Finite Group Databasebeta

← C2×#13073226 #14923145

Subgroups — C2×#13073226 #14923145

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073226C2116yesmaximal, direct product factor
2C2×C11⋊#401C212yesmaximal
3C2×#10622271C212yesmaximal
4C2×#10622843C211yesmaximal, characteristic
5C2×#10622843C211yesmaximal, characteristic
6C2×#10622586C211yesmaximal, characteristic
7C2×#10622265C212yesmaximal
8C2×#10622264C212yesmaximal
9C2×#10622549C211yesmaximal, characteristic
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic
12C2×C11×#391C211yesmaximal, characteristic
13C23×Q8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C11×#391C2218yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27#10622843C2218yes—
28#10622843C2218yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C4⋊C4×Dic11C2218yes—
40#10622586C2218yes—
41#10622549C2218yes—
42C4×Dic11⋊C4C2218yes—
43C11⋊#401C22116yes—
44#10622271C22116yes—
45#10622265C22116yes—
46#10622264C22116yes—
47C22×Q8×C11—24no—
48C22×Q8×C11—24no—
49C22×Q8×C11—24no—
50C22×Q8×C11C2314yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4C2314yes—
64C2×C42×C11—24no—
65C2×C42×C11C2314yes—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11C2314yes—
69C2×C4⋊Dic11C2314yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—28no—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2318yes—
75C2×Dic11⋊C4C2314yes—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—28no—
79C2×C4×Dic11C2318yes—
80C2×C4×Dic11C2314yes—
81C2×C4×Dic11C2314yes—
82C11×#95C2318yes—
83C11×#95C2318yes—
84C11⋊#95C2314yes—
85C11⋊#95C2318yes—
86C11⋊#95C2318yes—
87C11⋊#95C2318yes—
88C11⋊#95C2318yes—
89C11⋊#95C2318yes—
90C11⋊#95C2318yes—
91C11⋊#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2314yes—
94C2×#2514—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C2×Q8×C11—28no—
97C2×Q8×C11—28no—
98C2×Q8×C11—28no—
99C2×Q8×C11—416no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11#4114yes—
113C22×C4×C11#4114yes—
114C22×C4×C11#4114yes—
115C22×C4×C11C2414yes—
116C22×C4×C11C2412yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2414yes—
119C22×C4×C11C2412yes—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11#4114yes—
137C22×Dic11#4114yes—
138C22×Dic11C2412yes—
139C22×Dic11C2412yes—
140C22×Dic11C2414yes—
141C22×Dic11C2414yes—
142C22×Dic11C2412yes—
143C22×Dic11C2412yes—
144C11×C4⋊C4—28no—
145C42×C11—28no—
146C4⋊Dic11—28no—
147C4⋊Dic11—28no—
148Dic11⋊C4—28no—
149Dic11⋊C4—216no—
150Dic11⋊C4—28no—
151C4×Dic11—216no—
152C4×Dic11—28no—
153C4×Dic11—28no—
154#2514—1116no—
155C2×#401—112no—
156C2×#400—112no—
157C2×#391—111no—
158C2×#391—111no—
159C2×#391D1111yescharacteristic
160C2×#389—111no—
161C2×#387—112no—
162C2×#383—112no—
163C2×#382—111no—
164C2×C4×C4⋊C4—111no—
165C2×C4×C4⋊C4—111no—
166C23×C11C2×#4112yes—
167C23×C11C2×#4112yes—
168C23×C11C2×#4112yes—
169C23×C11C2×#4112yes—
170C23×C11C2×#4112yes—
171C23×C112−1+412yes—
172C23×C112−1+412yes—
173C23×C11C2511yescharacteristic
174Q8×C11—416no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
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—22no—
186C2×C4×C11—22no—
187C2×C4×C11—48no—
188C2×C4×C11—48no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11#126116yes—
192C2×C4×C11C2×#4114yes—
193C2×C4×C11C2×#4114yes—
194C2×C4×C11C2×#4114yes—
195C2×Dic11—28no—
196C2×Dic11—28no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—44no—
214C2×Dic11—48no—
215C2×Dic11—48no—
216C2×Dic11—44no—
217C2×Dic11C2×#4114yes—
218C2×Dic11C2×#4114yes—
219C23×Q8C2×D1111yescharacteristic
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—111no—
224C22×C4⋊C4—111no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C42—111no—
227C22×C42—112no—
228C22×C42—111no—
229C22×C42C2×D1111yescharacteristic
230#401—1116no—
231#400—1116no—
232#391—118no—
233#391—118no—
234#391C2×D1118yes—
235#389—118no—
236#387—1116no—
237#383—1116no—
238#382—118no—
239C4×C4⋊C4—118no—
240C4×C4⋊C4—118no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95—111no—
246C2×#95—112no—
247C2×#95—112no—
248C2×#95—112no—
249C2×#95—111no—
250C2×#95—112no—
251C2×#95C2×D1112yes—
252C2×#95C2×D1112yes—
253C22×C11C2×#12614yes—
254C22×C11#52914yes—
255C22×C11#54114yes—
256C22×C11#55214yes—
257C22×C11#55614yes—
258C22×C11#55614yes—
259C22×C11#55614yes—
260C22×C11C22×#4111yescharacteristic
261C22×C11C22×#4111yescharacteristic
262C22×C11C22×#4111yescharacteristic
