristic
187C2×D13—28no—
188C2×D13—24no—
189C2×D13C2×C4×D414yes—
190C4×C13—24no—
191C4×C13C2×C4×D414yes—
192Dic13—28no—
193Dic13—24no—
194Dic13C2×C4×D412yes—
195Dic13C23×D411yescharacteristic
196Dic13C22×#4111yescharacteristic
197C2×#41—138no—
198C2×#41—138no—
199C2×#41—268no—
200C2×#41—268no—
201C22×Q8—132no—
202C22×D4—134no—
203C22×D4C2×#26112yes—
204C22×D4C2×#26114yes—
205C23×C4—131no—
206C23×C4—134no—
207C23×C4—132no—
208#131—2664no—
209C2×M16—138no—
210C2×M16—1316no—
211C2×M16—2616no—
212C2×M16—268no—
213C22×C8—132no—
214C22×C8—134no—
215C22×C8—138no—
216C22×C8—134no—
217C22×C8—1316no—
218C22×C8—132no—
219C22×C8—134no—
220C22×C8—2616no—
221C22×C8—264no—
222C4⋊Q8—138no—
223#127C2×#26118yes—
224#124—1316no—
225#121—1332no—
226C4×D4—1316no—
227C4×D4—1316no—
228C2×C4⋊C4—134no—
229C2×C22⋊C4—138no—
230C2×C42—132no—
231C2×C42—131no—
232C2×C42—134no—
233C2×C42—134no—
234C2×C42C2×#26111yescharacteristic
235C4⋊C8—1316no—
236C22⋊C8—1332no—
237#97—1316no—
238C2×C13—48no—
239C2×C13#293214yescomplemented
240C2×C13C22×C4×D411yescharacteristic
241C2×C13C2×#56812yes—
242D13—24no—
243C24—131no—
244C24C22×#26114yes—
245#41—2616no—
246#41—2616no—
247#41—2632no—
248C2×Q8—138no—
249C2×Q8—268no—
250C2×D4—28no—
251C2×D4—48no—
252C2×D4—1316no—
253C2×D4—2616no—
254C2×D4C22×#26118yes—
255C2×D4C22×#261116yes—
256C22×C4—131no—
257C22×C4—134no—
258C22×C4—134no—
259C22×C4—132no—
260C22×C4—132no—
261C22×C4—138no—
262C22×C4—138no—
263C22×C4—132no—
264C22×C4—134no—
265C22×C4—138no—
266C22×C4—268no—
267C22×C4—268no—
268C22×C4—524no—
269C22×C4C22×#26112yes—
270C22×C4C22×#26111yescharacteristic
271M16—2632no—
272M16—2616no—
273C2×C8—134no—
274C2×C8—138no—
275C2×C8—1316no—
276C2×C8—134no—
277C2×C8—138no—
278C2×C8—2632no—
279C2×C8—268no—
280C2×C8—268no—
281C2×C8—264no—
282C4⋊C4—1316no—
283C22⋊C4—1332no—
284C42—134no—
285C42—134no—
286C42—134no—
287C42C22×#26114yes—
288C13C2×#293211yescharacteristic, complemented, Sylow
289C23—216no—
290C23—28no—
291C23—134no—
292C23—132no—
293C23—264no—
294C23C23×#26118yes—
295C23C23×#26111yescharacteristic
296Q8—2616no—
297D4—216no—
298D4—416no—
299D4—2632no—
300C2×C4—24no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—134no—
306C2×C4—134no—
307C2×C4—138no—
308C2×C4—134no—
309C2×C4—138no—
310C2×C4—268no—
311C2×C4—2616no—
312C2×C4—268no—
313C2×C4—264no—
314C2×C4—268no—
315C2×C4—528no—
316C2×C4D4×#26114yes—
317C2×C4C23×#26114yes—
318C2×C4C23×#26112yes—
319C8—138no—
320C8—264no—
321C8—268no—
322C22—28no—
323C22—216no—
324C22—416no—
325C22—134no—
326C22—268no—
327C22—264no—
328C22#1171962114yes—
329C22C2×D4×#26112yes—
330C22C24×#26111yescharacteristic
331C4—24no—
332C4—132no—
333C4—131no—
334C4—131no—
335C4—268no—
336C4—264no—
337C4C2×D4×#26114yes—
338C2—48no—
339C2—264no—
340C2#1313156514yesdirect product factor
341C2C22×D4×#26111yescharacteristic
342C2C2×#1171962112yes—
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#127C4
socleC23×C13C23×C4
prime radicalC2×#11719421C2
cosocleC2×Dic13C25
hypercenterC2×#127#261
hypocenterC13C2×#2932
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×#88238C2semidirect
2. #13131565C2direct (N × H)
3. C2×#11719144C2semidirect
4. C2×#11719053C2semidirect
5. C2×#11719147C2semidirect
6. C2×#11719047C2semidirect
12. C2×#88238C22semidirect
25. #11719147C22semidirect
26. #11719144C22semidirect
29. #11719053C22semidirect
30. #11719047C22semidirect
53. C2×D13⋊C8D4semidirect
111. D13⋊C8C2×D4semidirect
239. C2×C13#2932semidirect
288. C13C2×#2932semidirect
340. C2#13131565direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882382
#131315652
C2×#117191442
C2×#117190532
C2×#117191472
C2×#117190472
C2×#117194212
C2×#293213