Finite Group Databasebeta

← C2×#13113605 #15831973

Subgroups — C2×#13113605 #15831973

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718346C211yesmaximal, characteristic
2C2×#11718498C211yesmaximal, characteristic
3C2×D13×C4⋊C8C211yesmaximal, characteristic
4#13113605C218yesmaximal, direct product factor
5C2×#11718049C211yesmaximal, characteristic, complemented
6C2×#11718072C211yesmaximal, characteristic, complemented
7C2×#11718072C211yesmaximal, characteristic, complemented
8C2×C13×#334C211yesmaximal, characteristic, complemented
9C22×#6094—21no—
10C22×C8×D13—21no—
11C2×C42×D13C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88060C411yescharacteristic
16C2×#88060C411yescharacteristic
17C2×#88054—21no—
18C2×#88054—21no—
19C2×#88054C411yescharacteristic
20C2×#88054C411yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24#11718498—22no—
25#11718498C2214yes—
26D13×C4⋊C8—22no—
27D13×C4⋊C8C2214yes—
28#11718346C414yes—
29#11718346C2214yes—
30C13×#334C2214yescomplemented
31#11718072C2214yescomplemented
32#11718072C2214yescomplemented
33#11718049C2214yescomplemented
34C22×C4×D13C2×C411yescharacteristic
35C22×C4×D13D411yescharacteristic
36C22×C4×D13Q811yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13C2×C411yescharacteristic
41C2×C42×C13C2311yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13Q811yescharacteristic
45C22×#1055—21no—
46C22×#1055—21no—
47C22×#1055C2×C411yescharacteristic
48C22×#1055C2×C411yescharacteristic
49C2×#6094—24no—
50C2×#6094—44no—
51C2×C8×D13—24no—
52C2×C8×D13—44no—
53C42×D13C2×C412yes—
54C42×D13D412yes—
55C42×D13Q812yes—
56C42×D13C2312yes—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8C2312yes—
60C13×C4⋊C8C2312yes—
61C4×C8×C13C2×C412yes—
62C4×C8×C13C2312yes—
63#88060C2×C414yes—
64#88060C2×C414yes—
65#88054—24no—
66#88054—24no—
67#88054C2×C414yes—
68#88054C2×C414yes—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055C2312yes—
72C4⋊#1055C2312yes—
73C4×#1055C2×C412yes—
74C4×#1055C2312yes—
75C2×#1570—131nomaximal, Sylow
76C23×D13C4⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C22×Dic13C4⋊C411yescharacteristic
81C22×Dic13C4⋊C411yescharacteristic
82C22×Dic13C4⋊C411yescharacteristic
83C2×C4×D13—22no—
84C2×C4×D13—22no—
85C2×C4×D13—42no—
86C2×C4×D13C4⋊C412yes—
87C2×C4×D13C4⋊C412yes—
88C2×C4×D13C4⋊C412yes—
89C2×C4×D13SD1614yes—
90C2×C4×D13SD1614yes—
91C2×C4×D13C22×C412yes—
92C2×C4×D13C2×D412yes—
93C2×C4×D13C2×Q812yes—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—42no—
99C2×C8×C13—42no—
100C2×C8×C13C22×C412yes—
101C2×C8×C13C22×C412yes—
102C42×C13C22×C411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×Q811yescharacteristic
105C42×C13C2411yescharacteristic
106C4×Dic13C4⋊C412yes—
107C4×Dic13C4⋊C412yes—
108C4×Dic13C4⋊C412yes—
109C4×Dic13C22×C412yes—
110C4×Dic13C2×D412yes—
111C4×Dic13C2×Q812yes—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—22no—
116C2×#1055—42no—
117C2×#1055—42no—
118C2×#1055C22×C412yes—
119C2×#1055C22×C412yes—
