Finite Group Databasebeta

← C2×#13077177 #15617392

Subgroups — C2×#13077177 #15617392

Order 2816.

2830 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4313C211yesmaximal, characteristic
2C22×M16×D11C211yesmaximal, characteristic
3C2×D11×#117C211yesmaximal, characteristic
4#13077177C2116yesmaximal, direct product factor
5C2×#10622732C211yesmaximal, characteristic, complemented
6C2×#10622612C211yesmaximal, characteristic, complemented
7C2×#10622715C211yesmaximal, characteristic, complemented
8C2×#10622452C214yesmaximal, complemented
9C2×#10622450C214yesmaximal, complemented
10C2×C11×#424C211yesmaximal, characteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×M16×D11—28no—
19C2×M16×D11C2218yes—
20C22×#4313—28no—
21C22×#4313C2212yes—
22C22×#4313C2212yes—
23C22×#4313C2212yes—
24C22×#4313C2218yes—
25C22×C8×D11C2212yes—
26D11×#117C418yes—
27D11×#117C2218yes—
28C2×#66945C412yes—
29C2×C4⋊C4×D11C412yes—
30C2×C22⋊C4×D11C412yes—
31C2×#66930C412yes—
32C2×#66925C2212yes—
33C2×C42×D11C2212yes—
34C11×#424C2218yescomplemented
35C2×C11×C4⋊C8C2214yescomplemented
36#10622732C2218yescomplemented
37#10622715C2218yescomplemented
38C2×Dic11⋊C8C2214yescomplemented
39C2×Dic11⋊C8C2214yescomplemented
40#10622612C2218yescomplemented
41C2×C4⋊(C11⋊C8)C2214yescomplemented
42#10622452C22132yescomplemented
43#10622450C22132yescomplemented
44C24×D11C2×C411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C22×C4×D11C2×C414yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C414yes—
51C22×C4×D11D418yes—
52C22×C4×D11Q818yes—
53C22×C4×D11C2311yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2314yes—
56C2×C11×M16—24no—
57C2×C11×M16C2314yes—
58C22×C8×C11—24no—
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C22×C8×C11C2314yes—
62C11×#117C2×C414yes—
63C11×#117C2314yes—
64C2×C11×C4⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C42×C11C2312yes—
67C2×C22⋊Dic11C2×C412yes—
68C2×(C2×D11)⋊C4C2×C414yes—
69#66979C2×C414yes—
70#66979C2314yes—
71C2×C4⋊Dic11C2×C412yes—
72C2×Dic11⋊C4C2×C414yes—
73C2×C4×Dic11C2×C414yes—
74C2×C4×Dic11C2312yes—
75C2×#4318—24no—
76C2×#4318C2314yes—
77C22×C11⋊C8—24no—
78C22×C11⋊C8C2314yes—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81M16×D11—232no—
82C2×#4313—28no—
83C2×#4313—28no—
84C2×#4313—232no—
85C2×#4313—28no—
86C2×#4313C2318yes—
87C2×#4313C2318yes—
88C2×#4313C2318yes—
89C2×C8×D11—28no—
90C2×C8×D11C2318yes—
91#66945C2×C4116yes—
92C4⋊C4×D11C2×C4116yes—
93C22⋊C4×D11C2×C4116yes—
94#66930C2×C4116yes—
95#66925C2×C418yes—
96#66925C2318yes—
97C42×D11C2×C418yes—
98C42×D11C2318yes—
99C11×C4⋊C8C23116yescomplemented
100Dic11⋊C8C23116yescomplemented
101Dic11⋊C8C23116yescomplemented
102C4⋊(C11⋊C8)C23116yescomplemented
103C2×#2905—111nomaximal, Sylow
104C24×C11C22×C411yescharacteristic
105C23×D11—44no—
106C23×D11C4⋊C418yes—
107C23×D11C22×C411yescharacteristic
108C23×D11C22×C411yescharacteristic
