Finite Group Databasebeta

← C4×#10622792 #14907102

Subgroups — C4×#10622792 #14907102

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic
2C4×#66957C211yesmaximal, characteristic
3#13070485C212yesmaximal, complemented
4#13070478C212yesmaximal, complemented
5C4×#66893C212yesmaximal, complemented
6C4×#66892C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070336C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic
10C4×#66876C211yesmaximal, characteristic, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×#66957C2211yescharacteristic
15C4×#4339—21no—
16C4×C11×Q16—21no—
17C4×C11×Q16—21no—
18C4×C11×Q16C2212yes—
19C4×C11×Q16C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#103—21no—
22C2×C4×C8×C11C2211yescharacteristic
23C2×#66893C2212yes—
24#10622792C418yesdirect product factor
25C2×#66892C2212yes—
26#10622726—21no—
27#10622719C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30C4×Dic44C2211yescharacteristic
31C4×Dic44C2211yescharacteristic
32C4×D88C2211yescharacteristic
33C4×D88C2211yescharacteristic
34C4×#4314—21no—
35C4×#4314—21no—
36#10622202C2212yes—
37#10622202C2212yes—
38#10622130C2212yes—
39#10622129C2212yes—
40#10622128C2212yes—
41#10622127C2212yes—
42#10622099C2212yes—
43C4×C11⋊C16C2212yes—
44C22×Q8×C11—21no—
45C2×#4339—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—22no—
48C2×C11×Q16C2×C414yescomplemented
49C2×C11×Q16C2312yes—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—41no—
55C4×Q8×C11—41no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—41no—
58C2×C42×C11—41no—
59C2×C42×C11D411yescharacteristic
60C4×C22⋊D11—41no—
61C4×C22⋊D11—41no—
62#66979—21no—
63C2×Dic44C2311yescharacteristic
64#66957—22no—
65#66957C2×C414yes—
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×#103—22no—
77C11×#103—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66893C2×C418yescomplemented
83#66892C2×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×#510—111nomaximal, Sylow
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—41no—
99C2×Q8×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11D811yescharacteristic
103C22×C4×C11D811yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106#4339—24no—
107#4339—42no—
108C2×D44—21no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C11×Q16—24no—
114C11×Q16—22no—
115C11×Q16C22×C414yes—
116C2×C8×C11—22no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—22no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C42×C11—42no—
128C42×C11—42no—
129C42×C11D811yescharacteristic
130C42×C11D811yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C4×Dic11—41no—
143Dic44—21no—
144Dic44C22×C412yes—
145D88—21no—
146D88C22×C412yes—
147#4314—24no—
148C11⋊C16—22no—
149C11⋊C16C22×C414yes—
150C2×#510—111no—
151C4×#135—111no—
152C2×C4×Q16D1111yescharacteristic, complemented
153#2176—112no—
154#2175—112no—
155C4×Q32—112no—
156C4×SD32—112no—
157#2159—111no—
158#2141—111no—
159#2139—111no—
160C4×M32—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—41no—
163Q8×C11—24no—
164Q8×C11—42no—
165Q8×C11—44no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11#13512yes—
179C2×C4×C11C22×D411yescharacteristic
180C22⋊D11—44no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184D44—22no—
185D44—41no—
186C4×D11—44no—
187C4×D11—82no—
188C4×D11—82no—
189Dic22—22no—
190Dic22—41no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11C4×D412yes—
194C8×C11C23×C411yescharacteristic
195C8×C11C2×#4111yescharacteristic
196C2×#135—111no—
197C22×Q16C2×D1111yescharacteristic
198C4×#41—221no—
199C2×C4×Q8—21no—
200#510—118no—
201C2×Q32—112no—
202C2×SD32—112no—
203C2×M32—111no—
204C2×M32—111no—
205C4×Q16—21no—
206C4×Q16—21no—
207C4×Q16—111no—
208C4×Q16—111no—
209C4×Q16C2×D1112yes—
210C4×Q16C2×D1112yes—
211C4×SD16—221no—
212C4×SD16—221no—
213C4×D8—111no—
214C4×D8—111no—
215#427—111no—
216C2×#107C2×D1111yescharacteristic
217#416—221no—
218C2×#103—21no—
219C2×C4×C8C2×D1111yescharacteristic
220#367—112no—
221#366—112no—
222#358—112no—
223#358—112no—
224#358—112no—
225#357—112no—
226#346—112no—
227C4×C16—112no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11C4×D812yes—
231C22×C11C22×D811yescharacteristic
