Finite Group Databasebeta

← C2×#13077043 #15617182

Subgroups — C2×#13077043 #15617182

Order 2816.

3278 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C211yesmaximal, characteristic
2C22×#66954C211yesmaximal, characteristic
3C2×#10623053C211yesmaximal, characteristic
4#13077043C2116yesmaximal, direct product factor
5C2×#10622321C212yesmaximal, complemented
6C2×#10622610C211yesmaximal, characteristic, complemented
7C2×#10622302C212yesmaximal, complemented
8C2×M16×Dic11C211yesmaximal, characteristic, complemented
9C2×C4×#4313C212yesmaximal, complemented
10C22×#66879C211yesmaximal, characteristic, complemented
11C2×D11×#97C212yesmaximal, complemented
12C2×C11×#405C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×#66960C4116yescomplemented
21C2×#66960C2218yes—
22C2×#66954C4116yescomplemented
23C2×#66954C2218yes—
24C22×#4313C2212yes—
25C22×#4313C2212yes—
26C22×C8×D11C2212yes—
27C22×C8×D11C2212yes—
28#10623053C418yes—
29#10623053C2218yes—
30C2×#66946C412yes—
31C2×#66940C412yes—
32C2×(C22⋊D11)⋊C4C414yes—
33C2×#66925C2212yes—
34C2×C42×D11C2212yes—
35C11×#405C2218yescomplemented
36C2×C11×#97C2212yes—
37C2×C4×C8×C11C2212yes—
38M16×Dic11C2218yescomplemented
39C2×#66879C2211yescharacteristic
40C2×#66879C2212yes—
41C2×#66879C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×#66879C2211yescharacteristic
44C2×#66879C2218yescomplemented
45C2×C8×Dic11C2212yes—
46#10622610C2218yescomplemented
47C2×#66867C2212yes—
48C2×C4×C11⋊C8C2212yes—
49#10622321C22116yescomplemented
50D11×#97C22116yescomplemented
51#10622302C22116yescomplemented
52C4×#4313C22116yescomplemented
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C412yes—
55C23×Dic11C2×C412yes—
56C2×#4339C2×C418yes—
57C2×#4339C2×C418yes—
58C2×#4339C2×C414yes—
59C2×#4339C2314yes—
60C22×D44C2×C411yescharacteristic
61C22×C4×D11C2×C414yes—
62C22×C4×D11C2312yes—
63C22×Dic22C2×C411yescharacteristic
64C2×C11×M16C2×C418yescomplemented
65C2×C11×M16C2314yes—
66C22×C8×C11C2×C418yescomplemented
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2314yes—
71C11×#117C2×C414yes—
72C11×#117C2314yes—
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C412yes—
75C2×C42×C11C2312yes—
76C2×(C2×D11)⋊C4C2×C414yes—
77C2×Dic11⋊C4C2×C414yes—
78C2×C4×Dic11C2×C414yes—
79C2×C4×Dic11C2×C412yes—
80C2×C4×Dic11C2×C414yes—
81C2×C4×Dic11C2314yes—
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2×C418yescomplemented
85C2×#4318C2314yes—
86C22×C11⋊C8C2×C418yescomplemented
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2314yes—
91#66960C2×C4164yescomplemented
92#66954C2×C4164yescomplemented
93C2×#4313C2×C4116yescomplemented
94C2×#4313C2×C4116yescomplemented
95C2×#4313C2318yes—
96C2×#4313C2318yes—
97C2×C8×D11C2×C4116yescomplemented
98C2×C8×D11C2×C4116yescomplemented
99C2×C8×D11C2318yes—
100C2×C8×D11C2318yes—
101#66946C2×C4116yes—
102#66940C2×C4116yes—
103(C22⋊D11)⋊C4C2×C4132yes—
104#66925C2×C418yes—
105#66925C2318yes—
106C42×D11C2×C418yes—
107C42×D11C2318yes—
108C11×#97C2318yes—
109C4×C8×C11C2318yes—
110#66879C2318yes—
111#66879C2314yes—
112#66879C2314yes—
113#66879C2314yes—
114#66879C2314yes—
115C8×Dic11C2318yes—
