Finite Group Databasebeta

← #14771424

Subgroups — #14771424

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2#13071492C212yesmaximal
3#13069350C211yesmaximal, characteristic, complemented
4#13069211C212yesmaximal, complemented
5#13069205C212yesmaximal, complemented
6#13068705C212yesmaximal
7#13068642C211yesmaximal, characteristic
8#107×Dic11C211yesmaximal, characteristic, complemented
9C4×#66882C211yesmaximal, characteristic, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic
11C11×#1942C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#389C2212yes—
18C2×(C2×D11)⋊C8C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21C2×C8×Dic11C2211yescharacteristic
22#10622600—22no—
23#10622600C2212yes—
24#10622598C2212yes—
25#10622591—22no—
26C4⋊C4×Dic11C2212yes—
27C2×#66871C2212yes—
28C4×(C2×D11)⋊C4C2211yescharacteristic
29C4×C4⋊Dic11C2212yes—
30D11×#107C418yescomplemented
31#10622279—22no—
32#10622268—22no—
33C11×#340C2212yes—
34#10622189C2212yes—
35#10622188C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×C4×D11—22no—
41C22×C4×D11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C42×C11C2311yescharacteristic
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11C2312yes—
53C2×C4⋊Dic11C2312yes—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60C2×C8×D11—22no—
61C2×C8×D11—22no—
62C2×C8×D11C2×C414yes—
63C4⋊C4×D11—24no—
64C4⋊C4×D11C2×C418yes—
65C11×#107—22no—
66C11×#107C2×C414yes—
67C4×C8×C11—22no—
68C11×#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75(C2×D11)⋊C8—22no—
76#66882—22no—
77#66882C2×C414yes—
78C8×Dic11—22no—
79#66871C2×C418yes—
80#22612—111nomaximal, Sylow
81C23×D11C2×D411yescharacteristic
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11C2×D411yescharacteristic
90C22×Dic11C2×D411yescharacteristic
91C22×Dic11C2×D411yescharacteristic
92C2×C4×D11—28no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—82no—
98C2×C4×D11—82no—
99C2×C4×D11C22×C412yes—
100C2×C4×D11#4112yes—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11C22×C412yes—
105C2×C8×C11#4112yes—
106C2×C8×C11#4112yes—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—82no—
111C11×C4⋊C4C22×C414yes—
112C42×C11—21no—
113C42×C11—21no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4Q1614yes—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—82no—
121C4⋊Dic11C22×C414yes—
122Dic11⋊C4—28no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—82no—
126C4×Dic11—82no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8C22×C412yes—
133C8×D11—28no—
134C22×#107—111no—
135#2345—112no—
136#1942—111no—
137#1942D1111yescharacteristic, complemented
138#1921—112no—
139#1921—112no—
140#1824—112no—
141#1808—111no—
142C4×#107—111no—
143C4×#107—111no—
144C8×C22⋊C4—111no—
145C23×C11C22×D411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11C4×D412yes—
151C22×D11C2×Q1612yes—
152C22×D11#13512yes—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—24no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C2×Q1612yes—
165C2×C4×C11C23×C411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C112−1+411yescharacteristic
170C2×C4×C112−1+411yescharacteristic
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—24no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11C4×D412yes—
185C2×Dic11C2×Q1612yes—
186C4×D11—22no—
187C4×D11—22no—
188C4×D11—22no—
189C4×D11—22no—
190C4×D11—88no—
191C8×C11—41no—
192C8×C11#11714yes—
193C11⋊C8—22no—
194C11⋊C8—41no—
195C23×C8—111no—
196C22×C4⋊C4—112no—
197C2×#107—111no—
198C2×#107—112no—
199C2×#107—118no—
200C2×#107—111no—
201C2×#107C2×D1111yescharacteristic
202C2×#107C2×D1111yescharacteristic
203C2×C22⋊C8—111no—
204C2×C4×C8—111no—
205C2×C4×C8C2×D1111yescharacteristic
206#389—112no—
207#389C2×D1112yes—
208#387—222no—
209#387—222no—
210#380—112no—
211#380—222no—
212C4×C4⋊C4—112no—
213C4×C4⋊C4—112no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—222no—
216#340—112no—
217#340—112no—
218#340—112no—
219#340—112no—
220#340C2×D1112yes—
221#336—111no—
222#336—111no—
223C22×C11C2×C4×D411yescharacteristic
224C22×C11#54711yescharacteristic
225C22×C11#54711yescharacteristic
226C22×C11C22×Q1611yescharacteristic
227C22×C11C2×#13511yescharacteristic
228C22×C11#57611yescharacteristic
229C22×C11#57611yescharacteristic
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11C4×Q1614yes—
