Finite Group Databasebeta

← C2×#13066951 #14719627

Subgroups — C2×#13066951 #14719627

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622339C212yesmaximal, complemented
3#13066951C218yesmaximal, direct product factor
4C2×#10622107C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D11C411yescharacteristic
8C24×Dic11C411yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×(C2×D11)⋊C4C411yescharacteristic
12C22×Dic11⋊C4C2211yescharacteristic
13C22×C4×Dic11C411yescharacteristic
14C22×#4313—22no—
15C2×(C22⋊D11)⋊C4—22no—
16C2×(C22⋊D11)⋊C4—22no—
17C2×(C22⋊D11)⋊C4—24no—
18C2×(C22⋊D11)⋊C4C414yes—
19C2×(C22⋊D11)⋊C4C2214yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×(C2×D11)⋊C8—22no—
23#10622339—24no—
24#10622339C2218yescomplemented
25C11×#323C2214yescomplemented
26#10622163C2214yescomplemented
27#10622107C2218yescomplemented
28C25×C11C2×C411yescharacteristic
29C24×D11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—24no—
33C22×C22⋊D11—22no—
34C22×C22⋊D11—22no—
35C22×C22⋊D11—24no—
36C22×C22⋊D11C2×C414yes—
37C23×Dic11—22no—
38C23×Dic11—21no—
39C23×Dic11—21no—
40C23×Dic11—44no—
41C23×Dic11C2×C411yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C23×Dic11C2×C414yes—
44C23×Dic11C2×C411yescharacteristic
45C22×C4×D11—44no—
46C22×C4×D11C2×C412yes—
47C22×C4×D11D412yes—
48C22×C4×D11D412yes—
49C22×C4×D11D414yes—
50C22×C4×D11C2312yes—
51C22×C8×C11—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2312yes—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4C2×C414yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4C2×C412yes—
62C2×Dic11⋊C4C2312yes—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11C2×C414yes—
67C22×C11⋊C8—22no—
68C2×#4313—28no—
69C2×#4313—48no—
70(C22⋊D11)⋊C4—28no—
71(C22⋊D11)⋊C4—28no—
72(C22⋊D11)⋊C4—28no—
73(C22⋊D11)⋊C4—28no—
74C11×C22⋊C8—22no—
75C11×C22⋊C8C2314yes—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78(C2×D11)⋊C8—28no—
79C2×#1465—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—22no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11M1614yescomplemented
86C24×C11C22×C411yescharacteristic
87C24×C11C22×C412yes—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11C22⋊C412yes—
93C23×D11C22⋊C412yes—
94C23×D11C22×C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C2×C22⋊D11—216no—
105C2×C22⋊D11—216no—
106C2×C22⋊D11—28no—
107C2×C22⋊D11—28no—
108C2×C22⋊D11—28no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—42no—
118C22×Dic11—48no—
119C22×Dic11—48no—
120C22×Dic11—44no—
121C22×Dic11—44no—
122C22×Dic11C22⋊C412yes—
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11M1614yescomplemented
126C22×Dic11C22×C412yes—
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129C2×C4×D11—28no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—48no—
133C2×C4×D11—44no—
134C2×C4×D11C22⋊C414yes—
135C2×C4×D11C22⋊C414yes—
136C2×C4×D11C2×D414yes—
137C2×C4×D11C2×D414yes—
138C2×C8×C11—24no—
139C2×C8×C11—44no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142(C2×D11)⋊C4—28no—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145C4×Dic11—24no—
146C4×Dic11—24no—
147C2×C11⋊C8—24no—
148C2×C11⋊C8—44no—
149#4313—416no—
150C22×C4×D4—111no—
151C2×#407—112no—
152#1465—118no—
153C2×#324—112no—
154C2×#323—111no—
155C2×#323D1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—42no—
163C23×C11—48no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—48no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11C2×C22⋊C411yescharacteristic
171C23×C11C2×C22⋊C411yescharacteristic
172C23×C11C2×M1612yes—
173C23×C11C2×M1612yes—
174C23×C11C2×M1614yescomplemented
175C23×C11C23×C411yescharacteristic
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—24no—
179C22×D11—24no—
180C22×D11—24no—
181C22×D11—24no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—48no—
187C22×D11—48no—
188C22×D11C2×C22⋊C414yes—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11C22×D412yes—
199C22⋊D11—232no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—22no—
208C2×Dic11—48no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—48no—
212C2×Dic11—42no—
213C2×Dic11#9914yes—
214C2×Dic11C2×C22⋊C412yes—
215C2×Dic11C2×C22⋊C412yes—
216C2×Dic11C2×M1614yescomplemented
217C4×D11—28no—
218C4×D11—28no—
219C4×D11—44no—
220C4×D11—44no—
221C8×C11—44no—
222C11⋊C8—44no—
223C23×D4—111no—
224C24×C4—111no—
225C24×C4—111no—
226C22×M16—222no—
227C2×C4×D4—114no—
228C2×C4×D4—114no—
229C2×C4×D4—222no—
230C2×C4×D4—222no—
231C2×C4×D4—224no—
232C22×C4⋊C4—111no—
233C22×C22⋊C4—111no—
234C22×C22⋊C4C2×D1111yescharacteristic
235C22×C42—111no—
236#407—118no—
237#407—224no—
238C2×C22⋊C8—112no—
239C2×C22⋊C8—222no—
240C2×C22⋊C8C2×D1112yes—
241#324—118no—
242#323—114no—
243#323C2×D1114yescomplemented
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—48no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—48no—
257C22×C11#40712yes—
258C22×C11#40712yes—
259C22×C11C2×#9912yes—
260C22×C11#41312yes—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11C22×M1611yescharacteristic
