Finite Group Databasebeta

← C2×#13081825 #15660379

Subgroups — C2×#13081825 #15660379

Order 2816.

11210 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67040C211yesmaximal, characteristic
2#13081825C2132yesmaximal, direct product factor
3C2×#10623105C214yesmaximal, complemented
4C2×#10623054C216yesmaximal, complemented
5C2×#10623103C214yesmaximal, complemented
6C2×C4×#4343C214yesmaximal, complemented
7C2×#10623053C216yesmaximal, complemented
8C22×Q8×Dic11C211yesmaximal, characteristic, complemented
9C2×C4×Q8×D11C214yesmaximal, complemented
10C2×C11×#519C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2211yescharacteristic
12C2×#67040C4132yescomplemented
13C2×#67040C22116yes—
14C22×#4343C2214yes—
15C22×Q8×D11C2214yes—
16C22×#4339C2216yes—
17C11×#519C22116yescomplemented
18C2×C4×Q8×C11C2214yes—
19C2×C4×Q8×C11C2214yes—
20C2×C11×#117C2216yes—
21C2×Q8×Dic11C2214yes—
22C2×Q8×Dic11C2214yes—
23C2×Q8×Dic11C22116yescomplemented
24C22×C4⋊Dic11C2213yes—
25C22×C4×Dic11C2213yes—
26#10623105C22164yescomplemented
27C4×#4343C22164yescomplemented
28#10623103C22164yescomplemented
29C4×Q8×D11C22164yescomplemented
30#10623054C22196yescomplemented
31#10623053C22196yescomplemented
32C2×#66946C2216yes—
33C2×#66946C2216yes—
34C2×#66945C22112yes—
35C2×C4⋊C4×D11C22112yes—
36C2×#66940C2216yes—
37C2×#66940C2216yes—
38C2×(C22⋊D11)⋊C4C2214yes—
39C2×(C22⋊D11)⋊C4C22112yes—
40C2×C4×D44C22112yes—
41C2×#66925C22112yes—
42C2×C42×D11C22112yes—
43C2×C4×Dic22C22112yes—
44C22×Q8×C11C2×C4116yescomplemented
45C22×Q8×C11C2314yes—
46C22×Q8×C11C2318yes—
47C23×C4×C11C2313yes—
48C22×C22⋊D11C2314yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2313yes—
51#67040C2×C41256yescomplemented
52C2×#4343C2×C4164yescomplemented
53C2×#4343C23132yes—
54C2×Q8×D11C2×C4164yescomplemented
55C2×Q8×D11C23132yes—
56C2×#4339C2×C4196yescomplemented
57C2×#4339C23148yes—
58C22×D44C2316yes—
59C22×C4×D11C2314yes—
60C22×C4×D11C23112yes—
61C22×C4×D11C23112yes—
62C22×Dic22C2316yes—
63C4×Q8×C11C23132yes—
64C4×Q8×C11C23132yes—
65C11×#117C23148yes—
66C2×C11×C4⋊C4C2316yes—
67C2×C11×C4⋊C4C2316yes—
68C2×C11×C22⋊C4C2314yes—
69C2×C42×C11C23112yes—
70Q8×Dic11C23132yes—
71Q8×Dic11C23132yes—
72C2×(C2×D11)⋊C4C2314yes—
73C2×(C2×D11)⋊C4C23112yes—
74C2×C4⋊Dic11C23112yes—
75C2×C4⋊Dic11C23124yes—
76C2×Dic11⋊C4C23112yes—
77C2×Dic11⋊C4C2314yes—
78C2×C4×Dic11C23112yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2316yes—
81C2×C4×Dic11C2316yes—
82C2×C4×Dic11C23124yes—
83#66946C23148yes—
84#66946C23148yes—
85#66945C23196yes—
86C4⋊C4×D11C23196yes—
87#66940C23148yes—
88#66940C23148yes—
89(C22⋊D11)⋊C4C23132yes—
90(C22⋊D11)⋊C4C23196yes—
