Finite Group Databasebeta

← C2×#13076686 #14960310

Subgroups — C2×#13076686 #14960310

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C22×#66942C211yesmaximal, characteristic
3#13076686C2116yesmaximal, direct product factor
4C2×#10622273C212yesmaximal
5C2×#10622272C211yesmaximal, characteristic
6C2×#10622599C211yesmaximal, characteristic
7C2×#10622270C212yesmaximal
8C2×#10622597C212yesmaximal
9C2×#10622593C212yesmaximal
10C2×#10622593C211yesmaximal, characteristic
11C2×#10622263C211yesmaximal, characteristic
12C2×C11×#398C211yesmaximal, characteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×#66943—28no—
28C2×#66943C2218yes—
29C2×#66942—28no—
30C2×#66942C2218yes—
31C11×#398C2218yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622599C2218yes—
42#10622597C22116yes—
43#10622593C2218yes—
44#10622593C22116yes—
45#10622273C22116yes—
46#10622272C2218yes—
47#10622270C22116yes—
48#10622263C2218yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—44no—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2318yes—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—28no—
69C2×C4⋊Dic11C2314yes—
70C2×C4⋊Dic11C2314yes—
71C2×C4⋊Dic11C2318yes—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—44no—
78C2×Dic11⋊C4—44no—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×Dic11⋊C4C2314yes—
82C2×Dic11⋊C4C2314yes—
83C2×Dic11⋊C4C2318yes—
84C2×Dic11⋊C4C2318yes—
85C2×Dic11⋊C4C2318yes—
86C2×C4×Dic11D418yes—
87C2×C4×Dic11C2314yes—
88#66943—232no—
89#66942—232no—
90C11×#95C2314yes—
91C11×#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2314yes—
94C11⋊#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C2×#2822—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2414yes—
115C22×C4×C11C2412yes—
116C22×C4×C11C2412yes—
117C22×C4×C11C2414yes—
118C22×C4×C11C2412yes—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—28no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11C2×D414yes—
133C22×Dic11C2×D414yes—
134C22×Dic11C2414yes—
135C22×Dic11C2412yes—
136C22×Dic11C2414yes—
137C22×Dic11C2412yes—
138C22×Dic11C2412yes—
139C22×Dic11C2412yes—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—48no—
143C4⋊Dic11—28no—
144C4⋊Dic11—216no—
145C4⋊Dic11—28no—
146Dic11⋊C4—28no—
147Dic11⋊C4—28no—
148Dic11⋊C4—28no—
149Dic11⋊C4—216no—
150Dic11⋊C4—28no—
151Dic11⋊C4—48no—
152Dic11⋊C4—48no—
153C4×Dic11C2×D4116yes—
154C22×#125—111no—
155C22×#125—111no—
156#2822—1116no—
157C2×#400—111no—
158C2×#400—112no—
159C2×#400—111no—
160C2×#398—112no—
161C2×#398—112no—
162C2×#398—111no—
163C2×#398—112no—
164C2×#398D1111yescharacteristic
165C2×#382—111no—
166C23×C11C22×D412yes—
167C23×C11H(5,𝔽2)12yes—
168C23×C112−1+414yes—
169C23×C112−1+414yes—
170C23×C112−1+412yes—
171C23×C11C2511yescharacteristic
172C2×C4×C11—28no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—44no—
186C2×C4×C11—44no—
187C2×C4×C11—48no—
188C2×C4×C11—48no—
189C2×C4×C11C22×D414yes—
190C2×Dic11—28no—
191C2×Dic11—28no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—28no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—48no—
206C2×Dic11—44no—
207C2×Dic11—44no—
208C2×Dic11—48no—
209C2×Dic11C22×D414yes—
210C2×Dic11C22×D414yes—
211C2×#125—118no—
212C2×#125—118no—
213C2×#125—228no—
214C2×#125—228no—
215C22×C4⋊C4—112no—
216C22×C4⋊C4—111no—
217C22×C4⋊C4—111no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—111no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1112yes—
228C22×C42—111no—
229#400—118no—
230#400—118no—
231#400—1116no—
232#398—118no—
233#398—1116no—
234#398—1116no—
235#398—1116no—
236#398C2×D1118yes—
237#382—118no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95—112no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—111no—
245C2×#95C2×D1112yes—
246C2×#95C2×D1111yescharacteristic
247C22×C11#53614yes—
248C22×C11#53614yes—
249C22×C11#53714yes—
250C22×C11#56318yes—
251C22×C11#56418yes—