232C2×D11—42no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—44no—
239C4×C11—82no—
240C4×C11C4×D812yes—
241C4×C11#51012yescomplemented
242C4×C11C2×C4×D411yescharacteristic
243C4×C11C2×#13511yescharacteristic
244Dic11—42no—
245Dic11—81no—
246Dic11—81no—
247C2×#41—221no—
248C22×Q8—21no—
249#135—114no—
250#135—222no—
251C2×Q16—22no—
252C2×Q16—21no—
253C2×Q16—111no—
254C2×Q16C4×D1114yescomplemented
255C2×Q16C22×D1112yes—
256C2×SD16—221no—
257C2×D8—111no—
258C22×C8C22⋊D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—41no—
263C4×Q8—41no—
264C4×Q8—221no—
265C4×Q8—221no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—441no—
269C4×D4—441no—
270#117—221no—
271#117—441no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—41no—
274C2×C42—41no—
275C2×C42—441no—
276C2×C42C22⋊D1111yescharacteristic
277Q32—118no—
278SD32—118no—
279M32—114no—
280M32—222no—
281C2×C16—112no—
282C2×C16—112no—
283#107—21no—
284#107—111no—
285#107—111no—
286#107C22×D1112yes—
287#106—221no—
288#103—22no—
289#103—22no—
290#103—221no—
291#103—221no—
292#102—221no—
293#102—221no—
294C4×C8C22⋊D1111yescharacteristic
295C4×C8C22⋊D1111yescharacteristic
296C4×C8C22×D1111yescharacteristic
297C4×C8C22×D1111yescharacteristic
298C2×C11—22no—
299C2×C11C2×C4×D811yescharacteristic
300C2×C11C2×#51011yescharacteristic
301C2×C11#341411yescharacteristic
302D11—82no—
303#41—224no—
304#41—442no—
305C2×Q8—24no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×Q8—42no—
309C2×Q8—221no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4—441no—
317C22×C4#432311yescharacteristic
318C22×C4#432311yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—24no—
321Q16—22no—
322Q16—112no—
323Q16—221no—
324Q16C2×C4×D1114yes—
325SD16—224no—
326D8—112no—
327D8—221no—
328C2×C8—22no—
329C2×C8C2×C4×D1112yes—
330C2×C8#433912yes—
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C23×D1111yescharacteristic
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—42no—
347C42—42no—
348C42—441no—
349C42—441no—
350C42—441no—
351C42#432311yescharacteristic
352C42#432311yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C16—114no—
356C16—222no—
357C11C4×#51011yescharacteristic, complemented, Sylow
358C23—441no—
359C23C2×#432311yescharacteristic
360Q8—24no—
361Q8—42no—
362Q8—44no—
363Q8—222no—
364Q8—441no—
365D4—222no—
366D4—444no—
367D4—441no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—441no—
375C2×C4—444no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—882no—
379C2×C4—882no—
380C2×C4C4×C22⋊D1112yes—
381C2×C4C2×#432311yescharacteristic
382C2×C4C2×#432311yescharacteristic
383C2×C4C2×#432311yescharacteristic
384C2×C4C2×#432311yescharacteristic
385C2×C4C2×#432311yescharacteristic
386C2×C4#6700312yes—
387C2×C4C22×C22⋊D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8C4×C22⋊D1112yes—
391C8C22×C4×D1111yescharacteristic
392C8C2×#433911yescharacteristic
393C22—21no—
394C22—21no—
395C22—442no—
396C22—881no—
397C22—881no—
398C22C4×#432312yes—
399C22C22×#432311yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—442no—
406C4—881no—
407C4—881no—
408C4C4×#432312yes—
409C4#1062279212yesdirect product factor
410C4C2×C4×C22⋊D1111yescharacteristic
411C4C2×#6700311yescharacteristic
412C2—22no—
413C2—882no—
414C2C2×C4×#432311yescharacteristic
415C2C2×#1062279211yescharacteristic
416C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C4×C11×Q16C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11C4×#510
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #13070485C2semidirect
4. #13070478C2semidirect
5. C4×#66893C2semidirect
6. C4×#66892C2semidirect
7. #13070402C2semidirect
8. #13070336C2semidirect
10. C4×#66876C2semidirect
11. C2×C4×C11×Q16C2semidirect
24. #10622792C4direct (N × H)
48. C2×C11×Q16C2×C4semidirect
82. #66893C2×C4semidirect
83. #66892C2×C4semidirect
92. #66876C2×C4semidirect
152. C2×C4×Q16D11semidirect
241. C4×C11#510semidirect
254. C2×Q16C4×D11semidirect
357. C11C4×#510semidirect
409. C4#10622792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227922
C4×#669572
#130704852
#130704782
C4×#668932
C4×#668922
#130704022
#130703362
#130703262
C4×#668762
C2×C4×C11×Q162
C4×#51011