Finite Group Databasebeta

← C2×#13070063 #14782671

Subgroups — C2×#13070063 #14782671

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66881C211yesmaximal, characteristic, complemented
2C2×#10622746C212yesmaximal
3C2×#10622723C211yesmaximal, characteristic
4#13070063C218yesmaximal, direct product factor
5C2×#10622192C212yesmaximal, complemented
6C2×C11×#341C211yesmaximal, characteristic, complemented
7C22×#4339C2211yescharacteristic
8C22×C11×M16C2212yes—
9C23×C8×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C22×#4318C2211yescharacteristic
12#10622746—24no—
13#10622746C2218yes—
14C2×#66885—22no—
15#10622723—22no—
16#10622723C2214yes—
17C2×(C2×D11)⋊C8—22no—
18C2×#66881—22no—
19C2×#66881—22no—
20C2×#66881C2214yescomplemented
21C2×#66880—22no—
22C11×#341C2214yescomplemented
23#10622192C2218yescomplemented
24C23×C4×C11C2311yescharacteristic
25C22×C22⋊D11—21no—
26C23×Dic11—22no—
27C2×#4339—21no—
28C2×#4339—21no—
29C2×#4339—24no—
30C2×#4339—24no—
31C2×#4339D412yes—
32C2×#4339C2312yes—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×Dic22D411yescharacteristic
36C2×C11×M16—22no—
37C2×C11×M16—24no—
38C2×C11×M16—24no—
39C2×C11×M16C2314yes—
40C22×C8×C11—24no—
41C22×C8×C11—22no—
42C22×C8×C11D412yes—
43C22×C8×C11D412yes—
44C22×C8×C11C2312yes—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2314yes—
51C2×#4318—21no—
52C2×#4318—24no—
53C2×#4318C2312yes—
54C22×C11⋊C8—21no—
55#66885—28no—
56(C2×D11)⋊C8—28no—
57#66881—28no—
58#66880—28no—
59C2×#2079—111nomaximal, Sylow
60C24×C11#4111yescharacteristic
61C23×D11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4114yes—
68C22×C4×C11#4114yes—
69C22×C4×C11C2411yescharacteristic
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—44no—
73C22×Dic11—21no—
74C22×Dic11—24no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—84no—
78#4339—28no—
79#4339—24no—
80#4339—24no—
81#4339—42no—
82#4339—42no—
83#4339—44no—
84C2×D44—21no—
85C2×D44—24no—
86C2×D44C2×D412yes—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×Dic22—21no—
92C2×Dic22—24no—
93C2×Dic22C2×D412yes—
94C11×M16—24no—
95C11×M16—24no—
96C11×M16—44no—
97C2×C8×C11—24no—
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C2×C8×C11—44no—
102C2×C8×C11C2×D414yes—
103C4⋊Dic11—24no—
104C4⋊Dic11—24no—
105C4⋊Dic11—42no—
106C4⋊Dic11—42no—
107#4318—24no—
108#4318—42no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—42no—
111C22×#106—111no—
112C2×#417—112no—
113C2×#408—111no—
114#2079—118no—
115C2×#343—112no—
116C2×#341D1111yescharacteristic, complemented
117C23×C11—24no—
118C23×C11#12111yescharacteristic
119C23×C11#12111yescharacteristic
120C23×C11#12614yes—
121C23×C11C2×#4111yescharacteristic
122C22×D11—22no—
123C22×D11—42no—
124C22×D11—44no—
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12314yes—
128C2×C4×C11#12314yes—
129C2×C4×C11#12312yes—
130C2×C4×C11#12312yes—
131C2×C4×C11#12412yes—
132C2×C4×C11#12412yes—
133C2×C4×C11#12614yes—
134C2×C4×C11C22×D411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C2×#4112yes—
137C2×C4×C11C2×#4112yes—
138C22⋊D11—44no—
139C22⋊D11—44no—
140C2×Dic11—22no—
141C2×Dic11—42no—
142C2×Dic11—44no—
143C2×Dic11—84no—
144C2×Dic11—84no—
145C2×Dic11—84no—
146D44—24no—
147D44—42no—
148C4×D11—42no—
149C4×D11—42no—
150C4×D11—44no—
151Dic22—24no—
152Dic22—42no—
153C8×C11—24no—
154C8×C11—44no—
155C11⋊C8—42no—
156C22×#41—111no—
157C22×M16—111no—
158C22×M16C2×D1112yes—
159C23×C8C2×D1111yescharacteristic
160C22×C4⋊C4—112no—
161C2×#106—114no—
162C2×#106—222no—
163C2×#106—222no—
164#417—118no—
165#417—224no—
166C2×#103—222no—
167C2×#102—222no—
168#408—114no—
169#408—222no—
170C2×C22⋊C8—222no—
171#343—118no—
172#341C2×D1114yescomplemented
173C22×C11—28no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11#39712yes—
177C22×C11#39712yes—
178C22×C11#47114yes—
179C22×C11C2×#12111yescharacteristic
