Finite Group Databasebeta

← C2×#13123485 #16726663

Subgroups — C2×#13123485 #16726663

Order 3328.

2134 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
1C2×C4×#6127C211yesmaximal, characteristic
2#13123485C2116yesmaximal, direct product factor
3C2×#11718370C214yesmaximal, complemented
4C2×#11718366C214yesmaximal, complemented
5C2×#11718763C212yesmaximal, complemented
6C2×#11718771C212yesmaximal
7C2×C4×#6099C211yesmaximal, characteristic, complemented
8C22×C13×#97C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C23×C8×C13C2212yes—
11C22×C42×C13C2211yescharacteristic
12C2×C4×C22⋊D13C414yes—
13C2×#88180C2211yescharacteristic
14C22×#6099C2212yes—
15C4×#6127C418yes—
16C4×#6127C2218yes—
17C2×C4×D52C412yes—
18C2×#88126C2212yes—
19C2×C42×D13C2212yes—
20C2×C4×Dic26C412yes—
21C2×C13×#97C2212yes—
22C2×C13×#97C2212yes—
23C2×C13×#97C2218yescomplemented
24#11718771C22116yes—
25C2×#88060C2218yes—
26#11718763C22116yescomplemented
27C2×#88054C2218yes—
28C4×#6099C2218yescomplemented
29C2×#88043C2212yes—
30C2×C4×#1055C2212yes—
31#11718370C22132yescomplemented
32#11718366C22132yescomplemented
33C23×C4×C13C2×C412yes—
34C23×C4×C13C2311yescharacteristic
35C22×C22⋊D13C2×C412yes—
36C2×#6127—28no—
37C2×#6127C2×C414yes—
38C2×#6127C2314yes—
39C22×D52C2×C411yescharacteristic
40C22×C4×D13C2×C414yes—
41C22×C4×D13C2312yes—
42C22×Dic26C2×C411yescharacteristic
43C22×C8×C13—28no—
44C22×C8×C13C2314yes—
45C22×C8×C13C2318yes—
46C2×C42×C13C2×C412yes—
47C2×C42×C13C2×C414yes—
48C2×C42×C13C2311yescharacteristic
49C2×C42×C13C2311yescharacteristic
50C2×C42×C13C2314yes—
51C2×C22⋊Dic13C2×C412yes—
52C4×C22⋊D13C2×C4132yes—
53C2×#6103C2×C414yes—
54#88180C2×C414yes—
55#88180C2314yes—
56C2×C4⋊Dic13C2×C412yes—
57C2×#6101C2×C414yes—
58C2×C4×Dic13C2×C414yes—
59C2×C4×Dic13C2312yes—
60C2×#6099—28no—
61C2×#6099C2318yes—
62C22×#1055C2314yes—
63C4×D52C2×C4116yes—
64#88126C2×C418yes—
65#88126C2318yes—
66C42×D13C2×C418yes—
67C42×D13C2318yes—
68C4×Dic26C2×C4116yes—
69C13×#97C2318yes—
70C13×#97C2318yes—
71#88060C23132yes—
72#88054C23132yes—
73#88043C2318yes—
74C4×#1055C2318yes—
75C2×#2923—131nomaximal, Sylow
76C24×C13C22×C411yescharacteristic
77C23×D13C22×C412yes—
78C22×C4×C13—44no—
79C22×C4×C13C22×C412yes—
80C22×C4×C13C22×C412yes—
81C22×C4×C13C22×C418yes—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C412yes—
84C22×C4×C13#4118yes—
85C22×C4×C13C2412yes—
86C22×C4×C13C2411yescharacteristic
87C2×C22⋊D13—28no—
88C2×C22⋊D13C22×C418yes—
89C22×Dic13C22×C412yes—
90C22×Dic13C22×C414yes—
91#6127—216no—
92#6127—216no—
93C2×D52—24no—
94C2×D52C22×C414yes—
95C2×C4×D13—28no—
96C2×C4×D13—48no—
97C2×C4×D13C22×C414yes—
98C2×C4×D13C22×C4116yes—
99C2×C4×D13C2414yes—
100C2×Dic26—24no—
101C2×Dic26C22×C414yes—
102C2×C8×C13—28no—
103C2×C8×C13—216no—
104C2×C8×C13C2418yes—
105C42×C13C22×C418yes—
106C42×C13C22×C412yes—