120#6094—48no—
121C8×D13—48no—
122C2×#431—131no—
123C2×#423—131no—
124C22×C4⋊C8—131no—
125#1570—138no—
126C2×#334—131no—
127C2×#334—131no—
128C2×#334—131no—
129C2×#334D1311yescharacteristic, complemented
130C23×C13C2×C4⋊C411yescharacteristic
131C22×D13—22no—
132C22×D13—22no—
133C22×D13#10614yes—
134C22×D13C2×C4⋊C412yes—
135C2×C4×C13—22no—
136C2×C4×C13C2×C4⋊C411yescharacteristic
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13C2×C4⋊C411yescharacteristic
139C2×C4×C13#13112yes—
140C2×C4×C13#13112yes—
141C2×C4×C13C2×SD1612yes—
142C2×C4×C13C2×SD1612yes—
143C2×C4×C13C23×C411yescharacteristic
144C2×C4×C13C22×D411yescharacteristic
145C2×C4×C13C22×Q811yescharacteristic
146C2×Dic13—22no—
147C2×Dic13—22no—
148C2×Dic13#10614yes—
149C2×Dic13C2×C4⋊C412yes—
150C2×Dic13C2×C4⋊C412yes—
151C2×Dic13C2×C4⋊C412yes—
152C4×D13—22no—
153C4×D13—22no—
154C4×D13—24no—
155C4×D13—42no—
156C4×D13—42no—
157C4×D13#10618yes—
158C4×D13C2×SD1614yes—
159C4×D13C2×SD1614yes—
160C8×C13—22no—
161C8×C13—22no—
162C8×C13—42no—
163C8×C13—42no—
164#1055—22no—
165#1055—22no—
166#1055—42no—
167#1055—42no—
168C22×M16—261no—
169C23×C8—261no—
170C22×C42—131no—
171#431—134no—
172#431—134no—
173#423—134no—
174#423—262no—
175C2×C4⋊C8—131no—
176C2×C4⋊C8—131no—
177C2×C4⋊C8—131no—
178C2×C4⋊C8—131no—
179C2×C4⋊C8—134no—
180C2×C4⋊C8—262no—
181C2×C4⋊C8—261no—
182C2×C4⋊C8—261no—
183C2×C4⋊C8C2×D1311yescharacteristic
184C2×C4⋊C8C2×D1311yescharacteristic
185C2×C22⋊C8—131no—
186C2×C22⋊C8—131no—
187C2×C4×C8—131no—
188C2×C4×C8C2×D1311yescharacteristic
189#334—134no—
190#334—134no—
191#334—134no—
192#334C2×D1314yescomplemented
193C22×C13#42412yes—
194C22×C13C2×#10612yes—
195C22×C13#43012yes—
196C22×C13C22×C4⋊C411yescharacteristic
197C2×D13—28no—
198C2×D13—22no—
199C2×D13—22no—
200C2×D13C2×#10614yes—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13#42412yes—
204C4×C13C2×#10612yes—
205C4×C13C2×#13111yescharacteristic
206C4×C13C2×#13111yescharacteristic
207C4×C13C22×SD1611yescharacteristic
208C4×C13C22×SD1611yescharacteristic
209Dic13—22no—
210Dic13—22no—
211Dic13C2×#10614yes—
212C23×C4—131no—
213C23×C4—131no—
214C23×C4—131no—
215C2×M16—264no—
216C2×M16—524no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—131no—
220C22×C8—131no—
221C22×C8—264no—
222C22×C8—261no—
223C22×C8—261no—
224C22×C8—524no—
225C22×C8C4×D1311yescharacteristic
226C22×C8C4×D1311yescharacteristic
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—132no—
231C2×C42—132no—
232C2×C42—132no—
233C2×C42—132no—
234C2×C42C22×D1311yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—134no—
238C4⋊C8—134no—
239C4⋊C8—132no—
240C4⋊C8—132no—
241C4⋊C8—264no—
242C4⋊C8—264no—
243C4⋊C8—261no—
244C4⋊C8—261no—
245C4⋊C8C22×D1312yes—
246C4⋊C8C22×D1312yes—
247C22⋊C8—134no—
248C22⋊C8—134no—
249C4×C8—132no—
250C4×C8—132no—
251C4×C8C4×D1312yes—
252C4×C8C22×D1312yes—
253C2×C13#157014yescomplemented
254C2×C13C2×#42411yescharacteristic
255C2×C13C22×#10611yescharacteristic
256C2×C13C2×#43011yescharacteristic