252C22×C11C23×D411yescharacteristic
253C22×C11C2×H(5,𝔽2)11yescharacteristic
254C22×C11C2×2−1+412yes—
255C22×C11C2×2−1+412yes—
256C22×C11C2×2−1+411yescharacteristic
257C4×C11—24no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—44no—
261C4×C11—44no—
262Dic11—24no—
263Dic11—24no—
264Dic11—42no—
265Dic11—44no—
266Dic11—42no—
267Dic11—44no—
268C23×C4—111no—
269C23×C4—111no—
270C23×C4—111no—
271C23×C4—112no—
272C23×C4—111no—
273C23×C4—112no—
274C23×C4C22×D1112yes—
275C23×C4C22×D1111yescharacteristic
276C23×C4C22×D1111yescharacteristic
277C23×C4C22×D1112yes—
278C23×C4C22×D1111yescharacteristic
279#125—2232no—
280#125—2232no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—118no—
287C2×C4⋊C4—114no—
288C2×C4⋊C4—114no—
289C2×C4⋊C4—118no—
290C2×C4⋊C4—114no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4—118no—
293C2×C4⋊C4—118no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4—224no—
296C2×C4⋊C4—228no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—228no—
300C2×C4⋊C4—224no—
301C2×C4⋊C4—224no—
302C2×C4⋊C4—444no—
303C2×C4⋊C4—444no—
304C2×C4⋊C4C22×D1114yes—
305C2×C4⋊C4C22×D1114yes—
306C2×C4⋊C4C22×D1118yes—
307C2×C42—118no—
308C2×C42—114no—
309#95—118no—
310#95—114no—
311#95—118no—
312#95—118no—
313#95—118no—
314#95—118no—
315#95—118no—
316#95C22×D1114yes—
317#95C22×D1118yes—
318C2×C11#282218yescomplemented
319C2×C11C2×#53611yescharacteristic
320C2×C11C2×#53611yescharacteristic
321C2×C11C2×#53711yescharacteristic
322C2×C11C2×#56312yes—
323C2×C11C2×#56412yes—
324C24C23×D1111yescharacteristic
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—222no—
346C22×C4—224no—
347C22×C4—222no—
348C22×C4—224no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—224no—
353C22×C4—228no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4D4×D1114yes—
359C22×C4C23×D1114yes—
360C22×C4C23×D1112yes—
361C22×C4C23×D1112yes—
362C22×C4C23×D1114yes—
363C22×C4C23×D1112yes—
364C4⋊C4—28no—
365C4⋊C4—28no—
366C4⋊C4—48no—
367C4⋊C4—228no—
368C4⋊C4—228no—
369C4⋊C4—2216no—
370C4⋊C4—228no—
371C4⋊C4—228no—
372C4⋊C4—2216no—
373C4⋊C4—228no—
374C4⋊C4—228no—
375C4⋊C4—448no—
376C4⋊C4—448no—
377C42—1116no—
378C11C2×#282211yescharacteristic, complemented, Sylow
379C23C2×D4×D1112yes—
380C23#6703712yes—
381C23#6704014yes—
382C23#6704312yes—
383C23#6704314yes—
384C23C24×D1111yescharacteristic
385C2×C4—28no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—44no—
399C2×C4—48no—
400C2×C4—48no—
401C2×C4—44no—
402C2×C4—114no—
403C2×C4—114no—
404C2×C4—228no—
405C2×C4—228no—
406C2×C4—222no—
407C2×C4—224no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—224no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—224no—
414C2×C4—228no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—222no—
418C2×C4—224no—
419C2×C4—448no—
420C2×C4—444no—
421C2×C4—448no—
422C2×C4—444no—
423C2×C4C2×D4×D1114yes—
424C22#1062313914yes—
425C22#1062317718yes—
426C22#1062317914yes—
427C22C11⋊#56418yes—
428C22#1062325514yes—
429C22C22×D4×D1111yescharacteristic
430C22C2×#6703711yescharacteristic
431C22C2×#6704012yes—
432C22C2×#6704312yes—
433C22C2×#6704311yescharacteristic
434C4—24no—
435C4—42no—
436C4—42no—
437C4—44no—
438C4—44no—
439C4—224no—
440C4—224no—
441C4—442no—
442C4—444no—
443C4—442no—
444C4—444no—
445C2#1307668618yesdirect product factor
446C2C2×#1062317911yescharacteristic
447C2C2×#1062325511yescharacteristic
448C2C2×#1062313911yescharacteristic
449C2C2×#1062317712yes—
450C2C2×C11⋊#56412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socle, prime radicalC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13076686C2direct (N × H)
318. C2×C11#2822semidirect
378. C11C2×#2822semidirect
445. C2#13076686direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#669422
#130766862
C2×#106222732
C2×#106222722
C2×#106225992
C2×#106222702
C2×#106225972
C2×#106225932
C2×#106222632
C2×C11×#3982
C2×#282211