263C22×C11C22×M1611yescharacteristic
264C2×D11—24no—
265C2×D11—24no—
266C2×D11—24no—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—48no—
270C2×D11—48no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—42no—
274Dic11—24no—
275Dic11—22no—
276Dic11—42no—
277Dic11C2×#9914yes—
278C25—111no—
279C25C4×D1111yescharacteristic
280C22×D4—114no—
281C22×D4—224no—
282C22×D4—222no—
283C22×D4—222no—
284C22×D4—224no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—112no—
288C23×C4—112no—
289C23×C4—112no—
290C23×C4—114no—
291C23×C4—112no—
292C23×C4—111no—
293C23×C4—114no—
294C23×C4—221no—
295C23×C4—222no—
296C23×C4—221no—
297C23×C4—444no—
298C23×C4—444no—
299C23×C4C4×D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C2×M16—228no—
302C2×M16—448no—
303C22×C8—22no—
304C22×C8—222no—
305C4×D4—228no—
306C4×D4—228no—
307C4×D4—228no—
308C4×D4—228no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—114no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4C4×D1112yes—
319C2×C22⋊C4C22×D1112yes—
320C2×C42—114no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42—221no—
324C22⋊C8—22no—
325C22⋊C8—114no—
326C22⋊C8—228no—
327C22⋊C8—222no—
328C22⋊C8C22×D1114yes—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—22no—
332C2×C11—44no—
333C2×C11#146514yescomplemented
334C2×C11C2×#40711yescharacteristic
335C2×C11C22×#9911yescharacteristic
336C2×C11C2×#41311yescharacteristic
337D11—44no—
338C24—21no—
339C24—21no—
340C24—22no—
341C24—42no—
342C24—42no—
343C24—112no—
344C24—112no—
345C24—112no—
346C24—222no—
347C24—222no—
348C24—442no—
349C24—442no—
350C24#431314yescomplemented
351C24C2×C4×D1111yescharacteristic
352C24C2×C4×D1112yes—
353C2×D4—228no—
354C2×D4—228no—
355C2×D4—2216no—
356C2×D4—2216no—
357C2×D4—228no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—111no—
363C22×C4—112no—
364C22×C4—111no—
365C22×C4—114no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—114no—
369C22×C4—114no—
370C22×C4—114no—
371C22×C4—114no—
372C22×C4—112no—
373C22×C4—228no—
374C22×C4—224no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—222no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—448no—
385C22×C4—444no—
386C22×C4—444no—
387C22×C4—448no—
388C22×C4—444no—
389C22×C4—448no—
390C22×C4—442no—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4D4×D1112yes—
394C22×C4D4×D1112yes—
395C22×C4C23×D1111yescharacteristic
396M16—4416no—
397C2×C8—24no—
398C2×C8—44no—
399C2×C8—224no—
400C2×C8—444no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—228no—
406C42—224no—
407C42—224no—
408C11C2×#146511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—24no—
414C23—24no—
415C23—42no—
416C23—48no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—48no—
421C23—42no—
422C23—42no—
423C23—114no—
424C23—222no—
425C23—222no—
426C23—224no—
427C23—224no—
428C23—224no—
429C23—224no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—448no—
435C23—448no—
436C23C22⋊C4×D1111yescharacteristic
437C23C22⋊C4×D1111yescharacteristic
438C23C2×#431312yes—
439C23C2×#431314yescomplemented
440C23M16×D1112yes—
441C23C22×C4×D1111yescharacteristic
442D4—2232no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—112no—
452C2×C4—114no—
453C2×C4—112no—
454C2×C4—114no—
455C2×C4—228no—
456C2×C4—228no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—444no—
466C2×C4—444no—
467C2×C4—448no—
468C2×C4—448no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4C22⋊C4×D1112yes—
473C2×C4C2×D4×D1112yes—
474C8—44no—
475C8—444no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—44no—
484C22—44no—
485C22—48no—
486C22—42no—
487C22—42no—
488C22—48no—
489C22—224no—
490C22—224no—
491C22—224no—
492C22—444no—
493C22—444no—
494C22—448no—
495C22—448no—
496C22#1062233912yes—
497C22#1062233912yes—
498C22D11×#9912yes—
499C22#1062235812yes—
500C22C2×C22⋊C4×D1111yescharacteristic
501C22C22×#431311yescharacteristic
502C22C2×M16×D1111yescharacteristic
503C4—22no—
504C4—22no—
505C4—42no—
506C4—114no—
507C4—224no—
508C4—222no—
509C4—442no—
510C2—21no—
511C2—21no—
512C2—22no—
513C2—44no—
514C2—444no—
515C2#1306695114yesdirect product factor
516C2C2×#1062233911yescharacteristic
517C2C2×D11×#9911yescharacteristic
518C2C2×#1062235811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#323D11
hypocenterC11C2×#1465
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. #13066951C2direct (N × H)
4. C2×#10622107C2semidirect
5. C2×#10622163C2semidirect
6. C2×C11×#323C2semidirect
24. #10622339C22semidirect
25. C11×#323C22semidirect
26. #10622163C22semidirect
27. #10622107C22semidirect
85. C24×C11M16semidirect
125. C22×Dic11M16semidirect
155. C2×#323D11semidirect
174. C23×C11C2×M16semidirect
216. C2×Dic11C2×M16semidirect
243. #323C2×D11semidirect
333. C2×C11#1465semidirect
350. C24#4313semidirect
408. C11C2×#1465semidirect
439. C23C2×#4313semidirect
515. C2#13066951direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106223392
#130669512
C2×#106221072
C2×#106221632
C2×C11×#3232
C2×#146511