Finite Group Databasebeta

← #14787732

Subgroups — #14787732

Order 2816.

1134 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×#10623110C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13069817C212yesmaximal, complemented
5#13069623C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic
8#13068920C212yesmaximal, complemented
9#13068802C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999C2212yes—
16C2×#66999C2212yes—
17#10623110—24no—
18#10623110—24no—
19C2×#66949—22no—
20C2×C4⋊C4×D11C2212yes—
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66923—21no—
24C2×#66922C2211yescharacteristic
25C4×C11×Q16—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34#10622634—24no—
35#10622607—22no—
36#10622600C2212yes—
37C2×#66871C2212yes—
38#10622552—21no—
39#10622548C2211yescharacteristic
40#10622541—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11C2312yes—
50C22×Dic22—21no—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#66999—24no—
68#66999—24no—
69#66999—24no—
70#66999—42no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C22×C11⋊C8C2312yes—
85#66949—216no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88C4×D44—28no—
89C4×D44—22no—
90C4×D44—22no—
91#66923—28no—
92#66922—22no—
93#66922D414yes—
94C11×#107—22no—
95C11×#103—22no—
96C11×#103—22no—
97C4×C8×C11—22no—
98#66899—24no—
99#66899—42no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—42no—
103#66871—24no—
104C4⋊(C11⋊C8)—22no—
105#24122—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C2×D412yes—
118C2×Q8×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11C2×D412yes—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44Q1614yescomplemented
132C2×C4×D11—28no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—82no—
140C2×C4×D11—82no—
141C2×Dic22—24no—
142C2×Dic22—81no—
143C2×Dic22—81no—
144C11×Q16—28no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×D412yes—
157C42×C11—24no—
158C42×C11—42no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—82no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—81no—
172C4⋊Dic11C2×D414yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175Dic11⋊C4—44no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×#554—111no—
180C2×#477—111no—
181C2×C4×Q16D1111yescharacteristic, complemented
182#2538—111no—
183#2036—112no—
184#2001—112no—
185#1990—111no—
186#1954—111no—
187#1872—112no—
188#1852—112no—
189#1803—111no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11C2×Q1614yes—
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—22no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—41no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C2×Q1612yes—
223C2×C4×C11#13712yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239D44—28no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—42no—
243C4×D11—42no—
244C4×D11—88no—
245Dic22—84no—
246C8×C11—22no—
247C8×C11—41no—
248C11⋊C8—42no—
249C22×Q16C2×D1111yescharacteristic
250#554—224no—
251#554—224no—
252C2×C4⋊Q8—111no—
253C2×#125—221no—
254C2×C22⋊Q8—112no—
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8—222no—
257C2×C4×Q8C2×D1111yescharacteristic
258C2×C4×Q8C2×D1111yescharacteristic
259C2×C4×D4—111no—
260C2×C4×D4—221no—
261C22×C4⋊C4—112no—
262#477—224no—
263C4×Q16—24no—
264C2×#107—112no—
265C2×#107C2×D1111yescharacteristic
266C2×C4⋊C8—111no—
267C2×#103—112no—
268C2×#103—112no—
269C2×#103C2×D1111yescharacteristic
270C2×#103C2×D1111yescharacteristic
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273C2×C4×C8C2×D1111yescharacteristic
274#396—222no—
275#390—221no—
276#389—221no—
277#384—111no—
278#380—112no—
279#340—112no—
280#340—112no—
281#340—112no—
282C22×C11C2×#12011yescharacteristic
283C22×C11#54611yescharacteristic
284C22×C11#54711yescharacteristic
285C22×C11C22×Q1611yescharacteristic
286C22×C11C2×#13711yescharacteristic
287C22×C11#57611yescharacteristic
288C22×C11#57711yescharacteristic
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11#45114yes—
302C4×C11#52511yescharacteristic
303C4×C11#53711yescharacteristic
304C4×C11#54811yescharacteristic
305C4×C11#55011yescharacteristic
306Dic11—42no—
307Dic11—44no—
308Dic11—82no—
