Finite Group Databasebeta

← #14647163

Subgroups — #14647163

Order 2816.

588 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#13071018C211yesmaximal, characteristic
2#13068682C211yesmaximal, characteristic
3#13066840C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4×Dic11C2211yescharacteristic
9C2×#66930—21no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622589C411yescharacteristic, complemented
19#10622589C411yescharacteristic, complemented
20C4⋊C4×Dic11C411yescharacteristic, complemented
21C4⋊C4×Dic11C411yescharacteristic, complemented
22#10622555—21no—
23#10622263—21no—
24#10622262—21no—
25#10622188—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⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C22×C11⋊C8—21no—
54#66930—42no—
55#66930—42no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11⋊#95—24no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—42no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#8716—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
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×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
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—21no—
98C22×Dic11—21no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C22×Dic11C22⋊C411yescharacteristic
110C22×Dic11D812yes—
111C22×Dic11SD1612yes—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—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—
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11—42no—
136C4×Dic11—42no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140#2285—111no—
141#1817—111no—
142#1434—111no—
143#1294—111no—
144#1294—111no—
145#1294—111no—
146#1294D1111yescharacteristic
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11C2×C22⋊C411yescharacteristic
152C23×C11#12311yescharacteristic
153C23×C11#12311yescharacteristic
154C23×C11C2×D811yescharacteristic
155C23×C11C2×SD1611yescharacteristic
156C23×C11#13711yescharacteristic
157C23×C11#13711yescharacteristic
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11#11711yescharacteristic
180C2×C4×C11#11711yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11#10212yes—
212C2×Dic11#10212yes—
213C2×Dic11#10412yes—
214C8×C11—81no—
215C11⋊C8—81no—
216C2×#117—221no—
217C22×C42—111no—
218C2×C22⋊C8—111no—
219C2×C22⋊C8C2×D1111yescharacteristic
220#384—111no—
221#384—111no—
222#382—221no—
223#380—111no—
224#380—221no—
225#380C2×D1111yescharacteristic
226C4×C4⋊C4—111no—
227C4×C4⋊C4—111no—
228C4×C4⋊C4—221no—
229C2×#95—111no—
230C2×#95—221no—
231C2×#95—221no—
232C2×#95C2×D1111yescharacteristic
233#336—221no—
234#336—221no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11#38111yescharacteristic
248C22×C11#41011yescharacteristic
249C22×C11#41011yescharacteristic
250C22×C11C2×#10211yescharacteristic
251C22×C11#41911yescharacteristic
252C22×C11C2×#10411yescharacteristic
253C22×C11#42111yescharacteristic
254C22×C11#48011yescharacteristic
255C22×C11#48011yescharacteristic
256C22×C11#48311yescharacteristic
257C22×C11#48311yescharacteristic
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—82no—
263C4×C11—81no—
264C4×C11—81no—
265Dic11—22no—
266Dic11—22no—
267Dic11—22no—
268Dic11—41no—
269Dic11—82no—
270Dic11—81no—
271Dic11—81no—
272C23×C4—21no—
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C22×C8—21no—
278C22×C8—221no—
279#117—442no—
280#117—442no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4C4×D1111yescharacteristic
288C2×C4⋊C4C4×D1111yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—221no—
291C2×C42—111no—
292C2×C42—111no—
293C2×C42—111no—
294C2×C42—111no—
295C2×C42—221no—
296C2×C42—221no—
297C2×C42—221no—
298C2×C42—221no—
299C2×C42—221no—
300C2×C42—221no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—221no—
304C22⋊C8—221no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—221no—
309#95—221no—
310#95—224no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—442no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11#150211yescharacteristic
320C2×C11#150611yescharacteristic
321C2×C11#151511yescharacteristic
322C2×C11#151711yescharacteristic
323C2×C11#182011yescharacteristic
324C2×C11#182311yescharacteristic
325C2×C11#182611yescharacteristic
326C24D4×D1111yescharacteristic
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—111no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4C2×C4×D1111yescharacteristic
362C22×C4#433911yescharacteristic
363C22×C4#433911yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4#434111yescharacteristic
366C22×C4#434311yescharacteristic
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C4⋊C4—442no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C42—221no—
386C42—221no—
387C42—221no—
388C42—221no—
389C42—221no—
390C42—221no—
391C42—221no—
392C42—221no—
393C42—442no—
394C42—442no—
395C11#871611yescharacteristic, complemented, Sylow
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23C22⋊C4×D1111yescharacteristic
401C23#6693611yescharacteristic
402C23#6694711yescharacteristic
403C23D8×D1111yescharacteristic
404C23SD16×D1111yescharacteristic
405C23#6696811yescharacteristic
406C23#6697111yescharacteristic
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—222no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—222no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—881no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4#6692511yescharacteristic
460C2×C4#6693611yescharacteristic
461C2×C4#6694511yescharacteristic
462C2×C4#6694711yescharacteristic
463C8—81no—
464C8—881no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#1062227711yescharacteristic
478C22#1062235311yescharacteristic
479C22#1062235311yescharacteristic
480C22D11×#10211yescharacteristic
481C22#1062238711yescharacteristic
482C22#1062241511yescharacteristic
483C22#1062241811yescharacteristic
484C22D11×#10411yescharacteristic
485C22#1062243411yescharacteristic
486C22#1062247511yescharacteristic
487C22#1062249511yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—82no—
493C4—81no—
494C4—81no—
495C4—222no—
496C4—222no—
497C4—222no—
498C4—441no—
499C4—882no—
500C4—881no—
501C4—881no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2#1306710911yescharacteristic
507C2#1306712611yescharacteristic
508C2#1306716511yescharacteristic
509C2#1306717411yescharacteristic
510C2#1306869211yescharacteristic
511C2#1306870111yescharacteristic
512C2#1306871411yescharacteristic
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#8716
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
18. #10622589C4semidirect
19. #10622589C4semidirect
20. C4⋊C4×Dic11C4semidirect
21. C4⋊C4×Dic11C4semidirect
395. C11#8716semidirect

Maximal subgroups

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

subgroupindex
#130710182
#130686822
#130668402
#130664962
#130664952
#130664942
C11×#12942
#871611