107C42×C13C22×C412yes—
108C42×C13C2412yes—
109C42×C13C2412yes—
110C22⋊Dic13C22×C418yes—
111#6103C22×C4116yes—
112C4⋊Dic13C22×C418yes—
113#6101C22×C4116yes—
114C4×Dic13C22×C4116yes—
115C4×Dic13C22×C414yes—
116C4×Dic13C2414yes—
117#6099—216no—
118C2×#1055—28no—
119C2×#1055C2418yes—
120C2×C4×#41—131no—
121#2923—1316no—
122C2×#433—134no—
123C2×#432—134no—
124C2×#424—132no—
125C2×#408—132no—
126C2×C4×M16—131no—
127C22×#97D1311yescharacteristic, complemented
128C23×C13—24no—
129C23×C13#11714yes—
130C23×C13C23×C412yes—
131C23×C13C23×C411yescharacteristic
132C22×D13—24no—
133C22×D13—28no—
134C22×D13C23×C414yes—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—48no—
138C2×C4×C13#11714yes—
139C2×C4×C13#11718yes—
140C2×C4×C13C23×C414yes—
141C2×C4×C13C23×C414yes—
142C2×C4×C13C23×C411yescharacteristic
143C2×C4×C13C23×C412yes—
144C2×C4×C13C2×#4114yes—
145C2×C4×C13C2×#4118yes—
146C2×C4×C13C2511yescharacteristic
147C22⋊D13—216no—
148C2×Dic13—24no—
149C2×Dic13—28no—
150C2×Dic13C23×C414yes—
151C2×Dic13C23×C418yes—
152D52—28no—
153C4×D13—28no—
154C4×D13—28no—
155C4×D13—416no—
156Dic26—28no—
157C8×C13—28no—
158#1055—28no—
159C22×#41—131no—
160C22×M16—132no—
161C23×C8C2×D1312yes—
162C4×#41—138no—
163C4×#41—138no—
164C2×C4×Q8—132no—
165C2×C4×D4—134no—
166C2×C4×D4—132no—
167C2×#117—131no—
168C2×#117—132no—
169C22×C42—132no—
170C22×C42C2×D1311yescharacteristic
171#433—1332no—
172#432—1332no—
173#424—1316no—
174C2×C4⋊C8—138no—
175#408—1316no—
176C2×C22⋊C8—138no—
177C4×M16—138no—
178C2×#97—132no—
179C2×#97C2×D1312yes—
180C2×#97C2×D1312yes—
181C2×#97C2×D1318yescomplemented
182C2×C4×C8—132no—
183C22×C13—28no—
184C22×C13—24no—
185C22×C13C2×#11714yes—
186C22×C13C2×#11712yes—
187C22×C13#56814yes—
188C22×C13C24×C411yescharacteristic
189C2×D13—24no—
190C2×D13—28no—
191C2×D13—48no—
192C4×C13—24no—
193C4×C13—24no—
194C4×C13C2×#11714yes—
195C4×C13C2×#11712yes—
196C4×C13C22×#4112yes—
197Dic13—24no—
198Dic13—28no—
199C2×#41—134no—
200C2×#41—134no—
201C2×#41—268no—
202C22×Q8—131no—
203C22×D4—132no—
204C22×D4—131no—
205C23×C4—132no—
206C23×C4—134no—
207C23×C4C4×D1312yes—
208C23×C4C22×D1311yescharacteristic
209C2×M16—138no—
210C2×M16—268no—
211C22×C8—28no—
212C22×C8—134no—
213C22×C8C22×D1318yes—
214C22×C8C22×D1314yes—
215C4×Q8—1316no—
216C4×D4—1332no—
217C4×D4—1316no—
218#117—134no—
219#117—134no—
220#117—138no—
221#117—138no—
222C2×C4⋊C4—134no—
223C2×C4⋊C4—132no—
224C2×C22⋊C4—132no—
225C2×C22⋊C4—134no—
226C2×C42—134no—
227C2×C42—132no—
228C2×C42—138no—
229C2×C42—138no—
230C2×C42C4×D1312yes—
231C2×C42C4×D1314yes—
232C2×C42C22×D1314yes—
233C2×C42C22×D1311yescharacteristic
234C2×C42C22×D1311yescharacteristic
235C4⋊C8—1332no—
236C22⋊C8—1332no—
237#97—138no—
238#97C22×D1318yes—
239#97C22×D1318yes—
240C4×C8—138no—
241C2×C13—24no—
242C2×C13#292314yescomplemented
