Finite Group Databasebeta

← C2×#13116662 #16016076

Subgroups — C2×#13116662 #16016076

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88052C211yesmaximal, characteristic, complemented
2C23×#6090C211yesmaximal, characteristic, complemented
3#13116662C218yesmaximal, direct product factor
4C2×C4⋊#6090C211yesmaximal, characteristic, complemented
5C2×C22⋊#6090C211yesmaximal, characteristic, complemented
6C2×C22⋊#6090C211yesmaximal, characteristic, complemented
7C2×#11718053C211yesmaximal, characteristic, complemented
8C2×C8×D4×C13C211yesmaximal, characteristic
9C23×C8×C13C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C2×C4×D4×C13C411yescharacteristic
12C8×D4×C13C414yes—
13C8×D4×C13C2214yes—
14C2×C13×C4⋊C8C411yescharacteristic
15C2×C13×C22⋊C8C411yescharacteristic
16C2×C13×C22⋊C8C411yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18C2×#88052—24no—
19C2×#88052C2214yescomplemented
20C22×#6090—24no—
21C22×#6090C2211yescharacteristic
22C22×#6090C2211yescharacteristic
23C22×#6090C2211yescharacteristic
24C22×#6090C2211yescharacteristic
25C22×#6090C2214yescomplemented
26C22⋊#6090C2214yescomplemented
27C22⋊#6090C2214yescomplemented
28C4⋊#6090C2214yescomplemented
29#11718053C2214yescomplemented
30C22×D4×C13C811yescharacteristic
31C23×C4×C13C2×C411yescharacteristic
32C23×C4×C13C2×C411yescharacteristic
33C22×C8×C13—22no—
34C22×C8×C13—22no—
35C22×C8×C13—22no—
36C22×C8×C13—22no—
37C22×C8×C13C2×C411yescharacteristic
38C22×C8×C13C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13C2×C412yes—
41C22×C8×C13C2×C412yes—
42C22×C8×C13C2312yes—
43C22×C8×C13C2312yes—
44C22×C8×C13C2311yescharacteristic
45C4×D4×C13C814yes—
46C4×D4×C13C2×C414yes—
47C2×C13×C4⋊C4C811yescharacteristic
48C2×C13×C22⋊C4C811yescharacteristic
49C2×C13×C22⋊C4C811yescharacteristic
50C2×C42×C13C2×C411yescharacteristic
51C13×C4⋊C8C2×C414yes—
52C13×C22⋊C8C2×C414yes—
53C13×C22⋊C8C2×C414yes—
54C4×C8×C13C2×C412yes—
55C4×C8×C13C2312yes—
56#88052—28no—
57C2×#6090—22no—
58C2×#6090—22no—
59C2×#6090—22no—
60C2×#6090—28no—
61C2×#6090D414yescomplemented
62C2×#6090C2312yes—
63C2×#6090C2312yes—
64C2×#6090C2312yes—
65C2×#6090C2312yes—
66C2×#2168—131nomaximal, Sylow
67C24×C13C2×C811yescharacteristic
68C24×C13C2×C811yescharacteristic
69C2×D4×C13—24no—
70C2×D4×C13C2×C814yes—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13C2×C811yescharacteristic
76C22×C4×C13C2×C811yescharacteristic
77C22×C4×C13C2×C811yescharacteristic
78C22×C4×C13C2×C811yescharacteristic
79C22×C4×C13C2×C812yes—
80C22×C4×C13C2×C812yes—
81C22×C4×C13C22×C412yes—
82C22×C4×C13C22×C412yes—
83C22×C4×C13C22×C411yescharacteristic
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—24no—
88C2×C8×C13—24no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13C22×C412yes—
94C2×C8×C13C22×C412yes—
95C2×C8×C13C22×C412yes—
96C2×C8×C13C22×C411yescharacteristic
97C2×C8×C13C2×D412yes—
98C2×C8×C13#4112yes—
99C2×C8×C13C2411yescharacteristic
