Finite Group Databasebeta

← #14646513

Subgroups — #14646513

Order 2816.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66983C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C11×#1434C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×C4×C22⋊D11—21no—
9C2×C4×D44C411yescharacteristic, complemented
10C2×C11×#95—21no—
11C2×C11×#95—21no—
12C2×C11×#95C2212yes—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622553—21no—
17#10622552C411yescharacteristic, complemented
18C4×(C2×D11)⋊C4—21no—
19C4×C4⋊Dic11C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×C4⋊(C11⋊C8)—21no—
22#10622162—21no—
23#10622089—24no—
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C2×C42×C11—42no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37#66983—21no—
38#66983—21no—
39#66983D412yes—
40#66983Q812yes—
41C4×C22⋊D11—44no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—22no—
52C4×D44—42no—
53C11×#95—24no—
54C11×#95—22no—
55C11×#95—22no—
56C11×#95—42no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—42no—
63#8575—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×Q811yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—22no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—42no—
94C2×C22⋊D11—42no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C2×D44—21no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44C4⋊C412yes—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—41no—
108C42×C11—41no—
109C22⋊Dic11—42no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11C4⋊C412yes—
119Dic11⋊C4—42no—
120C4×Dic11—42no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124C4×#121—111no—
125#1797—111no—
126C2×#327—112no—
127#1434D1111yescharacteristic, complemented
128#1294—112no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12111yescharacteristic
135C23×C11C22⋊Q811yescharacteristic
136C23×C11#13512yes—
137C23×C11AGL(1,ℤ/8)12yes—
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11—82no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11—82no—
172C2×C4×C11#9912yes—
173C2×C4×C11#10412yes—
174C2×C4×C11C2×C4⋊C411yescharacteristic
175C2×C4×C11#11711yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11C22⋊Q811yescharacteristic
178C22⋊D11—44no—
179C22⋊D11—44no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189D44—42no—
190D44—42no—
191C4×D11—84no—
192C11⋊C8—82no—
193C2×#121—111no—
194C2×C4×D4—111no—
195C2×C4×D4—221no—
196C22×C42C2×D1111yescharacteristic
197C2×C4⋊C8—221no—
198C2×C22⋊C8—112no—
199#390—111no—
200#389—111no—
201#388—221no—
202#386—221no—
203#380—111no—
204C4×C4⋊C4—111no—
205C4×C22⋊C4—221no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95C2×D1112yes—
209#336—221no—
210#327—224no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11#38011yescharacteristic
220C22×C11C2×#9911yescharacteristic
221C22×C11#41011yescharacteristic
222C22×C11#41611yescharacteristic
223C22×C11#41811yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C22×C11#42111yescharacteristic
226C22×C11#46312yes—
227C22×C11#47812yes—
228C2×D11—42no—
229C2×D11—42no—
230C2×D11—42no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—84no—
244Dic11—42no—
245Dic11—81no—
246Dic11—81no—
247C22×D4—111no—
248C22×D4—221no—
249C23×C4—22no—
250C23×C4—221no—
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C23×C4C22×D1111yescharacteristic
254C22×C8—222no—
255#121—112no—
256#121—112no—
257#121—221no—
258#121—221no—
259C4×D4—442no—
260C4×D4—444no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C42—42no—
271C2×C42—221no—
272C2×C42C4×D1111yescharacteristic
273C2×C42C4×D1111yescharacteristic
274C2×C42D4411yescharacteristic
275C2×C42D4411yescharacteristic
276C4⋊C8—442no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279#95—24no—
280#95—22no—
281#95—22no—
282#95—42no—
283#95—221no—
284#95—221no—
285#95—221no—
286C2×C11—22no—
287C2×C11—22no—
288C2×C11#150111yescharacteristic
289C2×C11#150511yescharacteristic
290C2×C11#151011yescharacteristic
291C2×C11#152111yescharacteristic
292C2×C11#179911yescharacteristic
293C2×C11#180411yescharacteristic
294C2×C11#180611yescharacteristic
295D11—82no—
296C24—221no—
297C24C2×C22⋊D1111yescharacteristic
298C2×D4—112no—
299C2×D4—222no—
300C2×D4—222no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—442no—
305C2×D4—442no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4(C2×D11)⋊C411yescharacteristic
328C22×C4(C2×D11)⋊C411yescharacteristic
329C22×C4(C2×D11)⋊C411yescharacteristic
330C22×C4(C2×D11)⋊C411yescharacteristic
331C22×C4C2×C4×D1111yescharacteristic
332C22×C4C2×D4411yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4#434111yescharacteristic
335C22×C4Q8×D1111yescharacteristic
336C22×C4#434311yescharacteristic
337C2×C8—442no—
338C2×C8—442no—
339C2×C8—442no—
340C4⋊C4—112no—
341C4⋊C4—221no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—442no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C42—22no—
352C42—22no—
353C42—41no—
354C42—41no—
355C42—442no—
356C11#857511yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—222no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23C2×(C2×D11)⋊C411yescharacteristic
369C23#6699111yescharacteristic
370C23#6699911yescharacteristic
371C23#6700212yes—
372C23#6700312yes—
373D4—442no—
374D4—442no—
375D4—444no—
376D4—444no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—222no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—884no—
414C2×C4#6686912yes—
415C2×C4#6687012yes—
416C2×C4C4⋊C4×D1111yescharacteristic
417C2×C4#6694511yescharacteristic
418C2×C4#6694811yescharacteristic
419C2×C4#6695011yescharacteristic
420C8—882no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—442no—
430C22—442no—
431C22—442no—
432C22—881no—
433C22—881no—
434C22—881no—
435C22—881no—
436C22C2×#6686911yescharacteristic
437C22C2×#6687011yescharacteristic
438C22#1062260011yescharacteristic
439C22#1062261411yescharacteristic
440C22#1062261511yescharacteristic
441C22#1062261811yescharacteristic
442C22#1062261911yescharacteristic
443C22#1062267012yes—
444C22#1062267912yes—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—22no—
450C4—22no—
451C4—41no—
452C4—41no—
453C4—84no—
454C4—442no—
455C4—881no—
456C4—881no—
457C2—22no—
458C2—22no—
459C2—882no—
460C2#1306710511yescharacteristic
461C2#1306712311yescharacteristic
462C2#1306714411yescharacteristic
463C2#1306719111yescharacteristic
464C2#1306860111yescharacteristic
465C2#1306862311yescharacteristic
466C2#1306863711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8575
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13068596C2semidirect
4. #13066495C2semidirect
5. C11×#1434C2semidirect
9. C2×C4×D44C4semidirect
17. #10622552C4semidirect
19. C4×C4⋊Dic11C4semidirect
20. #10622541C4semidirect
127. #1434D11semidirect
356. C11#8575semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
#130685962
C2×#106220892
#130664952
C11×#14342
#857511