Finite Group Databasebeta

← #14760506

Subgroups — #14760506

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622748C211yesmaximal, characteristic
2C2×#10622482C211yesmaximal, characteristic, complemented
3C2×#10622735C211yesmaximal, characteristic, complemented
4#13071305C212yesmaximal, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069342C211yesmaximal, characteristic, complemented
7#13069311C212yesmaximal, complemented
8#13069042C212yesmaximal, complemented
9#13068515C211yesmaximal, characteristic, complemented
10#13068430C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×#66983C2212yes—
14C2×#66979C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×#66946C2212yes—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C11×#380C2212yes—
21#10622748C418yescomplemented
22#10622735—24no—
23C2×#66885C2212yes—
24C2×#66881C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66873C2212yes—
34#10622570—22no—
35#10622569—22no—
36#10622482—24no—
37#10622283—22no—
38#10622281—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16C2×C414yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—22no—
54C2×C22⋊Dic11D412yes—
55#66983—24no—
56#66983C2×C418yescomplemented
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61#66979—22no—
62#66979—22no—
63C2×C4⋊Dic11D412yes—
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8—22no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×D88—22no—
75C2×D88—22no—
76C2×D88C2×C414yes—
77#66946—24no—
78#66946—24no—
79C11×#107—22no—
80C11×#106—22no—
81C11×#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66885C2×C418yescomplemented
85#66881C2×C414yescomplemented
86#66879—22no—
87#66879D414yescomplemented
88C8×Dic11—22no—
89C8×Dic11—22no—
90#66873—24no—
91#66873—24no—
92#21541—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4112yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—28no—
106C2×C22⋊D11—82no—
107C2×C22⋊D11—82no—
108C22×Dic11—22no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44C22×C414yes—
117C2×C4×D11—44no—
118C2×C4×D11—82no—
119C2×C4×D11—82no—
120C11×M16—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C22⋊C4—82no—
132C22⋊Dic11—24no—
133(C2×D11)⋊C4—28no—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—82no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11C22×C414yes—
140Dic11⋊C4—82no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—82no—
144C4×Dic11C2×D412yes—
145C4×Dic11#4112yes—
146C2×C11⋊C8—28no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C2×D412yes—
152C2×C11⋊C8#4112yes—
153D88—28no—
154C2×#469—111no—
155C2×#442—111no—
156C2×#405—111no—
157#2324—112no—
158#1970—111no—
159#1941—111no—
160#1936—112no—
161#1893—112no—
162#1809D1111yescharacteristic, complemented
163#1776—111no—
164C4×#102—112no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11C4×D412yes—
170C23×C11C22×D411yescharacteristic
171C22×D11—24no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—88no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11#12114yes—
207D44—24no—
208D44—24no—
209D44—42no—
210D44—42no—
211C4×D11—88no—
212C8×C11—22no—
213C8×C11C4×D414yes—
214C11⋊C8—22no—
215C11⋊C8—22no—
216C22×D8—111no—
217C22×M16C2×D1111yescharacteristic
218C23×C8—111no—
219C2×#121—112no—
220C2×C4×D4—112no—
221C2×#117—111no—
222#469—118no—
223#442—224no—
224C2×#107C2×D1111yescharacteristic
225C2×#106—111no—
226C2×#106C2×D1111yescharacteristic
227C2×#102—112no—
228C2×#102—112no—
229C2×#102—112no—
230#405—224no—
231C2×#97—111no—
232C2×#97—111no—
233C2×C4×C8—111no—
234C2×C4×C8—111no—
235#390—112no—
236#390—222no—
237#389—112no—
238#388—222no—
239#386—222no—
240#385—222no—
241#380C2×D1112yes—
242C4×C4⋊C4—112no—
243#340—112no—
244#340—112no—
245#340C2×D1112yes—
246C22×C11—24no—
247C22×C11—22no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—42no—
251C22×C11C2×C4×D411yescharacteristic
252C22×C11C2×#12111yescharacteristic
253C22×C11#53211yescharacteristic
254C22×C11#57612yes—
255C22×C11#57712yes—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C4×C11—22no—
264C4×C11—82no—
265C4×C11—82no—
266C4×C11C2×C4×D411yescharacteristic
267C4×C11C4×#4111yescharacteristic
268C4×C11#52511yescharacteristic
269C4×C11#52911yescharacteristic
