Finite Group Databasebeta

← C2×#13071258 #14912421

Subgroups — C2×#13071258 #14912421

Order 2816.

3046 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2#13071258C2116yesmaximal, direct product factor
3C2×#10622570C212yesmaximal
4C2×#10622585C212yesmaximal, complemented
5C2×#10622603C212yesmaximal, complemented
6C2×#10622557C212yesmaximal, complemented
7C2×#10622824C211yesmaximal, characteristic, complemented
8C2×#10622277C211yesmaximal, characteristic, complemented
9C2×#10622280C211yesmaximal, characteristic, complemented
10C2×#10622262C211yesmaximal, characteristic, complemented
11C2×#10622261C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C4116yescomplemented
21C2×C4×C22⋊D11C2218yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C11×#380C2218yescomplemented
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34#10622824C2218yescomplemented
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622603C22116yescomplemented
41#10622585C22116yescomplemented
42#10622570C22116yes—
43#10622557C22116yescomplemented
44#10622280C2218yescomplemented
45#10622277C2218yescomplemented
46#10622262C2218yescomplemented
47#10622261C2218yescomplemented
48C25×C11C2311yescharacteristic
49C24×D11C2311yescharacteristic
50C23×C4×C11—44no—
51C23×C4×C11C2×C418yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2314yes—
57C22×C22⋊D11—28no—
58C22×C22⋊D11C2×C418yes—
59C22×C22⋊D11C2314yes—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C22×C4×D11—44no—
66C22×C4×D11C2×C418yes—
67C22×C4×D11C2314yes—
68C2×C11×C4⋊C4—44no—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C22⋊C4—44no—
71C2×C11×C22⋊C4C2318yes—
72C2×C22⋊Dic11—44no—
73C2×C22⋊Dic11C2×C418yes—
74C2×C22⋊Dic11C2318yes—
75C2×C22⋊Dic11C2314yes—
76C4×C22⋊D11C2×C4164yescomplemented
77C2×(C2×D11)⋊C4—44no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4C2×C418yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×Dic11⋊C4—28no—
84C2×Dic11⋊C4—44no—
85C2×Dic11⋊C4C2×C418yes—
86C2×Dic11⋊C4C2318yes—
87C2×Dic11⋊C4C2318yes—
88C2×Dic11⋊C4C2314yes—
89C2×C4×Dic11—28no—
90C2×C4×Dic11—44no—
91C2×C4×Dic11C2×C418yes—
92C2×C4×Dic11C2318yes—
93C2×C4×Dic11C2318yes—
94C2×C4×Dic11C2314yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2318yes—
99C11⋊#95C2314yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C2×#2319—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11C22×C414yes—
108C24×C11C2412yes—
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—22no—
114C23×D11C22×C414yes—
115C23×D11C2412yes—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—416no—
125C22×C4×C11—48no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C4116yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C2×C22⋊D11—232no—
134C2×C22⋊D11—216no—
135C2×C22⋊D11C22×C4116yes—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11C22×C414yes—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C414yes—
148C22×Dic11#4118yes—
149C22×Dic11C2414yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×C4×D11—416no—
155C2×C4×D11—48no—
156C2×C4×D11C22×C4116yes—
157C11×C4⋊C4—48no—
158C11×C22⋊C4—48no—
159C22⋊Dic11—48no—
160C22⋊Dic11C22×C4116yes—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163(C2×D11)⋊C4C22×C4116yes—
164Dic11⋊C4—216no—
165Dic11⋊C4—48no—
166Dic11⋊C4C22×C4116yes—
167C4×Dic11—216no—
168C4×Dic11—48no—
169C4×Dic11C22×C4116yes—
170C22×C4×D4—111no—
171#2319—1116no—
172C2×#390—112no—
173C2×#389—112no—
174C2×#388—112no—
175C2×#388—112no—
176C2×#381—111no—
177C2×#381—111no—
178C2×#380—111no—