116#66867C2318yes—
117C4×C11⋊C8C2318yes—
118C2×#2875—111nomaximal, Sylow
119C24×C11C22×C411yescharacteristic
120C23×D11C22×C412yes—
121C22×C4×C11C22×C414yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11C42116yes—
129C2×C22⋊D11C22×C418yes—
130C22×Dic11—44no—
131C22×Dic11C22×C412yes—
132C22×Dic11C22×C412yes—
133C22×Dic11C22×C418yes—
134C22×Dic11C22×C412yes—
135#4339C42132yes—
136#4339C22×C4116yes—
137#4339C22×C4116yes—
138C2×D44C4218yes—
139C2×D44C22×C414yes—
140C2×C4×D11—48no—
141C2×C4×D11C22×C418yes—
142C2×C4×D11C22×C418yes—
143C2×C4×D11C22×C4116yes—
144C2×C4×D11C22×C414yes—
145C2×C4×D11C2414yes—
146C2×Dic22C4218yes—
147C2×Dic22C22×C414yes—
148C11×M16C22×C4116yescomplemented
149C2×C8×C11C22×C414yes—
150C2×C8×C11C22×C418yes—
151C2×C8×C11C22×C414yes—
152C2×C8×C11C22×C4116yescomplemented
153C2×C8×C11C2414yes—
154C2×C8×C11C2412yes—
155C2×C8×C11C2412yes—
156C11×C4⋊C4C22×C418yes—
157C11×C22⋊C4C22×C418yes—
158C42×C11C22×C414yes—
159C42×C11C2414yes—
160(C2×D11)⋊C4C22×C4116yes—
161Dic11⋊C4C22×C4116yes—
162C4×Dic11C22×C412yes—
163C4×Dic11C22×C4116yes—
164C4×Dic11C22×C412yes—
165C4×Dic11C22×C418yes—
166C4×Dic11C2412yes—
167C4×Dic11C2412yes—
168#4318C22×C4116yescomplemented
169C2×C11⋊C8C22×C414yes—
170C2×C11⋊C8C22×C418yes—
171C2×C11⋊C8C22×C414yes—
172C2×C11⋊C8C22×C4116yescomplemented
173C2×C11⋊C8C2412yes—
174C2×C11⋊C8C2414yes—
175C2×C11⋊C8C2412yes—
176#4313C22×C4132yescomplemented
177#4313C22×C4132yescomplemented
178C8×D11C22×C4132yescomplemented
179C8×D11C22×C4132yescomplemented
180C22×#131—111no—
181C22×#131—111no—
182C2×C4×#41—111no—
183#2875—1116no—
184C2×#405—112no—
185C2×#405—112no—
186C2×#405—111no—
187C2×#405D1111yescharacteristic, complemented
188C2×C4×M16—112no—
189C2×C4×M16—111no—
190C22×#97—112no—
191C22×#97—111no—
192C23×C11—24no—
193C23×C11C2×C4214yes—
194C23×C11C23×C412yes—
195C23×C11C23×C411yescharacteristic
196C22×D11—28no—
197C22×D11C2×C4218yes—
198C22×D11C23×C414yes—
199C2×C4×C11—28no—
200C2×C4×C11C2×C4214yes—
201C2×C4×C11C2×C4218yes—
202C2×C4×C11C23×C418yes—
203C2×C4×C11C23×C412yes—
204C2×C4×C11C23×C412yes—
205C2×C4×C11C23×C414yes—
206C2×C4×C11C23×C414yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C23×C412yes—
209C2×C4×C11C2511yescharacteristic
210C22⋊D11C2×C42132yes—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—48no—
214C2×Dic11C2×C4218yes—
215C2×Dic11C23×C414yes—
216C2×Dic11C23×C414yes—
217C2×Dic11C23×C414yes—
218D44C2×C42116yes—
219C4×D11—416no—
220C4×D11C2×C42116yes—
221C4×D11C23×C418yes—
222C4×D11C23×C418yes—
223Dic22C2×C42116yes—
224C8×C11C23×C414yes—
225C8×C11C23×C418yes—
226C8×C11C23×C414yes—
227C11⋊C8C23×C414yes—
228C11⋊C8C23×C418yes—
229C11⋊C8C23×C414yes—
230C22×#41—111no—
231C2×#131—118no—
232C2×#131—1116no—
233C2×#131—118no—
234C2×#131—1116no—
235C22×M16—111no—
236C22×M16—112no—
237C22×M16—112no—
238C22×M16C2×D1111yescharacteristic
239C23×C8—111no—
240C23×C8—112no—
241C23×C8—112no—
242C23×C8C2×D1111yescharacteristic
243C4×#41—118no—
244C4×#41—118no—
245C2×C4×Q8—112no—
246C2×C4×D4—112no—
247C2×C4×D4—114no—
248C2×#117—112no—
249C2×#117C2×D1111yescharacteristic
250C22×C42—111no—
251C22×C42—112no—
252#405—118no—