243C2×C13C22×#11711yescharacteristic
244C2×C13C2×#56812yes—
245D13—44no—
246C24—132no—
247C24C2×C4×D1311yescharacteristic
248#41—2616no—
249#41—2616no—
250C2×Q8—134no—
251C2×Q8—264no—
252C2×D4—138no—
253C2×D4—134no—
254C2×D4—268no—
255C2×D4—264no—
256C22×C4—44no—
257C22×C4—134no—
258C22×C4—132no—
259C22×C4—134no—
260C22×C4—134no—
261C22×C4—1316no—
262C22×C4—268no—
263C22×C4—528no—
264C22×C4C2×C4×D1312yes—
265C22×C4C2×C4×D1312yes—
266C22×C4C2×C4×D1318yes—
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4C2×C4×D1312yes—
269C22×C4#612718yes—
270C22×C4C23×D1312yes—
271C22×C4C23×D1311yescharacteristic
272M16—2616no—
273C2×C8—28no—
274C2×C8—216no—
275C2×C8—138no—
276C2×C8—268no—
277C2×C8C23×D1318yes—
278C4⋊C4—1316no—
279C4⋊C4—138no—
280C22⋊C4—138no—
281C22⋊C4—1316no—
282C42—134no—
283C42—1316no—
284C42—134no—
285C42C2×C4×D1312yes—
286C42C2×C4×D1312yes—
287C42C2×C4×D1318yes—
288C42C23×D1312yes—
289C42C23×D1312yes—
290C13C2×#292311yescharacteristic, complemented, Sylow
291C23—24no—
292C23—134no—
293C23—264no—
294C23—268no—
295C23#8812614yes—
296C23C22×C4×D1312yes—
297C23C22×C4×D1311yescharacteristic
298Q8—268no—
299D4—2616no—
300D4—268no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—48no—
304C2×C4—138no—
305C2×C4—134no—
306C2×C4—264no—
307C2×C4—268no—
308C2×C4—268no—
309C2×C4—268no—
310C2×C4—5216no—
311C2×C4#8812614yes—
312C2×C4#8812618yes—
313C2×C4C22×C4×D1314yes—
314C2×C4C22×C4×D1314yes—
315C2×C4C22×C4×D1311yescharacteristic
316C2×C4C22×C4×D1312yes—
317C2×C4C2×#612714yes—
318C2×C4C2×#612718yes—
319C2×C4C24×D1311yescharacteristic
320C8—28no—
321C8—268no—
322C22—24no—
323C22—28no—
324C22—264no—
325C22—268no—
326C22—528no—
327C22C2×#8812614yes—
328C22C2×#8812612yes—
329C22#1171945014yes—
330C22C23×C4×D1311yescharacteristic
331C4—24no—
332C4—24no—
333C4—264no—
334C4—268no—
335C4C2×#8812612yes—
336C4C2×#8812614yes—
337C4C22×#612712yes—
338C2—24no—
339C2—524no—
340C2#1312348514yesdirect product factor
341C2C22×#8812611yescharacteristic
342C2C2×#1171945012yes—
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#97C2
socleC23×C13C23×C4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC22×#97D13
hypocenterC13C2×#2923
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. #13123485C2direct (N × H)
3. C2×#11718370C2semidirect
4. C2×#11718366C2semidirect
5. C2×#11718763C2semidirect
7. C2×C4×#6099C2semidirect
8. C22×C13×#97C2semidirect
23. C2×C13×#97C22semidirect
26. #11718763C22semidirect
28. C4×#6099C22semidirect
31. #11718370C22semidirect
32. #11718366C22semidirect
127. C22×#97D13semidirect
181. C2×#97C2×D13semidirect
242. C2×C13#2923semidirect
290. C13C2×#2923semidirect
340. C2#13123485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#61272
#131234852
C2×#117183702
C2×#117183662
C2×#117187632
C2×#117187712
C2×C4×#60992
C22×C13×#972
C2×#292313