Finite Group Databasebeta

← #14804231

Subgroups — #14804231

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2C2×#10622641C212yesmaximal
3C2×#10622696C211yesmaximal, characteristic
4#13073611C211yesmaximal, characteristic
5#13069938C212yesmaximal, complemented
6#13069709C212yesmaximal
7#13069539C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068957C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#2365C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×#4326C2212yes—
15C22×#4326C2212yes—
16C22×#4325C2212yes—
17C2×#66928C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#391C2212yes—
21C11×#389—21no—
22C11×#387—22no—
23C4×C11×C4⋊C4—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66899C2212yes—
27#10622705—24no—
28#10622696—24no—
29#10622641—28no—
30#10622600—21no—
31#10622600—21no—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36#10622542C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622287—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D414yes—
50C4×Q8×C11—24no—
51C4×Q8×C11—42no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11—22no—
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×#4326—24no—
64C2×#4326—24no—
65C2×#4326—24no—
66C2×#4326—24no—
67C2×#4326—42no—
68C2×#4326—42no—
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—42no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66928—24no—
82#66928—42no—
83C4×D44—22no—
84C4×D44—22no—
85#66922—22no—
86#66922—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95D412yes—
91#66899—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66874—24no—
95#66874—42no—
96#66873—22no—
97#66873D414yes—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—24no—
100C4×C11⋊C8—22no—
101#25365—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C2×D414yes—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—22no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44C2×D412yes—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4C2×D412yes—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—44no—
146C42×C11—42no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149#4326—48no—
150#4326—48no—
151#4325—48no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—42no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—42no—
158C4⋊Dic11—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8C2×D412yes—
167C2×C11⋊C8#4112yes—
168C2×#494—111no—
169C2×#464—112no—
170C2×#461—111no—
171#2547—111no—
172#2365D1111yescharacteristic, complemented
173#2056—112no—
174#2015—112no—
175#1981—111no—
176#1939—111no—
177#1878—112no—
178C4×#102—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187Q8×C11—24no—
188Q8×C11—24no—
189Q8×C11—42no—
190Q8×C11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11#13512yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224D44—22no—
225D44—22no—
226D44—41no—
227D44—41no—
228C4×D11—84no—
229Dic22—42no—
230Dic22—42no—
231Dic22—42no—
232Dic22—42no—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C22×Q16—112no—
237C22×Q16—112no—
238C22×SD16—112no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#124—112no—
242C2×C4×Q8C2×D1112yes—
243C2×C4×D4—111no—
244#494—224no—
245#464—228no—
246#461—224no—
247C2×C4⋊C8—112no—
248C2×C4⋊C8—111no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×#102—111no—
253C2×#102—111no—
254C2×C4×C8—111no—
255#397—222no—
256#391—112no—
257#391C2×D1112yes—
258#389—21no—
259#387—22no—
260#380—221no—
261#380—221no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4C2×D1111yescharacteristic
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—111no—
266#340—111no—
267#336—112no—
268C22×C11C2×#12111yescharacteristic
269C22×C11D4211yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57811yescharacteristic
274C22×C11#57811yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—22no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—81no—
288C4×C11#46414yescomplemented
289C4×C11#53211yescharacteristic
290C4×C11#54011yescharacteristic
291C4×C11D4211yescharacteristic
292C4×C11#54611yescharacteristic
293Dic11—82no—
294Dic11—81no—
295C22×Q8—112no—
296C22×Q8C22×D1112yes—
297C22×D4—111no—
298C23×C4—221no—
299C2×Q16—224no—
300C2×Q16—224no—
301C2×Q16—224no—
302C2×Q16—224no—
303C2×Q16—442no—
304C2×Q16—442no—
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8—112no—
311C4⋊Q8—22no—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314C4⋊Q8D4414yes—
315#124—224no—
316#124—442no—
317C4×Q8—24no—
318C4×Q8—42no—
319C4×D4—222no—
320C4×D4—222no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—221no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—22no—
335C2×C42—21no—
336C2×C42C22×D1112yes—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—224no—
339C4⋊C8—222no—
340#103—224no—
341#103—224no—
342#103—442no—
343#102—114no—
344#102—222no—
345C4×C8—222no—
346#95—22no—
347#95—21no—
348#95—22no—
349#95—222no—
350#95—222no—
351#95C22⋊D1112yes—
352C2×C11#242811yescharacteristic
353C2×C11C2×#46411yescharacteristic
354C2×C11#304411yescharacteristic
355C2×C11#327611yescharacteristic
356C2×C11#328311yescharacteristic
357C2×C11#339311yescharacteristic
358C2×C11#339811yescharacteristic
359D11—82no—
360C24—221no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—222no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8C2×D4414yes—
373C2×D4—112no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—221no—
383C22×C4—222no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—448no—
393Q16—448no—
394SD16—448no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—44no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C4⋊C4D4×D1112yes—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C22⋊C4—442no—
420C42—22no—
421C42—22no—
422C42—44no—
423C42—42no—
424C42C2×D4412yes—
425C42#433912yes—
426C11#2536511yescharacteristic, complemented, Sylow
427C23—222no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23C22×C22⋊D1111yescharacteristic
435Q8—24no—
436Q8—24no—
437Q8—42no—
438Q8—42no—
439Q8—442no—
440Q8—442no—
441Q8—442no—
442Q8—442no—
443D4—222no—
444D4—222no—
445D4—441no—
446D4—441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—441no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—884no—
471C2×C4#6698312yes—
472C2×C4#6698312yes—
473C2×C4#6699512yes—
474C2×C4#6700312yes—
475C2×C4C22×D4411yescharacteristic
476C2×C4C2×#433911yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4#6703711yescharacteristic
479C2×C4#41×D1111yescharacteristic
480C2×C4#6704211yescharacteristic
481C8—222no—
482C8—222no—
483C8—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×#6698311yescharacteristic
492C22D4×C22⋊D1111yescharacteristic
493C22C2×#6699511yescharacteristic
494C22C2×#6700311yescharacteristic
495C22#1062336511yescharacteristic
496C22#1062336911yescharacteristic
497C22#1062336911yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—44no—
502C4—42no—
503C4—81no—
504C4—881no—
505C4—882no—
506C4#1062264114yescomplemented
507C4#1062307911yescharacteristic
508C4D4×D4411yescharacteristic
509C4#1062308511yescharacteristic
510C4#1062309311yescharacteristic
511C2—882no—
512C2#1307219811yescharacteristic
513C2C2×#1062264111yescharacteristic
514C2#1307814611yescharacteristic
515C2#1308026211yescharacteristic
516C2#1308033411yescharacteristic
517C2#1308160011yescharacteristic
518C2#1308164311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2365D11
hypocenterC11#25365
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
5. #13069938C2semidirect
7. #13069539C2semidirect
8. #13069335C2semidirect
9. #13068957C2semidirect
11. C11×#2365C2semidirect
172. #2365D11semidirect
288. C4×C11#464semidirect
426. C11#25365semidirect
506. C4#10622641semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106226412
C2×#106226962
#130736112
#130699382
#130697092
#130695392
#130693352
#130689572
C4×#668732
C11×#23652
#2536511