253#405—1116no—
254#405—1116no—
255#405C2×D1118yescomplemented
256C4×M16—118no—
257C4×M16—1116no—
258C2×#97—111no—
259C2×#97—112no—
260C2×#97—111no—
261C2×#97—111no—
262C2×#97—111no—
263C2×#97—118no—
264C2×#97—112no—
265C2×#97—1116no—
266C2×#97C2×D1112yes—
267C2×C4×C8—112no—
268C2×C4×C8—112no—
269C2×C4×C8C2×D1112yes—
270C22×C11—28no—
271C22×C11—24no—
272C22×C11C22×C4214yes—
273C22×C11C22×C4212yes—
274C22×C11#56814yes—
275C22×C11C24×C411yescharacteristic
276C2×D11—216no—
277C2×D11—28no—
278C2×D11C22×C4218yes—
279C4×C11—28no—
280C4×C11C22×C4214yes—
281C4×C11C22×C4212yes—
282C4×C11C24×C411yescharacteristic
283C4×C11C24×C411yescharacteristic
284Dic11—24no—
285Dic11—24no—
286Dic11C22×C4218yes—
287C2×#41—114no—
288C2×#41—118no—
289C2×#41—118no—
290C2×#41—114no—
291C22×Q8—111no—
292C22×D4—112no—
293C22×D4—111no—
294C23×C4—112no—
295C23×C4—112no—
296C23×C4—114no—
297C23×C4C22×D1111yescharacteristic
298#131—1164no—
299#131—1164no—
300C2×M16—118no—
301C2×M16—114no—
302C2×M16—1116no—
303C2×M16—1116no—
304C2×M16—118no—
305C2×M16—118no—
306C2×M16C4×D1118yescomplemented
307C2×M16C22×D1114yes—
308C22×C8—118no—
309C22×C8—114no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8—112no—
313C22×C8—1116no—
314C22×C8—1116no—
315C22×C8—118no—
316C22×C8—118no—
317C22×C8C4×D1118yescomplemented
318C22×C8C22×D1111yescharacteristic
319C22×C8C22×D1112yes—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1114yes—
322C4×Q8—1116no—
323C4×D4—1116no—
324C4×D4—1132no—
325#117—118no—
326#117—118no—
327#117C4×D1114yes—
328#117C22×D1114yes—
329C2×C4⋊C4—114no—
330C2×C4⋊C4C4×D1112yes—
331C2×C22⋊C4—114no—
332C2×C22⋊C4C4×D1112yes—
333C2×C42—114no—
334C2×C42—112no—
335C2×C42—114no—
336C2×C42—114no—
337C2×C42—111no—
338C2×C42—111no—
339C2×C42—118no—
340C2×C42—118no—
341C2×C42C22×D1112yes—
342#97—114no—
343#97—118no—
344#97—114no—
345#97—114no—
346#97—114no—
347#97—118no—
348#97C22×D1118yes—
349C4×C8—118no—
350C4×C8—118no—
351C4×C8C22×D1118yes—
352C2×C11—24no—
353C2×C11#287514yescomplemented
354C2×C11C23×C4211yescharacteristic
355C2×C11C2×#56812yes—
356D11—28no—
357C24—112no—
358C24C2×C4×D1111yescharacteristic
359#41—1132no—
360#41—1116no—
361#41—1116no—
362C2×Q8—118no—
363C2×Q8—114no—
364C2×D4—1116no—
365C2×D4—118no—
366C2×D4—118no—
367C2×D4—114no—
368C22×C4—112no—
369C22×C4—114no—
370C22×C4—118no—
371C22×C4—118no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—118no—
376C22×C4—1116no—
377C22×C4—448no—
378C22×C4—444no—
379C22×C4C2×C4×D1114yes—
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4C2×C4×D1112yes—
382C22×C4C2×C4×D1114yes—
383C22×C4C2×C4×D1114yes—
384C22×C4C23×D1112yes—
385C22×C4C23×D1111yescharacteristic
386M16—1116no—
387M16—1132no—
388M16—1132no—
389M16C2×C4×D11116yescomplemented
390C2×C8—114no—
391C2×C8—114no—
392C2×C8—118no—
393C2×C8—1116no—
394C2×C8—114no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—1132no—
398C2×C8—1132no—
399C2×C8C2×C4×D1114yes—
400C2×C8C2×C4×D1118yes—
401C2×C8C2×C4×D1114yes—
402C2×C8C2×C4×D11116yescomplemented
403C2×C8C23×D1114yes—
404C2×C8C23×D1112yes—
405C2×C8C23×D1112yes—
406C4⋊C4—1116no—
407C4⋊C4C2×C4×D1118yes—
408C22⋊C4—1116no—
