Finite Group Databasebeta

← C2×#13130960 #16799098

Subgroups — C2×#13130960 #16799098

Order 3328.

2094 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×#88112C211yesmaximal, characteristic, complemented
2C22×C22⋊#1057C214yesmaximal, complemented
3C22×#88110C211yesmaximal, characteristic, complemented
4#13130960C218yesmaximal, direct product factor
5C22×D4×Dic13C211yesmaximal, characteristic
6C23×D4×C13C411yescharacteristic
7C24×Dic13C2212yes—
8C23×#1057C2212yes—
9C23×#1057C2212yes—
10C22×C22⋊Dic13C412yes—
11C2×D4×Dic13—24no—
12C2×D4×Dic13—24no—
13C2×D4×Dic13C414yes—
14C2×D4×Dic13C2214yes—
15C22×C4⋊Dic13C411yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×C22⋊#1057—216no—
18C2×C22⋊#1057C22116yescomplemented
19C2×#88112—24no—
20C2×#88112C2214yescomplemented
21C2×#88110—24no—
22C2×#88110C2214yescomplemented
23C25×C13C2×C412yes—
24C22×D4×C13—28no—
25C22×D4×C13—24no—
26C22×D4×C13C2×C414yes—
27C23×C4×C13C2×C411yescharacteristic
28C23×Dic13—28no—
29C23×Dic13—24no—
30C23×Dic13—24no—
31C23×Dic13—28no—
32C23×Dic13C2×C412yes—
33C23×Dic13C2×C414yes—
34C23×Dic13C2×C411yescharacteristic
35C23×Dic13C2314yes—
36C23×Dic13C2311yescharacteristic
37C22×#1057—24no—
38C22×#1057—24no—
39C22×#1057—28no—
40C22×#1057—24no—
41C22×#1057D418yescomplemented
42C22×#1057C2314yes—
43C22×#1057C2314yes—
44C2×C22⋊Dic13—28no—
45C2×C22⋊Dic13C2×C418yes—
46D4×Dic13—216no—
47D4×Dic13—28no—
48D4×Dic13—28no—
49C2×C4⋊Dic13—24no—
50C2×C4⋊Dic13C2×C414yes—
51C2×C4×Dic13C2×C412yes—
52C2×C4×Dic13D414yes—
53C2×C4×Dic13D414yes—
54C2×C4×Dic13C2312yes—
55C22⋊#1057—232no—
56#88112—28no—
57#88110—28no—
58C2×#1955—131nomaximal, Sylow
59C24×C13—24no—
60C24×C13—28no—
61C24×C13—24no—
62C24×C13—28no—
63C24×C13M1618yes—
64C24×C13C22×C414yes—
65C24×C13C22×C411yescharacteristic
66C2×D4×C13—232no—
67C2×D4×C13—216no—
68C2×D4×C13—28no—
69C22×C4×C13—24no—
70C22×C4×C13C22⋊C414yes—
71C22×C4×C13C22×C412yes—
72C22×Dic13—24no—
73C22×Dic13—24no—
74C22×Dic13—28no—
75C22×Dic13—28no—
76C22×Dic13—216no—
77C22×Dic13—28no—
78C22×Dic13—24no—
79C22×Dic13—24no—
80C22×Dic13—28no—
81C22×Dic13—416no—
82C22×Dic13—48no—
83C22×Dic13—48no—
84C22×Dic13C22⋊C414yes—
85C22×Dic13C22×C414yes—
86C22×Dic13C22×C412yes—
87C22×Dic13C22×C411yescharacteristic
88C22×Dic13C2×D412yes—
89C22×Dic13C2×D412yes—
90C22×Dic13C2×D414yes—
91C22×Dic13#4114yes—
92C22×Dic13C2411yescharacteristic
93C2×#1057—216no—
94C2×#1057—24no—
95C2×#1057—24no—
96C2×#1057—24no—
97C2×#1057—28no—
98C2×#1057—48no—
99C2×#1057C2×D418yescomplemented
100C22⋊Dic13—216no—
101C4⋊Dic13—28no—
102C4×Dic13C22⋊C418yes—
103C4×Dic13C2×D414yes—
104C4×Dic13C2×D414yes—
105C22×C4×D4—131no—
106C22×C4⋊C8—131no—
