Finite Group Databasebeta

← C2×#13116278 #15891811

Subgroups — C2×#13116278 #15891811

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88058C211yesmaximal, characteristic, complemented
2C2×#11718794C212yesmaximal
3C2×#11718771C211yesmaximal, characteristic
4#13116278C218yesmaximal, direct product factor
5C2×#11718146C212yesmaximal, complemented
6C2×C13×#341C211yesmaximal, characteristic, complemented
7C22×#6127C2211yescharacteristic
8C22×C13×M16C2212yes—
9C23×C8×C13C2211yescharacteristic
10C22×C4⋊Dic13C2212yes—
11C22×#6099C2211yescharacteristic
12#11718794—24no—
13#11718794C2218yes—
14C2×#88061—22no—
15#11718771—22no—
16#11718771C2214yes—
17C2×#88060—22no—
18C2×#88058—22no—
19C2×#88058—22no—
20C2×#88058C2214yescomplemented
21C2×#88056—22no—
22C13×#341C2214yescomplemented
23#11718146C2218yescomplemented
24C23×C4×C13C2311yescharacteristic
25C22×C22⋊D13—21no—
26C23×Dic13—22no—
27C2×#6127—21no—
28C2×#6127—21no—
29C2×#6127—24no—
30C2×#6127—24no—
31C2×#6127D412yes—
32C2×#6127C2312yes—
33C22×D52D411yescharacteristic
34C22×C4×D13—21no—
35C22×Dic26D411yescharacteristic
36C2×C13×M16—22no—
37C2×C13×M16—24no—
38C2×C13×M16—24no—
39C2×C13×M16C2314yes—
40C22×C8×C13—24no—
41C22×C8×C13—22no—
42C22×C8×C13D412yes—
43C22×C8×C13D412yes—
44C22×C8×C13C2312yes—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×C4⋊Dic13—22no—
48C2×C4⋊Dic13—22no—
49C2×C4⋊Dic13—22no—
50C2×C4⋊Dic13C2314yes—
51C2×#6099—21no—
52C2×#6099—24no—
53C2×#6099C2312yes—
54C22×#1055—21no—
55#88061—28no—
56#88060—28no—
57#88058—28no—
58#88056—28no—
59C2×#2078—131nomaximal, Sylow
60C24×C13#4111yescharacteristic
61C23×D13—21no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4114yes—
67C22×C4×C13#4114yes—
68C22×C4×C13#4111yescharacteristic
69C22×C4×C13C2411yescharacteristic
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—44no—
73C22×Dic13—21no—
74C22×Dic13—24no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—84no—
78#6127—28no—
79#6127—24no—
80#6127—24no—
81#6127—42no—
82#6127—42no—
83#6127—44no—
84C2×D52—24no—
85C2×D52—21no—
86C2×D52C2×D412yes—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—42no—
90C2×C4×D13—42no—
91C2×Dic26—24no—
92C2×Dic26—21no—
93C2×Dic26C2×D412yes—
94C13×M16—24no—
95C13×M16—24no—
96C13×M16—44no—
97C2×C8×C13—24no—
98C2×C8×C13—24no—
99C2×C8×C13—24no—
100C2×C8×C13—24no—
101C2×C8×C13—44no—
102C2×C8×C13C2×D414yes—
103C4⋊Dic13—24no—
104C4⋊Dic13—24no—
105C4⋊Dic13—42no—
106C4⋊Dic13—42no—
107#6099—24no—
108#6099—42no—
109C2×#1055—22no—
110C2×#1055—42no—
111C22×#107—131no—
112C2×#417—132no—
113C2×#408—131no—
114#2078—138no—
115C2×#343—132no—
116C2×#341D1311yescharacteristic, complemented
117C23×C13—22no—
118C23×C13—22no—
119C23×C13#12111yescharacteristic
120C23×C13#12111yescharacteristic
121C23×C13#12614yes—
122C23×C13C2×#4111yescharacteristic
123C22×D13—22no—
124C22×D13—42no—
125C22×D13—42no—
126C22×D13—42no—
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12314yes—
130C2×C4×C13#12314yes—
131C2×C4×C13#12312yes—
132C2×C4×C13#12312yes—
133C2×C4×C13#12412yes—
134C2×C4×C13#12412yes—
135C2×C4×C13#12614yes—
136C2×C4×C13C22×D411yescharacteristic
137C2×C4×C13C22×D411yescharacteristic
138C2×C4×C13C2×#4112yes—
139C2×C4×C13C2×#4112yes—
140C22⋊D13—44no—
141C22⋊D13—44no—
142C2×Dic13—22no—
143C2×Dic13—42no—
144C2×Dic13—44no—
145C2×Dic13—84no—
146C2×Dic13—84no—
147C2×Dic13—84no—
148D52—24no—
149D52—42no—
150C4×D13—42no—
151C4×D13—42no—
152C4×D13—44no—
153Dic26—24no—
154Dic26—42no—
155C8×C13—24no—
156C8×C13—44no—
157#1055—42no—
158C22×#41—131no—
159C22×M16—131no—
160C22×M16C2×D1312yes—
161C23×C8C2×D1311yescharacteristic
162C22×C4⋊C4—132no—
163C2×#107—134no—
164C2×#107—262no—
165C2×#107—262no—
166#417—138no—
167#417—264no—
168C2×#103—262no—
169C2×#102—262no—
170#408—134no—
171#408—262no—
172C2×C22⋊C8—262no—
173#343—138no—
174#341C2×D1314yescomplemented
175C22×C13—28no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#39712yes—
181C22×C13#39712yes—
182C22×C13#47212yes—
183C22×C13#47312yes—
184C22×C13C2×#12111yescharacteristic
185C22×C13C2×#12612yes—
186C2×D13—42no—
187C2×D13—42no—
188C2×D13—42no—
189C2×D13—84no—
190C4×C13#39712yes—