100C13×C4⋊C4C2×C814yes—
101C13×C22⋊C4C2×C814yes—
102C13×C22⋊C4C2×C814yes—
103C42×C13C2×C812yes—
104C42×C13C22×C412yes—
105#6090—22no—
106#6090—22no—
107#6090—22no—
108#6090C2×D414yescomplemented
109C22×M32—131no—
110C23×C16—131no—
111C2×C8×D4D1311yescharacteristic
112#2168—138no—
113C2×C4⋊C16—131no—
114C2×C22⋊C16—131no—
115C2×C22⋊C16—131no—
116C2×#346—131no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13M3214yescomplemented
123C23×C13C22×C812yes—
124C23×C13C22×C812yes—
125C23×C13C22×C811yescharacteristic
126D4×C13—28no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13C4×D412yes—
138C2×C4×C13C22×C812yes—
139C2×C4×C13C22×C812yes—
140C2×C4×C13C22×C812yes—
141C2×C4×C13C22×C812yes—
142C2×C4×C13C22×C811yescharacteristic
143C2×C4×C13#13112yes—
144C2×C4×C13C23×C411yescharacteristic
145C8×C13—22no—
146C8×C13—22no—
147C8×C13—22no—
148C8×C13C4×D412yes—
149C8×C13C22×D411yescharacteristic
150C8×C13C2×#4111yescharacteristic
151C23×C8C2×D1311yescharacteristic
152C23×C8C2×D1311yescharacteristic
153C2×C4×D4Dic1311yescharacteristic
154C2×M32—134no—
155C2×M32—264no—
156C22×C16—131no—
157C22×C16—134no—
158C22×C16—131no—
159C22×C16—131no—
160C22×C16—131no—
161C22×C16—264no—
162C8×D4Dic1314yes—
163C8×D4C2×D1314yes—
164C2×C4⋊C8Dic1311yescharacteristic
165C2×C22⋊C8Dic1311yescharacteristic
166C2×C22⋊C8Dic1311yescharacteristic
167C2×C4×C8C2×D1311yescharacteristic
168C4⋊C16—134no—
169C22⋊C16—134no—
170C22⋊C16—134no—
171#346—134no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—28no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—44no—
179C22×C13C8×D412yes—
180C22×C13C2×M3212yes—
181C22×C13C2×M3214yescomplemented
182C22×C13#50412yes—
183C22×C13C23×C811yescharacteristic
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—22no—
188C4×C13C8×D412yes—
189C4×C13C2×C4×D411yescharacteristic
190C4×C13C2×#13111yescharacteristic
191C22×D4#105511yescharacteristic
192C23×C4C2×Dic1311yescharacteristic
193C23×C4C2×Dic1311yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8C2×Dic1311yescharacteristic
199C22×C8C2×Dic1311yescharacteristic
200C22×C8C2×Dic1312yes—
201C22×C8C2×Dic1312yes—
202C22×C8C2×Dic1311yescharacteristic
203C22×C8C22×D1312yes—
204C22×C8C22×D1312yes—
205C22×C8C22×D1311yescharacteristic
206C4×D4#105514yes—
207C4×D4C2×Dic1314yes—
208C2×C4⋊C4#105511yescharacteristic
209C2×C22⋊C4#105511yescharacteristic
210C2×C22⋊C4#105511yescharacteristic
211C2×C42C2×Dic1311yescharacteristic
212M32—268no—
213C2×C16—134no—
214C2×C16—132no—
215C2×C16—132no—
216C2×C16—132no—
217C2×C16—132no—
218C2×C16—268no—
219C2×C16—262no—
220C2×C16—262no—
221C2×C16—262no—
222C4⋊C8C2×Dic1314yes—
223C22⋊C8C2×Dic1314yes—
224C22⋊C8C2×Dic1314yes—
225C4×C8C2×Dic1312yes—
226C4×C8C22×D1312yes—
227C2×C13—24no—
228C2×C13—42no—
229C2×C13#216814yescomplemented
230C2×C13C2×C8×D411yescharacteristic
231C2×C13C22×M3211yescharacteristic
232C2×C13C2×#50411yescharacteristic
233C24C2×#105511yescharacteristic
