Finite Group Databasebeta

← #14752787

Subgroups — #14752787

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic
2#13071081C211yesmaximal, characteristic
3#13068493C211yesmaximal, characteristic, complemented
4#13068488C211yesmaximal, characteristic, complemented
5C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
6#13068402C211yesmaximal, characteristic, complemented
7#13068397C211yesmaximal, characteristic, complemented
8#13068390C211yesmaximal, characteristic, complemented
9C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
10#13068384C211yesmaximal, characteristic, complemented
11#13068384C211yesmaximal, characteristic, complemented
12#13068364C211yesmaximal, characteristic, complemented
13#13068314C211yesmaximal, characteristic, complemented
14#13068312C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#435C418yescomplemented
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28#10622834C412yes—
29C4×C22⋊Dic11C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622624C418yescomplemented
40#10622598C412yes—
41#10622564C412yes—
42#10622564C412yes—
43C4×C4⋊Dic11C2211yescharacteristic
44C42×Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622188C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57C22×D4×C11C2×C411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×M16—41no—
61C2×C11×M16—41no—
62C2×C11×M16C2×C414yes—
63C22×C8×C11—41no—
64C22×C8×C11—41no—
65C22×C8×C11C2×C414yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11C2×C414yes—
71C4×D4×C11C2×C414yes—
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11C2×C412yes—
77C2×C22⋊Dic11C2×C412yes—
78C2×C22⋊Dic11C2×C412yes—
79C2×C22⋊Dic11C2×C412yes—
80#66979—41no—
81#66979—41no—
82#66979—41no—
83#66979—41no—
84C2×C4⋊Dic11C2×C412yes—
85C2×C4⋊Dic11C2×C412yes—
86C2×C4⋊Dic11C2×C412yes—
87C2×C4×Dic11C2×C412yes—
88C2×C4×Dic11C2×C412yes—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—41no—
94C2×#4318—41no—
95C2×#4318C2×C414yes—
96C22×C11⋊C8—41no—
97C22×C11⋊C8—41no—
98C22×C11⋊C8C2×C414yes—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×C4⋊C8C2×C414yes—
104C11×C22⋊C8C2×C414yes—
105C11×C22⋊C8C2×C414yes—
106C11×#97C2×C414yes—
107C11⋊#95C2×C412yes—
108C11⋊#95C2×C412yes—
109C11⋊#95C2×C412yes—
110C22⋊(C11⋊C8)C2×C414yes—
111C22⋊(C11⋊C8)C2×C414yes—
112#66879—41no—
113#66879—41no—
114C8×Dic11—41no—
115C8×Dic11—41no—
116C8×Dic11—41no—
117C8×Dic11—41no—
118C4⋊(C11⋊C8)C2×C414yes—
119#66867C2×C414yes—
120#20566—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C24×C11C22×C411yescharacteristic
123C2×D4×C11—42no—
124C2×D4×C11C4214yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C11×M16—44no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—44no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C22×C412yes—
160C11×C4⋊C4C4214yes—
161C11×C22⋊C4C4214yes—
162C11×C22⋊C4C4214yes—
163C42×C11C22×C412yes—
164C42×C11C22×C412yes—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C4⋊Dic11—42no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172C4×Dic11—24no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—42no—
182#4318—44no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—44no—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8C22×C412yes—
194C2×C11⋊C8C22×C412yes—
195C2×C11⋊C8C22×C412yes—
196C2×#435—111no—
197C2×#435D1111yescharacteristic
198#2293—111no—
199#1771—111no—
200#1771—111no—
201C4×C4⋊C8—111no—
202#1753—111no—
203#1753—111no—
204C8×C22⋊C4—111no—
205C8×C22⋊C4—111no—
206#1750—111no—
207#1750—111no—
208#1745—111no—
209#1729—111no—
210#1729—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11C2×C4212yes—
220C23×C11C2×C4212yes—
221C23×C11C23×C411yescharacteristic
222D4×C11—44no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11C2×C4212yes—
238C2×C4×C11C2×C4212yes—
239C2×C4×C11C2×C4212yes—
240C2×C4×C11C2×C4212yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11#13114yes—
259C8×C11—22no—
260C8×C11—22no—
261C8×C11—22no—
262C8×C11—22no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×M16—111no—
268C22×M16C2×D1111yescharacteristic
269C23×C8—111no—
270C23×C8C2×D1111yescharacteristic
271C2×C4×D4C2×D1111yescharacteristic
272C2×#117—111no—
273C2×#117—111no—
274#435—118no—
275#435Dic1118yescomplemented
276C2×C4⋊C8—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×C22⋊C8—111no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8C2×D1111yescharacteristic
282C2×#97—111no—
283C2×#97—111no—
284C2×#97—111no—
285C2×#97C2×D1111yescharacteristic
286C2×C4×C8—111no—
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290#390—112no—
291#389—112no—
292#388—112no—
293#388—112no—
294C4×C4⋊C4—111no—
295C4×C22⋊C4—111no—
296C4×C22⋊C4—111no—
297C43—111no—
298#336—111no—
299#336—111no—
300#336—111no—
301#336—111no—
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11C22×C4211yescharacteristic
