Finite Group Databasebeta

← #14690472

Subgroups — #14690472

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622289C211yesmaximal, characteristic, complemented
2C2×#10622570C213yesmaximal
3C2×#10622585C213yesmaximal, complemented
4#13066859C213yesmaximal, complemented
5#13066858C213yesmaximal, complemented
6#95×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#396C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C22×C11×C4⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C22×C22⋊Dic11C2213yes—
12C22×(C2×D11)⋊C4C2213yes—
13C22×(C2×D11)⋊C4C2213yes—
14C22×Dic11⋊C4C2213yes—
15C22×Dic11⋊C4C2213yes—
16C22×C4×Dic11C2213yes—
17C11×#396—24no—
18C2×C11×#95C2211yescharacteristic
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22#10622585—212no—
23#10622570—212no—
24#10622289—24no—
25C25×C11C2311yescharacteristic
26C24×D11C2311yescharacteristic
27C23×C4×C11C2313yes—
28C23×C4×C11C2313yes—
29C22×C22⋊D11—26no—
30C22×C22⋊D11—26no—
31C22×C22⋊D11Q814yes—
32C23×Dic11C2313yes—
33C23×Dic11C2313yes—
34C23×Dic11C2311yescharacteristic
35C2×C11×C4⋊C4—26no—
36C2×C11×C4⋊C4—26no—
37C2×C11×C4⋊C4—43no—
38C2×C11×C22⋊C4—26no—
39C2×C11×C22⋊C4—26no—
40C2×C11×C22⋊C4—43no—
41C2×C22⋊Dic11—26no—
42C2×C22⋊Dic11—26no—
43C2×C22⋊Dic11—43no—
44C2×(C2×D11)⋊C4—26no—
45C2×(C2×D11)⋊C4—26no—
46C2×(C2×D11)⋊C4—26no—
47C2×(C2×D11)⋊C4—26no—
48C2×(C2×D11)⋊C4—43no—
49C2×(C2×D11)⋊C4—43no—
50C2×Dic11⋊C4—26no—
51C2×Dic11⋊C4—26no—
52C2×Dic11⋊C4—26no—
53C2×Dic11⋊C4—26no—
54C2×Dic11⋊C4—43no—
55C2×Dic11⋊C4D4112yes—
56C2×C4×Dic11—26no—
57C2×C4×Dic11—26no—
58C2×C4×Dic11—26no—
59C11×#95D414yescomplemented
60C11⋊#95—26no—
61C11⋊#95—26no—
62C11⋊#95—26no—
63#15141—111nomaximal, Sylow
64C24×C11—23no—
65C24×C11—21no—
66C24×C11—23no—
67C24×C11—23no—
68C24×C11—23no—
69C24×C11—21no—
70C24×C11C2×Q812yes—
71C24×C11C2411yescharacteristic
72C23×D11—21no—
73C23×D11—23no—
74C23×D11—23no—
75C23×D11—23no—
76C23×D11—23no—
77C23×D11—21no—
78C23×D11C2×Q812yes—
79C22×C4×C11—23no—
80C22×C4×C11—23no—
81C22×C4×C11—23no—
82C22×C4×C11—23no—
83C22×C4×C11—23no—
84C22×C4×C11—23no—
85C22×C4×C11—23no—
86C22×C4×C11—23no—
87C22×C4×C11—23no—
88C22×C4×C11—23no—
89C22×C4×C11—23no—
90C22×C4×C11—23no—
91C22×C4×C11C2×D416yes—
92C22×C4×C11C2×D416yes—
93C2×C22⋊D11—224no—
94C2×C22⋊D11—412no—
95C2×C22⋊D11—44no—
96C22×Dic11—23no—
97C22×Dic11—23no—
98C22×Dic11—23no—
99C22×Dic11—23no—
100C22×Dic11—23no—
101C22×Dic11—23no—
102C22×Dic11—23no—
103C22×Dic11—23no—
104C22×Dic11—23no—
105C22×Dic11—23no—
106C22×Dic11—23no—
107C22×Dic11—23no—
108C22×Dic11C2×D416yes—
109C22×Dic11C2×D416yes—
110C22×Dic11C2×Q812yes—
111C22×Dic11#4116yes—
112C22×Dic11#4116yes—
113C11×C4⋊C4—412no—
114C11×C22⋊C4—412no—
115C22⋊Dic11—412no—
116(C2×D11)⋊C4—412no—
117(C2×D11)⋊C4—412no—
118Dic11⋊C4—224no—
119Dic11⋊C4—412no—
120C4×Dic11—412no—
121C2×#396—111no—
122C2×#396D1111yescharacteristic, complemented
123C2×#390—113no—
124C2×#389—113no—
125#1439—113no—
126#1439—113no—
127C4×#95—111no—
128C23×C11—26no—
129C23×C11—22no—
130C23×C11—26no—
131C23×C11—43no—
132C23×C11—41no—
133C23×C11—43no—
134C23×C11—43no—
135C23×C11—43no—
136C23×C11—43no—
137C23×C11—43no—
138C23×C11—43no—
139C23×C11—43no—
140C23×C11—43no—
141C23×C11C22×D413yes—
