Finite Group Databasebeta

← #14780335

Subgroups — #14780335

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071895C211yesmaximal, characteristic
2#13068914C211yesmaximal, characteristic, complemented
3#13068912C212yesmaximal, complemented
4#13068911C212yesmaximal, complemented
5#13068910C212yesmaximal, complemented
6#13068910C212yesmaximal, complemented
7#13068908C212yesmaximal, complemented
8#13068760C212yesmaximal, complemented
9C11×#1869C211yesmaximal, characteristic, complemented
10C23×C8×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×C4×C22⋊D11C2212yes—
13C2×C4×C22⋊D11C2212yes—
14C22×#4318C2211yescharacteristic
15C22×#4313C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2212yes—
19#10622836C412yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×(C2×D11)⋊C8C2212yes—
23C2×(C2×D11)⋊C8C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25#10622605C412yes—
26#10622573C411yescharacteristic
27#10622573C411yescharacteristic
28#10622562C411yescharacteristic
29#10622562C411yescharacteristic
30#10622545C2211yescharacteristic
31C11×#336C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2×C412yes—
42C22×D44C2×C411yescharacteristic
43C22×C4×D11C2312yes—
44C22×C8×C11—41no—
45C22×C8×C11—42no—
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C4×D4×C11—41no—
49C4×D4×C11—41no—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C22⋊C4C2×C411yescharacteristic
52C2×C11×C22⋊C4C2×C411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11C2×C412yes—
55C2×C22⋊Dic11C2×C412yes—
56C4×C22⋊D11—42no—
57C4×C22⋊D11—42no—
58C4×C22⋊D11—42no—
59C4×C22⋊D11—42no—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4C2×C412yes—
65C2×Dic11⋊C4C2×C412yes—
66C2×C4×Dic11C2312yes—
67C2×#4318—41no—
68C2×#4318—42no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2312yes—
71C2×#4313—42no—
72C2×#4313—42no—
73C2×#4313—42no—
74C4×D44—41no—
75C4×D44—41no—
76C11×C22⋊C8—41no—
77C11×C22⋊C8—42no—
78C11⋊#95C2×C411yescharacteristic
79C11⋊#95C2×C411yescharacteristic
80C11⋊#95C2×C412yes—
81C22⋊(C11⋊C8)—41no—
82C22⋊(C11⋊C8)—42no—
83(C2×D11)⋊C8—42no—
84(C2×D11)⋊C8—42no—
85(C2×D11)⋊C8—42no—
86#23359—111nomaximal, Sylow
87C24×C11C22×C411yescharacteristic
88C24×C11C22×C411yescharacteristic
89C23×D11C22×C412yes—
90C2×D4×C11—22no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C2×C22⋊D11—24no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C2×C22⋊D11—42no—
112C22×Dic11C22×C412yes—
113C22×Dic11C22×C412yes—
114C22×Dic11C22×C412yes—
115C2×D44—41no—
116C2×D44—42no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—44no—
130C11×C4⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—21no—
134C42×C11—21no—
135C22⋊Dic11—42no—
136C22⋊Dic11—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—41no—
141Dic11⋊C4—42no—
142Dic11⋊C4—42no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145#4318—44no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152#4313—48no—
153#2397—111no—
154#1870—112no—
155#1870—112no—
156#1870—112no—
157#1870—112no—
158#1870—111no—
159#1869—112no—
160#1869D1111yescharacteristic, complemented
161#1840—112no—
162C23×C11—22no—
163C23×C11—21no—
164C23×C11—22no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—22no—
171C23×C11#13112yes—
172C23×C11C23×C411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180D4×C11—44no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C11H(5,𝔽2)12yes—
199C2×C4×C11H(5,𝔽2)12yes—
200C22⋊D11—48no—
201C22⋊D11—48no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211D44—44no—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C8×C11—42no—
217C8×C11—42no—
218C11⋊C8—42no—
219C11⋊C8—42no—
220C22×M16—111no—
221C22×M16—112no—
222C23×C8C2×D1111yescharacteristic
223C2×C4×D4—112no—
224C2×C4×D4—112no—
225C2×C4×D4—111no—
226C2×C4×D4C2×D1111yescharacteristic
227C2×C22⋊C8—112no—
228C2×C22⋊C8—111no—
229C2×C22⋊C8—112no—
230C2×C22⋊C8—112no—
231C2×C22⋊C8—112no—
232C2×C22⋊C8C2×D1112yes—
233C2×C22⋊C8C2×D1111yescharacteristic
234#399—112no—
235#399—111no—
236#399—111no—
237#392—112no—
238#392—111no—
239#392—111no—
240#376—111no—
241#336—112no—
242#336—112no—
243#336—112no—
244#336—112no—
245#336—112no—
246#336C2×D1112yes—
247C22×C11—22no—
248C22×C11—24no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—42no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—42no—