319C22×C11#51811yescharacteristic
320C22×C11#52011yescharacteristic
321C22×C11C2×#13112yes—
322C22×C11#56812yes—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11#51811yescharacteristic
328C4×C11#51811yescharacteristic
329C4×C11#52011yescharacteristic
330C4×C11#52011yescharacteristic
331Dic11—24no—
332Dic11—42no—
333Dic11—42no—
334Dic11—42no—
335C22×D4C4×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×M16—41no—
339C2×M16—41no—
340C2×M16—114no—
341C2×M16—441no—
342C2×M16—441no—
343C2×M16C2×Dic1114yes—
344C22×C8—41no—
345C22×C8—41no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—114no—
351C22×C8—441no—
352C22×C8—441no—
353C22×C8C2×Dic1114yes—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C4×D4C4×D1114yes—
359C4×D4C2×Dic1114yes—
360#117—441no—
361#117—441no—
362#117—441no—
363#117—441no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4C4×D1111yescharacteristic
368C2×C22⋊C4—112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4C4×D1111yescharacteristic
373C2×C22⋊C4C4×D1111yescharacteristic
374C2×C42—112no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—112no—
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—114no—
382C4⋊C8C2×Dic1114yes—
383C22⋊C8—114no—
384C22⋊C8—114no—
385C22⋊C8C2×Dic1114yes—
386C22⋊C8C2×Dic1114yes—
387#97—114no—
388#97—441no—
389#97—441no—
390#97C2×Dic1114yes—
391C4×C8—441no—
392C4×C8—441no—
393C4×C8—441no—
394C4×C8—441no—
395#95—112no—
396#95—112no—
397#95—112no—
398C2×C11—42no—
399C2×C11—42no—
400C2×C11#227511yescharacteristic
401C2×C11#287311yescharacteristic
402C2×C11C4×#13111yescharacteristic
403C2×C11#298112yes—
404C2×C11#299212yes—
405C24C2×C4×D1111yescharacteristic
406C24C2×C4×D1111yescharacteristic
407C2×D4—42no—
408C2×D4C4×Dic1114yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4C2×C4×D1111yescharacteristic
422C22×C4C2×C4×D1111yescharacteristic
423C22×C4C2×C4×D1111yescharacteristic
424C22×C4C2×C4×D1111yescharacteristic
425C22×C4C2×C4×D1112yes—
426C22×C4C2×C4×D1112yes—
427C22×C4C22×Dic1112yes—
428C22×C4C22×Dic1112yes—
429C22×C4C23×D1111yescharacteristic
430M16—44no—
431M16—444no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—44no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—444no—
454C2×C8C22×Dic1112yes—
455C2×C8C22×Dic1112yes—
456C2×C8C22×Dic1112yes—
457C2×C8C22×Dic1112yes—
458C4⋊C4—442no—
459C4⋊C4—442no—
460C4⋊C4—442no—
461C4⋊C4C4×Dic1114yes—
462C22⋊C4—224no—
463C22⋊C4—224no—
464C22⋊C4—442no—
465C22⋊C4—442no—
466C22⋊C4C4×Dic1114yes—
467C22⋊C4C4×Dic1114yes—
468C42—224no—
469C42—221no—
470C42—221no—
471C42—221no—
472C42—221no—
473C42—221no—
474C42—221no—
475C42—221no—
476C42—221no—
477C42—442no—
478C42C2×C4×D1112yes—
479C42C22×Dic1112yes—
480C11#2056611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23C2×C4×Dic1112yes—
490C23C2×C4×Dic1112yes—
491C23C22×C4×D1111yescharacteristic
492D4—44no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—114no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4C2×C4×Dic1112yes—
520C2×C4C2×C4×Dic1112yes—
521C2×C4C2×C4×Dic1112yes—
522C2×C4C2×C4×Dic1112yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4#6703711yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704311yescharacteristic
528C2×C4C23×Dic1111yescharacteristic
529C8—22no—
530C8—22no—
531C8—22no—
532C8—22no—
533C8—222no—
534C8—222no—
535C8—222no—
536C8—222no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22#1062307611yescharacteristic
548C22#1062307711yescharacteristic
549C22#1062327612yes—
550C22D11×#13112yes—
551C22C22×C4×Dic1111yescharacteristic
552C4—22no—
553C4—22no—
554C4—22no—
555C4—22no—
556C4—224no—
557C4—442no—
558C4—442no—
559C4—442no—
560C4#1062307611yescharacteristic
561C4#1062307711yescharacteristic
562C4#1062332911yescharacteristic
563C4#1062335811yescharacteristic
564C2—42no—
565C2—42no—
566C2#1307097711yescharacteristic
567C2#1307703411yescharacteristic
568C2#131×Dic1111yescharacteristic
569C2#1307768812yes—
570C2#1307775112yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#435C2
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#20566
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #13068493C2semidirect
4. #13068488C2semidirect
5. C4⋊C8×Dic11C2semidirect
6. #13068402C2semidirect
7. #13068397C2semidirect
8. #13068390C2semidirect
9. C8×C22⋊Dic11C2semidirect
10. #13068384C2semidirect
11. #13068384C2semidirect
12. #13068364C2semidirect
13. #13068314C2semidirect
14. #13068312C2semidirect
23. C11×#435C4semidirect
39. #10622624C4semidirect
275. #435Dic11semidirect
480. C11#20566semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
#130710812
#130684932
#130684882
C4⋊C8×Dic112
#130684022
#130683972
#130683902
C8×C22⋊Dic112
#130683842
#130683642
#130683142
#130683122
C2×C11×#4352
#2056611