142C23×C11C22×D411yescharacteristic
143C23×C11C22×Q811yescharacteristic
144C23×C11C2×#4113yes—
145C23×C11C2×#4113yes—
146C23×C11H(5,𝔽2)13yes—
147C23×C112−1+411yescharacteristic
148C22×D11—26no—
149C22×D11—22no—
150C22×D11—26no—
151C22×D11—43no—
152C22×D11—41no—
153C22×D11—43no—
154C22×D11—43no—
155C22×D11—43no—
156C22×D11—43no—
157C22×D11—43no—
158C22×D11—43no—
159C22×D11—43no—
160C22×D11—43no—
161C2×C4×C11—26no—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11—26no—
165C2×C4×C11—26no—
166C2×C4×C11—26no—
167C2×C4×C11—43no—
168C2×C4×C11—43no—
169C2×C4×C11—43no—
170C2×C4×C11—43no—
171C2×C4×C11—43no—
172C2×C4×C11—43no—
173C2×C4×C11—43no—
174C2×C4×C11—43no—
175C22⋊D11—416no—
176C2×Dic11—26no—
177C2×Dic11—26no—
178C2×Dic11—26no—
179C2×Dic11—26no—
180C2×Dic11—26no—
181C2×Dic11—26no—
182C2×Dic11—43no—
183C2×Dic11—43no—
184C2×Dic11—43no—
185C2×Dic11—43no—
186C2×Dic11—43no—
187C2×Dic11—43no—
188C2×Dic11—43no—
189C2×Dic11—43no—
190C2×Dic11#121112yes—
191C2×Dic11C22⋊Q8112yes—
192C2×Dic11#12614yes—
193C23×D4—111no—
194C22×C4⋊C4—113no—
195C22×C4⋊C4—113no—
196C22×C4⋊C4C2×D1113yes—
197C22×C22⋊C4—113no—
198C22×C22⋊C4—113no—
199C22×C22⋊C4—113no—
200C22×C22⋊C4C2×D1113yes—
201C22×C42—113no—
202#396—24no—
203#396—224no—
204#390—2212no—
205#389—2212no—
206C2×#95—113no—
207C2×#95—113no—
208C2×#95—113no—
209C2×#95C2×D1111yescharacteristic
210C22×C11—42no—
211C22×C11—46no—
212C22×C11—46no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—83no—
216C22×C11—83no—
217C22×C11C2×#12113yes—
218C22×C11C2×C22⋊Q813yes—
219C22×C11C2×#12611yescharacteristic
220C22×C11#52913yes—
221C22×C11#53213yes—
222C22×C11#54013yes—
223C22×C11#54213yes—
224C22×C11D4213yes—
225C22×C11#54613yes—
226C22×C11#54813yes—
227C22×C11D4×Q811yescharacteristic
228C22×C11#55013yes—
229C22×C11#55413yes—
230C2×D11—42no—
231C2×D11—46no—
232C2×D11—46no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—83no—
236C2×D11—83no—
237C4×C11—46no—
238C4×C11—46no—
239Dic11—46no—
240Dic11—46no—
241Dic11#39618yescomplemented
242C25—111no—
243C25C22×D1111yescharacteristic
244C22×D4—114no—
245C22×D4—226no—
246C22×D4—226no—
247C23×C4—111no—
248C23×C4—113no—
249C23×C4—113no—
250C23×C4C22×D1113yes—
251C23×C4C22×D1113yes—
252C2×C4⋊C4—26no—
253C2×C4⋊C4—26no—
254C2×C4⋊C4—43no—
255C2×C4⋊C4—1112no—
256C2×C4⋊C4—226no—
257C2×C4⋊C4—226no—
258C2×C4⋊C4—226no—
259C2×C4⋊C4—226no—
260C2×C4⋊C4—443no—
261C2×C22⋊C4—26no—
262C2×C22⋊C4—26no—
263C2×C22⋊C4—43no—
264C2×C22⋊C4—226no—
265C2×C22⋊C4—226no—
266C2×C22⋊C4—226no—
267C2×C22⋊C4—226no—
268C2×C22⋊C4—226no—
269C2×C22⋊C4—226no—
270C2×C22⋊C4—443no—
271C2×C22⋊C4—443no—
272C2×C22⋊C4—443no—
273C2×C42—226no—
274C2×C42—226no—
275C2×C42—226no—
276#95—226no—
277#95—226no—
278#95—226no—
279#95C22⋊D1114yescomplemented
280C2×C11—82no—
281C2×C11C2×#39611yescharacteristic
282C2×C11#242613yes—
283C2×C11#242813yes—
284C2×C11#245213yes—
285C2×C11#245413yes—
286C2×C11#264411yescharacteristic
287C2×C11#286011yescharacteristic
288D11—82no—
289C24—23no—
290C24—23no—
291C24—21no—
292C24—23no—
293C24—23no—
294C24—21no—
295C24—112no—
296C24—223no—
297C24—223no—
298C24—221no—
299C24—223no—
300C24—223no—
301C24—221no—
302C24Q8×D1112yes—
303C24C23×D1111yescharacteristic
304C2×D4—2224no—
