Finite Group Databasebeta

← C2×#13070058 #14782665

Subgroups — C2×#13070058 #14782665

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66882C211yesmaximal, characteristic, complemented
2C2×#10622746C212yesmaximal
3C2×#10622723C211yesmaximal, characteristic
4#13070058C218yesmaximal, 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×#66882—22no—
19C2×#66882—22no—
20C2×#66882C2214yescomplemented
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#66882—28no—
58#66880—28no—
59C2×#2078—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×#107—111no—
112C2×#417—112no—
113C2×#408—111no—
114#2078—118no—
115C2×#343—112no—
116C2×#341D1111yescharacteristic, complemented
117C23×C11—22no—
118C23×C11—22no—
119C23×C11#12111yescharacteristic
120C23×C11#12111yescharacteristic
121C23×C11#12614yes—
122C23×C11C2×#4111yescharacteristic
123C22×D11—22no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12314yes—
130C2×C4×C11#12314yes—
131C2×C4×C11#12312yes—
132C2×C4×C11#12312yes—
133C2×C4×C11#12412yes—
134C2×C4×C11#12412yes—
135C2×C4×C11#12614yes—
136C2×C4×C11C22×D411yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C2×#4112yes—
139C2×C4×C11C2×#4112yes—
140C22⋊D11—44no—
141C22⋊D11—44no—
142C2×Dic11—22no—
143C2×Dic11—42no—
144C2×Dic11—44no—
145C2×Dic11—84no—
146C2×Dic11—84no—
147C2×Dic11—84no—
148D44—24no—
149D44—42no—
150C4×D11—42no—
151C4×D11—42no—
152C4×D11—44no—
153Dic22—24no—
154Dic22—42no—
155C8×C11—24no—
156C8×C11—44no—
157C11⋊C8—42no—
158C22×#41—111no—
159C22×M16—111no—
160C22×M16C2×D1112yes—
161C23×C8C2×D1111yescharacteristic
162C22×C4⋊C4—112no—
163C2×#107—114no—
164C2×#107—222no—
165C2×#107—222no—
166#417—118no—
167#417—224no—
168C2×#103—222no—
169C2×#102—222no—
170#408—114no—
171#408—222no—
172C2×C22⋊C8—222no—
173#343—118no—
174#341C2×D1114yescomplemented
175C22×C11—28no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39712yes—
181C22×C11#39712yes—
182C22×C11#47212yes—
183C22×C11#47312yes—
184C22×C11C2×#12111yescharacteristic
185C22×C11C2×#12612yes—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—84no—
190C4×C11#39712yes—
191C4×C11#39712yes—
192C4×C11C2×#12312yes—
193C4×C11C2×#12311yescharacteristic
194C4×C11C2×#12411yescharacteristic
195Dic11—42no—
196Dic11—84no—
197C2×#41—112no—
198C2×#41—112no—
199C2×#41—221no—
200C2×#41—221no—
201C2×#41—224no—
202C2×#41—224no—
203C22×Q8—111no—
204C22×D4—111no—
205C22×D4—221no—
206C23×C4—221no—
207C23×C4—222no—
208C23×C4C22×D1111yescharacteristic
209C2×M16—22no—
210C2×M16—24no—
211C2×M16—24no—
212C2×M16—112no—
213C2×M16—221no—
214C2×M16—224no—
215C2×M16C22×D1114yes—
216C22×C8—24no—
217C22×C8—22no—
218C22×C8—221no—
219C22×C8D4412yes—
220C22×C8D4412yes—
221C22×C8C22×D1112yes—
222C2×C4⋊C4—114no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—222no—
228#107—228no—
229#103—228no—
230#102—228no—
231C22⋊C8—228no—
232C2×C11—22no—
233C2×C11—22no—
234C2×C11#207814yescomplemented
235C2×C11C2×#39711yescharacteristic
236C2×C11C2×#47211yescharacteristic
237C2×C11C2×#47311yescharacteristic
238D11—82no—
239C24—221no—
240C24#434311yescharacteristic
241#41—228no—
242#41—224no—
243#41—224no—
244#41—442no—
245#41—442no—
246#41—444no—
247C2×Q8—112no—
248C2×Q8—221no—
249C2×Q8—224no—
250C2×D4—112no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—224no—
254C2×D4—221no—
255C2×D4—444no—
256C22×C4—221no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4—224no—
260C22×C4—442no—
261C22×C4—442no—
262C22×C4—442no—
263C22×C4—442no—
264C22×C4—884no—
265C22×C4C2×D4411yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4#433914yes—
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4#434114yes—
271C22×C4#434311yescharacteristic
272C22×C4C23×D1111yescharacteristic
273M16—24no—
274M16—24no—
275M16—44no—
276M16—224no—
277M16—442no—
278C2×C8—24no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—44no—
283C2×C8—222no—
284C2×C8—442no—
285C2×C8C2×D4414yes—
286C4⋊C4—224no—
287C4⋊C4—224no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C11C2×#207811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—222no—
294C23—442no—
295C23—442no—
296C23—442no—
297C23#6694811yescharacteristic
298C23#6694811yescharacteristic
299C23#6695114yes—
300C23C2×#434311yescharacteristic
301Q8—224no—
302Q8—442no—
303D4—224no—
304D4—444no—
305D4—444no—
306D4—442no—
307C2×C4—222no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—444no—
312C2×C4—444no—
313C2×C4—884no—
314C2×C4—884no—
315C2×C4—884no—
316C2×C4#6692812yes—
317C2×C4#6692812yes—
318C2×C4#6693614yes—
319C2×C4#6693614yes—
320C2×C4#6693912yes—
321C2×C4#6693912yes—
322C2×C4#6694811yescharacteristic
323C2×C4#6694811yescharacteristic
324C2×C4#6695114yes—
325C2×C4C22×D4411yescharacteristic
326C2×C4C2×#433912yes—
327C2×C4C2×D4×D1111yescharacteristic
328C2×C4C2×#434112yes—
329C8—24no—
330C8—44no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—28no—
337C22—442no—
338C22—442no—
339C22—442no—
340C22—884no—
341C22#1062228712yes—
342C22#1062228712yes—
343C22#1062250912yes—
344C22#1062251012yes—
345C22C2×#6694811yescharacteristic
346C22C2×#6695112yes—
347C4—442no—
348C4—884no—
349C4#1062228712yes—
350C4#1062228712yes—
351C4C2×#6692811yescharacteristic
352C4C2×#6693612yes—
353C4C2×#6693911yescharacteristic
354C2—22no—
355C2—22no—
356C2—882no—
357C2#1307005814yesdirect product factor
358C2C2×#1062228711yescharacteristic
359C2C2×#1062251011yescharacteristic
360C2C2×#1062250911yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#341C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC2×#341D11
hypocenterC11C2×#2078
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×#66882C2semidirect
4. #13070058C2direct (N × H)
5. C2×#10622192C2semidirect
6. C2×C11×#341C2semidirect
20. C2×#66882C22semidirect
22. C11×#341C22semidirect
23. #10622192C22semidirect
116. C2×#341D11semidirect
174. #341C2×D11semidirect
234. C2×C11#2078semidirect
290. C11C2×#2078semidirect
357. C2#13070058direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668822
C2×#106227462
C2×#106227232
#130700582
C2×#106221922
C2×C11×#3412
C2×#207811