Finite Group Databasebeta

← C2×#13066957 #14719634

Subgroups — C2×#13066957 #14719634

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C212yesmaximal, complemented
2#13066957C218yesmaximal, direct product factor
3C2×#10622163C214yesmaximal, complemented
4C22×C4×D4×C11C211yesmaximal, characteristic
5C23×D4×C11C411yescharacteristic
6C24×C4×C11C412yes—
7C2×C4×D4×C11—22no—
8C2×C4×D4×C11—22no—
9C2×C4×D4×C11—24no—
10C2×C4×D4×C11C414yes—
11C2×C4×D4×C11C2214yes—
12C22×C11×C4⋊C4C411yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2214yes—
16#10622539—24no—
17#10622539C2218yescomplemented
18C2×C4⋊(C11⋊C8)—22no—
19C2×#66867—22no—
20#10622163C22116yescomplemented
21C25×C11C2×C412yes—
22C22×D4×C11—28no—
23C22×D4×C11—22no—
24C22×D4×C11—22no—
25C22×D4×C11C2×C414yes—
26C23×C4×C11—24no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—48no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C418yes—
34C23×C4×C11C2311yescharacteristic
35C4×D4×C11—28no—
36C4×D4×C11—28no—
37C4×D4×C11—28no—
38C4×D4×C11—28no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4C2×C414yes—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4C2×C414yes—
45C2×C11×C22⋊C4C2314yes—
46C2×C42×C11C2×C412yes—
47C2×C42×C11D412yes—
48C2×C42×C11D412yes—
49C2×C42×C11D414yes—
50C2×C42×C11C2312yes—
51C22×C11⋊C8—24no—
52C22⋊(C11⋊C8)—24no—
53C22⋊(C11⋊C8)C2318yes—
54C4⋊(C11⋊C8)—28no—
55#66867—28no—
56C2×#1466—111nomaximal, Sylow
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—24no—
60C24×C11—44no—
61C24×C11—44no—
62C24×C11M1618yes—
63C24×C11C22×C411yescharacteristic
64C24×C11C22×C414yes—
65C2×D4×C11—216no—
66C2×D4×C11—216no—
67C2×D4×C11—216no—
68C2×D4×C11—28no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—28no—
74C22×C4×C11—28no—
75C22×C4×C11—42no—
76C22×C4×C11—48no—
77C22×C4×C11—416no—
78C22×C4×C11—416no—
79C22×C4×C11—48no—
80C22×C4×C11—44no—
81C22×C4×C11C22⋊C412yes—
82C22×C4×C11C22⋊C412yes—
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C412yes—
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C11×C4⋊C4—28no—
94C11×C22⋊C4—28no—
95C11×C22⋊C4—28no—
96C42×C11C22⋊C414yes—
97C42×C11C22⋊C414yes—
98C42×C11C2×D414yes—
99C42×C11C2×D414yes—
100C2×C11⋊C8—28no—
101C2×C11⋊C8—48no—
102C22×C4×D4D1111yescharacteristic
103C2×#432—112no—
104#1466—118no—
105C2×#323—114no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—24no—
109C23×C11—24no—
110C23×C11—28no—
111C23×C11—28no—
112C23×C11—44no—
113C23×C11—416no—
114C23×C11—44no—
115C23×C11—44no—
116C23×C11—44no—
117C23×C11—416no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11C2×C22⋊C411yescharacteristic
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11C2×M1614yes—
123C23×C11C2×M1618yes—
124C23×C11C23×C411yescharacteristic
125D4×C11—232no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—416no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—416no—
141C2×C4×C11—44no—
142C2×C4×C11#10014yes—
143C2×C4×C11C2×C22⋊C412yes—
144C2×C4×C11C2×C22⋊C414yes—
145C2×C4×C11C2×C22⋊C412yes—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C22×D412yes—
148C11⋊C8—48no—
149C23×D4Dic1111yescharacteristic
150C24×C4Dic1112yes—
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4—24no—
154C2×C4×D4Dic1114yes—
155C2×C4×D4C2×D1114yes—
156C22×C4⋊C4Dic1111yescharacteristic
157C22×C22⋊C4C2×D1112yes—
158C22×C42C2×D1111yescharacteristic
159#432—118no—
160#432—224no—
161C2×C4⋊C8—222no—
162C2×C22⋊C8—114no—
163C2×#97—222no—
164#323—1116no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—28no—
170C22×C11—28no—
171C22×C11—48no—
172C22×C11—48no—
173C22×C11—416no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—416no—
177C22×C11#40712yes—
178C22×C11#40712yes—
179C22×C11#41012yes—
180C22×C11C2×#10012yes—
181C22×C11C22×C22⋊C411yescharacteristic
182C22×C11C22×M1612yes—
