Finite Group Databasebeta

← C2×#13115552 #15866182

Subgroups — C2×#13115552 #15866182

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88054C212yesmaximal
2C22×C4×#1055C211yesmaximal, characteristic
3C2×C4×C4⋊Dic13C211yesmaximal, characteristic
4#13115552C218yesmaximal, direct product factor
5C2×#11718142C212yesmaximal
6C22×C13×C4⋊C8C211yesmaximal, characteristic
7C23×C8×C13C2212yes—
8C22×C42×C13C2211yescharacteristic
9C22×C4⋊Dic13C411yescharacteristic
10C22×C4⋊Dic13C411yescharacteristic
11C22×C4×Dic13C2212yes—
12C23×#1055C2211yescharacteristic
13C23×#1055C2211yescharacteristic
14C2×C13×C4⋊C8—24no—
15C2×C13×C4⋊C8C2214yes—
16C2×#88071C412yes—
17C2×#88054—28no—
18C2×#88054C2218yes—
19C4×C4⋊Dic13C414yes—
20C4×C4⋊Dic13C2214yes—
21C2×C4×#1055—24no—
22C2×C4×#1055C2214yes—
23#11718142C2218yes—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2×C412yes—
28C23×Dic13C2×C412yes—
29C22×C8×C13—24no—
30C22×C8×C13—24no—
31C22×C8×C13—24no—
32C22×C8×C13C2314yes—
33C2×C42×C13C2×C412yes—
34C2×C42×C13D414yes—
35C2×C42×C13Q814yes—
36C2×C42×C13C2312yes—
37C2×C4⋊Dic13—24no—
38C2×C4⋊Dic13C818yescomplemented
39C2×C4⋊Dic13C2×C414yes—
40C2×C4⋊Dic13C2×C414yes—
41C2×C4×Dic13—24no—
42C2×C4×Dic13—24no—
43C2×C4×Dic13C2×C414yes—
44C2×C4×Dic13C2314yes—
45C22×#1055—22no—
46C22×#1055—22no—
47C22×#1055—22no—
48C22×#1055—22no—
49C22×#1055D414yes—
50C22×#1055Q814yes—
51C22×#1055C2312yes—
52C22×#1055C2312yes—
53C13×C4⋊C8—28no—
54#88071C2×C418yes—
55#88054—216no—
56C4×#1055—28no—
57C2×#1939—131nomaximal, Sylow
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13C4⋊C414yes—
62C22×C4×C13C4⋊C414yes—
63C22×C4×C13C2×C814yes—
64C22×C4×C13M1614yes—
65C22×C4×C13C22×C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C22×C412yes—
68C22×C4×C13C2×D412yes—
69C22×C4×C13C2×D412yes—
70C22×C4×C13C2×Q812yes—
71C22×C4×C13C2×Q812yes—
72C22×C4×C13#4112yes—
73C22×C4×C13#4112yes—
74C22×C4×C13C2411yescharacteristic
75C22×Dic13—24no—
76C22×Dic13—24no—
77C22×Dic13—24no—
78C22×Dic13—24no—
79C22×Dic13—24no—
80C22×Dic13C2×C818yes—
81C22×Dic13C22×C414yes—
82C22×Dic13C22×C414yes—
83C2×C8×C13—24no—
84C2×C8×C13—24no—
85C2×C8×C13—24no—
86C2×C8×C13—48no—
87C42×C13C4⋊C418yes—
88C42×C13C2×D414yes—
89C42×C13C2×Q814yes—
90C4⋊Dic13—28no—
91C4⋊Dic13C2×C8116yescomplemented
92C4×Dic13—28no—
93C4×Dic13—24no—
94C4×Dic13—24no—
95C2×#1055—28no—
96C2×#1055—28no—
97C2×#1055—22no—
98C2×#1055—22no—
99C2×#1055—22no—
100C2×#1055—22no—
101C2×#1055C2×D414yes—
102C2×#1055C2×Q814yes—
103C22×C4⋊C8—132no—
104C22×C4⋊C8D1311yescharacteristic
105C22×C4×C8—131no—
106C2×C4×C4⋊C4—131no—
107#1939—138no—
108C2×#336—132no—
109C23×C13C2×C4⋊C412yes—
110C23×C13C4×D412yes—
111C23×C13C4×Q812yes—
112C23×C13C22×C812yes—
113C23×C13C2×M1612yes—
114C23×C13#13112yes—
115C23×C13#13112yes—
116C23×C13C23×C411yescharacteristic
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—28no—
120C2×C4×C13C4⋊C8116yescomplemented
121C2×C4×C13C2×C4⋊C414yes—
122C2×C4×C13C2×C4⋊C412yes—
123C2×C4×C13C2×C4⋊C414yes—