179C2×#380D1111yescharacteristic, complemented
180C2×C4×C4⋊C4—111no—
181C2×#376—111no—
182C23×C11—28no—
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—48no—
190C23×C11—48no—
191C23×C11C23×C414yes—
192C23×C11C23×C412yes—
193C23×C11C2×#4114yes—
194C23×C11H(5,𝔽2)14yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C112−1+412yes—
197C23×C11C2511yescharacteristic
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—24no—
202C22×D11—22no—
203C22×D11—24no—
204C22×D11—22no—
205C22×D11—48no—
206C22×D11—48no—
207C22×D11C23×C414yes—
208C2×C4×C11—28no—
209C2×C4×C11—28no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—416no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11C23×C414yes—
222C2×C4×C11C23×C414yes—
223C22⋊D11—232no—
224C2×Dic11—28no—
225C2×Dic11—28no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—48no—
236C2×Dic11—48no—
237C2×Dic11#117116yes—
238C2×Dic11C23×C414yes—
239C2×Dic11C23×C414yes—
240C2×Dic11C23×C414yes—
241C2×Dic11C2×#4118yes—
242C4×D11—416no—
243C23×D4—111no—
244C24×C4—111no—
245C24×C4C2×D1111yescharacteristic
246C2×C4×D4—118no—
247C2×C4×D4—1116no—
248C22×C4⋊C4—111no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4—112no—
251C22×C4⋊C4C2×D1112yes—
252C22×C22⋊C4—111no—
253C22×C22⋊C4—111no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4C2×D1112yes—
258C22×C42—111no—
259C22×C42—112no—
260C22×C42—112no—
261#390—1116no—
262#389—1116no—
263#388—1116no—
264#388—1116no—
265#381—118no—
266#381—118no—
267#380—118no—
268#380C2×D1118yescomplemented
269C4×C4⋊C4—118no—
270#376—118no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—111no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95C2×D1111yescharacteristic
277C2×#95C2×D1111yescharacteristic
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—416no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11C2×#11714yes—
285C22×C11#51814yes—
286C22×C11#52014yes—
287C22×C11#54018yes—
288C22×C11#54218yes—
289C22×C11C24×C411yescharacteristic
290C22×C11C22×#4112yes—
291C22×C11C2×H(5,𝔽2)12yes—
292C22×C11C2×H(5,𝔽2)11yescharacteristic
293C22×C11C2×2−1+411yescharacteristic
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—416no—
298C2×D11—44no—
299C2×D11—44no—
300C4×C11—24no—
301C4×C11—24no—
302C4×C11—44no—
303C4×C11—44no—
304Dic11—24no—
305Dic11—24no—
306Dic11—44no—
307Dic11—44no—
308Dic11C2×#11718yes—
309C25—111no—
310C25C22×D1111yescharacteristic
311C22×D4—118no—
312C22×D4—114no—
313C22×D4—228no—
314C23×C4—44no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—118no—
319C23×C4—114no—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4—444no—
323C23×C4C4×D1118yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1114yes—
329C4×D4—1164no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—228no—
336C2×C4⋊C4—444no—
337C2×C4⋊C4C22×D1118yes—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—114no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4—444no—
348C2×C22⋊C4—444no—
349C2×C22⋊C4C22×D1118yes—
350C2×C42—118no—
351C2×C42—114no—
352C2×C42—118no—
353C2×C42—118no—
354C2×C42—228no—
355C2×C42—444no—
356#95—114no—
357#95—118no—
358#95—114no—
359#95—118no—
360#95—118no—
361#95C22×D1114yes—
362#95C22×D1114yes—
363C2×C11—44no—
364C2×C11#231918yescomplemented
365C2×C11C22×#11711yescharacteristic
366C2×C11C2×#51811yescharacteristic
367C2×C11C2×#52011yescharacteristic
368C2×C11C2×#54012yes—
369C2×C11C2×#54212yes—
370D11—44no—
371C24—22no—
372C24—24no—
373C24—22no—
374C24—24no—
375C24—114no—
376C24—112no—
377C24—222no—
378C24—224no—
379C24—222no—
380C24—224no—