180C22×C11C2×#12612yes—
181C2×D11—42no—
182C2×D11—44no—
183C2×D11—84no—
184C4×C11#39712yes—
185C4×C11#39712yes—
186C4×C11C2×#12312yes—
187C4×C11C2×#12311yescharacteristic
188C4×C11C2×#12411yescharacteristic
189Dic11—42no—
190Dic11—84no—
191C2×#41—112no—
192C2×#41—112no—
193C2×#41—221no—
194C2×#41—221no—
195C2×#41—224no—
196C2×#41—224no—
197C22×Q8—111no—
198C22×D4—111no—
199C22×D4—221no—
200C23×C4—221no—
201C23×C4—222no—
202C23×C4C22×D1111yescharacteristic
203C2×M16—22no—
204C2×M16—24no—
205C2×M16—24no—
206C2×M16—112no—
207C2×M16—221no—
208C2×M16—224no—
209C2×M16C22×D1114yes—
210C22×C8—24no—
211C22×C8—22no—
212C22×C8—221no—
213C22×C8D4412yes—
214C22×C8D4412yes—
215C22×C8C22×D1112yes—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222#106—228no—
223#103—228no—
224#102—228no—
225C22⋊C8—228no—
226C2×C11—22no—
227C2×C11—22no—
228C2×C11#207914yescomplemented
229C2×C11C2×#39711yescharacteristic
230C2×C11C2×#47112yes—
231D11—82no—
232C24—221no—
233C24#434311yescharacteristic
234#41—228no—
235#41—224no—
236#41—224no—
237#41—442no—
238#41—442no—
239#41—444no—
240C2×Q8—112no—
241C2×Q8—221no—
242C2×Q8—224no—
243C2×D4—112no—
244C2×D4—222no—
245C2×D4—222no—
246C2×D4—224no—
247C2×D4—221no—
248C2×D4—444no—
249C22×C4—221no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—224no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4—884no—
258C22×C4C2×D4411yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4#433914yes—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4#434114yes—
264C22×C4#434311yescharacteristic
265C22×C4C23×D1111yescharacteristic
266M16—24no—
267M16—24no—
268M16—44no—
269M16—224no—
270M16—442no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—44no—
276C2×C8—222no—
277C2×C8—442no—
278C2×C8C2×D4414yes—
279C4⋊C4—224no—
280C4⋊C4—224no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C11C2×#207911yescharacteristic, complemented, Sylow
284C23—24no—
285C23—222no—
286C23—444no—
287C23—442no—
288C23#6694811yescharacteristic
289C23#6694811yescharacteristic
290C23#6695114yes—
291C23C2×#434311yescharacteristic
292Q8—224no—
293Q8—442no—
294D4—224no—
295D4—444no—
296D4—444no—
297D4—442no—
298C2×C4—222no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—444no—
303C2×C4—444no—
304C2×C4—884no—
305C2×C4—884no—
306C2×C4—884no—
307C2×C4#6692812yes—
308C2×C4#6692812yes—
309C2×C4#6693614yes—
310C2×C4#6693614yes—
311C2×C4#6693912yes—
312C2×C4#6693912yes—
313C2×C4#6694811yescharacteristic
314C2×C4#6694811yescharacteristic
315C2×C4#6695114yes—
316C2×C4C22×D4411yescharacteristic
317C2×C4C2×#433912yes—
318C2×C4C2×D4×D1111yescharacteristic
319C2×C4C2×#434112yes—
320C8—24no—
321C8—44no—
322C8—442no—
323C22—22no—
324C22—22no—
325C22—28no—
326C22—444no—
327C22—442no—
328C22—884no—
329C22#1062228712yes—
330C22#1062228712yes—
331C22#1062251114yes—
332C22C2×#6694811yescharacteristic
333C22C2×#6695112yes—
334C4—442no—
335C4—884no—
336C4#1062228712yes—
337C4#1062228712yes—
338C4C2×#6692811yescharacteristic
339C4C2×#6693612yes—
340C4C2×#6693911yescharacteristic
341C2—22no—
342C2—22no—
343C2—882no—
344C2#1307006314yesdirect product factor
345C2C2×#1062228711yescharacteristic
346C2C2×#1062251112yes—
subgroupG/H
centerC23#66948
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#341C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC2×#341D11
hypocenterC11C2×#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C22×#66881C2semidirect
4. #13070063C2direct (N × H)
5. C2×#10622192C2semidirect
6. C2×C11×#341C2semidirect
20. C2×#66881C22semidirect
22. C11×#341C22semidirect
23. #10622192C22semidirect
116. C2×#341D11semidirect
172. #341C2×D11semidirect
228. C2×C11#2079semidirect
283. C11C2×#2079semidirect
344. C2#13070063direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668812
C2×#106227462
C2×#106227232
#130700632
C2×#106221922
C2×C11×#3412
C2×#207911