Finite Group Databasebeta

← C4×#10622806 #14907089

Subgroups — C4×#10622806 #14907089

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×#10622806C211yesmaximal, characteristic
2C2×C4×D88C211yesmaximal, characteristic, complemented
3#13070490C212yesmaximal, complemented
4#13070478C212yesmaximal, complemented
5C4×#66892C212yesmaximal, complemented
6C4×#66890C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070331C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C4×C11×#135C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C4×C11×#41—21no—
14C22×D88C2211yescharacteristic
15C2×C4×D44—21no—
16C4×C11×Q16C2211yescharacteristic, complemented
17C4×C11×Q16C2211yescharacteristic, complemented
18C4×C11×SD16—21no—
19C4×C11×SD16—21no—
20C4×C11×D8C2211yescharacteristic, complemented
21C4×C11×D8C2211yescharacteristic, complemented
22C11×#427C2211yescharacteristic
23C11×#416—21no—
24C2×C4×C8×C11C2211yescharacteristic
25#10622806C418yesdirect product factor
26C2×#66892C2212yes—
27C2×#66890C2212yes—
28C2×#66885—21no—
29C2×#66882C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32C4×D88—21no—
33C4×D88—21no—
34C4×D88C2212yes—
35C4×D88C2212yes—
36#10622202C2212yescomplemented
37#10622200C2212yescomplemented
38#10622129C2212yes—
39#10622129C2212yes—
40#10622128C2212yescomplemented
41#10622127C2212yescomplemented
42#10622099C2212yescomplemented
43C4×C11⋊C16C2212yescomplemented
44C2×C11×#41—21no—
45C22×D44—21no—
46C22×C4×D11—41no—
47C11×#135—22no—
48C11×#135C2×C414yescomplemented
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—21no—
51C2×C11×D8C2311yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—41no—
59C4×D4×C11—41no—
60C11×#117—21no—
61C11×#117—41no—
62C2×C42×C11—41no—
63C2×C42×C11D411yescharacteristic
64C2×(C2×D11)⋊C4—41no—
65C2×C4⋊Dic11—21no—
66C2×D88—21no—
67C2×D88—22no—
68C2×D88C2×C414yescomplemented
69C2×D88C2312yes—
70C4×D44—22no—
71C4×D44—22no—
72C4×D44—41no—
73C4×D44—41no—
74C11×#107C2311yescharacteristic
75C11×#107C2311yescharacteristic
76C11×#106—21no—
77C11×#103—21no—
78C11×#103—21no—
79C11×#102—21no—
80C11×#102—21no—
81C4×C8×C11D411yescharacteristic
82C4×C8×C11D411yescharacteristic
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66892C2×C418yescomplemented
86#66890C2×C418yescomplemented
87#66885—22no—
88#66885—22no—
89#66882—21no—
90#66882C2312yes—
91#66876—22no—
92#66876C2×C414yescomplemented
93C2×C11⋊C16C2312yes—
94C2×C11⋊C16C2312yes—
95C4×#509—111nomaximal, Sylow
96C23×D11—41no—
97C11×#41—24no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×Dic11—41no—
109C2×D44—24no—
110C2×D44—22no—
111C2×D44—41no—
112C2×D44—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—84no—
116C11×Q16—21no—
117C11×Q16C22×C412yescomplemented
118C11×SD16—24no—
119C11×D8—21no—
120C11×D8C22×C412yescomplemented
121C2×C8×C11—22no—
122C2×C8×C11C22×C412yes—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11—41no—
136C42×C11—41no—
137C42×C11—41no—
138C42×C11D811yescharacteristic
139C42×C11D811yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—42no—
144C4⋊Dic11—22no—
145C4⋊Dic11—41no—
146D88—24no—
147D88—22no—
148D88C22×C414yes—
149C11⋊C16—22no—
150C11⋊C16C22×C414yescomplemented
151C2×#509—111no—
152C4×#135D1111yescharacteristic, complemented
153C2×C4×D8—111no—
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—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—42no—
165C22×D11—44no—
166C22×D11—82no—
167C22×D11—82no—
168Q8×C11—22no—
169Q8×C11—41no—
170D4×C11—22no—
171D4×C11—44no—
172D4×C11—41no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—82no—
180C2×C4×C11—82no—
181C2×C4×C11C4×D412yes—
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11#13512yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×Dic11—42no—
190C2×Dic11—82no—
191D44—24no—
192D44—42no—
193D44—44no—
194C4×D11—84no—
195C4×D11—84no—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11C4×D412yes—
199C8×C11C23×C411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C2×#135C2×D1111yescharacteristic
202C22×D8—111no—
203C4×#41—21no—
204C2×C4×D4—221no—
205#509—118no—
206C2×SD32—112no—
207C2×D16—112no—
208C2×M32—111no—
209C2×M32—111no—
210C4×Q16C2×D1111yescharacteristic, complemented
211C4×Q16C2×D1111yescharacteristic, complemented
212C4×SD16—21no—
213C4×SD16—21no—
214C4×D8—112no—
215C4×D8—112no—
216C4×D8—221no—
217C4×D8—221no—
218C4×D8C2×D1111yescharacteristic, complemented
219C4×D8C2×D1111yescharacteristic, complemented
220#427C2×D1111yescharacteristic
221C2×#107—111no—
222#416—21no—
223C2×#102—221no—
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—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C4×D812yes—