263C22×C11C22×#4111yescharacteristic
264C22×C11C22×#4111yescharacteristic
265C22×C11C2×2−1+411yescharacteristic
266C22×C11C2×2−1+411yescharacteristic
267C4×C11—44no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11C2×#12618yes—
272Dic11—24no—
273Dic11—24no—
274Dic11—42no—
275Dic11—42no—
276Dic11—44no—
277Dic11—44no—
278C22×Q8—24no—
279C22×Q8—24no—
280C22×Q8—24no—
281C22×Q8C22×D1114yes—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—112no—
285C23×C4—112no—
286C23×C4—111no—
287C23×C4—111no—
288C23×C4C22×D1112yes—
289C23×C4C22×D1111yescharacteristic
290C23×C4C22×D1111yescharacteristic
291C23×C4C22×D1112yes—
292C23×C4C22×D1111yescharacteristic
293C2×C4⋊C4—24no—
294C2×C4⋊C4—114no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—118no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—224no—
301C2×C4⋊C4—228no—
302C2×C4⋊C4—224no—
303C2×C4⋊C4—224no—
304C2×C4⋊C4C22×D1114yes—
305C2×C42—24no—
306C2×C42—114no—
307C2×C42—118no—
308C2×C42—114no—
309C2×C42—228no—
310C2×C42—224no—
311C2×C42—224no—
312C2×C42C22×D1114yes—
313#95—114no—
314#95—118no—
315#95—114no—
316#95—118no—
317#95—118no—
318#95—118no—
319#95—118no—
320#95—118no—
321#95—118no—
322#95—118no—
323#95C22×D1118yes—
324#95C22×D1118yes—
325C2×C11#251418yescomplemented
326C2×C11C22×#12611yescharacteristic
327C2×C11C2×#52911yescharacteristic
328C2×C11C2×#54111yescharacteristic
329C2×C11C2×#55211yescharacteristic
330C2×C11C2×#55611yescharacteristic
331C2×C11C2×#55611yescharacteristic
332C2×C11C2×#55611yescharacteristic
333C24C23×D1111yescharacteristic
334C2×Q8—28no—
335C2×Q8—28no—
336C2×Q8—28no—
337C2×Q8—416no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—114no—
351C22×C4—114no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—112no—
355C22×C4—114no—
356C22×C4—112no—
357C22×C4—114no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—222no—
371C22×C4—224no—
372C22×C4—224no—
373C22×C4—222no—
374C22×C4#433914yes—
375C22×C4#434114yes—
376C22×C4#434114yes—
377C22×C4C23×D1114yes—
378C22×C4C23×D1112yes—
379C22×C4C23×D1112yes—
380C22×C4C23×D1114yes—
381C22×C4C23×D1112yes—
382C4⋊C4—28no—
383C4⋊C4—228no—
384C4⋊C4—228no—
385C4⋊C4—2216no—
386C4⋊C4—228no—
387C4⋊C4—228no—
388C42—28no—
389C42—2216no—
390C42—228no—
391C42—228no—
392C11C2×#251411yescharacteristic, complemented, Sylow
393C23C2×#433912yes—
394C23C2×#434112yes—
395C23C2×#434112yes—
396C23#6704012yes—
397C23#6704012yes—
398C23#41×D1112yes—
399C23#41×D1112yes—
400C23C24×D1111yescharacteristic
401Q8—416no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—48no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—48no—
418C2×C4—114no—
419C2×C4—114no—
420C2×C4—228no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—228no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—224no—
436C2×C4—222no—
437C2×C4—224no—
438C2×C4—444no—
439C2×C4—448no—
440C2×C4—448no—
441C2×C4—444no—
442C2×C4#66932116yes—
443C2×C4C2×#433914yes—
444C2×C4C2×#434114yes—
445C2×C4C2×#434114yes—
446C22C2×#6693214yes—
447C22#1062309914yes—
448C22#1062309914yes—
449C22#1062317014yes—
450C22#1062317214yes—
451C22#1062321114yes—
452C22#1062326214yes—
453C22C22×#433911yescharacteristic
454C22C22×#434111yescharacteristic
455C22C22×#434111yescharacteristic
456C22C2×#6704011yescharacteristic
457C22C2×#6704011yescharacteristic
458C22C2×#41×D1111yescharacteristic
459C22C2×#41×D1111yescharacteristic
460C4—42no—
461C4—44no—
462C4—44no—
463C4—42no—
464C4—224no—
465C4—224no—
466C4—442no—
467C4—444no—
468C4—444no—
469C4—442no—
470C4C2×#6693218yes—
471C2#1307322618yesdirect product factor
472C2C22×#6693211yescharacteristic
473C2C2×#1062321111yescharacteristic
474C2C2×#1062326211yescharacteristic
475C2C2×#1062317011yescharacteristic
476C2C2×#1062317211yescharacteristic
477C2C2×#1062309911yescharacteristic
478C2C2×#1062309911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#391C2
socle, prime radicalC24×C11C24
hypercenterC2×#391D11
hypocenterC11C2×#2514
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #13073226C2direct (N × H)
325. C2×C11#2514semidirect
392. C11C2×#2514semidirect
471. C2#13073226direct (N × H)

Maximal subgroups

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

subgroupindex
#130732262
C2×C11⋊#4012
C2×#106222712
C2×#106228432
C2×#106225862
C2×#106222652
C2×#106222642
C2×#106225492
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
C2×C11×#3912
C2×#251411