Finite Group Databasebeta

← C2×#13077079 #15617246

Subgroups — C2×#13077079 #15617246

Order 2816.

4818 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×#67040C211yesmaximal, characteristic
2C2×#10623343C211yesmaximal, characteristic, complemented
3#13077079C2116yesmaximal, direct product factor
4C2×#10622619C2112yesmaximal, complemented
5C2×C11×#519C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C2×#67040—24no—
8C2×#67040—24no—
9C2×#67040—24no—
10C2×#67040—24no—
11C2×#67040C418yescomplemented
12C2×#67040C2218yes—
13C22×#4343C414yescomplemented
14C22×Q8×D11C414yescomplemented
15C22×#4339C2216yes—
16C11×#519—24no—
17C11×#519C2218yescomplemented
18C2×C4×Q8×C11—24no—
19C2×C11×#117C2216yes—
20#10623343—24no—
21#10623343C2218yescomplemented
22C2×Q8×Dic11—24no—
23C2×#66979C2216yes—
24#10622619C22196yescomplemented
25C2×#66870C22116yes—
26C22×Q8×C11C2×C414yes—
27C22×Q8×C11C2×C414yes—
28C22×Q8×C11D414yes—
29C22×Q8×C11D414yes—
30C22×Q8×C11D414yes—
31C22×Q8×C11D414yes—
32C22×Q8×C11C2314yes—
33C23×C4×C11C2313yes—
34C22×C22⋊D11C2314yes—
35#67040—232no—
36#67040—232no—
37#67040—232no—
38#67040—232no—
39C2×#4343—216no—
40C2×#4343—216no—
41C2×#4343C2×C4132yescomplemented
42C2×Q8×D11—216no—
43C2×Q8×D11—216no—
44C2×Q8×D11C2×C4132yescomplemented
45C2×#4339—212no—
46C2×#4339—212no—
47C2×#4339—212no—
48C2×#4339—212no—
49C2×#4339C2×C4124yes—
50C2×#4339C23124yes—
51C22×D44C2×C416yes—
52C22×C4×D11C2×C4112yes—
53C22×Dic22C2×C416yes—
54C4×Q8×C11—232no—
55C11×#117—212no—
56C11×#117C23124yes—
57C2×C11×C4⋊C4—26no—
58C2×C11×C22⋊C4C2314yes—
59C2×C42×C11—26no—
60C2×C22⋊Dic11C2314yes—
61Q8×Dic11—232no—
62#66979—212no—
63#66979C23124yes—
64C2×C4⋊Dic11—26no—
65C2×C4×Dic11—26no—
66#66870C23164yes—
67C2×#2884—111nomaximal, Sylow
68C24×C11C2411yescharacteristic
69C23×D11C22×C414yes—
70C2×Q8×C11C22⋊C4116yes—
71C2×Q8×C11C22⋊C4116yes—
72C2×Q8×C11C22⋊C4116yes—
73C2×Q8×C11C22⋊C4116yes—
74C2×Q8×C11C22×C4116yes—
75C2×Q8×C11C2×D4116yes—
76C2×Q8×C11C2×D4116yes—
77C22×C4×C11—24no—
78C22×C4×C11C22×C416yes—
79C22×C4×C11C22×C416yes—
80C22×C4×C11C2×D416yes—
81C22×C4×C11C2×D416yes—
82C22×C4×C11C2×D416yes—
83C22×C4×C11C2×D416yes—
84C22×C4×C11C2416yes—
85C2×C22⋊D11—24no—
86C2×C22⋊D11—24no—
87C2×C22⋊D11—24no—
88C2×C22⋊D11—24no—
89C2×C22⋊D11C22×C418yes—
90C2×C22⋊D11C2418yes—
91C22×Dic11—24no—
92C22×Dic11C22×C414yes—
93#4343—2128no—
94Q8×D11—2128no—
95#4339—248no—
96#4339—248no—
97#4339—248no—
98#4339—248no—
99C2×D44—212no—
100C2×D44—212no—
101C2×D44C22×C4124yes—
102C2×C4×D11—224no—
103C2×C4×D11—224no—
104C2×C4×D11C22×C4148yes—
105C2×Dic22—212no—
106C2×Dic22—212no—
107C2×Dic22C22×C4124yes—
108C11×C4⋊C4—224no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4C2418yes—
111C42×C11—224no—
112C22⋊Dic11—24no—
113C22⋊Dic11C2418yes—
114C4⋊Dic11—224no—
115C4×Dic11—224no—
116C22×2−1+4—111no—
117C2×#519—111no—
118C2×#519D1111yescharacteristic, complemented