409C22⋊C4C2×C4×D1118yes—
410C42—112no—
411C42—112no—
412C42—1116no—
413C42—118no—
414C42—112no—
415C42—112no—
416C42C2×C4×D1114yes—
417C42C23×D1114yes—
418C11C2×#287511yescharacteristic, complemented, Sylow
419C23—24no—
420C23—118no—
421C23—114no—
422C23—228no—
423C23C42×D1114yes—
424C23C22×C4×D1112yes—
425C23C22×C4×D1111yescharacteristic
426Q8—1116no—
427D4—1132no—
428D4—1116no—
429C2×C4—28no—
430C2×C4—118no—
431C2×C4—114no—
432C2×C4—1116no—
433C2×C4—118no—
434C2×C4—118no—
435C2×C4—114no—
436C2×C4—114no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—4416no—
440C2×C4—448no—
441C2×C4C42×D1114yes—
442C2×C4C42×D1118yes—
443C2×C4C22×C4×D1118yes—
444C2×C4C22×C4×D1111yescharacteristic
445C2×C4C22×C4×D1112yes—
446C2×C4C22×C4×D1112yes—
447C2×C4C22×C4×D1112yes—
448C2×C4C22×C4×D1114yes—
449C2×C4C22×C4×D1114yes—
450C2×C4C24×D1111yescharacteristic
451C8—114no—
452C8—114no—
453C8—118no—
454C8C22×C4×D1114yes—
455C8C22×C4×D1118yes—
456C8C22×C4×D1114yes—
457C22—28no—
458C22—24no—
459C22—118no—
460C22—2216no—
461C22—228no—
462C22C2×C42×D1114yes—
463C22C2×C42×D1112yes—
464C22#1062328114yes—
465C22C23×C4×D1111yescharacteristic
466C4—28no—
467C4—118no—
468C4—224no—
469C4—224no—
470C4C2×C42×D1112yes—
471C4C2×C42×D1114yes—
472C4C23×C4×D1111yescharacteristic
473C4C23×C4×D1111yescharacteristic
474C2—24no—
475C2—228no—
476C2#1307704314yesdirect product factor
477C2C22×C42×D1111yescharacteristic
478C2C2×#1062328112yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
socleC23×C11C23×C4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#405D11
hypocenterC11C2×#2875
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
4. #13077043C2direct (N × H)
5. C2×#10622321C2semidirect
6. C2×#10622610C2semidirect
7. C2×#10622302C2semidirect
8. C2×M16×Dic11C2semidirect
9. C2×C4×#4313C2semidirect
10. C22×#66879C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#405C2semidirect
20. C2×#66960C4semidirect
22. C2×#66954C4semidirect
35. C11×#405C22semidirect
38. M16×Dic11C22semidirect
44. C2×#66879C22semidirect
46. #10622610C22semidirect
49. #10622321C22semidirect
50. D11×#97C22semidirect
51. #10622302C22semidirect
52. C4×#4313C22semidirect
64. C2×C11×M16C2×C4semidirect
66. C22×C8×C11C2×C4semidirect
84. C2×#4318C2×C4semidirect
86. C22×C11⋊C8C2×C4semidirect
91. #66960C2×C4semidirect
92. #66954C2×C4semidirect
93. C2×#4313C2×C4semidirect
94. C2×#4313C2×C4semidirect
97. C2×C8×D11C2×C4semidirect
98. C2×C8×D11C2×C4semidirect
148. C11×M16C22×C4semidirect
152. C2×C8×C11C22×C4semidirect
168. #4318C22×C4semidirect
172. C2×C11⋊C8C22×C4semidirect
176. #4313C22×C4semidirect
177. #4313C22×C4semidirect
178. C8×D11C22×C4semidirect
179. C8×D11C22×C4semidirect
187. C2×#405D11semidirect
255. #405C2×D11semidirect
306. C2×M16C4×D11semidirect
317. C22×C8C4×D11semidirect
353. C2×C11#2875semidirect
389. M16C2×C4×D11semidirect
402. C2×C8C2×C4×D11semidirect
418. C11C2×#2875semidirect
476. C2#13077043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C22×#669542
C2×#106230532
#130770432
C2×#106223212
C2×#106226102
C2×#106223022
C2×M16×Dic112
C2×C4×#43132
C22×#668792
C2×D11×#972
C2×C11×#4052
C2×#287511