124C2×C4×C13C4×D412yes—
125C2×C4×C13C4×Q812yes—
126C2×C4×C13#12114yes—
127C2×C4×C13C22⋊Q814yes—
128C2×C4×C13#12514yes—
129C2×C4×C13C4⋊Q814yes—
130C2×C4×C13C22×C814yes—
131C2×C4×C13C2×M1614yes—
132C2×C4×C13C22×D411yescharacteristic
133C2×C4×C13C22×D411yescharacteristic
134C2×C4×C13C22×Q811yescharacteristic
135C2×C4×C13C22×Q811yescharacteristic
136C2×C4×C13C2×#4111yescharacteristic
137C2×C4×C13C2×#4111yescharacteristic
138C2×Dic13—24no—
139C2×Dic13—24no—
140C2×Dic13—216no—
141C2×Dic13—24no—
142C2×Dic13—24no—
143C2×Dic13—24no—
144C2×Dic13—48no—
145C2×Dic13C22×C818yes—
146C8×C13—44no—
147#1055—24no—
148#1055—24no—
149C23×C8—131no—
150C23×C8—131no—
151C23×C8C2×D1312yes—
152C22×C4⋊C4—131no—
153C22×C4⋊C4—131no—
154C22×C42—132no—
155C22×C42C2×D1311yescharacteristic
156C2×C4⋊C8—24no—
157C2×C4⋊C8—138no—
158C2×C4⋊C8—268no—
159C2×C4⋊C8C2×D1314yes—
160C2×C4×C8—134no—
161C2×C4×C8—264no—
162C4×C4⋊C4—134no—
163C4×C4⋊C4—134no—
164C2×#95—132no—
165#336—138no—
166C22×C13#38914yes—
167C22×C13C2×C4⋊C814yes—
168C22×C13#42414yes—
169C22×C13C8×D414yes—
170C22×C13#43614yes—
171C22×C13C8×Q814yes—
172C22×C13#44614yes—
173C22×C13C22×C4⋊C411yescharacteristic
174C22×C13C2×C4×D411yescharacteristic
175C22×C13C2×C4×Q811yescharacteristic
176C22×C13C23×C811yescharacteristic
177C22×C13C22×M1611yescharacteristic
178C22×C13C2×#13111yescharacteristic
179C22×C13C2×#13111yescharacteristic
180C4×C13—24no—
181C4×C13#38914yes—
182C4×C13C2×C4⋊C818yescomplemented
183C4×C13C2×#12111yescharacteristic
184C4×C13C2×C22⋊Q811yescharacteristic
185C4×C13C2×#12511yescharacteristic
186C4×C13C2×C4⋊Q811yescharacteristic
187Dic13—28no—
188Dic13—44no—
189C23×C4—132no—
190C23×C4—132no—
191C23×C4C4×D1311yescharacteristic
192C23×C4C4×D1311yescharacteristic
193C23×C4C22×D1311yescharacteristic
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—24no—
197C22×C8—134no—
198C22×C8—134no—
199C22×C8—132no—
200C22×C8—132no—
201C22×C8—262no—
202C22×C8—262no—
203C22×C8—262no—
204C22×C8—262no—
205C22×C8C22×D1314yes—
206C2×C4⋊C4—138no—
207C2×C4⋊C4—134no—
208C2×C4⋊C4—134no—
209C2×C4⋊C4—264no—
210C2×C42—134no—
211C2×C42—134no—
212C2×C42—264no—
213C2×C42—264no—
214C2×C42Dic2614yes—
215C2×C42C4×D1312yes—
216C2×C42C22⋊D1314yes—
217C2×C42C22×D1312yes—
218C4⋊C8—28no—
219C4⋊C8—2616no—
220C4×C8—268no—
221#95—138no—
222C2×C13#193918yescomplemented
223C2×C13C2×#38911yescharacteristic
224C2×C13C22×C4⋊C811yescharacteristic
225C2×C13C2×#42411yescharacteristic
226C2×C13C2×C8×D411yescharacteristic
227C2×C13C2×#43611yescharacteristic
228C2×C13C2×C8×Q811yescharacteristic
229C2×C13C2×#44611yescharacteristic
230C24C2×C4×D1311yescharacteristic
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—138no—
234C22×C4—134no—
235C22×C4—134no—
236C22×C4—264no—
237C22×C4—264no—
238C22×C4—264no—
239C22×C4—264no—
240C22×C4—264no—
241C22×C4C8×D1314yes—
242C22×C4#609414yes—
243C22×C4#610114yes—
244C22×C4#610114yes—
245C22×C4C2×Dic2612yes—
246C22×C4C2×C4×D1312yes—
247C22×C4C2×C4×D1311yescharacteristic
248C22×C4C2×C4×D1312yes—