309C22×Q8—221no—
310C22×Q8C22×D1111yescharacteristic
311C22×Q8C22×D1111yescharacteristic
312C22×D4—111no—
313C23×C4—112no—
314C23×C4—222no—
315C2×Q16—22no—
316C2×Q16—22no—
317C2×Q16—22no—
318C22×C8—112no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—114no—
322C4⋊Q8—222no—
323#125—228no—
324C22⋊Q8—2216no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C22⋊Q8—442no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8C22⋊D1114yes—
333C4×D4—228no—
334C4×D4—222no—
335C4×D4—222no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C22⋊C4—112no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42C22×D1111yescharacteristic
358#107—22no—
359#107—224no—
360C4⋊C8—222no—
361#103—22no—
362#103—22no—
363#103—224no—
364#103—442no—
365C22⋊C8—224no—
366C22⋊C8—442no—
367C4×C8—22no—
368#95—222no—
369C2×C11#240711yescharacteristic
370C2×C11C2×#45111yescharacteristic
371C2×C11#301211yescharacteristic
372C2×C11#329911yescharacteristic
373C2×C11#333311yescharacteristic
374C2×C11#333811yescharacteristic
375C2×C11#335611yescharacteristic
376D11—44no—
377C24—112no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—224no—
389C2×Q8—881no—
390C2×Q8—881no—
391C2×Q8#433912yes—
392C2×Q8C2×C22⋊D1112yes—
393C2×D4—114no—
394C2×D4—222no—
395C2×D4—222no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—112no—
401C22×C4—228no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—882no—
411C22×C4—882no—
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4C23×D1111yescharacteristic
415Q16—28no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8#433912yes—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—42no—
430C4⋊C4—114no—
431C4⋊C4—228no—
432C4⋊C4—228no—
433C4⋊C4—222no—
434C4⋊C4—224no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—444no—
439C4⋊C4—442no—
440C4⋊C4—881no—
441C4⋊C4C2×C22⋊D1112yes—
442C22⋊C4—228no—
443C22⋊C4—224no—
444C22⋊C4—444no—
445C22⋊C4—882no—
446C42—24no—
447C42—42no—
448C42D4×D1112yes—
449C42C2×C22⋊D1112yes—
450C11#2412211yescharacteristic, complemented, Sylow
451C23—114no—
452C23—222no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23—222no—
457C23—222no—
458C23C2×D4×D1111yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—22no—
462Q8—22no—
463Q8—41no—
464Q8—41no—
465Q8—41no—
466Q8—41no—
467Q8—884no—
468D4—228no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—224no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—888no—
497C2×C4Q16×D1112yes—
498C2×C4#6697112yes—
499C2×C4#6699012yes—
500C2×C4#6699012yes—
501C2×C4C2×#433911yescharacteristic
502C2×C4C2×#433911yescharacteristic
503C2×C4C2×D4×D1111yescharacteristic
504C2×C4#6704211yescharacteristic
505C2×C4#6704311yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C8—22no—
508C8—41no—
509C8—442no—
510C22—224no—
511C22—224no—
512C22—224no—
513C22—442no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22#1062308111yescharacteristic
518C22#1062308211yescharacteristic
519C22C2×Q16×D1111yescharacteristic
520C22C2×#6697111yescharacteristic
521C22#1062330011yescharacteristic
522C22#1062330111yescharacteristic
523C22C2×#6699011yescharacteristic
524C4—22no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—442no—
530C4—444no—
531C4—882no—
532C4#1062279914yes—
533C4#1062308311yescharacteristic
534C4#1062308411yescharacteristic
535C4#1062332211yescharacteristic
536C4#1062336411yescharacteristic
537C2—444no—
538C2#1307196111yescharacteristic
539C2C2×#1062279911yescharacteristic
540C2#1307791611yescharacteristic
541C2#1308049411yescharacteristic
542C2#1308095611yescharacteristic
543C2#1308101011yescharacteristic
544C2#1308123311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×C4×Q16D11
hypocenterC11#24122
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
4. #13069817C2semidirect
5. #13069623C2semidirect
6. #13069577C2semidirect
8. #13068920C2semidirect
9. #13068802C2semidirect
10. #13068621C2semidirect
11. C2×C4×C11×Q16C2semidirect
131. C2×D44Q16semidirect
181. C2×C4×Q16D11semidirect
450. C11#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106226342
#130735342
#130698172
#130696232
#130695772
#130694102
#130689202
#130688022
#130686212
C2×C4×C11×Q162
#2412211