Finite Group Databasebeta

← C4×#10622760 #14907091

Subgroups — C4×#10622760 #14907091

Order 2816.

738 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×#10622760C211yesmaximal, characteristic
2C4×#66957C211yesmaximal, characteristic, complemented
3#13070490C212yesmaximal, complemented
4#13070480C212yesmaximal, complemented
5C4×#66891C212yesmaximal, complemented
6C4×#66890C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070332C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×#66957C2211yescharacteristic
15C4×#4339—21no—
16C4×C11×D8—21no—
17C4×C11×D8—21no—
18C4×C11×D8C2212yes—
19C4×C11×D8C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102—21no—
22C2×C4×C8×C11C2211yescharacteristic
23C2×#66891C2212yes—
24#10622760C418yesdirect product factor
25C2×#66890C2212yes—
26#10622726—21no—
27#10622719C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30C4×Dic44C2211yescharacteristic, complemented
31C4×Dic44C2211yescharacteristic, complemented
32C4×D88C2211yescharacteristic, complemented
33C4×D88C2211yescharacteristic, complemented
34C4×#4314—21no—
35C4×#4314—21no—
36#10622200C2212yes—
37#10622200C2212yes—
38#10622130C2212yescomplemented
39#10622129C2212yescomplemented
40#10622128C2212yescomplemented
41#10622127C2212yescomplemented
42#10622099C2212yescomplemented
43C4×C11⋊C16C2212yescomplemented
44C22×D4×C11—21no—
45C23×C4×C11—41no—
46C2×#4339—21no—
47C2×C11×D8—21no—
48C2×C11×D8—22no—
49C2×C11×D8C2×C414yescomplemented
50C2×C11×D8C2312yes—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—41no—
56C4×D4×C11—41no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C22⋊C4—41no—
59C2×C42×C11D411yescharacteristic
60C4×C22⋊D11—41no—
61C4×C22⋊D11—41no—
62#66979—21no—
63C2×Dic44C2311yescharacteristic
64#66957—22no—
65#66957C2×C414yescomplemented
66C2×D88C2311yescharacteristic
67C2×#4314—21no—
68C4×D44—21no—
69C4×D44—21no—
70#66925—41no—
71C42×D11—41no—
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#102—22no—
77C11×#102—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66891C2×C418yescomplemented
83#66890C2×C418yescomplemented
84#66885—21no—
85#66885—21no—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89#66880—21no—
90#66880—21no—
91#66876—22no—
92#66876C2×C414yescomplemented
93C2×C11⋊C16C2312yes—
94C2×C11⋊C16C2312yes—
95C4×#509—111nomaximal, Sylow
96C24×C11—41no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—84no—
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C2×C22⋊D11—41no—
109#4339—24no—
110#4339—42no—
111C2×D44—21no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×Dic22—21no—
116C11×D8—24no—
117C11×D8—22no—
118C11×D8C22×C414yes—
119C2×C8×C11—22no—
120C2×C8×C11C22×C412yes—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4112yes—
125C2×C8×C11C2411yescharacteristic
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11D811yescharacteristic
131C42×C11D811yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C22⋊Dic11—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11—41no—
142C4×Dic11—41no—
143C4×Dic11—41no—
144Dic44—21no—
145Dic44C22×C412yescomplemented
146D88—21no—
147D88C22×C412yescomplemented
148#4314—24no—
149C11⋊C16—22no—
150C11⋊C16C22×C414yescomplemented
151C2×#509—111no—
152C4×#135—111no—
153C2×C4×D8D1111yescharacteristic, complemented
154#2177—112no—
155#2175—112no—
156C4×SD32—112no—
157C4×D16—112no—
158#2159—111no—
159#2140—111no—
160#2139—111no—
161C4×M32—111no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11C2×D811yescharacteristic
167C22×D11—41no—
168D4×C11—24no—
169D4×C11—42no—
170D4×C11—44no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—84no—
175C2×C4×C11—82no—
176C2×C4×C11—84no—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11#13512yes—
184C2×C4×C11C22×D411yescharacteristic
185C22⋊D11—44no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189D44—22no—
190D44—41no—
191C4×D11—44no—
192C4×D11—82no—
193C4×D11—82no—
194Dic22—22no—
195Dic22—41no—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11C4×D412yes—
199C8×C11C23×C411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C2×#135—111no—
202C22×D8C2×D1111yescharacteristic
203C4×#41—221no—
204C2×C4×D4—21no—
205#509—118no—
206C2×SD32—112no—
207C2×D16—112no—
208C2×M32—111no—
209C2×M32—111no—
210C4×Q16—111no—
211C4×Q16—111no—
212C4×SD16—221no—
213C4×SD16—221no—
214C4×D8—21no—
215C4×D8—21no—
216C4×D8—111no—
217C4×D8—111no—
218C4×D8C2×D1112yes—
219C4×D8C2×D1112yes—
220#427—111no—
221C2×#107C2×D1111yescharacteristic
222#416—221no—
223C2×#102—21no—
224C2×C4×C8C2×D1111yescharacteristic
225#367—112no—
226#366—112no—
227#358—112no—
228#357—112no—
229#357—112no—
230#357—112no—
231#346—112no—
232C4×C16—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—44no—
236C22×C11—88no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11C4×D812yes—
