Finite Group Databasebeta

← C2×#13079141 #15623391

Subgroups — C2×#13079141 #15623391

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623260C212yesmaximal
2#13079141C2116yesmaximal, direct product factor
3C2×#10622469C212yesmaximal, complemented
4C2×#10622693C212yesmaximal, complemented
5C2×#10622296C211yesmaximal, characteristic, complemented
6C2×#10622471C211yesmaximal, characteristic, complemented
7C2×#10622468C211yesmaximal, characteristic, complemented
8C2×#10622474C212yesmaximal
9C2×#10622473C211yesmaximal, characteristic
10C2×D11×#106C211yesmaximal, characteristic
11C2×#10622302C211yesmaximal, characteristic
12C2×C11×#498C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2212yes—
14C2×#66999—22no—
15C2×#66997—22no—
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18#10623260—28no—
19#10623260C22116yes—
20C2×#66949—22no—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66943C2212yes—
24C2×#66942—22no—
25C2×#66941C2212yes—
26C2×#66925C2211yescharacteristic
27C2×#66923C2212yes—
28C11×#498C2218yescomplemented
29C2×C11×#106C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C2×#66882C2212yes—
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622693C22116yescomplemented
39C2×#66872C2212yes—
40C2×#66872C2212yes—
41C2×#66871C2212yes—
42C2×#66871C2212yes—
43C2×#66867C2211yescharacteristic
44#10622474C22116yes—
45#10622473C2218yes—
46D11×#106C2218yes—
47#10622471C2218yescomplemented
48#10622469C22116yescomplemented
49#10622468C2218yescomplemented
50#10622302C2218yes—
51#10622296C2218yescomplemented
52C22×Q8×C11—22no—
53C22×C4×D11—22no—
54C22×C4×D11C2311yescharacteristic
55C22×Dic22—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8C2318yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64#66999—216no—
65#66997—216no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4D412yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4D412yes—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×#4313Q818yescomplemented
82C2×#4313C2314yes—
83C2×C8×D11Q818yescomplemented
84C2×C8×D11C2314yes—
85#66949—216no—
86#66945—24no—
87#66945C2318yes—
88C4⋊C4×D11—24no—
89C4⋊C4×D11C2318yes—
90#66943—24no—
91#66943C2318yes—
92#66942—216no—
93#66941—24no—
94#66941C2318yes—
95#66925D414yes—
96#66925C2314yes—
97#66923—24no—
98#66923C2318yes—
99C11×#106C2314yes—
100C11×#106C2318yes—
101C11×#106C2314yes—
102C4×C8×C11C2314yes—
103#66882C2318yes—
104#66881C2314yes—
105#66881C2314yes—
106#66879C2314yes—
107C8×Dic11C2314yes—
108#66872C2318yes—
109#66872C2318yes—
110#66871C2318yes—
111#66871C2318yes—
112#66867C2314yes—
113C2×#3163—111nomaximal, Sylow
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—28no—
116C2×Q8×C11—84no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D411yescharacteristic
125C2×C4×D11—28no—
126C2×C4×D11—84no—
127C2×C4×D11C2×D412yes—
128C2×C4×D11C2×Q814yes—
129C2×C4×D11C2×Q814yes—
130C2×C4×D11C2412yes—
131C2×Dic22—28no—
132C2×Dic22—84no—
133C2×C8×C11C2×Q814yes—
134C2×C8×C11C2×Q814yes—
135C2×C8×C11C2412yes—
136C2×C8×C11C2412yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2414yes—
141C11×C4⋊C4C2414yes—
142C42×C11C2×D412yes—
143C42×C11C2412yes—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4C2×D418yes—