91C4×D44C23196yes—
92#66925C23196yes—
93C42×D11C23196yes—
94C4×Dic22C23196yes—
95C2×C4×2−1+4—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C23×D11C2414yes—
98C2×Q8×C11C22×C4132yes—
99C2×Q8×C11C22×C4164yescomplemented
100C2×Q8×C11C24116yes—
101C22×C4×C11C22×C4124yes—
102C22×C4×C11C2414yes—
103C22×C4×C11C2414yes—
104C22×C4×C11C2416yes—
105C22×C4×C11C24112yes—
106C2×C22⋊D11C22×C4132yes—
107C2×C22⋊D11C24116yes—
108C22×Dic11—24no—
109C22×Dic11—46no—
110C22×Dic11C2414yes—
111C22×Dic11C2411yescharacteristic
112C22×Dic11C2416yes—
113C22×Dic11C24112yes—
114C22×Dic11C2414yes—
115C22×Dic11C2411yescharacteristic
116#4343C22×C41256yescomplemented
117Q8×D11C22×C41256yescomplemented
118#4339C22×C41384yescomplemented
119C2×D44C22×C4148yes—
120C2×D44C24124yes—
121C2×C4×D11—216no—
122C2×C4×D11—424no—
123C2×C4×D11C22×C4196yes—
124C2×C4×D11C24116yes—
125C2×C4×D11C24148yes—
126C2×C4×D11C24148yes—
127C2×Dic22C22×C4148yes—
128C2×Dic22C24124yes—
129C11×C4⋊C4C24124yes—
130C11×C4⋊C4C24124yes—
131C11×C22⋊C4C24116yes—
132C42×C11C24148yes—
133(C2×D11)⋊C4C24116yes—
134(C2×D11)⋊C4C24148yes—
135C4⋊Dic11C24148yes—
136Dic11⋊C4C24148yes—
137Dic11⋊C4C24116yes—
138C4×Dic11C24148yes—
139C4×Dic11C24116yes—
140C4×Dic11C24124yes—
141C4×Dic11C24124yes—
142C22×2−1+4—111no—
143C4×2−1+4—1132no—
144C2×#520—114no—
145C2×#520—116no—
146C2×#519—114no—
147C2×#519D1111yescharacteristic, complemented
148C2×C4×#41—114no—
149C2×C4×#41—116no—
150C22×C4×Q8—111no—
151C22×C4×Q8—114no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11C23×C414yes—
155C23×C11C2512yes—
156C23×C11C2511yescharacteristic
157C22×D11—28no—
158C22×D11—28no—
159C22×D11C23×C4116yes—
160C22×D11C2518yes—
161Q8×C11C23×C4164yes—
162C2×C4×C11—28no—
163C2×C4×C11—28no—
164C2×C4×C11C23×C4124yes—
165C2×C4×C11C23×C4148yes—
166C2×C4×C11C2518yes—
167C2×C4×C11C2518yes—
168C2×C4×C11C25112yes—
169C22⋊D11C23×C4164yes—
170C2×Dic11—22no—
171C2×Dic11—212no—
172C2×Dic11—28no—
173C2×Dic11—412no—
174C2×Dic11C23×C4116yes—
175C2×Dic112−1+414yescomplemented
176C2×Dic11C2512yes—
177C2×Dic11C25112yes—
178C2×Dic11C2518yes—
179C2×Dic11C2512yes—
180D44C23×C4196yes—
181C4×D11—232no—
182C4×D11—448no—
183C4×D11C23×C41192yes—
184Dic22C23×C4196yes—
185C2×2−1+4—1116no—
186C2×2−1+4—1132no—
187C22×#41—114no—
188C22×#41—116no—
189C23×Q8—114no—
190C23×Q8C2×D1111yescharacteristic
191#520—1164no—
192#520—1196no—
193#519—1164no—
194#519C2×D11116yescomplemented
195C4×#41—1164no—
196C4×#41—1196no—
197C2×C4×Q8—114no—
198C2×C4×Q8—114no—
199C2×C4×Q8—1116no—
200C2×C4×Q8—1164no—
201C2×C4×Q8—116no—
202C2×C4×Q8—116no—
203C2×C4×Q8—1112no—
204C2×C4×Q8C2×D1114yes—
205C2×C4×Q8C2×D1114yes—
