Finite Group Databasebeta

← #14658184

Subgroups — #14658184

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074733C211yesmaximal, characteristic
2#13068804C211yesmaximal, characteristic
3#13066875C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1852C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×#107—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622597—21no—
20#10622592—21no—
21C2×#66871—21no—
22#10622555—21no—
23#10622270—21no—
24#10622269—21no—
25C11×#340—21no—
26#10622167—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—42no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C22×C11⋊C8—21no—
49#66931—42no—
50#66931—42no—
51C11×#107—42no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8Q812yescomplemented
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—42no—
62C11⋊#95—42no—
63C11⋊#95Q812yescomplemented
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)Q812yescomplemented
66#66871—42no—
67#10569—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2×Q811yescharacteristic
84C22×C4×C11C2×Q811yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11D812yes—
104C22×Dic11Q1612yes—
105C2×Dic22—42no—
106C2×Dic22—81no—
107C2×Dic22—81no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—42no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126Dic11⋊C4—81no—
127Dic11⋊C4—81no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#2659—111no—
132#1852—111no—
133#1852D1111yescharacteristic
134#1442—111no—
135#1294—111no—
136#1294—111no—
137#1280—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11#12011yescharacteristic
143C23×C11C22⋊Q811yescharacteristic
144C23×C11C4⋊Q811yescharacteristic
145C23×C11C2×D811yescharacteristic
146C23×C11C2×Q1611yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11C22⋊Q811yescharacteristic
171C2×C4×C11C22⋊Q811yescharacteristic
172C2×C4×C11C4⋊Q811yescharacteristic
173C2×C4×C11C4⋊Q811yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197Dic22—84no—
198C8×C11—42no—
199C11⋊C8—42no—
200C2×C22⋊Q8—221no—
201C22×C4⋊C4C2×D1111yescharacteristic
202C2×#107—21no—
203C2×#107—221no—
204C2×C22⋊C8—111no—
205C2×C22⋊C8C2×D1111yescharacteristic
206#398—221no—
207#398—221no—
208#395—221no—
209#395—221no—
210#380—111no—
211#380—221no—
212#380C2×D1111yescharacteristic
213C2×#95—111no—
214C2×#95—111no—
215C2×#95—221no—
216C2×#95—221no—
217#340—21no—
218#340—221no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11#39511yescharacteristic
232C22×C11#44711yescharacteristic
233C22×C11#45111yescharacteristic
234C22×C11#45411yescharacteristic
235C22×C11#45511yescharacteristic
236C22×C11B(4,𝔽2)11yescharacteristic
237C22×C11#45811yescharacteristic
238C22×C11#47411yescharacteristic
239C22×C11#47711yescharacteristic
240C22×C11#50011yescharacteristic
241C22×C11#50111yescharacteristic
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—81no—
247C4×C11—82no—
248C4×C11—81no—
249Dic11—42no—
250Dic11—42no—
251Dic11—82no—
252Dic11—81no—
253Dic11—81no—
254C22×Q8—221no—
255C23×C4—21no—
256C23×C4—111no—
257C23×C4—111no—
258C23×C4—221no—
259C23×C4C22×D1111yescharacteristic
260C22×C8—21no—
261C22×C8—221no—
262C22⋊Q8—442no—
263C22⋊Q8—442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C4⋊C4C22⋊D1111yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—221no—
278#107—42no—
279#107—442no—
280C22⋊C8—21no—
281C22⋊C8—112no—
282C22⋊C8—221no—
283C22⋊C8Dic2212yescomplemented
284#95—21no—
285#95—112no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95—221no—
291#95—221no—
292#95—442no—
293#95—442no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11#159811yescharacteristic
299C2×C11#160211yescharacteristic
300C2×C11#160711yescharacteristic
301C2×C11#161711yescharacteristic
302C2×C11#205711yescharacteristic
303C2×C11#206111yescharacteristic
304C2×C11#206211yescharacteristic
305C24D4×D1111yescharacteristic
306C2×Q8—442no—
307C2×Q8—881no—
308C2×Q8—881no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—112no—
321C22×C4—112no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—222no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4—441no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4C2×Dic2211yescharacteristic
340C22×C4#433911yescharacteristic
341C22×C4D4×D1111yescharacteristic
342C22×C4Q8×D1111yescharacteristic
343C22×C4Q8×D1111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—222no—
349C2×C8—441no—
350C2×C8—441no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—442no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C4⋊C4—881no—
363C4⋊C4—881no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C11#1056911yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23#6694111yescharacteristic
374C23#6694911yescharacteristic
375C23D8×D1111yescharacteristic
376C23#6696411yescharacteristic
377C23Q16×D1111yescharacteristic
378C23#6697111yescharacteristic
379C23#6699011yescharacteristic
380Q8—884no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4#6694111yescharacteristic
426C2×C4#6694911yescharacteristic
427C2×C4#6697711yescharacteristic
428C2×C4#6699711yescharacteristic
429C8—42no—
430C8—442no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22#1062248711yescharacteristic
444C22#1062248811yescharacteristic
445C22#1062248911yescharacteristic
446C22#1062250311yescharacteristic
447C22#1062259211yescharacteristic
448C22#1062264511yescharacteristic
449C22#1062266611yescharacteristic
450C22#1062276911yescharacteristic
451C22#1062279911yescharacteristic
452C22#1062281411yescharacteristic
453C22#1062281511yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—82no—
459C4—81no—
460C4—81no—
461C4—442no—
462C4—442no—
463C4—882no—
464C4—881no—
465C4—881no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—21no—
470C2#1306754911yescharacteristic
471C2#1306757111yescharacteristic
472C2#1306760011yescharacteristic
473C2#1306765611yescharacteristic
474C2#1306994211yescharacteristic
475C2#1306996411yescharacteristic
476C2#1306996911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1852C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1852D11
hypocenterC11#10569
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
53. C11×C22⋊C8Q8semidirect
63. C11⋊#95Q8semidirect
65. C22⋊(C11⋊C8)Q8semidirect
283. C22⋊C8Dic22semidirect
368. C11#10569semidirect

Maximal subgroups

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

subgroupindex
#130747332
#130688042
#130668752
#130664962
#130664942
#130664582
C11×#18522
#1056911