146C4⋊Dic11—28no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11C2414yes—
150C4⋊Dic11C2414yes—
151Dic11⋊C4—28no—
152Dic11⋊C4—28no—
153Dic11⋊C4—28no—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4C2×D418yes—
157C4×Dic11—28no—
158C4×Dic11C2×D412yes—
159C4×Dic11C2412yes—
160C2×C11⋊C8C2×Q814yes—
161C2×C11⋊C8C2×Q814yes—
162C2×C11⋊C8C2412yes—
163C2×C11⋊C8C2412yes—
164#4313C2×Q8116yescomplemented
165C8×D11C2×Q8116yescomplemented
166C2×#544—112no—
167#3163—1116no—
168C2×#501—112no—
169C2×#501—112no—
170C2×#499—111no—
171C2×#499—111no—
172C2×#498—111no—
173C2×#498D1111yescharacteristic, complemented
174C2×#428—112no—
175C2×#427—111no—
176C22×#106—111no—
177C2×#405—111no—
178C23×C11C22×D411yescharacteristic
179C22×D11—24no—
180C22×D11C4⋊Q814yes—
181C22×D11C22×D412yes—
182Q8×C11—88no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11C22×D414yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q812yes—
191C2×C4×C11C22×Q812yes—
192C2×C4×C11C2511yescharacteristic
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11C4⋊Q814yes—
199C2×Dic11C22×D414yes—
200C2×Dic11C22×D412yes—
201C4×D11—88no—
202C4×D11C4⋊Q818yes—
203C4×D11C22×Q814yes—
204C4×D11C22×Q814yes—
205Dic22—88no—
206C8×C11C22×Q814yes—
207C8×C11C22×Q814yes—
208C11⋊C8C22×Q814yes—
209C11⋊C8C22×Q814yes—
210C22×M16—111no—
211C23×C8—111no—
212#544—1116no—
213#544—228no—
214C2×C4⋊Q8—112no—
215C2×C4⋊Q8—222no—
216C2×C4⋊Q8C2×D1112yes—
217C2×#125—112no—
218C2×#125—112no—
219C2×#125—222no—
220C2×C22⋊Q8—222no—
221C2×C22⋊Q8—222no—
222C2×#117—111no—
223C2×#117—112no—
224C22×C4⋊C4—112no—
225#501—1116no—
226#501—1116no—
227#499—118no—
228#499—118no—
229#498—118no—
230#498C2×D1118yescomplemented
231#428—1116no—
232#427—118no—
233C2×#107—112no—
234C2×#107—112no—
235C2×#107—112no—
236C2×#106—111no—
237C2×#106—111no—
238C2×#106—112no—
239C2×#106—112no—
240C2×#106—118no—
241C2×#106C2×D1111yescharacteristic
242C2×#106C2×D1111yescharacteristic
243C2×#106C2×D1112yes—
244#405—118no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8C2×D1111yescharacteristic
249C22×C11C2×C4⋊Q812yes—
250C22×C11#57714yes—
251C22×C11C23×D411yescharacteristic
252C2×D11—28no—
253C2×D11—24no—
254C2×D11C2×C4⋊Q814yes—
255C4×C11—24no—
256C4×C11—44no—
257C4×C11—44no—
258C4×C11C2×C4⋊Q812yes—
259C4×C11C23×Q811yescharacteristic
260C4×C11C23×Q811yescharacteristic
261Dic11—24no—
262Dic11—44no—
263Dic11—44no—
264Dic11C2×C4⋊Q814yes—
265C22×Q8—22no—
266C22×Q8—222no—
267C23×C4—111no—
268C23×C4—222no—
269C2×M16—118no—
270C2×M16—114no—
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—118no—
274C22×C8—114no—
275C22×C8C22×D1111yescharacteristic
276C22×C8C22×D1111yescharacteristic
277C4⋊Q8—24no—
278C4⋊Q8—118no—
279C4⋊Q8—224no—
280C4⋊Q8—2216no—
281C4⋊Q8C22×D1118yes—
282#125—118no—
283#125—118no—
284#125—224no—
285#125—2216no—
286#125—224no—
287C22⋊Q8—2216no—
288C22⋊Q8—2216no—
289#117—114no—
290#117—114no—
291#117—118no—
292#117—224no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—118no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4C22×D1112yes—
306C2×C4⋊C4C22×D1112yes—
307C2×C22⋊C4—112no—
308C2×C22⋊C4—222no—
309C2×C42—111no—
310C2×C42—222no—
311C2×C42C22×D1111yescharacteristic
312#107—118no—
313#107—118no—
314#107—118no—
315#106—114no—
