Finite Group Databasebeta

← C2×#13067135 #14720893

Subgroups — C2×#13067135 #14720893

Order 2816.

1554 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13067135C218yesmaximal, direct product factor
4C2×#10622090C214yesmaximal, complemented
5C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C23×Dic22C411yescharacteristic, complemented
8C22×C11×C22⋊C4—21no—
9C22×C42×C11—21no—
10C22×C22⋊Dic11—21no—
11C22×C4⋊Dic11C411yescharacteristic, complemented
12C2×#66977—21no—
13C2×#66977—22no—
14C2×#66977—21no—
15C2×#66977—22no—
16C2×#66977C414yescomplemented
17C2×#66977C412yescomplemented
18C2×#66977C2212yes—
19C2×#66977C2214yes—
20C22×Dic11⋊C4—21no—
21C22×#4318—21no—
22C4×C11×C22⋊C4—22no—
23C4×C11×C22⋊C4C2214yes—
24C2×C11×#95C2212yes—
25#10622820—22no—
26#10622820C2214yes—
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622090C22116yescomplemented
30C25×C11D411yescharacteristic
31C23×C4×C11—22no—
32C23×C4×C11—44no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D412yes—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2×C412yes—
49C22×Dic22C2×C414yescomplemented
50C2×C11×C22⋊C4—28no—
51C2×C11×C22⋊C4—24no—
52C2×C42×C11—24no—
53C2×C42×C11—44no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—24no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2×C412yes—
61C2×C4⋊Dic11C2×C414yescomplemented
62#66977—24no—
63#66977—24no—
64#66977—24no—
65#66977—22no—
66#66977—24no—
67#66977—22no—
68#66977—24no—
69#66977C2×C414yes—
70#66977C2×C418yescomplemented
71#66977C2314yes—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—24no—
76C2×#4318—24no—
77C2×#4318—44no—
78C22×C11⋊C8—22no—
79C11×#95—22no—
80C11×#95C2314yes—
81C22⋊(C11⋊C8)—24no—
82C22⋊(C11⋊C8)—22no—
83C22⋊(C11⋊C8)C2314yes—
84C2×#1508—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—42no—
88C24×C11C22⋊C411yescharacteristic
89C24×C11C22⋊C412yes—
90C24×C11C22⋊C411yescharacteristic
91C24×C11C2×D412yes—
92C24×C11C2×D411yescharacteristic
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—28no—
97C22×C4×C11—24no—
98C22×C4×C11—44no—
99C22×C4×C11—44no—
100C22×C4×C11—44no—
101C22×C4×C11—44no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊C412yes—
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11C22⋊C412yes—
111C22×C4×C11C22⋊C412yes—
112C22×C4×C11C22⋊C412yes—
113C22×C4×C11C22⋊C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11—44no—
130C22×Dic11—44no—
131C2×Dic22—22no—
132C2×Dic22—24no—
133C2×Dic22—44no—
134C2×Dic22—48no—
135C2×Dic22—48no—
136C2×Dic22—44no—
137C2×Dic22C22×C414yes—
138C11×C22⋊C4—216no—
139C42×C11—48no—
140C22⋊Dic11—24no—
141C22⋊Dic11—28no—
142C22⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—24no—
145C4⋊Dic11C22×C414yes—
146Dic11⋊C4—24no—
147Dic11⋊C4—28no—
148Dic11⋊C4—24no—
149#4318—48no—
150C2×C11⋊C8—24no—
151C2×C11⋊C8—44no—
152C22×C22⋊Q8—111no—
153C2×#407—111no—
154C2×C4×C22⋊C4D1111yescharacteristic
155#1508—118no—
156C2×#328—114no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—416no—
171C23×C11#10414yes—
172C23×C11C2×C22⋊C412yes—
173C23×C11C2×C22⋊C411yescharacteristic
174C23×C11C2×C22⋊C412yes—
175C23×C11C2×C22⋊C411yescharacteristic
176C23×C11#13714yes—
177C23×C11C22×D411yescharacteristic
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—28no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—44no—
197C2×C4×C11—416no—
198C2×C4×C11—44no—
199C2×C4×C11#9914yes—
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—48no—
209C2×Dic11—44no—
210C2×Dic11—48no—
211C2×Dic11—44no—
212Dic22—44no—
213Dic22—48no—
214Dic22—44no—
215C11⋊C8—44no—
216C23×Q8—111no—
217C24×C4C2×D1111yescharacteristic
218C22×M16—221no—
219C2×C22⋊Q8—112no—
220C2×C22⋊Q8—114no—
221C2×C22⋊Q8—112no—
222C2×C22⋊Q8—114no—
223C2×C22⋊Q8—221no—
224C2×C22⋊Q8—222no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—222no—
227C22×C4⋊C4—111no—
228C22×C4⋊C4—221no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4—221no—
231C22×C42—21no—
232#407—114no—
233#407—222no—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—221no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4C2×D1114yes—
238C2×#95C2×D1112yes—
239#328—1116no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—28no—
247C22×C11—28no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—48no—
252C22×C11—48no—
253C22×C11—44no—
254C22×C11C2×#9912yes—
255C22×C11#41912yes—
256C22×C11#41912yes—
257C22×C11C2×#10414yes—
258C22×C11C2×#10412yes—
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11C2×#13712yes—
261C4×C11—21no—
262C4×C11—22no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—48no—
267C4×C11C2×#9914yes—
268Dic11—44no—
269Dic11—44no—
270C25C22⋊D1111yescharacteristic
271C22×Q8—112no—