206C2×C4×D4—116no—
207C2×C4×D4—116no—
208C2×C4×D4—114no—
209C2×C4×D4—1112no—
210C2×C4×D4—1112no—
211C2×#117—1112no—
212C2×#117—1112no—
213C2×#117C2×D1116yes—
214C22×C4⋊C4—113no—
215C22×C4⋊C4—1112no—
216C22×C42—113no—
217C22×C42—1112no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—28no—
221C22×C11C24×C414yes—
222C22×C11C24×C412yes—
223C22×C11C2×2−1+412yes—
224C22×C11#58512yes—
225C22×C11C2611yescharacteristic
226C2×D11—28no—
227C2×D11—28no—
228C2×D11—232no—
229C2×D11C24×C4116yes—
230C4×C11—28no—
231C4×C11—28no—
232C4×C11C24×C4124yes—
233Dic11—22no—
234Dic11—212no—
235Dic11C24×C4116yes—
236Dic11C2×2−1+414yescomplemented
2372−1+4—11256no—
238C2×#41—1164no—
239C2×#41—1132no—
240C2×#41—1196no—
241C2×#41—1148no—
242C22×Q8—1164no—
243C22×Q8—1132no—
244C22×Q8—116no—
245C22×Q8C4×D11116yescomplemented
246C22×Q8C22×D1114yes—
247C22×Q8C22×D1118yes—
248C22×D4—114no—
249C22×D4—116no—
250C23×C4—1112no—
251C23×C4—111no—
252C23×C4—113no—
253C23×C4—114no—
254C23×C4—1112no—
255C23×C4C22×D1113yes—
256C4×Q8—1132no—
257C4×Q8—1132no—
258C4×Q8—1148no—
259C4×Q8—1148no—
260C4×Q8—1196no—
261C4×Q8C22×D11132yes—
262C4×Q8C22×D11132yes—
263C4×D4—1148no—
264C4×D4—1148no—
265C4×D4—1132no—
266C4×D4—1196no—
267C4×D4—1196no—
268#117—1196no—
269#117—1196no—
270#117C22×D11148yes—
271C2×C4⋊C4—1112no—
272C2×C4⋊C4—1112no—
273C2×C4⋊C4—1124no—
274C2×C4⋊C4—114no—
275C2×C4⋊C4—1196no—
276C2×C4⋊C4C22×D1116yes—
277C2×C4⋊C4C22×D1116yes—
278C2×C22⋊C4—114no—
279C2×C22⋊C4—1112no—
280C2×C22⋊C4C22×D1114yes—
281C2×C42—1112no—
282C2×C42—116no—
283C2×C42—114no—
284C2×C42—116no—
285C2×C42—1124no—
286C2×C42—1196no—
287C2×C42C22×D11112yes—
288C2×C11—24no—
289C2×C11C4×2−1+414yescomplemented
290C2×C11C25×C411yescharacteristic
291C2×C11C22×2−1+411yescharacteristic
292C2×C11C2×#58511yescharacteristic
293D11—216no—
294C24—114no—
295C24C23×D1111yescharacteristic
296#41—11256no—
297#41—11384no—
298C2×Q8—11256no—
299C2×Q8—1148no—
300C2×Q8—1124no—
301C2×Q8C2×C4×D11132yes—
302C2×Q8C2×C4×D11164yescomplemented
303C2×Q8C23×D11116yes—
304C2×D4—1132no—
305C2×D4—1116no—
306C2×D4—1148no—
307C2×D4—1124no—
308C22×C4—111no—
309C22×C4—114no—
310C22×C4—1196no—
311C22×C4—1148no—
312C22×C4—114no—
313C22×C4—111no—
314C22×C4—116no—
315C22×C4—1112no—
316C22×C4—1116no—
317C22×C4—1148no—
318C22×C4—2216no—
319C22×C4—224no—
320C22×C4—4424no—
321C22×C4—446no—
322C22×C4C2×C4×D11124yes—
323C22×C4C23×D1114yes—
324C22×C4C23×D1114yes—
325C22×C4C23×D11112yes—
326C22×C4C23×D1116yes—
327C4⋊C4—1148no—
328C4⋊C4—1148no—
329C4⋊C4—1116no—
330C4⋊C4C23×D11124yes—
331C4⋊C4C23×D11124yes—
332C22⋊C4—1116no—
333C22⋊C4—1148no—
334C22⋊C4C23×D11116yes—