316#106—114no—
317#106—118no—
318#106—118no—
319#106C22×D1114yes—
320#106C22×D1114yes—
321#106C22×D1118yes—
322#97—114no—
323#97—114no—
324C4×C8—114no—
325C4×C8C22×D1114yes—
326C2×C11#316314yescomplemented
327C2×C11C22×C4⋊Q811yescharacteristic
328C2×C11C2×#57712yes—
329D11—24no—
330C24—111no—
331C2×Q8—28no—
332C2×Q8—84no—
333C2×Q8—228no—
334C2×Q8—884no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—111no—
338C22×C4—112no—
339C22×C4—114no—
340C22×C4—114no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—228no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—884no—
347C22×C4D4×D1112yes—
348C22×C4C23×D1111yescharacteristic
349M16—1116no—
350C2×C8—114no—
351C2×C8—114no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—1116no—
355C2×C8Q8×D1114yes—
356C2×C8Q8×D1114yes—
357C2×C8C23×D1112yes—
358C2×C8C23×D1112yes—
359C4⋊C4—28no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—118no—
363C4⋊C4—114no—
364C4⋊C4—114no—
365C4⋊C4—228no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—228no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—228no—
372C4⋊C4—228no—
373C4⋊C4C23×D1114yes—
374C4⋊C4C23×D1114yes—
375C22⋊C4—118no—
376C22⋊C4—228no—
377C42—112no—
378C42—112no—
379C42—228no—
380C42D4×D1112yes—
381C42C23×D1112yes—
382C11C2×#316311yescharacteristic, complemented, Sylow
383C23—114no—
384C23—112no—
385C23—224no—
386C23C2×D4×D1111yescharacteristic
387Q8—88no—
388Q8—888no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—114no—
395C2×C4—112no—
396C2×C4—118no—
397C2×C4—114no—
398C2×C4—114no—
399C2×C4—114no—
400C2×C4—224no—
401C2×C4—224no—
402C2×C4—224no—
403C2×C4—444no—
404C2×C4—444no—
405C2×C4—888no—
406C2×C4C2×D4×D1114yes—
407C2×C4C2×D4×D1111yescharacteristic
408C2×C4C2×Q8×D1112yes—
409C2×C4C2×Q8×D1112yes—
410C2×C4C24×D1111yescharacteristic
411C8—114no—
412C8—114no—
413C8C2×Q8×D1114yes—
414C8C2×Q8×D1114yes—
415C22—114no—
416C22—228no—
417C22—224no—
418C22D11×C4⋊Q812yes—
419C22#1062329314yes—
420C22C22×D4×D1111yescharacteristic
421C4—24no—
422C4—44no—
423C4—44no—
424C4—114no—
425C4—224no—
426C4—444no—
427C4—444no—
428C4D11×C4⋊Q812yes—
429C4C22×Q8×D1111yescharacteristic
430C4C22×Q8×D1111yescharacteristic
431C2—224no—
432C2#1307914114yesdirect product factor
433C2C2×D11×C4⋊Q811yescharacteristic
434C2C2×#1062329312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#498D11
hypocenterC11C2×#3163
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. #13079141C2direct (N × H)
3. C2×#10622469C2semidirect
4. C2×#10622693C2semidirect
5. C2×#10622296C2semidirect
6. C2×#10622471C2semidirect
7. C2×#10622468C2semidirect
12. C2×C11×#498C2semidirect
28. C11×#498C22semidirect
38. #10622693C22semidirect
47. #10622471C22semidirect
48. #10622469C22semidirect
49. #10622468C22semidirect
51. #10622296C22semidirect
81. C2×#4313Q8semidirect
83. C2×C8×D11Q8semidirect
164. #4313C2×Q8semidirect
165. C8×D11C2×Q8semidirect
173. C2×#498D11semidirect
230. #498C2×D11semidirect
326. C2×C11#3163semidirect
382. C11C2×#3163semidirect
432. C2#13079141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232602
#130791412
C2×#106224692
C2×#106226932
C2×#106222962
C2×#106224712
C2×#106224682
C2×#106224742
C2×#106224732
C2×D11×#1062
C2×#106223022
C2×C11×#4982
C2×#316311