119#2884—1116no—
120C2×#410—1112no—
121C23×C11—42no—
122C23×C11C23×C411yescharacteristic
123C23×C11C23×C411yescharacteristic
124C23×C11C22×D411yescharacteristic
125C23×C11C22×D411yescharacteristic
126C23×C11C22×D411yescharacteristic
127C23×C11C22×D411yescharacteristic
128C23×C11C2511yescharacteristic
129C22×D11—24no—
130C22×D11—24no—
131C22×D11—48no—
132C22×D11C23×C418yes—
133Q8×C11C2×C22⋊C4164yes—
134C2×C4×C11—28no—
135C2×C4×C11—48no—
136C2×C4×C11C2×C22⋊C4112yes—
137C2×C4×C11C2×C22⋊C4112yes—
138C2×C4×C11C2×C22⋊C4112yes—
139C2×C4×C11C2×C22⋊C4112yes—
140C2×C4×C11C23×C4112yes—
141C2×C4×C11C22×D4112yes—
142C2×C4×C11C22×D4112yes—
143C22⋊D11—28no—
144C22⋊D11—28no—
145C22⋊D11—28no—
146C22⋊D11—28no—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—28no—
150C2×Dic11—48no—
151C2×Dic11C23×C418yes—
152D44—248no—
153C4×D11—296no—
154Dic22—248no—
155C2×2−1+4—118no—
156C2×2−1+4—118no—
157C2×2−1+4—224no—
158C2×2−1+4—224no—
159C2×2−1+4—224no—
160C2×2−1+4—224no—
161C22×#41—114no—
162C22×#41—116no—
163C23×Q8—114no—
164C23×Q8C2×D1111yescharacteristic
165#519—24no—
166#519—118no—
167#519—224no—
168#519C2×D1118yescomplemented
169C2×C4×Q8—24no—
170C2×C4×Q8—224no—
171C2×#117—116no—
172C2×#117C2×D1116yes—
173#410—1196no—
174C2×#99—1116no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11C22×C22⋊C411yescharacteristic
183C22×C11C22×C22⋊C411yescharacteristic
184C22×C11C22×C22⋊C411yescharacteristic
185C22×C11C22×C22⋊C411yescharacteristic
186C22×C11C24×C411yescharacteristic
187C22×C11C23×D411yescharacteristic
188C22×C11C23×D411yescharacteristic
189C2×D11—28no—
190C2×D11—48no—
191C2×D11—48no—
192C2×D11—48no—
193C4×C11—48no—
194C4×C11C22×C22⋊C4124yes—
195Dic11—28no—
196Dic11—48no—
1972−1+4—2232no—
1982−1+4—2232no—
1992−1+4—2232no—
2002−1+4—2232no—
201C2×#41—1132no—
202C2×#41—1124no—
203C2×#41—1124no—
204C2×#41—2216no—
205C2×#41—2216no—
206C2×#41—2212no—
207C2×#41—2212no—
208C2×#41—2212no—
209C2×#41—2212no—
210C22×Q8—1132no—
211C22×Q8—116no—
212C22×Q8—2216no—
213C22×Q8—2216no—
214C22×Q8C4×D1114yes—
215C22×Q8C4×D1114yes—
216C22×Q8D4414yes—
217C22×Q8D4414yes—
218C22×Q8C22⋊D1114yes—
219C22×Q8C22⋊D1114yes—
220C22×Q8C22×D1114yes—
221C22×D4—114no—
222C22×D4—116no—
223C23×C4—1112no—
224C23×C4C22×D1113yes—
225C4×Q8—232no—
226C4×Q8—2232no—
227#117—212no—
228#117—1124no—
229#117—2212no—
230#117C22×D11124yes—
231C2×C4⋊C4—26no—
232C2×C4⋊C4—226no—
233C2×C22⋊C4—114no—
234C2×C22⋊C4C22×D1114yes—
235C2×C42—26no—
236C2×C42—226no—
237#99—1164no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#288412yescomplemented
245C2×C11C23×C22⋊C411yescharacteristic
246D11—48no—
247C24—114no—
248C24C23×D1111yescharacteristic
249#41—22128no—
250#41—2248no—
251#41—2248no—
252#41—2248no—
253#41—2248no—
254C2×Q8—1124no—
255C2×Q8—22128no—
256C2×Q8—2212no—
257C2×Q8—2212no—
258C2×Q8(C2×D11)⋊C4116yes—
259C2×Q8(C2×D11)⋊C4116yes—
260C2×Q8(C2×D11)⋊C4116yes—