109C23×D11C22×C414yes—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2×Q814yes—
115C22×C4×C11C2412yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11C4⋊C418yes—
118C22×Dic11C22×C414yes—
119C22×Dic11C22×C414yes—
120C22×Dic11C22×C411yescharacteristic
121C22×Dic11C22×C411yescharacteristic
122C2×C4×D11—48no—
123C2×C4×D11C4⋊C418yes—
124C2×C4×D11C4⋊C418yes—
125C2×C4×D11C4⋊C4132yes—
126C2×C4×D11C22×C4116yes—
127C2×C4×D11C22×C412yes—
128C2×C4×D11C22×C412yes—
129C2×C4×D11C22×C414yes—
130C2×C4×D11C22×C414yes—
131C2×C4×D11C2×D414yes—
132C2×C4×D11C2×D414yes—
133C2×C4×D11C2×D4116yes—
134C2×C4×D11C2×Q814yes—
135C2×C4×D11C2×Q814yes—
136C2×C4×D11C2×Q8116yes—
137C2×C4×D11C2412yes—
138C2×C4×D11C2412yes—
139C11×M16—28no—
140C2×C8×C11—24no—
141C2×C8×C11—24no—
142C2×C8×C11—28no—
143C2×C8×C11C2414yes—
144C2×C8×C11C2414yes—
145C11×C4⋊C4C22×C418yes—
146C11×C22⋊C4C22×C418yes—
147C42×C11C22×C414yes—
148C42×C11C2414yes—
149C22⋊Dic11C22×C418yes—
150(C2×D11)⋊C4C22×C4116yes—
151C4⋊Dic11C22×C418yes—
152Dic11⋊C4C22×C4116yes—
153C4×Dic11C22×C414yes—
154C4×Dic11C22×C4116yes—
155C4×Dic11C2414yes—
156#4318—28no—
157C2×C11⋊C8—24no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—28no—
160C2×C11⋊C8C2414yes—
161C2×C11⋊C8C2414yes—
162#4313—216no—
163#4313—216no—
164#4313—216no—
165C8×D11—216no—
166C23×M16—111no—
167C23×M16—111no—
168C22×#117—111no—
169#2905—1116no—
170C2×#424—114no—
171C2×#424—111no—
172C2×#424—111no—
173C2×#424—111no—
174C2×#424D1111yescharacteristic, complemented
175C2×#423—114no—
176C23×C11—24no—
177C23×C11C2×C4⋊C414yes—
178C23×C11C23×C412yes—
179C23×C11C23×C411yescharacteristic
180C22×D11—24no—
181C22×D11—24no—
182C22×D11—416no—
183C22×D11—48no—
184C22×D11C2×C4⋊C414yes—
185C22×D11C2×C4⋊C414yes—
186C22×D11C2×C4⋊C4116yes—
187C22×D11C23×C412yes—
188C22×D11C23×C412yes—
189C2×C4×C11—28no—
190C2×C4×C11C2×C4⋊C418yes—
191C2×C4×C11C2×C4⋊C414yes—
192C2×C4×C11C23×C418yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C23×C412yes—
195C2×C4×C11C22×D412yes—
196C2×C4×C11C22×D414yes—
197C2×C4×C11C22×Q814yes—
198C2×C4×C11C22×Q812yes—
199C2×C4×C11C2511yescharacteristic
200C2×Dic11—28no—
201C2×Dic11C2×C4⋊C4116yes—
202C2×Dic11C2×C4⋊C414yes—
203C2×Dic11C2×C4⋊C414yes—
204C2×Dic11C23×C418yes—
205C2×Dic11C23×C412yes—
206C2×Dic11C23×C412yes—
207C4×D11—416no—
208C4×D11C2×C4⋊C418yes—
209C4×D11C2×C4⋊C418yes—
210C4×D11C2×C4⋊C4116yes—
211C4×D11C2×C4⋊C4116yes—
212C4×D11C22×D414yes—
213C4×D11C22×D414yes—
214C4×D11C22×Q814yes—
215C4×D11C22×Q814yes—
216C8×C11—24no—
217C8×C11—24no—
218C11⋊C8—24no—
219C11⋊C8—24no—
220C24×C4—111no—
221C22×M16—111no—
222C22×M16—118no—
223C22×M16—112no—
224C22×M16—112no—
225C22×M16—112no—
226C22×M16—118no—
227C22×M16—228no—
228C22×M16—228no—
229C22×M16C2×D1111yescharacteristic
230C23×C8—111no—
231C23×C8—112no—
232C23×C8C2×D1111yescharacteristic
233C2×#117—111no—
234C2×#117—118no—
235C2×#117—118no—
236C2×#117—112no—
237C2×#117—112no—
238C2×#117—112no—
239C2×#117C2×D1111yescharacteristic