234C24C2×#105511yescharacteristic
235C2×D4—24no—
236C2×D4C2×#105514yes—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4C2×#105511yescharacteristic
242C22×C4C2×#105511yescharacteristic
243C22×C4C2×#105511yescharacteristic
244C22×C4C2×#105511yescharacteristic
245C22×C4C2×#105512yes—
246C22×C4C2×#105512yes—
247C22×C4C22×Dic1312yes—
248C22×C4C22×Dic1312yes—
249C22×C4C22×Dic1311yescharacteristic
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8D4×D1312yes—
260C2×C8#612912yes—
261C2×C8C22×Dic1312yes—
262C2×C8C22×Dic1312yes—
263C2×C8C22×Dic1312yes—
264C2×C8C22×Dic1311yescharacteristic
265C2×C8C23×D1311yescharacteristic
266C4⋊C4C2×#105514yes—
267C22⋊C4C2×#105514yes—
268C22⋊C4C2×#105514yes—
269C42C2×#105512yes—
270C42C22×Dic1312yes—
271C16—134no—
272C16—262no—
273C16—262no—
274C16—262no—
275C13C2×#216811yescharacteristic, complemented, Sylow
276C23—22no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23#8805214yescomplemented
282C23C22×#105512yes—
283C23C22×#105512yes—
284C23C22×#105511yescharacteristic
285D4—28no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4C22×#105512yes—
297C2×C4C22×#105512yes—
298C2×C4C22×#105512yes—
299C2×C4C22×#105512yes—
300C2×C4C22×#105511yescharacteristic
301C2×C4D4×Dic1312yes—
302C2×C4#8820212yes—
303C2×C4C23×Dic1311yescharacteristic
304C8—22no—
305C8—22no—
306C8—22no—
307C8D4×Dic1312yes—
308C8C2×D4×D1311yescharacteristic
309C8C2×#612911yescharacteristic
310C22—22no—
311C22—28no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—44no—
317C22D4×#105512yes—
318C22C2×#8805212yes—
319C22C2×#8805214yescomplemented
320C22#1171880112yes—
321C22C23×#105511yescharacteristic
322C4—22no—
323C4—22no—
324C4—22no—
325C4—22no—
326C4D4×#105512yes—
327C4C2×D4×Dic1311yescharacteristic
328C4C2×#8820211yescharacteristic
329C2—24no—
330C2—42no—
331C2#1311666214yesdirect product factor
332C2C2×D4×#105511yescharacteristic
333C2C22×#8805211yescharacteristic
334C2C2×#1171880111yescharacteristic
subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC2×C8×D4×C13C2
socleC23×C13C22×C8
prime radicalC22×D4×C13C8
cosocleC2×C8×C13C24
hypercenterC2×C8×D4D13
hypocenterC13C2×#2168
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88052C2semidirect
2. C23×#6090C2semidirect
3. #13116662C2direct (N × H)
4. C2×C4⋊#6090C2semidirect
5. C2×C22⋊#6090C2semidirect
6. C2×C22⋊#6090C2semidirect
7. C2×#11718053C2semidirect
19. C2×#88052C22semidirect
25. C22×#6090C22semidirect
26. C22⋊#6090C22semidirect
27. C22⋊#6090C22semidirect
28. C4⋊#6090C22semidirect
29. #11718053C22semidirect
61. C2×#6090D4semidirect
108. #6090C2×D4semidirect
122. C23×C13M32semidirect
181. C22×C13C2×M32semidirect
229. C2×C13#2168semidirect
275. C13C2×#2168semidirect
281. C23#88052semidirect
319. C22C2×#88052semidirect
331. C2#13116662direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880522
C23×#60902
#131166622
C2×C4⋊#60902
C2×C22⋊#60902
C2×#117180532
C2×C8×D4×C132
C2×#216813