191C4×C13#39712yes—
192C4×C13C2×#12312yes—
193C4×C13C2×#12311yescharacteristic
194C4×C13C2×#12411yescharacteristic
195Dic13—42no—
196Dic13—84no—
197C2×#41—132no—
198C2×#41—132no—
199C2×#41—261no—
200C2×#41—261no—
201C2×#41—264no—
202C2×#41—264no—
203C22×Q8—131no—
204C22×D4—131no—
205C22×D4—261no—
206C23×C4—261no—
207C23×C4—262no—
208C23×C4C22×D1311yescharacteristic
209C2×M16—22no—
210C2×M16—24no—
211C2×M16—24no—
212C2×M16—132no—
213C2×M16—261no—
214C2×M16—264no—
215C2×M16C22×D1314yes—
216C22×C8—24no—
217C22×C8—22no—
218C22×C8—261no—
219C22×C8D5212yes—
220C22×C8D5212yes—
221C22×C8C22×D1312yes—
222C2×C4⋊C4—134no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—262no—
225C2×C4⋊C4—262no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—262no—
228#107—268no—
229#103—268no—
230#102—268no—
231C22⋊C8—268no—
232C2×C13—22no—
233C2×C13—22no—
234C2×C13#207814yescomplemented
235C2×C13C2×#39711yescharacteristic
236C2×C13C2×#47211yescharacteristic
237C2×C13C2×#47311yescharacteristic
238D13—82no—
239C24—261no—
240C24#613111yescharacteristic
241#41—268no—
242#41—264no—
243#41—264no—
244#41—522no—
245#41—522no—
246#41—524no—
247C2×Q8—132no—
248C2×Q8—261no—
249C2×Q8—264no—
250C2×D4—132no—
251C2×D4—262no—
252C2×D4—262no—
253C2×D4—264no—
254C2×D4—261no—
255C2×D4—524no—
256C22×C4—261no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—264no—
260C22×C4—522no—
261C22×C4—522no—
262C22×C4—522no—
263C22×C4—522no—
264C22×C4—1044no—
265C22×C4C2×D5211yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C22×C4#612714yes—
268C22×C4D4×D1311yescharacteristic
269C22×C4D4×D1311yescharacteristic
270C22×C4#612914yes—
271C22×C4#613111yescharacteristic
272C22×C4C23×D1311yescharacteristic
273M16—24no—
274M16—24no—
275M16—44no—
276M16—264no—
277M16—522no—
278C2×C8—24no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—44no—
283C2×C8—262no—
284C2×C8—522no—
285C2×C8C2×D5214yes—
286C4⋊C4—264no—
287C4⋊C4—264no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C13C2×#207811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—262no—
294C23—522no—
295C23—522no—
296C23—522no—
297C23#8814911yescharacteristic
298C23#8814911yescharacteristic
299C23#8815214yes—
300C23C2×#613111yescharacteristic
301Q8—264no—
302Q8—522no—
303D4—264no—
304D4—524no—
305D4—524no—
306D4—522no—
307C2×C4—262no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—524no—
312C2×C4—524no—
313C2×C4—1044no—
314C2×C4—1044no—
315C2×C4—1044no—
316C2×C4#8812912yes—
317C2×C4#8812912yes—
318C2×C4#8813714yes—
319C2×C4#8813714yes—
320C2×C4#8814012yes—
321C2×C4#8814012yes—
322C2×C4#8814911yescharacteristic
323C2×C4#8814911yescharacteristic
324C2×C4#8815214yes—
325C2×C4C22×D5211yescharacteristic
326C2×C4C2×#612712yes—
327C2×C4C2×D4×D1311yescharacteristic
328C2×C4C2×#612912yes—
329C8—24no—
330C8—44no—
331C8—522no—
332C22—28no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—522no—
338C22—522no—
339C22—522no—
340C22—1044no—
341C22#1171833512yes—
342C22#1171833512yes—
343C22#1171855712yes—
344C22#1171855812yes—
345C22C2×#8814911yescharacteristic
346C22C2×#8815212yes—
347C4—522no—
348C4—1044no—
349C4#1171833512yes—
350C4#1171833512yes—
351C4C2×#8812911yescharacteristic
352C4C2×#8813712yes—
353C4C2×#8814011yescharacteristic
354C2—22no—
355C2—22no—
356C2—1042no—
357C2#1311627814yesdirect product factor
358C2C2×#1171833511yescharacteristic
359C2C2×#1171855811yescharacteristic
360C2C2×#1171855711yescharacteristic
subgroupG/H
centerC23#88149
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#341C2
socleC23×C13#121
prime radicalC22×#6127C22
hypercenterC2×#341D13
hypocenterC13C2×#2078
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C22×#88058C2semidirect
4. #13116278C2direct (N × H)
5. C2×#11718146C2semidirect
6. C2×C13×#341C2semidirect
20. C2×#88058C22semidirect
22. C13×#341C22semidirect
23. #11718146C22semidirect
116. C2×#341D13semidirect
174. #341C2×D13semidirect
234. C2×C13#2078semidirect
290. C13C2×#2078semidirect
357. C2#13116278direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880582
C2×#117187942
C2×#117187712
#131162782
C2×#117181462
C2×C13×#3412
C2×#207813