257D13—24no—
258C24—131no—
259C22×C4—131no—
260C22×C4—132no—
261C22×C4—134no—
262C22×C4—134no—
263C22×C4—132no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—132no—
267C22×C4—132no—
268C22×C4—132no—
269C22×C4—132no—
270C22×C4—262no—
271C22×C4—262no—
272C22×C4—522no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4D4×D1311yescharacteristic
275C22×C4Q8×D1311yescharacteristic
276M16—528no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—132no—
284C2×C8—132no—
285C2×C8—262no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—528no—
290C2×C8—522no—
291C2×C8—522no—
292C2×C8C2×C4×D1312yes—
293C2×C8C2×C4×D1312yes—
294C42—132no—
295C42—132no—
296C42—132no—
297C42—132no—
298C42—132no—
299C42—132no—
300C42C2×C4×D1311yescharacteristic
301C42D4×D1311yescharacteristic
302C42Q8×D1311yescharacteristic
303C42C23×D1311yescharacteristic
304C13C2×#157011yescharacteristic, complemented, Sylow
305C23—132no—
306C23—134no—
307C23—262no—
308C23—262no—
309C23C4⋊C4×D1311yescharacteristic
310C2×C4—22no—
311C2×C4—132no—
312C2×C4—134no—
313C2×C4—134no—
314C2×C4—134no—
315C2×C4—138no—
316C2×C4—132no—
317C2×C4—132no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—264no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4C4⋊C4×D1311yescharacteristic
326C2×C4C4⋊C4×D1311yescharacteristic
327C2×C4C4⋊C4×D1311yescharacteristic
328C2×C4#8815512yes—
329C2×C4#8816112yes—
330C2×C4SD16×D1312yes—
331C2×C4SD16×D1312yes—
332C2×C4C22×C4×D1311yescharacteristic
333C2×C4C2×D4×D1311yescharacteristic
334C2×C4C2×Q8×D1311yescharacteristic
335C8—22no—
336C8—22no—
337C8—42no—
338C8—42no—
339C8—262no—
340C8—262no—
341C8—522no—
342C8—522no—
343C22—134no—
344C22—268no—
345C22—262no—
346C22—262no—
347C22#1171850012yes—
348C22D13×#10612yes—
349C22#1171855412yes—
350C22C2×C4⋊C4×D1311yescharacteristic
351C4—21no—
352C4—21no—
353C4—134no—
354C4—262no—
355C4—262no—
356C4#1171850012yes—
357C4D13×#10612yes—
358C4C2×#8815511yescharacteristic
359C4C2×#8816111yescharacteristic
360C4C2×SD16×D1311yescharacteristic
361C4C2×SD16×D1311yescharacteristic
362C2—264no—
363C2#1311360514yesdirect product factor
364C2C2×#1171850011yescharacteristic
365C2C2×D13×#10611yescharacteristic
366C2C2×#1171855411yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#334C2
socleC23×C13C2×C4⋊C4
prime radicalC23×D13C4⋊C4
cosocleC42×C13C24
hypercenterC2×#334D13
hypocenterC13C2×#1570
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
4. #13113605C2direct (N × H)
5. C2×#11718049C2semidirect
6. C2×#11718072C2semidirect
7. C2×#11718072C2semidirect
8. C2×C13×#334C2semidirect
30. C13×#334C22semidirect
31. #11718072C22semidirect
32. #11718072C22semidirect
33. #11718049C22semidirect
129. C2×#334D13semidirect
192. #334C2×D13semidirect
253. C2×C13#1570semidirect
304. C13C2×#1570semidirect
363. C2#13113605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183462
C2×#117184982
C2×D13×C4⋊C82
#131136052
C2×#117180492
C2×#117180722
C2×C13×#3342
C2×#157013