240C22×C11C22×D811yescharacteristic
241C2×D11—42no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—82no—
248C4×C11C4×D812yes—
249C4×C11#50912yescomplemented
250C4×C11C2×C4×D411yescharacteristic
251C4×C11C2×#13511yescharacteristic
252Dic11—42no—
253Dic11—81no—
254Dic11—81no—
255C2×#41—221no—
256C22×D4—21no—
257C23×C4—41no—
258#135—114no—
259#135—222no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—22no—
263C2×D8—21no—
264C2×D8—111no—
265C2×D8C4×D1114yescomplemented
266C2×D8C22×D1112yes—
267C22×C8C22⋊D1111yescharacteristic
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—22no—
272C4×D4—22no—
273C4×D4—41no—
274C4×D4—41no—
275C4×D4—221no—
276C4×D4—221no—
277C4×D4—441no—
278C4×D4—441no—
279#117—221no—
280#117—441no—
281C2×C4⋊C4—21no—
282C2×C22⋊C4—41no—
283C2×C42—441no—
284C2×C42C22⋊D1111yescharacteristic
285SD32—118no—
286D16—118no—
287M32—114no—
288M32—222no—
289C2×C16—112no—
290C2×C16—112no—
291#107—21no—
292#107—111no—
293#107—111no—
294#107C22×D1112yes—
295#106—221no—
296#103—221no—
297#103—221no—
298#102—22no—
299#102—22no—
300#102—221no—
301#102—221no—
302C4×C8C22⋊D1111yescharacteristic
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C2×C11—22no—
307C2×C11—84no—
308C2×C11C2×C4×D811yescharacteristic
309C2×C11C2×#50911yescharacteristic
310C2×C11#341411yescharacteristic
311D11—82no—
312C24—41no—
313#41—224no—
314#41—442no—
315C2×Q8—221no—
316C2×D4—24no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—221no—
321C2×D4—441no—
322C22×C4—41no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—84no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4#432311yescharacteristic
330C22×C4#432311yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332Q16—112no—
333Q16—221no—
334SD16—224no—
335D8—24no—
336D8—22no—
337D8—112no—
338D8—221no—
339D8C2×C4×D1114yes—
340C2×C8—22no—
341C2×C8C2×C4×D1112yes—
342C2×C8#433912yes—
343C2×C8C2×C22⋊D1111yescharacteristic
344C2×C8C2×C22⋊D1111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—441no—
359C42—441no—
360C42—441no—
361C42#432311yescharacteristic
362C42#432311yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C16—114no—
366C16—222no—
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—42no—
369C23—44no—
370C23—82no—
371C23—82no—
372C23—441no—
373C23C2×#432311yescharacteristic
374Q8—222no—
375Q8—441no—
376D4—24no—
377D4—42no—
378D4—44no—
379D4—222no—
380D4—444no—
381D4—441no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—84no—
386C2×C4—82no—
387C2×C4—84no—
388C2×C4—441no—
389C2×C4—444no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—882no—
393C2×C4—882no—
394C2×C4C4×C22⋊D1112yes—
395C2×C4C2×#432311yescharacteristic
396C2×C4C2×#432311yescharacteristic
397C2×C4C2×#432311yescharacteristic
398C2×C4C2×#432311yescharacteristic
399C2×C4C2×#432311yescharacteristic
400C2×C4#6700312yes—
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—21no—
403C8—21no—
404C8C4×C22⋊D1112yes—
405C8C22×C4×D1111yescharacteristic
406C8C2×#433911yescharacteristic
407C22—21no—
408C22—21no—
409C22—44no—
410C22—88no—
411C22—82no—
412C22—82no—
413C22—442no—
414C22—881no—
415C22—881no—
416C22C4×#432312yes—
417C22C22×#432311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—442no—
423C4—881no—
424C4—881no—
425C4C4×#432312yes—
426C4#1062276012yesdirect product factor
427C4C2×C4×C22⋊D1111yescharacteristic
428C4C2×#6700311yescharacteristic
429C2—22no—
430C2—84no—
431C2—882no—
432C2C2×C4×#432311yescharacteristic
433C2C2×#1062276011yescharacteristic
434C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C4×C11×D8C2
socleC22×C11C22×D8
prime radicalC2×#10622760C2
cosocleC2×C8×C11C24
hypercenterC2×C4×D8D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#66957C2semidirect
3. #13070490C2semidirect
4. #13070480C2semidirect
5. C4×#66891C2semidirect
6. C4×#66890C2semidirect
7. #13070402C2semidirect
8. #13070332C2semidirect
9. #13070326C2semidirect
10. C4×#66876C2semidirect
11. C2×C4×C11×D8C2semidirect
24. #10622760C4direct (N × H)
30. C4×Dic44C22semidirect
31. C4×Dic44C22semidirect
32. C4×D88C22semidirect
33. C4×D88C22semidirect
38. #10622130C22semidirect
39. #10622129C22semidirect
40. #10622128C22semidirect
41. #10622127C22semidirect
42. #10622099C22semidirect
43. C4×C11⋊C16C22semidirect
49. C2×C11×D8C2×C4semidirect
65. #66957C2×C4semidirect
82. #66891C2×C4semidirect
83. #66890C2×C4semidirect
92. #66876C2×C4semidirect
145. Dic44C22×C4semidirect
147. D88C22×C4semidirect
150. C11⋊C16C22×C4semidirect
153. C2×C4×D8D11semidirect
249. C4×C11#509semidirect
265. C2×D8C4×D11semidirect
367. C11C4×#509semidirect
426. C4#10622760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227602
C4×#669572
#130704902
#130704802
C4×#668912
C4×#668902
#130704022
#130703322
#130703262
C4×#668762
C2×C4×C11×D82
C4×#50911