261C2×Q8(C2×D11)⋊C4116yes—
262C2×Q8C2×C4×D11116yes—
263C2×Q8C2×D44116yes—
264C2×Q8C2×C22⋊D11116yes—
265C2×D4—118no—
266C2×D4—118no—
267C2×D4—1124no—
268C2×D4—224no—
269C2×D4—224no—
270C2×D4—224no—
271C2×D4—224no—
272C2×D4—2212no—
273C2×D4—2212no—
274C22×C4—24no—
275C22×C4—114no—
276C22×C4—1148no—
277C22×C4—2224no—
278C22×C4—2224no—
279C22×C4—224no—
280C22×C4C2×C4×D1116yes—
281C22×C4C2×C4×D1116yes—
282C22×C4C2×D4416yes—
283C22×C4C2×D4416yes—
284C22×C4C2×C22⋊D1116yes—
285C22×C4C2×C22⋊D1116yes—
286C22×C4C23×D1116yes—
287C4⋊C4—224no—
288C4⋊C4—2224no—
289C22⋊C4—24no—
290C22⋊C4—118no—
291C22⋊C4—224no—
292C22⋊C4C23×D1118yes—
293C42—224no—
294C42—2224no—
295C11C2×#288411yescharacteristic, complemented, Sylow
296C23—42no—
297C23—118no—
298C23—224no—
299C23—224no—
300C23—448no—
301C23C22×C4×D1111yescharacteristic
302C23C22×C4×D1111yescharacteristic
303C23C22×D4411yescharacteristic
304C23C22×D4411yescharacteristic
305C23C22×C22⋊D1111yescharacteristic
306C23C22×C22⋊D1111yescharacteristic
307C23C24×D1111yescharacteristic
308Q8—2248no—
309Q8C2×(C2×D11)⋊C4164yes—
310D4—228no—
311D4—228no—
312D4—228no—
313D4—228no—
314D4—2248no—
315C2×C4—28no—
316C2×C4—48no—
317C2×C4—118no—
318C2×C4—224no—
319C2×C4—224no—
320C2×C4—2296no—
321C2×C4—228no—
322C2×C4—448no—
323C2×C4C2×(C2×D11)⋊C4112yes—
324C2×C4C2×(C2×D11)⋊C4112yes—
325C2×C4C2×(C2×D11)⋊C4112yes—
326C2×C4C2×(C2×D11)⋊C4112yes—
327C2×C4C22×C4×D11112yes—
328C2×C4C22×D44112yes—
329C2×C4C22×C22⋊D11112yes—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—228no—
338C22—448no—
339C22—448no—
340C22—448no—
341C22C22×(C2×D11)⋊C411yescharacteristic
342C22C22×(C2×D11)⋊C411yescharacteristic
343C22C22×(C2×D11)⋊C411yescharacteristic
344C22C22×(C2×D11)⋊C411yescharacteristic
345C22C23×C4×D1111yescharacteristic
346C22C23×D4411yescharacteristic
347C22C23×C22⋊D1111yescharacteristic
348C4—48no—
349C4—228no—
350C4—448no—
351C4C22×(C2×D11)⋊C4124yes—
352C2—21no—
353C2—21no—
354C2—21no—
355C2—21no—
356C2—21no—
357C2—21no—
358C2—448no—
359C2#1307707912yesdirect product factor
360C2C23×(C2×D11)⋊C411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#519C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#67040C2
cosocleC23×C11C25
hypercenterC2×#519D11
hypocenterC11C2×#2884
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#10623343C2semidirect
3. #13077079C2direct (N × H)
4. C2×#10622619C2semidirect
5. C2×C11×#519C2semidirect
11. C2×#67040C4semidirect
13. C22×#4343C4semidirect
14. C22×Q8×D11C4semidirect
17. C11×#519C22semidirect
21. #10623343C22semidirect
24. #10622619C22semidirect
41. C2×#4343C2×C4semidirect
44. C2×Q8×D11C2×C4semidirect
118. C2×#519D11semidirect
168. #519C2×D11semidirect
244. C2×C11#2884semidirect
295. C11C2×#2884semidirect
359. C2#13077079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
C2×#106233432
#130770792
C2×#106226192
C2×C11×#5192
C2×#288411