107C22×C22⋊C8—134no—
108C22×#97—131no—
109#1955—138no—
110C23×C13—24no—
111C23×C13—28no—
112C23×C13—24no—
113C23×C13—28no—
114C23×C13—216no—
115C23×C13—232no—
116C23×C13—48no—
117C23×C13—48no—
118C23×C13—416no—
119C23×C13C2×C22⋊C412yes—
120C23×C13C4×D414yes—
121C23×C13C2×M1618yes—
122C23×C13C2×M1614yes—
123C23×C13#13114yes—
124C23×C13C23×C411yescharacteristic
125D4×C13—232no—
126C2×C4×C13—24no—
127C2×C4×C13—28no—
128C2×C4×C13C2×C22⋊C414yes—
129C2×Dic13—24no—
130C2×Dic13—28no—
131C2×Dic13—24no—
132C2×Dic13—28no—
133C2×Dic13—48no—
134C2×Dic13—48no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—416no—
138C2×Dic13C2×C22⋊C414yes—
139C2×Dic13C2×C22⋊C412yes—
140C2×Dic13C4×D414yes—
141C2×Dic13#12118yes—
142C2×Dic13#12414yes—
143C2×Dic13#12714yes—
144C2×Dic13C22×D411yescharacteristic
145C2×Dic13C22×D412yes—
146C2×Dic13C22×D411yescharacteristic
147C2×Dic13C2×#4112yes—
148#1057—28no—
149#1057—44no—
150C23×D4#26111yescharacteristic
151C24×C4—132no—
152C23×C8—132no—
153C23×C8—132no—
154C2×C4×D4—134no—
155C2×C4×D4—134no—
156C2×C4×D4—264no—
157C2×C4×D4—264no—
158C22×C4⋊C4—131no—
159C22×C22⋊C4—132no—
160C22×C42—131no—
161C2×C4⋊C8—134no—
162C2×C4⋊C8—264no—
163C2×C22⋊C8—1316no—
164C2×C22⋊C8—2616no—
165C2×#97—134no—
166C2×#97—264no—
167C22×C13—28no—
168C22×C13—216no—
169C22×C13—44no—
170C22×C13—48no—
171C22×C13—432no—
172C22×C13—44no—
173C22×C13#39014yes—
174C22×C13#40714yes—
175C22×C13#40814yes—
176C22×C13#435116yes—
177C22×C13C22×C22⋊C411yescharacteristic
178C22×C13C2×C4×D412yes—
179C22×C13C22×M1612yes—
180C22×C13C2×#13112yes—
181C4×C13—24no—
182Dic13—24no—
183Dic13—44no—
184Dic13#39014yes—
185Dic13C2×#12112yes—
186Dic13C2×#12411yescharacteristic
187Dic13C2×#12711yescharacteristic
188C25C2×#26112yes—
189C22×D4—28no—
190C22×D4—24no—
191C22×D4C2×#26114yes—
192C23×C4—131no—
193C23×C4—131no—
194C23×C4—134no—
195C23×C4—134no—
196C23×C4—132no—
197C23×C4—264no—
198C23×C4—264no—
199C23×C4—268no—
200C23×C4—268no—
201C23×C4C2×#26111yescharacteristic
202C22×C8—134no—
203C22×C8—138no—
204C22×C8—134no—
205C22×C8—264no—
206C22×C8—264no—
207C22×C8—268no—
208C22×C8—264no—
209C4×D4—268no—
210C4×D4—268no—
211C4×D4—2616no—
212C2×C4⋊C4—134no—
213C2×C4⋊C4—264no—
214C2×C22⋊C4—138no—
215C2×C22⋊C4—268no—
216C2×C42—134no—
217C2×C42—134no—
218C2×C42—132no—
219C2×C42—132no—
220C4⋊C8—268no—
221C22⋊C8—2632no—
222#97—268no—
223C2×C13—48no—
224C2×C13#195518yescomplemented
225C2×C13C2×#39011yescharacteristic
226C2×C13C2×#40711yescharacteristic
227C2×C13C2×#40811yescharacteristic
228C2×C13C2×#43514yes—
229C24—28no—
230C24—28no—
231C24—24no—
232C24—24no—
233C24#612218yes—
234C24C22×#26114yes—
235C24C22×#26111yescharacteristic