183C4×C11—24no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—22no—
187C4×C11—44no—
188C4×C11C2×#10014yes—
189C25C2×Dic1112yes—
190C22×D4—28no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4C2×Dic1114yes—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—48no—
198C23×C4C2×Dic1111yescharacteristic
199C23×C4C2×Dic1111yescharacteristic
200C23×C4C2×Dic1112yes—
201C23×C4C2×Dic1118yes—
202C23×C4C22×D1111yescharacteristic
203C22×C8—224no—
204C4×D4—28no—
205C4×D4—28no—
206C4×D4—28no—
207C4×D4—28no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4C2×Dic1114yes—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—24no—
213C2×C22⋊C4C2×Dic1114yes—
214C2×C22⋊C4C22×D1114yes—
215C2×C42C2×Dic1112yes—
216C2×C42C22⋊D1112yes—
217C2×C42C22⋊D1112yes—
218C2×C42C22⋊D1114yes—
219C2×C42C22×D1112yes—
220C4⋊C8—228no—
221C22⋊C8—118no—
222C22⋊C8—224no—
223#97—228no—
224C2×C11—22no—
225C2×C11—22no—
226C2×C11—48no—
227C2×C11#146614yescomplemented
228C2×C11C2×#40711yescharacteristic
229C2×C11C2×#41011yescharacteristic
230C2×C11C22×#10011yescharacteristic
231C24—24no—
232C24—22no—
233C24—22no—
234C24—44no—
235C24—44no—
236C24#431818yes—
237C24C22×Dic1111yescharacteristic
238C24C22×Dic1114yes—
239C2×D4—216no—
240C2×D4—216no—
241C2×D4—216no—
242C2×D4—28no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—28no—
248C22×C4—28no—
249C22×C4—42no—
250C22×C4—48no—
251C22×C4—416no—
252C22×C4—416no—
253C22×C4—48no—
254C22×C4—44no—
255C22×C4C22⋊Dic1112yes—
256C22×C4C22⋊Dic1112yes—
257C22×C4C22⋊Dic1112yes—
258C22×C4C22⋊Dic1111yescharacteristic
259C22×C4C22⋊Dic1111yescharacteristic
260C22×C4C22×Dic1112yes—
261C22×C4C22×Dic1112yes—
262C22×C4C22×Dic1114yes—
263C22×C4C22×Dic1111yescharacteristic
264C22×C4C2×C22⋊D1112yes—
265C22×C4C2×C22⋊D1112yes—
266C22×C4C23×D1111yescharacteristic
267C2×C8—228no—
268C2×C8—448no—
269C4⋊C4—28no—
270C22⋊C4—28no—
271C22⋊C4—28no—
272C42C22⋊Dic1114yes—
273C42C22⋊Dic1114yes—
274C42C2×C22⋊D1114yes—
275C42C2×C22⋊D1114yes—
276C11C2×#146611yescharacteristic, complemented, Sylow
277C23—22no—
278C23—22no—
279C23—24no—
280C23—28no—
281C23—28no—
282C23—24no—
283C23—44no—
284C23—416no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—416no—
289C23—44no—
290C23—44no—
291C23C2×#431814yes—
292C23C2×#431818yes—
293C23C2×C22⋊Dic1111yescharacteristic
294C23C2×C22⋊Dic1111yescharacteristic
295C23C23×Dic1111yescharacteristic
296D4—232no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—416no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—416no—
312C2×C4—44no—
313C2×C4#6689714yes—
314C2×C4C2×C22⋊Dic1112yes—
315C2×C4C2×C22⋊Dic1114yes—
316C2×C4C2×C22⋊Dic1112yes—
317C2×C4C2×C22⋊Dic1112yes—
318C2×C4C22×C22⋊D1112yes—
319C8—448no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—28no—
325C22—28no—
326C22—48no—
327C22—48no—
328C22—416no—
329C22—44no—
330C22—44no—
331C22—416no—
332C22#1062282012yes—
333C22#1062282012yes—
334C22C2×#6689712yes—
335C22#1062285312yes—
336C22C22×#431812yes—
337C22C22×C22⋊Dic1111yescharacteristic
338C4—24no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—44no—
343C4C2×#6689714yes—
344C2—22no—
345C2—22no—
346C2—48no—
347C2#1306695714yesdirect product factor
348C2C2×#1062282011yescharacteristic
349C2C2×#1062285311yescharacteristic
350C2C22×#6689711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×D4×C11C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC22×C4×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#1466
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622539C2semidirect
2. #13066957C2direct (N × H)
3. C2×#10622163C2semidirect
17. #10622539C22semidirect
20. #10622163C22semidirect
227. C2×C11#1466semidirect
276. C11C2×#1466semidirect
347. C2#13066957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225392
#130669572
C2×#106221632
C22×C4×D4×C112
C2×#146611