Finite Group Databasebeta

← #14670710

Subgroups — #14670710

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622496C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C22×C8×D11C2211yescharacteristic
10C2×#66948—21no—
11C2×C4⋊C4×D11—21no—
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×#66882C2211yescharacteristic
16C22×C11⋊C16C2211yescharacteristic
17C2×#66873—21no—
18C2×#66871—21no—
19#10622496—22no—
20#10622496C414yescomplemented
21D11×#107—22no—
22D11×#107—22no—
23#10622147—22no—
24(C2×D11)⋊C16—22no—
25#10622129—22no—
26C22×D44—21no—
27C22×D44—41no—
28C22×C4×D11—41no—
29C22×C4×D11D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×(C2×D11)⋊C4—41no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—41no—
36C22×C11⋊C8D411yescharacteristic
37C2×D88—21no—
38C2×D88—21no—
39C2×D88—21no—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88C2×C412yescomplemented
43C2×C8×D11—21no—
44C2×C8×D11—21no—
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11C2×C412yes—
48C2×C8×D11D412yes—
49#66948—24no—
50#66948—42no—
51C4⋊C4×D11—24no—
52C4⋊C4×D11—42no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#107C2×C412yescomplemented
59C11×#107D412yescomplemented
60#66882—21no—
61#66882D412yescomplemented
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65#66873—24no—
66#66871—24no—
67#12991—111nomaximal, Sylow
68C23×D11—41no—
69C23×D11D811yescharacteristic
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—41no—
74C22×Dic11D811yescharacteristic
75C2×D44—22no—
76C2×D44—44no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—82no—
83C2×D44—82no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—44no—
89C2×C4×D11—82no—
90C2×C4×D11—82no—
91C2×C4×D11C22⋊C412yes—
92C2×C4×D11SD1612yes—
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103(C2×D11)⋊C4—44no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106Dic11⋊C4—44no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8C22⋊C412yes—
110D88—22no—
111D88—22no—
112D88—41no—
113D88—41no—
114C8×D11—22no—
115C8×D11—22no—
116C8×D11—22no—
117C8×D11—22no—
118C11×C16—41no—
119C11⋊C16—41no—
120C2×#466—111no—
121C22×#107—111no—
122C2×#357—111no—
123C2×#357—111no—
124C2×C22⋊C16—111no—
125#1380—111no—
126#1380D1111yescharacteristic, complemented
127C23×C11C2×D811yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—42no—
133C22×D11—81no—
134C22×D11—81no—
135C22×D11—81no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11#10212yes—
140C22×D11D1612yes—
141C22×D11SD3212yes—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—42no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11#10212yes—
160D44—42no—
161D44—42no—
162D44—88no—
163D44—81no—
164D44—81no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—22no—
169C4×D11—88no—
170C8×C11C4×D411yescharacteristic
171C8×C11C4×D411yescharacteristic
172C8×C11#12111yescharacteristic
173C8×C11#12111yescharacteristic
174C11⋊C8—22no—
175C22×D8—111no—
176C23×C8—111no—
177C2×#121—221no—
178C22×C4⋊C4—221no—
179C22×C16—111no—
180C22×C16C2×D1111yescharacteristic
181#466—114no—
182#466—222no—
183C2×#107—111no—
184C2×#107—222no—
185C2×#107—221no—
186C2×#107—222no—
187C2×#107C2×D1111yescharacteristic
188C2×#107C2×D1111yescharacteristic
189C2×#102—221no—
190#357—222no—
191#357—222no—
192C22⋊C16—222no—
193C22×C11C2×#10211yescharacteristic
194C22×C11#44711yescharacteristic
195C22×C11#48011yescharacteristic
196C22×C11C2×D1611yescharacteristic
197C22×C11C2×SD3211yescharacteristic
198C22×C11#50911yescharacteristic
199C22×C11#51011yescharacteristic
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—161no—
210C2×D11—161no—
211C2×D11—161no—
212C2×D11—161no—
213C2×D11#35714yescomplemented
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#38611yescharacteristic
217C4×C11#41711yescharacteristic
218C4×C11#44811yescharacteristic
219C4×C11#48111yescharacteristic
220Dic11—22no—
221Dic11—82no—
222C22×D4—221no—
223C22×D4—441no—
224C23×C4—111no—
225C23×C4—441no—
226C2×D8—112no—
227C2×D8—221no—
228C2×D8—221no—
229C2×D8—221no—
230C2×D8—221no—
231C2×D8—221no—
232C22×C8—111no—
233C22×C8—112no—
234C22×C8—112no—
235C22×C8—221no—