305C2×D4—444no—
306C2×D4—4412no—
307C22×C4—23no—
308C22×C4—23no—
309C22×C4—23no—
310C22×C4—23no—
311C22×C4—23no—
312C22×C4—23no—
313C22×C4—23no—
314C22×C4—23no—
315C22×C4—23no—
316C22×C4—23no—
317C22×C4—23no—
318C22×C4—23no—
319C22×C4—116no—
320C22×C4—112no—
321C22×C4—116no—
322C22×C4—116no—
323C22×C4—116no—
324C22×C4—223no—
325C22×C4—223no—
326C22×C4—223no—
327C22×C4—223no—
328C22×C4—223no—
329C22×C4—223no—
330C22×C4—223no—
331C22×C4—223no—
332C22×C4—223no—
333C22×C4—223no—
334C22×C4—223no—
335C22×C4—223no—
336C22×C4D4×D1116yes—
337C22×C4C2×C22⋊D1116yes—
338C4⋊C4—412no—
339C4⋊C4—2224no—
340C4⋊C4—4412no—
341C22⋊C4—412no—
342C22⋊C4—4412no—
343C22⋊C4—4412no—
344C22⋊C4—4412no—
345C42—4412no—
346C11#1514111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—26no—
349C23—26no—
350C23—41no—
351C23—43no—
352C23—43no—
353C23—43no—
354C23—43no—
355C23—43no—
356C23—43no—
357C23—43no—
358C23—43no—
359C23—43no—
360C23—222no—
361C23—226no—
362C23—226no—
363C23—441no—
364C23—443no—
365C23—443no—
366C23—443no—
367C23—443no—
368C23—443no—
369C23—443no—
370C23—443no—
371C23—443no—
372C23—443no—
373C23C2×D4×D1113yes—
374C23#6703713yes—
375C23C2×Q8×D1111yescharacteristic
376C23#6704011yescharacteristic
377C23#41×D1113yes—
378C23#41×D1113yes—
379C23C22×C22⋊D1111yescharacteristic
380D4—4416no—
381C2×C4—26no—
382C2×C4—26no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—43no—
388C2×C4—43no—
389C2×C4—43no—
390C2×C4—43no—
391C2×C4—43no—
392C2×C4—43no—
393C2×C4—43no—
394C2×C4—43no—
395C2×C4—114no—
396C2×C4—1112no—
397C2×C4—1112no—
398C2×C4—226no—
399C2×C4—226no—
400C2×C4—226no—
401C2×C4—226no—
402C2×C4—226no—
403C2×C4—226no—
404C2×C4—443no—
405C2×C4—443no—
406C2×C4—443no—
407C2×C4—443no—
408C2×C4—443no—
409C2×C4—443no—
410C2×C4—443no—
411C2×C4—443no—
412C22—46no—
413C22—46no—
414C22—42no—
415C22—83no—
416C22—83no—
417C22—81no—
418C22—81no—
419C22—446no—
420C22—446no—
421C22—442no—
422C22—883no—
423C22—883no—
424C22—881no—
425C22—881no—
426C22#1062313013yes—
427C22D11×#12113yes—
428C22#1062314113yes—
429C22#1062314613yes—
430C22D11×C22⋊Q813yes—
431C22#1062316413yes—
432C22#1062316713yes—
433C22#1062317113yes—
434C22D11×#12611yescharacteristic
435C22#1062323713yes—
436C22D4×C22⋊D1113yes—
437C22Q8×C22⋊D1111yescharacteristic
438C22#1062336313yes—
439C4—46no—
440C4—46no—
441C4—118no—
442C4—446no—
443C4—446no—
444C2—82no—
445C2—882no—
446C2D11×#39611yescharacteristic
447C2#1307217713yes—
448C2#1307220113yes—
449C2#1307246513yes—
450C2#1307248113yes—
451C2#1307457811yescharacteristic
452C2#1307698111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#396C2
prime radicalC23×C22⋊D11C22
hypercenterC2×#396D11
hypocenterC11#15141
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×#10622289C2semidirect
3. C2×#10622585C2semidirect
4. #13066859C2semidirect
5. #13066858C2semidirect
6. #95×Dic11C2semidirect
7. C2×C11×#396C2semidirect
59. C11×#95D4semidirect
122. C2×#396D11semidirect
241. Dic11#396semidirect
279. #95C22⋊D11semidirect
346. C11#15141semidirect

Maximal subgroups

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

subgroupindex
C2×#106222892
C2×#106225702
C2×#106225852
#130668592
#130668582
#95×Dic112
C2×C11×#3962
#1514111