270Dic11—24no—
271Dic11—44no—
272Dic11—42no—
273C22×D4—112no—
274C22×D4—222no—
275C23×C4—222no—
276C23×C4C22×D1111yescharacteristic
277C2×D8—114no—
278C2×D8—222no—
279C2×D8—222no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16C4×D1114yescomplemented
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—222no—
286C22×C8—222no—
287C22×C8—222no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290#121—118no—
291#121—224no—
292C4×D4—224no—
293C4×D4—224no—
294#117—222no—
295#117—222no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—112no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C42—111no—
308C2×C42—111no—
309C2×C42—222no—
310#107—22no—
311#106—22no—
312#106—114no—
313#102—118no—
314#102—224no—
315#102—224no—
316#97—114no—
317#97—222no—
318C4×C8—222no—
319C4×C8—222no—
320#95—22no—
321#95—222no—
322#95—222no—
323C2×C11—42no—
324C2×C11C4×#12111yescharacteristic
325C2×C11#294612yes—
326C2×C11#306212yes—
327C2×C11#317311yescharacteristic
328C2×C11#317611yescharacteristic
329D11—84no—
330C24—222no—
331C24D4×D1111yescharacteristic
332C2×D4—114no—
333C2×D4—228no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—882no—
340C2×D4—882no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—222no—
350C22×C4—444no—
351C22×C4—882no—
352C22×C4—882no—
353C22×C4C2×C4×D1112yes—
354C22×C4D4×D1111yescharacteristic
355C22×C4#434312yes—
356C22×C4C23×D1111yescharacteristic
357D8—228no—
358M16—28no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—112no—
362C2×C8—112no—
363C2×C8—228no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8C2×C4×D1112yes—
369C2×C8C2×C4×D1112yes—
370C2×C8D4×D1112yes—
371C2×C8#434112yes—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—114no—
377C4⋊C4—224no—
378C4⋊C4—222no—
379C4⋊C4—882no—
380C22⋊C4—82no—
381C22⋊C4—224no—
382C22⋊C4—228no—
383C22⋊C4—444no—
384C22⋊C4—882no—
385C22⋊C4—882no—
386C42—112no—
387C42—112no—
388C42—221no—
389C42—221no—
390C42—882no—
391C11#2154111yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—21no—
395C23—21no—
396C23—224no—
397C23—442no—
398C23—442no—
399C23—442no—
400C23—442no—
401C23—442no—
402C23—442no—
403C23#6694612yes—
404C23C2×D4×D1111yescharacteristic
405D4—224no—
406D4—224no—
407D4—442no—
408D4—442no—
409D4—888no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—114no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—224no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—888no—
432C2×C4#6694612yes—
433C2×C4C22×C4×D1111yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4C2×#434311yescharacteristic
437C2×C4#41×D1111yescharacteristic
438C2×C4#41×D1111yescharacteristic
439C8—22no—
440C8—222no—
441C8—222no—
442C8(C22⋊D11)⋊C414yes—
443C22—22no—
444C22—24no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—444no—
449C22—444no—
450C22—444no—
451C22—882no—
452C22—882no—
453C22—882no—
454C22—882no—
455C22C2×#6694611yescharacteristic
456C22#1062312711yescharacteristic
457C22D11×#12111yescharacteristic
458C22#1062330512yes—
459C22#1062330912yes—
460C4—22no—
461C4—82no—
462C4—82no—
463C4—224no—
464C4—442no—
465C4—444no—
466C4C2×(C22⋊D11)⋊C411yescharacteristic
467C4#1062305311yescharacteristic
468C4#1062315511yescharacteristic
469C4#1062315811yescharacteristic
470C2—42no—
471C2—884no—
472C2#1307112211yescharacteristic
473C2#1307744612yes—
474C2#1307829112yes—
475C2#1307923411yescharacteristic
476C2#1307926111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC2×#10622748C2
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C2×#10622735C2semidirect
4. #13071305C2semidirect
5. #13069480C2semidirect
6. #13069342C2semidirect
7. #13069311C2semidirect
8. #13069042C2semidirect
9. #13068515C2semidirect
10. #13068430C2semidirect
11. C11×#1809C2semidirect
21. #10622748C4semidirect
48. C2×C11×M16C2×C4semidirect
56. #66983C2×C4semidirect
84. #66885C2×C4semidirect
85. #66881C2×C4semidirect
87. #66879D4semidirect
162. #1809D11semidirect
282. C2×M16C4×D11semidirect
391. C11#21541semidirect

Maximal subgroups

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

subgroupindex
C2×#106227482
C2×#106224822
C2×#106227352
#130713052
#130694802
#130693422
#130693112
#130690422
#130685152
#130684302
C11×#18092
#2154111