272C22×Q8—114no—
273C22×Q8—222no—
274C22×Q8—221no—
275C22×Q8—444no—
276C23×C4—22no—
277C23×C4—44no—
278C23×C4—221no—
279C23×C4—221no—
280C23×C4C4×D1111yescharacteristic
281C23×C4C4×D1112yes—
282C23×C4C4×D1111yescharacteristic
283C23×C4D4411yescharacteristic
284C23×C4D4411yescharacteristic
285C23×C4D4412yes—
286C23×C4C22⋊D1111yescharacteristic
287C23×C4C22⋊D1112yes—
288C23×C4C22×D1111yescharacteristic
289C23×C4C22×D1112yes—
290C2×M16—224no—
291C2×M16—444no—
292C22×C8—222no—
293C22⋊Q8—114no—
294C22⋊Q8—118no—
295C22⋊Q8—114no—
296C22⋊Q8—224no—
297C22⋊Q8—224no—
298C22⋊Q8—224no—
299C22⋊Q8—224no—
300C22⋊Q8—222no—
301C22⋊Q8—224no—
302C22⋊Q8—222no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—222no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—224no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—224no—
316C2×C22⋊C4—222no—
317C2×C42—24no—
318C2×C42—44no—
319C22⋊C8—114no—
320C22⋊C8—222no—
321C22⋊C8—224no—
322#95—22no—
323#95C22×D1114yes—
324C2×C11—22no—
325C2×C11—22no—
326C2×C11—24no—
327C2×C11—42no—
328C2×C11#150814yescomplemented
329C2×C11C22×#9911yescharacteristic
330C2×C11C2×#41911yescharacteristic
331C2×C11C22×#10411yescharacteristic
332C24—24no—
333C24—24no—
334C24—42no—
335C24(C2×D11)⋊C411yescharacteristic
336C24(C2×D11)⋊C412yes—
337C24(C2×D11)⋊C411yescharacteristic
338C24C2×C22⋊D1112yes—
339C24C2×C22⋊D1111yescharacteristic
340C2×Q8—114no—
341C2×Q8—222no—
342C2×Q8—224no—
343C2×Q8—448no—
344C2×Q8—448no—
345C2×Q8—444no—
346C2×Q8—444no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—28no—
351C22×C4—24no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—44no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—444no—
366C22×C4—444no—
367C22×C4(C2×D11)⋊C412yes—
368C22×C4(C2×D11)⋊C412yes—
369C22×C4(C2×D11)⋊C412yes—
370C22×C4(C2×D11)⋊C411yescharacteristic
371C22×C4(C2×D11)⋊C412yes—
372C22×C4(C2×D11)⋊C412yes—
373C22×C4(C2×D11)⋊C411yescharacteristic
374C22×C4C2×C4×D1112yes—
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4C2×C4×D1112yes—
377C22×C4C2×C4×D1111yescharacteristic
378C22×C4C2×D4412yes—
379C22×C4C2×D4411yescharacteristic
380C22×C4C2×D4412yes—
381C22×C4C2×D4411yescharacteristic
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C23×D1111yescharacteristic
385M16—448no—
386C2×C8—224no—
387C2×C8—444no—
388C4⋊C4—114no—
389C4⋊C4—222no—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—228no—
393C4⋊C4—224no—
394C22⋊C4—216no—
395C22⋊C4—228no—
396C22⋊C4—224no—
397C22⋊C4—224no—
398C42—48no—
399C11C2×#150811yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—24no—
406C23—22no—
407C23—22no—
408C23—24no—
409C23—24no—
410C23—22no—
411C23—42no—
412C23—42no—
413C23—416no—
414C23#6686914yes—
415C23C2×(C2×D11)⋊C412yes—
416C23C2×(C2×D11)⋊C412yes—
417C23C2×(C2×D11)⋊C411yescharacteristic
418C23C2×(C2×D11)⋊C411yescharacteristic
419C23#6700414yes—
420C23C22×C22⋊D1111yescharacteristic
421Q8—444no—
422Q8—444no—
423Q8—448no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—28no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—44no—
443C2×C4—416no—
444C2×C4—44no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—448no—
448C2×C4—448no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4#6687014yes—
452C2×C4C2×(C2×D11)⋊C411yescharacteristic
453C2×C4C2×(C2×D11)⋊C412yes—
454C2×C4C2×(C2×D11)⋊C411yescharacteristic
455C2×C4C2×(C2×D11)⋊C412yes—
456C2×C4C22×C4×D1111yescharacteristic
457C2×C4C22×D4411yescharacteristic
458C8—444no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—28no—
463C22—28no—
464C22—22no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—48no—
471C22—48no—
472C22—44no—
473C22C2×#6686914yes—
474C22C2×#6686912yes—
475C22C2×#6687012yes—
476C22#1062261712yes—
477C22#1062261712yes—
478C22C22×(C2×D11)⋊C411yescharacteristic
479C22C2×#6700412yes—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—21no—
485C4—48no—
486C4—444no—
487C4—444no—
488C4C2×#6687014yes—
489C2—22no—
490C2—24no—
491C2—22no—
492C2—42no—
493C2#1306713514yesdirect product factor
494C2C22×#6687011yescharacteristic
495C2C2×#1062261711yescharacteristic
496C2C22×#6686911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#1508
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13067135C2direct (N × H)
4. C2×#10622090C2semidirect
7. C23×Dic22C4semidirect
11. C22×C4⋊Dic11C4semidirect
16. C2×#66977C4semidirect
17. C2×#66977C4semidirect
29. #10622090C22semidirect
49. C22×Dic22C2×C4semidirect
61. C2×C4⋊Dic11C2×C4semidirect
70. #66977C2×C4semidirect
328. C2×C11#1508semidirect
399. C11C2×#1508semidirect
493. C2#13067135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106228202
#130671352
C2×#106220902
C2×C4×C11×C22⋊C42
C2×#150811