Finite Group Databasebeta

← C2×#13066981 #14719745

Subgroups — C2×#13066981 #14719745

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066981C218yesmaximal, direct product factor
4C2×#10622107C214yesmaximal, complemented
5C2×C11×#407C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C23×Dic22C411yescharacteristic
8C22×C11×M16—21no—
9C22×C22⋊Dic11C412yes—
10C22×C4⋊Dic11C411yescharacteristic
11C2×#66977—21no—
12C2×#66977—21no—
13C2×#66977—22no—
14C2×#66977—21no—
15C2×#66977—21no—
16C2×#66977—22no—
17C2×#66977C414yes—
18C2×#66977C2214yes—
19C22×Dic11⋊C4C2212yes—
20C23×C11⋊C8—21no—
21C11×#407—22no—
22C11×#407C2214yes—
23C2×C11×C22⋊C8—21no—
24C2×C11×C22⋊C8C2212yes—
25C2×C22⋊(C11⋊C8)—22no—
26C2×C22⋊(C11⋊C8)—21no—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2214yes—
29#10622107C22116yescomplemented
30C25×C11C2×C411yescharacteristic
31C23×C4×C11—44no—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D412yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D412yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×Dic11C2×C412yes—
43C23×Dic11C2×C412yes—
44C22×Dic22—22no—
45C22×Dic22—21no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2×C414yes—
49C2×C11×M16—24no—
50C2×C11×M16—44no—
51C22×C8×C11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11C2×C418yes—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2×C414yes—
60#66977—24no—
61#66977—24no—
62#66977—24no—
63#66977—24no—
64#66977—24no—
65#66977—24no—
66#66977—24no—
67#66977—24no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4C2×C414yes—
73C2×Dic11⋊C4C2314yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—24no—
76C22×C11⋊C8—44no—
77C11×C22⋊C8—24no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8C2314yes—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)—24no—
82C22⋊(C11⋊C8)C2314yes—
83C2×#1472—111nomaximal, Sylow
84C24×C11—24no—
85C24×C11—24no—
86C24×C11—42no—
87C24×C11C22⋊C411yescharacteristic
88C24×C11C22⋊C412yes—
89C24×C11C22⋊C411yescharacteristic
90C24×C11C22×C412yes—
91C24×C11C22×C411yescharacteristic
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—44no—
96C22×C4×C11—44no—
97C22×C4×C11—44no—
98C22×C4×C11—44no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C412yes—
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C412yes—
106C22×C4×C11C22⋊C412yes—
107C22×C4×C11C22⋊C412yes—
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—28no—
125C22×Dic11—44no—
126C22×Dic11C22×C414yes—
127C22×Dic11C22×C414yes—
128C2×Dic22—24no—
129C2×Dic22—24no—
130C2×Dic22—44no—
131C2×Dic22—48no—
132C2×Dic22—48no—
133C2×Dic22—44no—
134C11×M16—48no—
135C2×C8×C11—24no—
136C2×C8×C11—44no—
137C22⋊Dic11—28no—
138C22⋊Dic11—28no—
139C4⋊Dic11—24no—
140C4⋊Dic11—24no—
141Dic11⋊C4—24no—
142Dic11⋊C4—24no—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—44no—
147C2×C11⋊C8—48no—
148C22×C22⋊Q8—111no—
149C2×#407D1111yescharacteristic
150C22×C22⋊C8—111no—
151#1472—118no—
152C2×#324—114no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—24no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—416no—
167C23×C11#10114yes—
168C23×C11C2×C22⋊C412yes—
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C22⋊C412yes—
171C23×C11C2×C22⋊C411yescharacteristic
172C23×C11#13114yes—
173C23×C11C23×C411yescharacteristic
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11#9914yes—
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11C2×C22⋊C411yescharacteristic
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—28no—
201C2×Dic11—44no—
202C2×Dic11—44no—
203C2×Dic11—44no—
204C2×Dic11—44no—
205C2×Dic11—44no—
206Dic22—48no—
207Dic22—48no—
208C8×C11—44no—
209C11⋊C8—44no—
210C23×Q8—111no—
211C24×C4C2×D1111yescharacteristic
212C22×M16—21no—
213C23×C8—221no—
214C2×C22⋊Q8—114no—
215C2×C22⋊Q8—114no—
216C2×C22⋊Q8—221no—
217C2×C22⋊Q8—222no—
218C2×C22⋊Q8—221no—
219C2×C22⋊Q8—221no—
220C2×C22⋊Q8—221no—
221C2×C22⋊Q8—222no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—111no—
224C22×C22⋊C4—112no—
225#407—22no—
226#407C2×D1114yes—
227C2×C22⋊C8—21no—
228C2×C22⋊C8—112no—
229C2×C22⋊C8—114no—
230C2×C22⋊C8—222no—
231C2×C22⋊C8—221no—
232C2×C22⋊C8C2×D1112yes—
233#324—1116no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—28no—
241C22×C11—28no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—48no—
246C22×C11—48no—
247C22×C11—44no—
248C22×C11#40812yes—
249C22×C11#40812yes—
250C22×C11C2×#9912yes—
251C22×C11C2×#10114yes—