240C22×C4⋊C4—112no—
241C22×C22⋊C4—112no—
242C22×C42—112no—
243#424—118no—
244#424—118no—
245#424—118no—
246#424—1132no—
247#424C2×D1118yescomplemented
248#423—1132no—
249C2×C4⋊C8—114no—
250C2×C4⋊C8—114no—
251C2×C4⋊C8—114no—
252C2×C4⋊C8C2×D1114yescomplemented
253C22×C11—28no—
254C22×C11—24no—
255C22×C11C22×C4⋊C414yes—
256C22×C11C22×C4⋊C412yes—
257C22×C11#56814yes—
258C22×C11C24×C411yescharacteristic
259C2×D11—28no—
260C2×D11—28no—
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—416no—
264C2×D11C22×C4⋊C414yes—
265C2×D11C22×C4⋊C414yes—
266C4×C11—28no—
267C4×C11C22×C4⋊C412yes—
268C4×C11C22×C4⋊C414yes—
269C4×C11C23×D411yescharacteristic
270C4×C11C23×Q811yescharacteristic
271Dic11—28no—
272Dic11C22×C4⋊C414yes—
273Dic11C22×C4⋊C414yes—
274C25—111no—
275C23×C4—111no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—114no—
279C23×C4—118no—
280C23×C4—118no—
281C23×C4—114no—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—114no—
285C23×C4C22×D1111yescharacteristic
286C2×M16—24no—
287C2×M16—114no—
288C2×M16—118no—
289C2×M16—118no—
290C2×M16—118no—
291C2×M16—228no—
292C2×M16—228no—
293C2×M16—2232no—
294C2×M16—228no—
295C2×M16—2232no—
296C2×M16—224no—
297C2×M16C22×D1114yes—
298C22×C8—24no—
299C22×C8—114no—
300C22×C8—112no—
301C22×C8—112no—
302C22×C8—118no—
303C22×C8—228no—
304C22×C8—224no—
305C22×C8C22×D1114yes—
306C22×C8C22×D1112yes—
307C22×C8C22×D1112yes—
308#117—114no—
309#117—114no—
310#117—1116no—
311#117—1116no—
312#117—118no—
313#117—118no—
314#117C4×D1114yes—
315#117C22×D1114yes—
316C2×C4⋊C4—114no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—1116no—
319C2×C4⋊C4C4×D1112yes—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—114no—
322C2×C22⋊C4—1116no—
323C2×C22⋊C4C4×D1112yes—
324C2×C42—114no—
325C2×C42—112no—
326C2×C42—118no—
327C2×C42—118no—
328C2×C42C22×D1112yes—
329C4⋊C8—1116no—
330C4⋊C8—1116no—
331C4⋊C8—1116no—
332C4⋊C8C22×D11116yescomplemented
333C2×C11—24no—
334C2×C11#290514yescomplemented
335C2×C11C23×C4⋊C411yescharacteristic
336C2×C11C2×#56812yes—
337D11—24no—
338D11—24no—
339C24—111no—
340C24—111no—
341C24—118no—
342C24—114no—
343C24—444no—
344C24C2×C4×D1111yescharacteristic
345C22×C4—118no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—114no—
349C22×C4—118no—
350C22×C4—118no—
351C22×C4—1132no—
352C22×C4—112no—
353C22×C4—114no—
354C22×C4—114no—
355C22×C4—112no—
356C22×C4—114no—
357C22×C4—1116no—
358C22×C4—114no—
359C22×C4—1116no—
360C22×C4—114no—
361C22×C4—114no—
362C22×C4—112no—
363C22×C4—112no—
364C22×C4—114no—
365C22×C4—1116no—
366C22×C4—448no—
367C22×C4C2×C4×D1114yes—
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4C2×C4×D1112yes—
370C22×C4D4×D1114yes—
371C22×C4Q8×D1114yes—
372C22×C4C23×D1112yes—
373C22×C4C23×D1111yescharacteristic
374M16—28no—
375M16—2216no—
376M16—2216no—
377M16—2216no—
378M16—228no—
379C2×C8—24no—
380C2×C8—28no—
381C2×C8—24no—
382C2×C8—114no—
383C2×C8—114no—
384C2×C8—2216no—
