Finite Group Databasebeta

← C2×#13116457 #16015609

Subgroups — C2×#13116457 #16015609

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88052C212yesmaximal, complemented
2#13116457C218yesmaximal, direct product factor
3C2×#11718145C214yesmaximal, complemented
4C22×C13×#131C211yesmaximal, characteristic
5C22×C13×#41C411yescharacteristic
6C2×C13×#131—22no—
7C2×C13×#131—22no—
8C2×C13×#131—24no—
9C2×C13×#131C414yes—
10C2×C13×#131C2214yes—
11C22×C13×M16C411yescharacteristic
12C22×C13×M16C2212yes—
13C23×C8×C13C412yes—
14C23×C8×C13C2211yescharacteristic
15C2×#88052—22no—
16C2×#88052—24no—
17C2×#88052C2214yes—
18C2×#88052C2218yescomplemented
19C22×#6090—22no—
20#11718145C22116yescomplemented
21C2×C13×#41—22no—
22C2×C13×#41—22no—
23C2×C13×#41—22no—
24C2×C13×#41—22no—
25C2×C13×#41C814yes—
26C2×C13×#41C2×C414yes—
27C22×Q8×C13C811yescharacteristic
28C22×D4×C13C812yes—
29C22×D4×C13C811yescharacteristic
30C23×C4×C13C2×C412yes—
31C23×C4×C13C2×C411yescharacteristic
32C13×#131—28no—
33C13×#131—28no—
34C13×#131—28no—
35C13×#131—28no—
36C2×C13×M16—22no—
37C2×C13×M16—22no—
38C2×C13×M16—24no—
39C2×C13×M16—24no—
40C2×C13×M16C2×C414yes—
41C2×C13×M16C2×C414yes—
42C2×C13×M16C2314yes—
43C22×C8×C13—24no—
44C22×C8×C13—22no—
45C22×C8×C13—22no—
46C22×C8×C13C2×C412yes—
47C22×C8×C13C2×C418yes—
48C22×C8×C13C2×C411yescharacteristic
49C22×C8×C13C2×C412yes—
50C22×C8×C13D412yes—
51C22×C8×C13D412yes—
52C22×C8×C13D414yes—
53C22×C8×C13C2311yescharacteristic
54C22×C8×C13C2312yes—
55#88052—24no—
56#88052—28no—
57#88052C2318yes—
58C2×#6090—24no—
59C2×#6090—28no—
60C2×#2115—131nomaximal, Sylow
61C24×C13C2×C812yes—
62C24×C13C2×C811yescharacteristic
63C13×#41—28no—
64C13×#41—28no—
65C13×#41—28no—
66C13×#41—28no—
67C2×Q8×C13—22no—
68C2×Q8×C13—22no—
69C2×Q8×C13C2×C814yes—
70C2×D4×C13—24no—
71C2×D4×C13—24no—
72C2×D4×C13—22no—
73C2×D4×C13—22no—
74C2×D4×C13C2×C818yes—
75C2×D4×C13C2×C814yes—
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13C22⋊C412yes—
81C22×C4×C13C22⋊C412yes—
82C22×C4×C13C2×C812yes—
83C22×C4×C13C2×C814yes—
84C22×C4×C13C2×C811yescharacteristic
85C22×C4×C13C2×C812yes—
86C22×C4×C13M1612yes—
87C22×C4×C13M1612yes—
88C22×C4×C13C22×C414yes—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C22×C412yes—
91C13×M16—28no—
92C13×M16—28no—
93C13×M16—28no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—28no—
97C2×C8×C13—28no—
98C2×C8×C13C22⋊C411yescharacteristic
99C2×C8×C13C22⋊C412yes—
100C2×C8×C13C22⋊C414yes—
101C2×C8×C13C22⋊C414yes—
102C2×C8×C13C22⋊C411yescharacteristic
103C2×C8×C13C22×C414yes—
104C2×C8×C13C22×C412yes—
105C2×C8×C13C22×C411yescharacteristic
106C2×C8×C13C2×D412yes—
107C2×C8×C13C2×D412yes—
108C2×C8×C13C2×D414yes—
109C2×C8×C13C2×D414yes—
110C2×C8×C13C2411yescharacteristic
111#6090—28no—
112C22×#131D1311yescharacteristic
113C22×M32—132no—
114#2115—138no—
115C2×#349—134no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—42no—