255C22×C11—41no—
256C22×C11—42no—
257C22×C11#51811yescharacteristic
258C22×C11#51812yes—
259C22×C11C2×#13111yescharacteristic
260C22×C11#56811yescharacteristic
261C22×C11#56812yes—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C4×C11—41no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—41no—
273C4×C11#56011yescharacteristic
274C4×C11#56012yes—
275C4×C11#56011yescharacteristic
276Dic11—42no—
277Dic11—42no—
278Dic11—42no—
279C22×D4—112no—
280C22×D4—112no—
281C22×D4—111no—
282C22×D4C4×D1111yescharacteristic
283C23×C4—112no—
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C2×M16—442no—
287C2×M16—442no—
288C2×M16—442no—
289C2×M16—441no—
290C2×M16—442no—
291C22×C8—42no—
292C22×C8—41no—
293C22×C8—112no—
294C22×C8—112no—
295C22×C8C22×D1112yes—
296C22×C8C22×D1112yes—
297C4×D4—41no—
298C4×D4—41no—
299C4×D4—441no—
300C4×D4—441no—
301C4×D4—442no—
302C4×D4—442no—
303C4×D4—442no—
304C4×D4—442no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4C4×D1111yescharacteristic
309C2×C22⋊C4—112no—
310C2×C22⋊C4—112no—
311C2×C22⋊C4—112no—
312C2×C22⋊C4—112no—
313C2×C22⋊C4—112no—
314C2×C22⋊C4C4×D1111yescharacteristic
315C2×C22⋊C4C4×D1111yescharacteristic
316C2×C42—112no—
317C2×C42C22×D1111yescharacteristic
318C22⋊C8—42no—
319C22⋊C8—41no—
320C22⋊C8—442no—
321C22⋊C8—442no—
322C22⋊C8—442no—
323C22⋊C8—441no—
324C22⋊C8—442no—
325#95—112no—
326#95—111no—
327#95—111no—
328C2×C11—42no—
329C2×C11—81no—
330C2×C11#238011yescharacteristic
331C2×C11#297612yes—
332C2×C11#297611yescharacteristic
333C2×C11#297811yescharacteristic
334C2×C11#297812yes—
335D11—82no—
336C24—112no—
337C24C2×C4×D1111yescharacteristic
338C24C2×C4×D1111yescharacteristic
339C2×D4—22no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—224no—
343C2×D4—441no—
344C2×D4—442no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—442no—
348C2×D4—442no—
349C2×D4—442no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4C2×C4×D1111yescharacteristic
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372M16—448no—
373M16—444no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—44no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C4⋊C4—41no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4—441no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—442no—
394C22⋊C4—442no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C42—21no—
399C42—21no—
400C42—222no—
401C42—222no—
402C11#2335911yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—22no—
411C23—22no—
412C23—222no—
413C23—222no—
414C23—222no—
415C23—222no—
416C23—222no—
417C23—222no—
418C23—222no—
419C23#6695412yes—
420C23C22×C4×D1111yescharacteristic
421D4—44no—
422D4—444no—
423D4—448no—
424D4—448no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4#6703712yes—
454C2×C4#6703711yescharacteristic
455C2×C4#6703711yescharacteristic
456C2×C4#6704212yes—
457C8—42no—
458C8—42no—
459C8—442no—
460C8—442no—
461C22—24no—
462C22—22no—
463C22—41no—
464C22—42no—
465C22—41no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22—42no—
470C22—41no—
471C22—442no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—442no—
477C22—442no—
478C22#1062301711yescharacteristic
479C22#1062307612yes—
480C22C2×#6695411yescharacteristic
481C22#1062327611yescharacteristic
482C22#1062328112yes—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—442no—
488C4—442no—
489C4—442no—
490C4#1062312611yescharacteristic
491C4#1062315112yes—
492C4#1062319711yescharacteristic
493C2—42no—
494C2—81no—
495C2—882no—
496C2#1307179111yescharacteristic
497C2#1307765812yes—
498C2#1307766111yescharacteristic
499C2#1307767411yescharacteristic
500C2#1307767512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radical#13071895C2
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#23359
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #13068914C2semidirect
3. #13068912C2semidirect
4. #13068911C2semidirect
5. #13068910C2semidirect
6. #13068910C2semidirect
7. #13068908C2semidirect
8. #13068760C2semidirect
9. C11×#1869C2semidirect
160. #1869D11semidirect
402. C11#23359semidirect

Maximal subgroups

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

subgroupindex
#130718952
#130689142
#130689122
#130689112
#130689102
#130689082
#130687602
C11×#18692
#2335911