236C22×C8—221no—
237C22×C8—221no—
238C22×C8—221no—
239C22×C8C22×D1111yescharacteristic
240#121—224no—
241#121—442no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—224no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—442no—
247C2×C4⋊C4—441no—
248C2×C22⋊C4—441no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—221no—
253C2×C16—221no—
254C2×C16—221no—
255#107—21no—
256#107—21no—
257#107—112no—
258#107—224no—
259#107—221no—
260#107C4×D1112yescomplemented
261#107D4412yescomplemented
262#102—224no—
263C2×C11#187411yescharacteristic
264C2×C11C2×#35711yescharacteristic
265C2×C11#213911yescharacteristic
266C2×C11#218411yescharacteristic
267C2×C11#218511yescharacteristic
268C2×C11#223211yescharacteristic
269C2×C11#223311yescharacteristic
270D11—24no—
271D11—162no—
272C24—111no—
273C24—441no—
274C2×D4—222no—
275C2×D4—444no—
276C2×D4—441no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—882no—
282C2×D4—882no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—111no—
286C22×C4—112no—
287C22×C4—112no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—444no—
293C22×C4—441no—
294C22×C4—882no—
295C22×C4—882no—
296C22×C4D4×D1111yescharacteristic
297D8—222no—
298D8—222no—
299D8—441no—
300D8—441no—
301C2×C8—112no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8C2×C4×D1111yescharacteristic
309C2×C8C2×D4411yescharacteristic
310C2×C8#433911yescharacteristic
311C2×C8D4×D1111yescharacteristic
312C2×C8D4×D1111yescharacteristic
313C2×C8#434311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—222no—
319C4⋊C4—444no—
320C4⋊C4—441no—
321C22⋊C4—444no—
322C16—41no—
323C16—441no—
324C11#1299111yescharacteristic, complemented, Sylow
325C23—112no—
326C23—112no—
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—442no—
333C23—881no—
334C23—881no—
335C23—881no—
336C23—881no—
337C23—881no—
338C23—881no—
339C23D8×D1111yescharacteristic
340D4—442no—
341D4—442no—
342D4—888no—
343D4—881no—
344D4—881no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—112no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—442no—
359C2×C4—888no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4C22⋊C4×D1111yescharacteristic
363C2×C4#6693511yescharacteristic
364C2×C4#6694711yescharacteristic
365C2×C4SD16×D1111yescharacteristic
366C2×C4#6696711yescharacteristic
367C2×C4#6697111yescharacteristic
368C8—222no—
369C8C4×D4411yescharacteristic
370C8#6693711yescharacteristic
371C8#6694611yescharacteristic
372C8#6694811yescharacteristic
373C22—114no—
374C22—222no—
375C22—222no—
376C22—222no—
377C22—222no—
378C22—222no—
379C22—222no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22—1761no—
384C22—1761no—
385C22—1761no—
386C22—1761no—
387C22D11×#10211yescharacteristic
388C22#1062238611yescharacteristic
389C22#1062249511yescharacteristic
390C22D11×D1611yescharacteristic
391C22D11×SD3211yescharacteristic
392C22#1062252711yescharacteristic
393C22#1062253111yescharacteristic
394C4—82no—
395C4—82no—
396C4—222no—
397C4—882no—
398C4#1062227811yescharacteristic
399C4#1062241611yescharacteristic
400C4#1062241911yescharacteristic
401C4#1062247611yescharacteristic
402C2—224no—
403C2—1762no—
404C2#1306893211yescharacteristic
405C2D11×#35711yescharacteristic
406C2#1307032711yescharacteristic
407C2#1307052911yescharacteristic
408C2#1307053411yescharacteristic
409C2#1307079811yescharacteristic
410C2#1307080311yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC2×#10622496C2
cosocleC22×C8×C11C23
hypercenter#1380D11
hypocenterC11#12991
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
3. C2×#10622147C2semidirect
4. C2×#10622129C2semidirect
5. C2×(C2×D11)⋊C16C2semidirect
6. #13066707C2semidirect
7. C11×#1380C2semidirect
20. #10622496C4semidirect
42. C2×D88C2×C4semidirect
58. C11×#107C2×C4semidirect
59. C11×#107D4semidirect
61. #66882D4semidirect
126. #1380D11semidirect
213. C2×D11#357semidirect
260. #107C4×D11semidirect
261. #107D44semidirect
324. C11#12991semidirect

Maximal subgroups

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

subgroupindex
C2×#106224962
C2×D11×#1072
C2×#106221472
C2×#106221292
C2×(C2×D11)⋊C162
#130667072
C11×#13802
#1299111