Finite Group Databasebeta

← #14787830

Subgroups — #14787830

Order 2816.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13073517C211yesmaximal, characteristic
4#13069816C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068933C212yesmaximal, complemented
9#13068804C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—22no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×#4325C2211yescharacteristic
23C2×#66983C2212yes—
24C2×C4×D44C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2212yes—
27#10622836—21no—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622700—24no—
32#10622639—24no—
33#10622606—21no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2212yes—
38#10622569—22no—
39#10622549C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yescomplemented
55C11×#125—28no—
56C11×C22⋊Q8—216no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yescomplemented
61C4×D4×C11—28no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4325—22no—
79C2×#4325—22no—
80C2×#4325—22no—
81#66983—24no—
82#66983—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C4×D44—22no—
91C4×D44—22no—
92#66899—22no—
93#66899—42no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66873—22no—
100#66873—24no—
101#66871—22no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24130—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C23×D11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—82no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—82no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—82no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44#4112yes—
145C2×C4×D11—42no—
146C2×C4×D11—82no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—24no—
158C42×C11—24no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C22⋊Dic11—82no—
162#4325—28no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—42no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8#4112yes—
178C2×#554D1111yescharacteristic, complemented
179C2×#474—111no—
180C2×#440—111no—
181#2535—111no—
182#2036—112no—
183#2000—112no—
184#1993—111no—
185#1955—111no—
186#1874—112no—
187#1852—112no—
188#1805—111no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11#13714yes—
196C23×C11C22×D411yescharacteristic
197C22×D11—22no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—42no—
201C22×D11—42no—
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—84no—
207D4×C11—28no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—88no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C22⋊D11—88no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—84no—
245C11⋊C8—22no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×SD16—111no—
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#125—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8C2×D1112yes—
255C2×#121—112no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4—111no—
259C2×C4×D4C2×D1111yescharacteristic
260C22×C4⋊C4C2×D1112yes—
261#474—224no—
262#440—224no—
263C2×#107—111no—
264C2×#107—112no—
265C2×C4⋊C8—111no—
266C2×#103—111no—
267C2×#103—112no—
268C2×#102—111no—
269C2×#102—112no—
270C2×C22⋊C8—112no—
271C2×C22⋊C8—112no—
272C2×#97—111no—
273#397—221no—
274#392—221no—
275#386—222no—
276#382—111no—
277#380—112no—
278#340—112no—
279#340—112no—
280#340—112no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54611yescharacteristic
290C22×C11#54711yescharacteristic
291C22×C11C2×#13712yes—
292C22×C11#57612yes—
293C2×D11—42no—
294C2×D11—44no—
295C2×D11—82no—
296C2×D11—81no—
297C2×D11—81no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11#52511yescharacteristic
305C4×C11#53711yescharacteristic
306C4×C11#54811yescharacteristic
307C4×C11#55011yescharacteristic
308Dic11—81no—
309Dic11—82no—
310C22×Q8—21no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4—111no—
313C22×D4—222no—
314C22×D4C22⋊D1111yescharacteristic
315C23×C4—22no—
316C23×C4—221no—
317C23×C4C22×D1112yes—
318C2×SD16—222no—
319C2×SD16—222no—
320C2×SD16—222no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—112no—
324C4⋊Q8—22no—
325C4⋊Q8C22⋊D1114yescomplemented
326#125—28no—
327C22⋊Q8—216no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330#121—224no—
331#121—442no—
332C4×Q8—22no—
333C4×Q8C22⋊D1114yescomplemented
334C4×D4—28no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—222no—
338C4×D4—222no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4C22⋊D1111yescharacteristic
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4C22⋊D1112yes—
355C2×C42—21no—
356C2×C42C22×D1111yescharacteristic
357#107—222no—
358#107—224no—
359C4⋊C8—222no—
360#103—222no—
361#103—442no—
362#102—222no—
363#102—224no—
364C22⋊C8—224no—
365C22⋊C8—442no—
366#97—222no—
367#95—222no—
368#95—221no—
369#95—221no—
370C2×C11—44no—
371C2×C11#240711yescharacteristic
372C2×C11#300411yescharacteristic
373C2×C11#300811yescharacteristic
374C2×C11#331412yes—
375C2×C11#334612yes—
376D11—82no—
377C24—221no—
378C24C2×C22⋊D1112yes—
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—82no—
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—112no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—444no—
396C2×D4—444no—
397C2×D4—882no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—28no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—222no—
411C22×C4—221no—
412C22×C4—442no—
413C22×C4—882no—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418SD16—228no—
419C2×C8—112no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—222no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4C2×C22⋊D1112yes—
440C4⋊C4C2×C22⋊D1114yes—
441C22⋊C4—28no—
442C22⋊C4—24no—
443C22⋊C4—444no—
444C22⋊C4—442no—
445C22⋊C4—882no—
446C42—24no—
447C42C2×C22⋊D1112yes—
448C42C2×C22⋊D1112yes—
449C11#2413011yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—222no—
457C23—442no—
458C23—441no—
459C23—442no—
460C23—441no—
461C23#6699514yes—
462C23C22×C22⋊D1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469D4—222no—
470D4—222no—
471D4—441no—
472D4—441no—
473D4—888no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—88no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—441no—
497C2×C4—884no—
498C2×C4#6700612yes—
499C2×C4#6700612yes—
500C2×C4#41×D1111yescharacteristic
501C2×C4#41×D1111yescharacteristic
502C2×C4#6704211yescharacteristic
503C2×C4#6704311yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—222no—
507C8—441no—
508C8—442no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—442no—
517C22—444no—
518C22—882no—
519C22—881no—
520C22—881no—
521C22C2×#6699512yes—
522C22#1062335511yescharacteristic
523C22#1062336011yescharacteristic
524C22#1062336612yes—
525C22C2×#6700611yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—44no—
532C4—882no—
533C4—881no—
534C4#1062335911yescharacteristic
535C4#1062336211yescharacteristic
536C4#1062336411yescharacteristic
537C4#1062336511yescharacteristic
538C2—44no—
539C2—882no—
540C2#1307195511yescharacteristic
541C2#1307785011yescharacteristic
542C2#1307788411yescharacteristic
543C2#1308069112yes—
544C2#1308109512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radical#13073517C2
hypercenterC2×#554D11
hypocenterC11#24130
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×#10622639C2semidirect
4. #13069816C2semidirect
5. #13069617C2semidirect
6. #13069590C2semidirect
7. #13069415C2semidirect
8. #13068933C2semidirect
9. #13068804C2semidirect
10. #13068631C2semidirect
11. C2×C11×#554C2semidirect
54. C11×C4⋊Q8D4semidirect
60. C4×Q8×C11D4semidirect
178. C2×#554D11semidirect
325. C4⋊Q8C22⋊D11semidirect
333. C4×Q8C22⋊D11semidirect
449. C11#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106226392
#130735172
#130698162
#130696172
#130695902
#130694152
#130689332
#130688042
#130686312
C2×C11×#5542
#2413011