Finite Group Databasebeta

← #14670708

Subgroups — #14670708

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×#10622770C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
5#13066708C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66991—21no—
10C22×C8×D11C2211yescharacteristic
11C2×C4⋊C4×D11—21no—
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×#66896—21no—
15#10622770—22no—
16#10622770C414yescomplemented
17C2×#66882C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C2×#66871—21no—
21D11×#107—22no—
22D11×#107—22no—
23C11×#357—22no—
24#10622200—22no—
25(C2×D11)⋊C16—22no—
26C22×D4×C11—21no—
27C22×C22⋊D11—41no—
28C22×C4×D11—41no—
29C22×C4×D11D411yescharacteristic
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8—21no—
35C2×C11×D8C2×C412yescomplemented
36C22×C8×C11C2311yescharacteristic
37C2×C11×C4⋊C4—21no—
38C2×C22⋊Dic11—41no—
39#66991—24no—
40#66991—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—41no—
44C22×C11⋊C8D411yescharacteristic
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11—21no—
48C2×C8×D11—21no—
49C2×C8×D11C2×C412yes—
50C2×C8×D11D412yes—
51C4⋊C4×D11—24no—
52C4⋊C4×D11—42no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C11×#107—21no—
57C11×#107D412yescomplemented
58#66896—24no—
59#66882—21no—
60#66882—21no—
61#66882C2×C412yescomplemented
62#66882D412yescomplemented
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16—21no—
66#66871—24no—
67#12991—111nomaximal, Sylow
68C24×C11—41no—
69C23×D11D811yescharacteristic
70C2×D4×C11—22no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—44no—
79C2×C22⋊D11—82no—
80C2×C22⋊D11—82no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11D811yescharacteristic
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—
93C11×D8—22no—
94C11×D8—22no—
95C11×D8—41no—
96C11×D8—41no—
97C2×C8×C11C22×C411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C22⋊Dic11—44no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—44no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8C22⋊C412yes—
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×#357D1111yescharacteristic, complemented
124C2×C22⋊C16—111no—
125#1380—111no—
126#1380—111no—
127C23×C11—42no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11—81no—
134C23×C11C2×D811yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11#10212yes—
140C22×D11D1612yes—
141C22×D11SD3212yes—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C22⋊D11—88no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11#10212yes—
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×D8C2×D1111yescharacteristic
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—111no—
185C2×#107—222no—
186C2×#107—221no—
187C2×#107—222no—
188C2×#107C2×D1111yescharacteristic
189C2×#102—221no—
190#357—22no—
191#357—222no—
192C22⋊C16—222no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—161no—
197C22×C11—161no—
198C22×C11—161no—
199C22×C11—161no—
200C22×C11C2×#10211yescharacteristic
201C22×C11#44711yescharacteristic
202C22×C11#48011yescharacteristic
203C22×C11C2×D1611yescharacteristic
204C22×C11C2×SD3211yescharacteristic
205C22×C11#50911yescharacteristic
206C22×C11#51011yescharacteristic
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—22no—
213C2×D11#35714yescomplemented
214C4×C11—82no—
215C4×C11#38611yescharacteristic
216C4×C11#41711yescharacteristic
217C4×C11#44811yescharacteristic
218C4×C11#48111yescharacteristic
219Dic11—22no—
220Dic11—82no—
221Dic11—82no—
222C22×D4—21no—
223C22×D4—441no—
224C23×C4—111no—
225C23×C4—441no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8C4×D1112yescomplemented
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—224no—
244C2×C4⋊C4—221no—
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—112no—
257#107—112no—
258#107—224no—
259#107—221no—
260#107—221no—
261#107C22⋊D1112yescomplemented
262#102—224no—
263C2×C11—162no—
264C2×C11#187411yescharacteristic
265C2×C11C2×#35711yescharacteristic
266C2×C11#213911yescharacteristic
267C2×C11#218411yescharacteristic
268C2×C11#218511yescharacteristic
269C2×C11#223211yescharacteristic
270C2×C11#223311yescharacteristic
271D11—24no—
272C24—41no—
273C24—111no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—444no—
281C2×D4—882no—
282C2×D4—882no—
283C22×C4—41no—
284C22×C4—111no—
285C22×C4—112no—
286C22×C4—112no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—444no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—882no—
295C22×C4—882no—
296C22×C4D4×D1111yescharacteristic
297D8—22no—
298D8—22no—
299D8—41no—
300D8—41no—
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×C8#433911yescharacteristic
310C2×C8D4×D1111yescharacteristic
311C2×C8D4×D1111yescharacteristic
312C2×C8#434111yescharacteristic
313C2×C8C2×C22⋊D1111yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C4⋊C4—444no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C22⋊C4—444no—
322C16—41no—
323C16—441no—
324C11#1299111yescharacteristic, complemented, Sylow
325C23—42no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—112no—
333C23—112no—
334C23—112no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23D8×D1111yescharacteristic
340D4—42no—
341D4—42no—
342D4—81no—
343D4—81no—
344D4—888no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—112no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—888no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4C22⋊C4×D1111yescharacteristic
363C2×C4#6693611yescharacteristic
364C2×C4#6696411yescharacteristic
365C2×C4SD16×D1111yescharacteristic
366C2×C4#6696811yescharacteristic
367C2×C4#6699011yescharacteristic
368C8—222no—
369C8(C22⋊D11)⋊C411yescharacteristic
370C8#6693711yescharacteristic
371C8C4×C22⋊D1111yescharacteristic
372C8#6699111yescharacteristic
373C22—82no—
374C22—82no—
375C22—82no—
376C22—114no—
377C22—161no—
378C22—161no—
379C22—161no—
380C22—161no—
381C22—222no—
382C22—222no—
383C22—222no—
384C22—222no—
385C22—222no—
386C22—222no—
387C22D11×#10211yescharacteristic
388C22#1062238711yescharacteristic
389C22D11×D1611yescharacteristic
390C22#1062252411yescharacteristic
391C22D11×SD3211yescharacteristic
392C22#1062252811yescharacteristic
393C22#1062276911yescharacteristic
394C4—82no—
395C4—222no—
396C4—882no—
397C4—882no—
398C4#1062238411yescharacteristic
399C4#1062239011yescharacteristic
400C4#1062256911yescharacteristic
401C4#1062278311yescharacteristic
402C2—162no—
403C2—224no—
404C2#1306893011yescharacteristic
405C2D11×#35711yescharacteristic
406C2#1307032511yescharacteristic
407C2#1307052611yescharacteristic
408C2#1307053111yescharacteristic
409C2#1307079511yescharacteristic
410C2#1307080011yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622770C2
cosocleC22×C8×C11C23
hypercenterC2×#357D11
hypocenterC11#12991
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
3. C2×#10622200C2semidirect
4. C2×(C2×D11)⋊C16C2semidirect
5. #13066708C2semidirect
6. #13066707C2semidirect
7. C2×C11×#357C2semidirect
16. #10622770C4semidirect
35. C2×C11×D8C2×C4semidirect
57. C11×#107D4semidirect
61. #66882C2×C4semidirect
62. #66882D4semidirect
123. C2×#357D11semidirect
213. C2×D11#357semidirect
231. C2×D8C4×D11semidirect
261. #107C22⋊D11semidirect
324. C11#12991semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
C2×D11×#1072
C2×#106222002
C2×(C2×D11)⋊C162
#130667082
#130667072
C2×C11×#3572
#1299111