119C23×C13—44no—
120C23×C13C22⋊C812yes—
121C23×C13C22⋊C812yes—
122C23×C13C22×C811yescharacteristic
123C23×C13C22×C814yes—
124C23×C13C22×C812yes—
125Q8×C13—28no—
126D4×C13—216no—
127D4×C13—28no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—24no—
131C2×C4×C13—24no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13C22⋊C812yes—
135C2×C4×C13C22⋊C812yes—
136C2×C4×C13C22⋊C814yes—
137C2×C4×C13C22⋊C814yes—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13C2×C22⋊C411yescharacteristic
140C2×C4×C13C2×C22⋊C414yes—
141C2×C4×C13C22×C814yes—
142C2×C4×C13C22×C811yescharacteristic
143C2×C4×C13C22×C812yes—
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13C2×M1611yescharacteristic
146C2×C4×C13C2×M1614yes—
147C2×C4×C13C23×C411yescharacteristic
148C8×C13—24no—
149C8×C13C2×C22⋊C412yes—
150C8×C13C2×C22⋊C412yes—
151C8×C13C2×C22⋊C412yes—
152C8×C13C22×D412yes—
153C22×#41Dic1311yescharacteristic
154C2×#131—22no—
155C2×#131—24no—
156C2×#131—22no—
157C2×#131Dic1314yes—
158C2×#131C2×D1314yes—
159C22×M16Dic1311yescharacteristic
160C22×M16C2×D1312yes—
161C23×C8Dic1312yes—
162C23×C8C2×D1311yescharacteristic
163C2×M32—134no—
164C2×M32—138no—
165C2×M32—262no—
166C2×M32—264no—
167C22×C16—262no—
168#349—1316no—
169C22×C13—22no—
170C22×C13—24no—
171C22×C13—24no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—44no—
175C22×C13—44no—
176C22×C13—44no—
177C22×C13C2×C22⋊C811yescharacteristic
178C22×C13C2×C22⋊C814yes—
179C22×C13C2×C22⋊C811yescharacteristic
180C22×C13C23×C811yescharacteristic
181C4×C13—24no—
182C4×C13C2×C22⋊C811yescharacteristic
183C4×C13C2×C22⋊C811yescharacteristic
184C4×C13C2×C22⋊C814yes—
185C4×C13C22×C22⋊C411yescharacteristic
186C4×C13C22×M1611yescharacteristic
187C2×#41—22no—
188C2×#41—22no—
189C2×#41—22no—
190C2×#41—22no—
191C2×#41#105514yes—
192C2×#41C2×Dic1314yes—
193C22×Q8#105511yescharacteristic
194C22×D4#105512yes—
195C22×D4#105511yescharacteristic
196C23×C4C2×Dic1312yes—
197C23×C4C2×Dic1311yescharacteristic
198#131—28no—
199#131—28no—
200#131—28no—
201#131—28no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—24no—
205C2×M16—24no—
206C2×M16C2×Dic1314yes—
207C2×M16C2×Dic1314yes—
208C2×M16C22×D1314yes—
209C22×C8—24no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8C2×Dic1312yes—
213C22×C8C2×Dic1318yes—
214C22×C8C2×Dic1312yes—
215C22×C8C2×Dic1311yescharacteristic
216C22×C8C22⋊D1312yes—
217C22×C8C22⋊D1314yes—
218C22×C8C22⋊D1312yes—
219C22×C8C22×D1311yescharacteristic
220C22×C8C22×D1312yes—
221M32—138no—
222M32—264no—
223M32—268no—
224C2×C16—264no—
225C2×C16—268no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—24no—
229C2×C13—44no—
230C2×C13#211512yescomplemented
231C2×C13C22×C22⋊C811yescharacteristic
232C24C2×#105512yes—
233C24C2×#105511yescharacteristic
234#41—28no—
235#41—28no—
236#41—28no—
237#41—28no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8C2×#105514yes—
