Finite Group Databasebeta

← #14653851

Subgroups — #14653851

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076924C211yesmaximal, characteristic
2#13068380C211yesmaximal, characteristic
3Dic11⋊#95C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×Dic11⋊C4—21no—
9C22×C4×Dic11C2211yescharacteristic
10C2×#66943C411yescharacteristic, complemented
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66879—21no—
19#10622598C411yescharacteristic, complemented
20#10622590C411yescharacteristic, complemented
21#10622586C411yescharacteristic, complemented
22#10622563—21no—
23#10622559—21no—
24#10622268—21no—
25#10622267—21no—
26#10622188—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—24no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—42no—
45C2×Dic11⋊C4—42no—
46C2×C4×Dic11—42no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8—21no—
52#66943—42no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8Q812yes—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—42no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)Q812yes—
68#66879—42no—
69#9887—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
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×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×Q811yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122Dic11⋊C4—48no—
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#2851—111no—
133#1749—111no—
134C4⋊#95—111no—
135#1294—111no—
136#1294—111no—
137#1294—111no—
138#1294D1111yescharacteristic
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11C2×C22⋊C411yescharacteristic
144C23×C11#12411yescharacteristic
145C23×C11C4⋊Q811yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149C23×C11#13711yescharacteristic
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11C4×Q811yescharacteristic
172C2×C4×C11C4×Q811yescharacteristic
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×C4×C11C22⋊Q811yescharacteristic
175C2×Dic11—24no—
176C2×Dic11—24no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—81no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11#9912yes—
203C2×Dic11#10412yes—
204C8×C11—42no—
205C11⋊C8—42no—
206C2×#125—111no—
207C22×C4⋊C4—221no—
208C22×C42—111no—
209C2×C22⋊C8—111no—
210C2×C22⋊C8C2×D1111yescharacteristic
211C2×#97—221no—
212#389—111no—
213#389—111no—
214#387—221no—
215#387—221no—
216#385—221no—
217#385—221no—
218#382—111no—
219#380—111no—
220#380C2×D1111yescharacteristic
221C2×#95—111no—
222C2×#95—221no—
223C2×#95C2×D1111yescharacteristic
224#336—221no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11#39111yescharacteristic
238C22×C11C2×#9911yescharacteristic
239C22×C11#41011yescharacteristic
240C22×C11#41711yescharacteristic
241C22×C11#41711yescharacteristic
242C22×C11C2×#10411yescharacteristic
243C22×C11#42111yescharacteristic
244C22×C11#49011yescharacteristic
245C22×C11#49111yescharacteristic
246C22×C11#50111yescharacteristic
247C22×C11#50111yescharacteristic
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—82no—
253C4×C11—81no—
254C4×C11—81no—
255Dic11—22no—
256Dic11—22no—
257Dic11—41no—
258Dic11—41no—
259Dic11—82no—
260Dic11—81no—
261Dic11—81no—
262C23×C4—21no—
263C23×C4—111no—
264C23×C4—111no—
265C23×C4—221no—
266C23×C4C22×D1111yescharacteristic
267C22×C8—21no—
268C22×C8—221no—
269#125—442no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—224no—
277C2×C4⋊C4—442no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4C4×D1111yescharacteristic
280C2×C4⋊C4C4×D1111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—221no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42—111no—
286C2×C42—111no—
287C2×C42—442no—
288C22⋊C8—21no—
289C22⋊C8—112no—
290C22⋊C8—221no—
291C22⋊C8Dic2212yes—
292#97—442no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—221no—
297#95—221no—
298#95—221no—
299#95—221no—
300#95—221no—
301#95—221no—
302#95—221no—
303#95—442no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—21no—
307C2×C11—21no—
308C2×C11#150411yescharacteristic
309C2×C11#150911yescharacteristic
310C2×C11#151211yescharacteristic
311C2×C11#151311yescharacteristic
312C2×C11#198611yescharacteristic
313C2×C11#199211yescharacteristic
314C2×C11#199611yescharacteristic
315C24D4×D1111yescharacteristic
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—222no—
332C22×C4—222no—
333C22×C4—221no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—222no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4C2×Dic2211yescharacteristic
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4#433911yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4#434111yescharacteristic
353C22×C4Q8×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—222no—
358C2×C8—441no—
359C2×C8—441no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C4⋊C4—448no—
367C4⋊C4—442no—
368C4⋊C4—442no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—441no—
372C22⋊C4—441no—
373C42—222no—
374C42—222no—
375C42—441no—
376C42—441no—
377C11#988711yescharacteristic, complemented, Sylow
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23C22⋊C4×D1111yescharacteristic
383C23#6693811yescharacteristic
384C23#6694111yescharacteristic
385C23#6696411yescharacteristic
386C23#6696711yescharacteristic
387C23#6696811yescharacteristic
388C23#6697111yescharacteristic
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—112no—
411C2×C4—112no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—881no—
436C2×C4—881no—
437C2×C4—881no—
438C2×C4—881no—
439C2×C4C4×Dic2211yescharacteristic
440C2×C4#6693111yescharacteristic
441C2×C4#6694011yescharacteristic
442C2×C4#6694911yescharacteristic
443C8—42no—
444C8—442no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22#1062225911yescharacteristic
458C22#1062235311yescharacteristic
459C22D11×#9911yescharacteristic
460C22#1062237711yescharacteristic
461C22#1062238411yescharacteristic
462C22#1062241011yescharacteristic
463C22#1062241611yescharacteristic
464C22D11×#10411yescharacteristic
465C22#1062243411yescharacteristic
466C22#1062246911yescharacteristic
467C22#1062248911yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—222no—
476C4—222no—
477C4—441no—
478C4—441no—
479C4—882no—
480C4—881no—
481C4—881no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—21no—
486C2#1306711711yescharacteristic
487C2#1306714011yescharacteristic
488C2#1306715111yescharacteristic
489C2#1306715811yescharacteristic
490C2#1306955811yescharacteristic
491C2#1306958311yescharacteristic
492C2#1306959911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9887
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
10. C2×#66943C4semidirect
19. #10622598C4semidirect
20. #10622590C4semidirect
21. #10622586C4semidirect
377. C11#9887semidirect

Maximal subgroups

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

subgroupindex
#130769242
#130683802
Dic11⋊#952
#130664962
#130664952
#130664942
C11×#12942
#988711