237C4×C11—22no—
238C4×C11—41no—
239C4×C11—44no—
240C4×C11—82no—
241C4×C11C2×#11711yescharacteristic
242C4×C11#51911yescharacteristic
243C4×C11#55211yescharacteristic
244C4×C11#55211yescharacteristic
245Dic11—22no—
246Dic11—22no—
247Dic11—41no—
248Dic11—44no—
249Dic11—82no—
250C23×C4—111no—
251C23×C4—222no—
252C22×C8—111no—
253C22×C8—114no—
254C22×C8—111no—
255C22×C8—222no—
256C22×C8—222no—
257C22×C8C22×D1111yescharacteristic
258C22×C8C22×D1111yescharacteristic
259C2×C4⋊C4—22no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—118no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—224no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4C22×D1112yes—
267C2×C4⋊C4C22×D1112yes—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—222no—
271C2×C42—111no—
272C2×C42—222no—
273C2×C42—222no—
274C2×C42C22×D1111yescharacteristic
275#107—22no—
276#107—114no—
277#107—118no—
278#107—222no—
279#107C4×D1114yes—
280C22⋊C8—222no—
281C4×C8—22no—
282C4×C8—222no—
283#95—22no—
284#95—111no—
285#95—111no—
286#95—222no—
287#95—222no—
288#95—222no—
289#95—222no—
290C2×C11#234411yescharacteristic
291C2×C11C2×C4×Q1611yescharacteristic
292C2×C11#294811yescharacteristic
293C2×C11#333811yescharacteristic
294C2×C11#333811yescharacteristic
295C2×C11#333911yescharacteristic
296C2×C11#333911yescharacteristic
297D11—24no—
298C24—111no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—112no—
304C22×C4—112no—
305C22×C4—111no—
306C22×C4—228no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—882no—
314C22×C4—882no—
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4C23×D1111yescharacteristic
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—112no—
322C2×C8—221no—
323C2×C8—221no—
324C2×C8—228no—
325C2×C8—221no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8C2×C4×D1112yes—
329C2×C8#434112yes—
330C2×C8#434312yes—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—82no—
335C4⋊C4—114no—
336C4⋊C4—228no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—882no—
341C4⋊C4C2×C4×D1114yes—
342C22⋊C4—114no—
343C22⋊C4—222no—
344C22⋊C4—444no—
345C42—21no—
346C42—21no—
347C42—221no—
348C42—221no—
349C42—882no—
350C42—882no—
351C11#2261211yescharacteristic, complemented, Sylow
352C23—112no—
353C23—112no—
354C23—112no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23C2×D4×D1111yescharacteristic
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—24no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—112no—
372C2×C4—112no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—224no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—888no—
391C2×C4Q16×D1112yes—
392C2×C4C22×C4×D1111yescharacteristic
393C2×C4C2×#434111yescharacteristic
394C2×C4C2×#434311yescharacteristic
395C2×C4#6704011yescharacteristic
396C2×C4#41×D1111yescharacteristic
397C2×C4#6704311yescharacteristic
398C8—41no—
399C8—222no—
400C8—441no—
401C8#6694514yes—
402C22—114no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22—222no—
407C22—222no—
408C22—222no—
409C22C4×D4×D1111yescharacteristic
410C22#1062314211yescharacteristic
411C22#1062325711yescharacteristic
412C22#1062328811yescharacteristic
413C22C2×Q16×D1111yescharacteristic
414C22D11×#13511yescharacteristic
415C22#1062330011yescharacteristic
416C4—22no—
417C4—41no—
418C4—44no—
419C4—82no—
420C4—222no—
421C4—222no—
422C4—441no—
423C4—444no—
424C4—882no—
425C4C2×#6694511yescharacteristic
426C4#1062310311yescharacteristic
427C4#1062317011yescharacteristic
428C4#1062322511yescharacteristic
429C2—224no—
430C2#1307148411yescharacteristic
431C2C4×Q16×D1111yescharacteristic
432C2#1307746311yescharacteristic
433C2#1308100511yescharacteristic
434C2#1308100811yescharacteristic
435C2#1308101311yescharacteristic
436C2#1308101711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1942C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1942D11
hypocenterC11#22612
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
3. #13069350C2semidirect
4. #13069211C2semidirect
5. #13069205C2semidirect
8. #107×Dic11C2semidirect
9. C4×#66882C2semidirect
11. C11×#1942C2semidirect
30. D11×#107C4semidirect
137. #1942D11semidirect
351. C11#22612semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
#130714922
#130693502
#130692112
#130692052
#130687052
#130686422
#107×Dic112
C4×#668822
C8×(C2×D11)⋊C42
C11×#19422
#2261211