385C2×C8—224no—
386C2×C8—224no—
387C2×C8—228no—
388C2×C8C23×D1114yes—
389C2×C8C23×D1114yes—
390C4⋊C4—1116no—
391C4⋊C4—118no—
392C4⋊C4C2×C4×D1118yes—
393C22⋊C4—118no—
394C22⋊C4—1116no—
395C22⋊C4C2×C4×D1118yes—
396C42—1116no—
397C42—114no—
398C42—114no—
399C42C2×C4×D1114yes—
400C42C23×D1114yes—
401C11C2×#290511yescharacteristic, complemented, Sylow
402C23—24no—
403C23—114no—
404C23—114no—
405C23—112no—
406C23—112no—
407C23—1116no—
408C23—224no—
409C23—224no—
410C23—4416no—
411C23—448no—
412C23C4⋊C4×D1114yes—
413C23C22×C4×D1112yes—
414C23C22×C4×D1111yescharacteristic
415C2×C4—28no—
416C2×C4—1116no—
417C2×C4—114no—
418C2×C4—114no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—118no—
422C2×C4—1116no—
423C2×C4—118no—
424C2×C4—1116no—
425C2×C4—114no—
426C2×C4—114no—
427C2×C4—114no—
428C2×C4—114no—
429C2×C4—118no—
430C2×C4—228no—
431C2×C4—4416no—
432C2×C4C4⋊C4×D1118yes—
433C2×C4C4⋊C4×D1114yes—
434C2×C4C22×C4×D1118yes—
435C2×C4C22×C4×D1111yescharacteristic
436C2×C4C22×C4×D1112yes—
437C2×C4C2×D4×D1112yes—
438C2×C4C2×D4×D1114yes—
439C2×C4C2×Q8×D1114yes—
440C2×C4C2×Q8×D1112yes—
441C2×C4C24×D1111yescharacteristic
442C8—24no—
443C8—24no—
444C8—224no—
445C8—224no—
446C22—28no—
447C22—24no—
448C22—114no—
449C22—114no—
450C22—228no—
451C22—228no—
452C22—224no—
453C22—224no—
454C22—4416no—
455C22C2×C4⋊C4×D1114yes—
456C22C2×C4⋊C4×D1112yes—
457C22#1062328114yes—
458C22C23×C4×D1111yescharacteristic
459C4—28no—
460C4—114no—
461C4—114no—
462C4—228no—
463C4C2×C4⋊C4×D1112yes—
464C4C2×C4⋊C4×D1114yes—
465C4C22×D4×D1111yescharacteristic
466C4C22×Q8×D1111yescharacteristic
467C2—24no—
468C2—224no—
469C2—224no—
470C2#1307717714yesdirect product factor
471C2C22×C4⋊C4×D1111yescharacteristic
472C2C2×#1062328112yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#424C2
socleC23×C11C23×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
hypercenterC2×#424D11
hypocenterC11C2×#2905
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #13077177C2direct (N × H)
5. C2×#10622732C2semidirect
6. C2×#10622612C2semidirect
7. C2×#10622715C2semidirect
8. C2×#10622452C2semidirect
9. C2×#10622450C2semidirect
10. C2×C11×#424C2semidirect
34. C11×#424C22semidirect
35. C2×C11×C4⋊C8C22semidirect
36. #10622732C22semidirect
37. #10622715C22semidirect
38. C2×Dic11⋊C8C22semidirect
39. C2×Dic11⋊C8C22semidirect
40. #10622612C22semidirect
41. C2×C4⋊(C11⋊C8)C22semidirect
42. #10622452C22semidirect
43. #10622450C22semidirect
99. C11×C4⋊C8C23semidirect
100. Dic11⋊C8C23semidirect
101. Dic11⋊C8C23semidirect
102. C4⋊(C11⋊C8)C23semidirect
174. C2×#424D11semidirect
247. #424C2×D11semidirect
252. C2×C4⋊C8C2×D11semidirect
332. C4⋊C8C22×D11semidirect
334. C2×C11#2905semidirect
401. C11C2×#2905semidirect
470. C2#13077177direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43132
C22×M16×D112
C2×D11×#1172
#130771772
C2×#106227322
C2×#106226122
C2×#106227152
C2×#106224522
C2×#106224502
C2×C11×#4242
C2×#290511