236C2×D4—232no—
237C2×D4—216no—
238C2×D4—28no—
239C22×C4—24no—
240C22×C4—134no—
241C22×C4—134no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—134no—
247C22×C4—132no—
248C22×C4—134no—
249C22×C4—268no—
250C22×C4—264no—
251C22×C4—264no—
252C22×C4—268no—
253C22×C4—268no—
254C22×C4—2616no—
255C22×C4—264no—
256C22×C4—268no—
257C22×C4—264no—
258C22×C4—5216no—
259C22×C4—528no—
260C22×C4—528no—
261C22×C4C22⋊#26114yes—
262C22×C4C22×#26112yes—
263C2×C8—138no—
264C2×C8—264no—
265C2×C8—264no—
266C2×C8—2616no—
267C2×C8—268no—
268C2×C8—264no—
269C2×C8—528no—
270C4⋊C4—268no—
271C22⋊C4—2616no—
272C42—134no—
273C42—134no—
274C42—138no—
275C13C2×#195511yescharacteristic, complemented, Sylow
276C23—216no—
277C23—28no—
278C23—28no—
279C23—24no—
280C23—24no—
281C23—232no—
282C23—416no—
283C23—48no—
284C23—48no—
285C23#8823814yes—
286C23D4×#26114yes—
287C23C2×#612218yes—
288C23C2×#612214yes—
289C23C2×C22⋊#26112yes—
290C23C23×#26111yescharacteristic
291D4—232no—
292C2×C4—28no—
293C2×C4—24no—
294C2×C4—132no—
295C2×C4—132no—
296C2×C4—134no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—132no—
300C2×C4—138no—
301C2×C4—134no—
302C2×C4—134no—
303C2×C4—134no—
304C2×C4—264no—
305C2×C4—268no—
306C2×C4—268no—
307C2×C4—264no—
308C2×C4—528no—
309C2×C4—524no—
310C2×C4—524no—
311C2×C4—5216no—
312C2×C4—528no—
313C2×C4C2×C22⋊#26114yes—
314C8—268no—
315C8—524no—
316C22—216no—
317C22—28no—
318C22—48no—
319C22—44no—
320C22—44no—
321C22—432no—
322C22#11719144116yes—
323C22#1171914714yes—
324C22#1171915114yes—
325C22#1171916914yes—
326C22C2×#8823812yes—
327C22C2×D4×#26112yes—
328C22C22×#612212yes—
329C22C22×C22⋊#26111yescharacteristic
330C4—24no—
331C4—132no—
332C4—131no—
333C4—131no—
334C4—134no—
335C4—264no—
336C4—524no—
337C2—48no—
338C2#1313096018yesdirect product factor
339C2C2×#1171915111yescharacteristic
340C2C2×#1171916911yescharacteristic
341C2C2×#1171914711yescharacteristic
342C2C2×#1171914414yes—
subgroupG/H
centerC24C22×#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
Fitting, prime radicalC23×D4×C13C4
socleC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC23×D4#261
hypocenterC13C2×#1955
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88112C2semidirect
2. C22×C22⋊#1057C2semidirect
3. C22×#88110C2semidirect
4. #13130960C2direct (N × H)
18. C2×C22⋊#1057C22semidirect
20. C2×#88112C22semidirect
22. C2×#88110C22semidirect
41. C22×#1057D4semidirect
99. C2×#1057C2×D4semidirect
224. C2×C13#1955semidirect
275. C13C2×#1955semidirect
338. C2#13130960direct (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×C22⋊#10572
C22×#881102
#131309602
C22×D4×Dic132
C2×#195513