335C42—1116no—
336C42—1124no—
337C42—1148no—
338C42—1124no—
339C42C23×D11148yes—
340C11C2×C4×2−1+411yescharacteristic, complemented, Sylow
341C23—22no—
342C23—22no—
343C23—1116no—
344C23—118no—
345C23—228no—
346C23—228no—
347C23C22×C4×D1114yes—
348C23C24×D1112yes—
349C23C24×D1111yescharacteristic
350Q8—1196no—
351Q8C22×C4×D11164yes—
352D4—1164no—
353D4—1196no—
354C2×C4—28no—
355C2×C4—28no—
356C2×C4—1116no—
357C2×C4—114no—
358C2×C4—112no—
359C2×C4—118no—
360C2×C4—11192no—
361C2×C4—112no—
362C2×C4—1112no—
363C2×C4—2232no—
364C2×C4—228no—
365C2×C4—222no—
366C2×C4—2212no—
367C2×C4—4448no—
368C2×C4—4412no—
369C2×C4C22×C4×D11124yes—
370C2×C4C22×C4×D11148yes—
371C2×C4C24×D1118yes—
372C2×C4C24×D1118yes—
373C2×C4C24×D11112yes—
374C22—22no—
375C22—22no—
376C22—28no—
377C22—1116no—
378C22—228no—
379C22—228no—
380C22—2232no—
381C22C23×C4×D1114yes—
382C22C23×C4×D1112yes—
383C22D11×2−1+412yes—
384C22#1062345712yes—
385C22C25×D1111yescharacteristic
386C4—28no—
387C4—28no—
388C4—1116no—
389C4—114no—
390C4—222no—
391C4—2212no—
392C4C23×C4×D11124yes—
393C2—24no—
394C2—2216no—
395C2#1308182514yesdirect product factor
396C2C24×C4×D1111yescharacteristic
397C2C2×D11×2−1+411yescharacteristic
398C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC2×C11×#519C2
socleC23×C11C25
prime radicalC22×#67040C2
cosocleC22×C11C26
hypercenterC2×#519D11
hypocenterC11C2×C4×2−1+4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #13081825C2direct (N × H)
3. C2×#10623105C2semidirect
4. C2×#10623054C2semidirect
5. C2×#10623103C2semidirect
6. C2×C4×#4343C2semidirect
7. C2×#10623053C2semidirect
8. C22×Q8×Dic11C2semidirect
9. C2×C4×Q8×D11C2semidirect
10. C2×C11×#519C2semidirect
12. C2×#67040C4semidirect
17. C11×#519C22semidirect
23. C2×Q8×Dic11C22semidirect
26. #10623105C22semidirect
27. C4×#4343C22semidirect
28. #10623103C22semidirect
29. C4×Q8×D11C22semidirect
30. #10623054C22semidirect
31. #10623053C22semidirect
44. C22×Q8×C11C2×C4semidirect
51. #67040C2×C4semidirect
52. C2×#4343C2×C4semidirect
54. C2×Q8×D11C2×C4semidirect
56. C2×#4339C2×C4semidirect
99. C2×Q8×C11C22×C4semidirect
116. #4343C22×C4semidirect
117. Q8×D11C22×C4semidirect
118. #4339C22×C4semidirect
147. C2×#519D11semidirect
175. C2×Dic112−1+4semidirect
194. #519C2×D11semidirect
236. Dic11C2×2−1+4semidirect
245. C22×Q8C4×D11semidirect
289. C2×C11C4×2−1+4semidirect
302. C2×Q8C2×C4×D11semidirect
340. C11C2×C4×2−1+4semidirect
395. C2#13081825direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
#130818252
C2×#106231052
C2×#106230542
C2×#106231032
C2×C4×#43432
C2×#106230532
C22×Q8×Dic112
C2×C4×Q8×D112
C2×C11×#5192
C2×C4×2−1+411