Finite Group Databasebeta

← #14646526

Subgroups — #14646526

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C2×#10622175C212yesmaximal
3#13066846C211yesmaximal, characteristic, complemented
4#13066494C212yesmaximal, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic, complemented
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11—21no—
11C11×#390C411yescharacteristic, complemented
12C11×#389C411yescharacteristic, complemented
13C11×#388—21no—
14C11×#386—21no—
15C11×#380C2211yescharacteristic
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C4⋊(C11⋊C8)—21no—
22#10622175—24no—
23#10622162—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121D412yes—
34C11×#121Q812yes—
35C4×D4×C11—42no—
36C4×D4×C11—42no—
37C4×D4×C11—42no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—21no—
48C2×C42×C11—42no—
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—42no—
55C2×C4⋊Dic11—42no—
56C22×C11⋊C8—22no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—42no—
63C22⋊(C11⋊C8)—22no—
64C22⋊(C11⋊C8)—22no—
65C4⋊(C11⋊C8)—42no—
66#8577—111nomaximal, Sylow
67C24×C11—21no—
68C24×C11C2×D411yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11C4⋊C412yescomplemented
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11D812yes—
98C22×C4×C11SD1612yes—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×Q811yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—24no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C22×Dic11—42no—
109C22×Dic11—42no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4C4⋊C412yescomplemented
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11—42no—
129C4⋊Dic11—48no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C4×#121D1111yescharacteristic
134#1797—111no—
135C2×#327—112no—
136C4⋊#95—111no—
137#1294—112no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11#12111yescharacteristic
151C23×C11C22⋊Q811yescharacteristic
152C23×C11C2×D811yescharacteristic
153C23×C11C2×SD1611yescharacteristic
154C23×C11AGL(1,ℤ/8)11yescharacteristic
155C23×C11#13711yescharacteristic
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—84no—
192C2×C4×C11#9912yes—
193C2×C4×C11#10212yes—
194C2×C4×C11#10212yes—
195C2×C4×C11#10412yes—
196C2×C4×C11C2×C4⋊C411yescharacteristic
197C2×C4×C11#11711yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11C22⋊Q811yescharacteristic
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—44no—
203C2×Dic11—82no—
204C2×Dic11—82no—
205C2×Dic11—82no—
206C2×Dic11—82no—
207C11⋊C8—82no—
208C2×#121C2×D1111yescharacteristic
209C2×C4×D4—21no—
210C2×C4×D4Dic1111yescharacteristic, complemented
211C22×C4⋊C4—221no—
212C22×C42C2×D1111yescharacteristic
213C2×C4⋊C8—221no—
214C2×C22⋊C8—112no—
215#390Dic1111yescharacteristic, complemented
216#389Dic1111yescharacteristic, complemented
217#388—21no—
218#386—21no—
219#380C2×D1111yescharacteristic
220C4×C4⋊C4Dic1111yescharacteristic, complemented
221C4×C22⋊C4—21no—
222C2×#95—112no—
223C2×#95—221no—
224#336—221no—
225#327—224no—
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—21no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11#38011yescharacteristic
246C22×C11C2×#9911yescharacteristic
247C22×C11#41011yescharacteristic
248C22×C11C2×#10211yescharacteristic
249C22×C11#41711yescharacteristic
250C22×C11C2×#10411yescharacteristic
251C22×C11#42111yescharacteristic
252C22×C11#45911yescharacteristic
253C22×C11#46111yescharacteristic
254C22×C11#47411yescharacteristic
255C22×C11#47611yescharacteristic
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—81no—
266C4×C11—81no—
267Dic11—84no—
268C22×D4—21no—
269C22×D4C2×Dic1111yescharacteristic
270C23×C4—21no—
271C23×C4—222no—
272C23×C4C22⋊D1111yescharacteristic
273C23×C4C22⋊D1111yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C22×C8—222no—
276#121—21no—
277#121—21no—
278#121Dic2212yes—
279#121D4412yes—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—224no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4C2×Dic1111yescharacteristic