249C22×C4D4×D1312yes—
250C22×C4#612912yes—
251C22×C4Q8×D1312yes—
252C22×C4#613112yes—
253C22×C4C2×C22⋊D1312yes—
254C22×C4C23×D1311yescharacteristic
255C2×C8—24no—
256C2×C8—24no—
257C2×C8—24no—
258C2×C8—48no—
259C2×C8—134no—
260C2×C8—134no—
261C2×C8—268no—
262C2×C8—268no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—262no—
267C4⋊C4—1316no—
268C4⋊C4—268no—
269C42—268no—
270C42—264no—
271C42—264no—
272C42#610118yes—
273C42C2×Dic2614yes—
274C42C2×C22⋊D1314yes—
275C13C2×#193911yescharacteristic, complemented, Sylow
276C23#8814112yes—
277C23#8814712yes—
278C23C2×C8×D1312yes—
279C23C2×#609412yes—
280C23#8816112yes—
281C23#8816112yes—
282C23C2×#610112yes—
283C23C22×C4×D1311yescharacteristic
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—28no—
287C2×C4—138no—
288C2×C4—264no—
289C2×C4—264no—
290C2×C4—2616no—
291C2×C4—264no—
292C2×C4—264no—
293C2×C4—264no—
294C2×C4—528no—
295C2×C4#88054116yescomplemented
296C2×C4#8814112yes—
297C2×C4#8814214yes—
298C2×C4#8814414yes—
299C2×C4#8814712yes—
300C2×C4C2×C8×D1314yes—
301C2×C4C2×#609414yes—
302C2×C4C2×#610114yes—
303C2×C4C2×#610114yes—
304C2×C4C2×#610112yes—
305C2×C4#8819214yes—
306C2×C4#8820014yes—
307C2×C4C22×Dic2611yescharacteristic
308C2×C4C2×D4×D1311yescharacteristic
309C2×C4C2×#612911yescharacteristic
310C2×C4C2×Q8×D1311yescharacteristic
311C2×C4C2×#613111yescharacteristic
312C2×C4C22×C22⋊D1311yescharacteristic
313C8—44no—
314C8—264no—
315C8—264no—
316C22#1171849114yes—
317C22#1171849214yes—
318C22#1171849514yes—
319C22#1171849914yes—
320C22#1171863414yes—
321C22C2×#8805414yes—
322C22#1171878014yes—
323C22C2×#8814111yescharacteristic
324C22C2×#8814711yescharacteristic
325C22C22×C8×D1311yescharacteristic
326C22C22×#609411yescharacteristic
327C22C2×#8816111yescharacteristic
328C22C2×#8816111yescharacteristic
329C22C22×#610111yescharacteristic
330C4—24no—
331C4—268no—
332C4—524no—
333C4#1171863414yes—
334C4C2×#8805418yescomplemented
335C4C2×#8814211yescharacteristic
336C4C2×#8814411yescharacteristic
337C4C2×#8819211yescharacteristic
338C4C2×#8820011yescharacteristic
339C2#1311555218yesdirect product factor
340C2C2×#1171863411yescharacteristic
341C2C22×#8805411yescharacteristic
342C2C2×#1171878011yescharacteristic
343C2C2×#1171849511yescharacteristic
344C2C2×#1171849911yescharacteristic
345C2C2×#1171849111yescharacteristic
346C2C2×#1171849211yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC22×C13×C4⋊C8C2
socle, prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC22×C4⋊C8D13
hypocenterC13C2×#1939
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #13115552C2direct (N × H)
38. C2×C4⋊Dic13C8semidirect
91. C4⋊Dic13C2×C8semidirect
120. C2×C4×C13C4⋊C8semidirect
182. C4×C13C2×C4⋊C8semidirect
222. C2×C13#1939semidirect
275. C13C2×#1939semidirect
295. C2×C4#88054semidirect
334. C4C2×#88054semidirect
339. C2#13115552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880542
C22×C4×#10552
C2×C4×C4⋊Dic132
#131155522
C2×#117181422
C22×C13×C4⋊C82
C2×#193913