381C24C2×C4×D1114yes—
382C24C23×D1112yes—
383C24C23×D1111yescharacteristic
384C2×D4—1116no—
385C2×D4—2232no—
386C2×D4—2216no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—48no—
396C22×C4—416no—
397C22×C4—114no—
398C22×C4—118no—
399C22×C4—112no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—1116no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—222no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—4416no—
417C22×C4—448no—
418C22×C4C2×C4×D1114yes—
419C22×C4C2×C4×D1114yes—
420C22×C4C2×C4×D11116yes—
421C22×C4C23×D1114yes—
422C22×C4C23×D1114yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1112yes—
425C4⋊C4—48no—
426C4⋊C4—1116no—
427C4⋊C4—2216no—
428C4⋊C4—448no—
429C22⋊C4—48no—
430C22⋊C4—1116no—
431C22⋊C4—1116no—
432C22⋊C4—448no—
433C22⋊C4—448no—
434C22⋊C4—448no—
435C42—1116no—
436C42—2216no—
437C42—448no—
438C11C2×#231911yescharacteristic, complemented, Sylow
439C23—28no—
440C23—28no—
441C23—28no—
442C23—22no—
443C23—24no—
444C23—22no—
445C23—24no—
446C23—48no—
447C23—48no—
448C23—114no—
449C23—228no—
450C23—228no—
451C23—228no—
452C23—222no—
453C23—224no—
454C23—222no—
455C23—224no—
456C23—448no—
457C23—448no—
458C23C22×C4×D1114yes—
459C23C22×C4×D1112yes—
460C23#6703714yes—
461C23#6703712yes—
462C23#6704012yes—
463C23#41×D1114yes—
464C23C24×D1111yescharacteristic
465D4—2232no—
466C2×C4—28no—
467C2×C4—28no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—416no—
477C2×C4—48no—
478C2×C4—48no—
479C2×C4—1116no—
480C2×C4—114no—
481C2×C4—118no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—228no—
485C2×C4—228no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—4416no—
496C2×C4—448no—
497C2×C4—448no—
498C2×C4C22×C4×D1114yes—
499C2×C4C22×C4×D1114yes—
500C22—24no—
501C22—24no—
502C22—24no—
503C22—44no—
504C22—44no—
505C22—416no—
506C22—224no—
507C22—224no—
508C22—224no—
509C22—444no—
510C22—444no—
511C22—4416no—
512C22#1062301714yes—
513C22#1062303514yes—
514C22D11×#11714yes—
515C22#1062314618yes—
516C22#1062317118yes—
517C22C23×C4×D1111yescharacteristic
518C22C2×#6703711yescharacteristic
519C22C2×#6703712yes—
520C22C2×#6704011yescharacteristic
521C22C2×#41×D1112yes—
522C4—24no—
523C4—24no—
524C4—44no—
525C4—44no—
526C4—118no—
527C4—224no—
528C4—224no—
529C4—444no—
530C4—444no—
531C2—44no—
532C2—444no—
533C2#1307125818yesdirect product factor
534C2C2×D11×#11711yescharacteristic
535C2C2×#1062301711yescharacteristic
536C2C2×#1062303511yescharacteristic
537C2C2×#1062314612yes—
538C2C2×#1062317112yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2319
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071258C2direct (N × H)
4. C2×#10622585C2semidirect
5. C2×#10622603C2semidirect
6. C2×#10622557C2semidirect
7. C2×#10622824C2semidirect
8. C2×#10622277C2semidirect
9. C2×#10622280C2semidirect
10. C2×#10622262C2semidirect
11. C2×#10622261C2semidirect
12. C2×C11×#380C2semidirect
20. C2×C4×C22⋊D11C4semidirect
31. C11×#380C22semidirect
34. #10622824C22semidirect
40. #10622603C22semidirect
41. #10622585C22semidirect
43. #10622557C22semidirect
44. #10622280C22semidirect
45. #10622277C22semidirect
46. #10622262C22semidirect
47. #10622261C22semidirect
76. C4×C22⋊D11C2×C4semidirect
179. C2×#380D11semidirect
268. #380C2×D11semidirect
364. C2×C11#2319semidirect
438. C11C2×#2319semidirect
533. C2#13071258direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130712582
C2×#106225702
C2×#106225852
C2×#106226032
C2×#106225572
C2×#106228242
C2×#106222772
C2×#106222802
C2×#106222622
C2×#106222612
C2×C11×#3802
C2×#231911