239C22×C11C22×D811yescharacteristic
240C2×D11—44no—
241C2×D11—88no—
242C2×D11—82no—
243C2×D11—82no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11C4×D812yes—
251C4×C11#50912yescomplemented
252C4×C11C2×C4×D411yescharacteristic
253C4×C11C2×#13511yescharacteristic
254Dic11—82no—
255C2×#41—21no—
256C22×D4—221no—
257C23×C4—441no—
258#135—22no—
259#135C4×D1114yescomplemented
260C2×Q16C22×D1111yescharacteristic
261C2×SD16—21no—
262C2×D8—114no—
263C2×D8—112no—
264C2×D8—222no—
265C2×D8—221no—
266C2×D8C22×D1111yescharacteristic
267C22×C8C22⋊D1111yescharacteristic
268C22×C8C22×D1111yescharacteristic
269C4×Q8—21no—
270C4×Q8—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—41no—
274C4×D4—41no—
275C4×D4—222no—
276C4×D4—222no—
277C4×D4—441no—
278C4×D4—441no—
279#117—21no—
280#117—41no—
281C2×C4⋊C4—221no—
282C2×C22⋊C4—441no—
283C2×C42—41no—
284C2×C42C22⋊D1111yescharacteristic
285SD32—118no—
286D16—118no—
287M32—114no—
288M32—222no—
289C2×C16—112no—
290C2×C16—112no—
291#107—112no—
292#107—221no—
293#107C22×D1111yescharacteristic
294#107C22×D1111yescharacteristic
295#106—21no—
296#103—21no—
297#103—21no—
298#102—21no—
299#102—21no—
300#102—222no—
301#102—222no—
302C4×C8C22⋊D1111yescharacteristic
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C2×C11—22no—
307C2×C11—82no—
308C2×C11C2×C4×D811yescharacteristic
309C2×C11C2×#50911yescharacteristic
310C2×C11#341411yescharacteristic
311D11—84no—
312C24—441no—
313#41—24no—
314#41—42no—
315C2×Q8—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—224no—
319C2×D4—222no—
320C2×D4—441no—
321C2×D4—442no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—441no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—884no—
329C22×C4#432311yescharacteristic
330C22×C4#432311yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332Q16—21no—
333Q16C2×C4×D1112yescomplemented
334SD16—24no—
335D8—21no—
336D8—114no—
337D8—224no—
338D8—222no—
339D8C2×C4×D1112yescomplemented
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—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—222no—
352C4⋊C4—441no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—442no—
357C22⋊C4—442no—
358C42—41no—
359C42—41no—
360C42—41no—
361C42#432311yescharacteristic
362C42#432311yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C16—114no—
366C16—222no—
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—41no—
369C23—442no—
370C23—444no—
371C23—882no—
372C23—882no—
373C23C2×#432311yescharacteristic
374Q8—22no—
375Q8—41no—
376D4—22no—
377D4—44no—
378D4—41no—
379D4—224no—
380D4—442no—
381D4—444no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—442no—
391C2×C4—884no—
392C2×C4—882no—
393C2×C4—884no—
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—42no—
410C22—81no—
411C22—81no—
412C22—444no—
413C22—888no—
414C22—882no—
415C22—882no—
416C22C4×#432312yes—
417C22C22×#432311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—882no—
425C4C4×#432312yes—
426C4#1062280612yesdirect product factor
427C4C2×C4×C22⋊D1111yescharacteristic
428C4C2×#6700311yescharacteristic
429C2—22no—
430C2—82no—
431C2—884no—
432C2C2×C4×#432311yescharacteristic
433C2C2×#1062280611yescharacteristic
434C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×#135C2
socleC22×C11C22×D8
prime radicalC2×#10622806C2
cosocleC2×C8×C11C24
hypercenterC4×#135D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. C2×C4×D88C2semidirect
3. #13070490C2semidirect
4. #13070478C2semidirect
5. C4×#66892C2semidirect
6. C4×#66890C2semidirect
7. #13070405C2semidirect
8. #13070331C2semidirect
9. #13070328C2semidirect
10. C4×#66876C2semidirect
11. C4×C11×#135C2semidirect
16. C4×C11×Q16C22semidirect
17. C4×C11×Q16C22semidirect
20. C4×C11×D8C22semidirect
21. C4×C11×D8C22semidirect
25. #10622806C4direct (N × H)
36. #10622202C22semidirect
37. #10622200C22semidirect
40. #10622128C22semidirect
41. #10622127C22semidirect
42. #10622099C22semidirect
43. C4×C11⋊C16C22semidirect
48. C11×#135C2×C4semidirect
68. C2×D88C2×C4semidirect
85. #66892C2×C4semidirect
86. #66890C2×C4semidirect
92. #66876C2×C4semidirect
117. C11×Q16C22×C4semidirect
120. C11×D8C22×C4semidirect
150. C11⋊C16C22×C4semidirect
152. C4×#135D11semidirect
210. C4×Q16C2×D11semidirect
211. C4×Q16C2×D11semidirect
218. C4×D8C2×D11semidirect
219. C4×D8C2×D11semidirect
251. C4×C11#509semidirect
259. #135C4×D11semidirect
333. Q16C2×C4×D11semidirect
339. D8C2×C4×D11semidirect
367. C11C4×#509semidirect
426. C4#10622806direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×C4×D882
#130704902
#130704782
C4×#668922
C4×#668902
#130704052
#130703312
#130703282
C4×#668762
C4×C11×#1352
C4×#50911