241C2×D4—24no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4C2×#105518yes—
246C2×D4C2×#105514yes—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4C2×#105512yes—
252C22×C4C2×#105514yes—
253C22×C4C2×#105511yescharacteristic
254C22×C4C2×#105512yes—
255C22×C4#609912yes—
256C22×C4#609912yes—
257C22×C4C22⋊Dic1312yes—
258C22×C4C22⋊Dic1312yes—
259C22×C4C22×Dic1314yes—
260C22×C4C22×Dic1311yescharacteristic
261C22×C4C22×Dic1312yes—
262M16—28no—
263M16—28no—
264M16—28no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—28no—
268C2×C8—28no—
269C2×C8C22⋊Dic1311yescharacteristic
270C2×C8C22⋊Dic1312yes—
271C2×C8C22⋊Dic1314yes—
272C2×C8C22⋊Dic1314yes—
273C2×C8C22⋊Dic1311yescharacteristic
274C2×C8C22×Dic1314yes—
275C2×C8C22×Dic1312yes—
276C2×C8C22×Dic1311yescharacteristic
277C2×C8C2×C22⋊D1312yes—
278C2×C8C2×C22⋊D1314yes—
279C2×C8C2×C22⋊D1312yes—
280C2×C8C2×C22⋊D1314yes—
281C2×C8C23×D1311yescharacteristic
282C16—268no—
283C13C2×#211511yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23—42no—
287C23—44no—
288C23C22⋊#105512yes—
289C23C22⋊#105512yes—
290C23C22×#105511yescharacteristic
291C23C22×#105514yes—
292C23C22×#105512yes—
293Q8—28no—
294D4—216no—
295D4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4C22⋊#105512yes—
303C2×C4C22⋊#105512yes—
304C2×C4C22⋊#105514yes—
305C2×C4C22⋊#105514yes—
306C2×C4C22×#105514yes—
307C2×C4C22×#105511yescharacteristic
308C2×C4C22×#105512yes—
309C2×C4C2×#609911yescharacteristic
310C2×C4C2×#609911yescharacteristic
311C2×C4C2×#609914yes—
312C2×C4C2×C22⋊Dic1311yescharacteristic
313C2×C4C2×C22⋊Dic1311yescharacteristic
314C2×C4C2×C22⋊Dic1314yes—
315C2×C4C23×Dic1311yescharacteristic
316C8—24no—
317C8C2×C22⋊Dic1312yes—
318C8C2×C22⋊Dic1312yes—
319C8C2×C22⋊Dic1312yes—
320C8C22×C22⋊D1312yes—
321C22—22no—
322C22—24no—
323C22—24no—
324C22—42no—
325C22—42no—
326C22—44no—
327C22—44no—
328C22—44no—
329C22C2×C22⋊#105511yescharacteristic
330C22C2×C22⋊#105514yes—
331C22C2×C22⋊#105511yescharacteristic
332C22C23×#105511yescharacteristic
333C4—24no—
334C4C2×C22⋊#105511yescharacteristic
335C4C2×C22⋊#105511yescharacteristic
336C4C2×C22⋊#105514yes—
337C4C22×#609911yescharacteristic
338C4C22×C22⋊Dic1311yescharacteristic
339C2—21no—
340C2—21no—
341C2—24no—
342C2—44no—
343C2#1311645712yesdirect product factor
344C2C22×C22⋊#105511yescharacteristic
subgroupG/H
centerC2×C8C22⋊Dic13
commutatorC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC22×C13×#131C2
socleC22×C13C2×C22⋊C8
prime radicalC22×C13×#41C4
cosocleC2×C8×C13C24
hypercenterC22×#131D13
hypocenterC13C2×#2115
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C22×#88052C2semidirect
2. #13116457C2direct (N × H)
3. C2×#11718145C2semidirect
18. C2×#88052C22semidirect
20. #11718145C22semidirect
230. C2×C13#2115semidirect
283. C13C2×#2115semidirect
343. C2#13116457direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880522
#131164572
C2×#117181452
C22×C13×#1312
C2×#211513