252C22×C11C2×#10112yes—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11C2×#13112yes—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—22no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11C2×#9914yes—
261Dic11—44no—
262Dic11—44no—
263C25C4×D1111yescharacteristic
264C22×Q8—114no—
265C22×Q8—222no—
266C22×Q8—221no—
267C22×Q8—221no—
268C22×Q8—444no—
269C23×C4—44no—
270C23×C4—112no—
271C23×C4—112no—
272C23×C4C4×D1111yescharacteristic
273C23×C4C4×D1112yes—
274C23×C4D4411yescharacteristic
275C23×C4D4412yes—
276C23×C4D4411yescharacteristic
277C23×C4C22⋊D1111yescharacteristic
278C23×C4C22⋊D1111yescharacteristic
279C23×C4C22⋊D1112yes—
280C23×C4C22×D1111yescharacteristic
281C23×C4C22×D1112yes—
282C2×M16—24no—
283C2×M16—44no—
284C22×C8—22no—
285C22×C8—224no—
286C22×C8—222no—
287C22×C8—444no—
288C22⋊Q8—224no—
289C22⋊Q8—224no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—224no—
293C22⋊Q8—224no—
294C22⋊Q8—224no—
295C22⋊Q8—224no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—114no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C22⋊C4—118no—
307C2×C22⋊C4—224no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C22⋊C8—24no—
311C22⋊C8—22no—
312C22⋊C8—114no—
313C22⋊C8—222no—
314C22⋊C8—224no—
315C22⋊C8C22×D1114yes—
316C2×C11—22no—
317C2×C11—22no—
318C2×C11—24no—
319C2×C11—42no—
320C2×C11#147214yescomplemented
321C2×C11C2×#40811yescharacteristic
322C2×C11C22×#9911yescharacteristic
323C2×C11C22×#10111yescharacteristic
324C24—24no—
325C24—24no—
326C24—42no—
327C24(C2×D11)⋊C411yescharacteristic
328C24(C2×D11)⋊C412yes—
329C24(C2×D11)⋊C411yescharacteristic
330C24C2×C4×D1112yes—
331C24C2×C4×D1111yescharacteristic
332C2×Q8—224no—
333C2×Q8—224no—
334C2×Q8—448no—
335C2×Q8—444no—
336C2×Q8—448no—
337C2×Q8—444no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—44no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—228no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—444no—
356C22×C4(C2×D11)⋊C412yes—
357C22×C4(C2×D11)⋊C412yes—
358C22×C4(C2×D11)⋊C412yes—
359C22×C4(C2×D11)⋊C411yescharacteristic
360C22×C4(C2×D11)⋊C412yes—
361C22×C4(C2×D11)⋊C412yes—
362C22×C4(C2×D11)⋊C411yescharacteristic
363C22×C4C2×C4×D1112yes—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4C2×D4412yes—
366C22×C4C2×D4411yescharacteristic
367C22×C4C2×D4411yescharacteristic
368C22×C4C2×D4412yes—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C2×C22⋊D1112yes—
373C22×C4C23×D1111yescharacteristic
374M16—48no—
375C2×C8—24no—
376C2×C8—44no—
377C2×C8—224no—
378C2×C8—444no—
379C2×C8—448no—
380C4⋊C4—224no—
381C4⋊C4—224no—
382C4⋊C4—224no—
383C4⋊C4—224no—
384C4⋊C4—224no—
385C4⋊C4—224no—
386C22⋊C4—228no—
387C22⋊C4—228no—
388C11C2×#147211yescharacteristic, complemented, Sylow
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—24no—
394C23—22no—
395C23—24no—
396C23—22no—
397C23—24no—
398C23—24no—
399C23—22no—
400C23—42no—
401C23—42no—
402C23—416no—
403C23#6688814yes—
404C23#6696014yes—
405C23C2×(C2×D11)⋊C412yes—
406C23C2×(C2×D11)⋊C411yescharacteristic
407C23C2×(C2×D11)⋊C412yes—
408C23C2×(C2×D11)⋊C411yescharacteristic
409C23C22×C4×D1111yescharacteristic
410Q8—448no—
411Q8—448no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—228no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4—444no—
435C2×C4—444no—
436C2×C4—444no—
437C2×C4#6687014yes—
438C2×C4C2×(C2×D11)⋊C411yescharacteristic
439C2×C4C2×(C2×D11)⋊C411yescharacteristic
440C2×C4C2×(C2×D11)⋊C412yes—
441C2×C4C2×(C2×D11)⋊C412yes—
442C2×C4C22×D4411yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—44no—
445C8—444no—
446C22—22no—
447C22—21no—
448C22—21no—
449C22—22no—
450C22—21no—
451C22—21no—
452C22—28no—
453C22—28no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—48no—
458C22—48no—
459C22—44no—
460C22C2×#6687012yes—
461C22#1062274212yes—
462C22#1062274212yes—
463C22C2×#6688814yes—
464C22C2×#6688812yes—
465C22C2×#6696012yes—
466C22C22×(C2×D11)⋊C411yescharacteristic
467C4—21no—
468C4—21no—
469C4—22no—
470C4—21no—
471C4—21no—
472C4—444no—
473C4—444no—
474C4C2×#6687014yes—
475C2—22no—
476C2—24no—
477C2—22no—
478C2—42no—
479C2#1306698114yesdirect product factor
480C2C2×#1062274211yescharacteristic
481C2C22×#6687011yescharacteristic
482C2C22×#6688811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11C2×#1472
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13066981C2direct (N × H)
4. C2×#10622107C2semidirect
29. #10622107C22semidirect
320. C2×C11#1472semidirect
388. C11C2×#1472semidirect
479. C2#13066981direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C22⋊(C11⋊C8)2
#130669812
C2×#106221072
C2×C11×#4072
C2×#147211