288C2×C4⋊C4C2×Dic1111yescharacteristic
289C2×C4⋊C4C2×Dic1111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C42—21no—
296C2×C42—42no—
297C2×C42C2×Dic1111yescharacteristic
298C2×C42C2×Dic1111yescharacteristic
299C2×C42C22⋊D1111yescharacteristic
300C2×C42C22⋊D1111yescharacteristic
301C4⋊C8—442no—
302C22⋊C8—222no—
303C22⋊C8—222no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—222no—
308#95—222no—
309#95—442no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—82no—
315C2×C11#150211yescharacteristic
316C2×C11#150411yescharacteristic
317C2×C11#151211yescharacteristic
318C2×C11#151911yescharacteristic
319C2×C11#179911yescharacteristic
320C2×C11#180211yescharacteristic
321C2×C11#180611yescharacteristic
322C24—21no—
323C24C2×C22⋊D1111yescharacteristic
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4C4⋊Dic1112yescomplemented
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—224no—
349C22×C4—442no—
350C22×C4—442no—
351C22×C4—442no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4#432312yes—
356C22×C4#432412yes—
357C22×C4C22⋊Dic1111yescharacteristic
358C22×C4C22⋊Dic1111yescharacteristic
359C22×C4C22⋊Dic1111yescharacteristic
360C22×C4C22⋊Dic1111yescharacteristic
361C22×C4C2×Dic2211yescharacteristic
362C22×C4C2×D4411yescharacteristic
363C22×C4#433911yescharacteristic
364C22×C4#433911yescharacteristic
365C22×C4C22×Dic1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C2×C8—442no—
368C2×C8—442no—
369C2×C8—442no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—42no—
374C4⋊C4—448no—
375C4⋊C4C4⋊Dic1112yescomplemented
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C42—22no—
384C42—22no—
385C42—41no—
386C42—41no—
387C42—42no—
388C11#857711yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23#6697711yescharacteristic
401C23#6698311yescharacteristic
402C23C2×#432311yescharacteristic
403C23C2×#432411yescharacteristic
404C23#6700211yescharacteristic
405C23#6700411yescharacteristic
406C23C2×C22⋊Dic1111yescharacteristic
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—84no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4—882no—
447C2×C4—882no—
448C2×C4—882no—
449C2×C4—882no—
450C2×C4#6689612yes—
451C2×C4#6689612yes—
452C2×C4#6689812yes—
453C2×C4#6690112yes—
454C2×C4#6697711yescharacteristic
455C2×C4C2×C4⋊Dic1111yescharacteristic
456C2×C4#6697911yescharacteristic
457C2×C4#6698311yescharacteristic
458C8—882no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#1062262011yescharacteristic
479C22#1062262111yescharacteristic
480C22#1062262811yescharacteristic
481C22#1062263211yescharacteristic
482C22#1062282511yescharacteristic
483C22C2×#6689611yescharacteristic
484C22C2×#6689811yescharacteristic
485C22#1062284511yescharacteristic
486C22C2×#6690111yescharacteristic
487C22#1062284911yescharacteristic
488C22#1062285311yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—42no—
498C4—81no—
499C4—81no—
500C4—884no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—82no—
506C2#1306711111yescharacteristic
507C2#1306712011yescharacteristic
508C2#1306715411yescharacteristic
509C2#1306718411yescharacteristic
510C2#1306860411yescharacteristic
511C2#1306861611yescharacteristic
512C2#1306863611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC4×#121D11
hypocenterC11#8577
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
3. #13066846C2semidirect
4. #13066494C2semidirect
8. C2×C4×D4×C11C4semidirect
11. C11×#390C4semidirect
12. C11×#389C4semidirect
16. C4×C11×C4⋊C4C4semidirect
78. C2×D4×C11C4⋊C4semidirect
116. C11×C4⋊C4C4⋊C4semidirect
210. C2×C4×D4Dic11semidirect
215. #390Dic11semidirect
216. #389Dic11semidirect
220. C4×C4⋊C4Dic11semidirect
333. C2×D4C4⋊Dic11semidirect
375. C4⋊C4C4⋊Dic11semidirect
388. C11#8577semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221752
#130668462
#130664942
C4×C11×#1212
#857711