Finite Group Databasebeta

← #14787728

Subgroups — #14787728

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×#10623074C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal, complemented
5#13069624C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13068924C212yesmaximal, complemented
9#13068803C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4326C2211yescharacteristic
16C2×D4×Dic11—21no—
17C22×C4⋊Dic11C2212yes—
18C2×#66977C2212yes—
19#10623074—24no—
20#10623074—24no—
21C2×#66943—21no—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#396—22no—
26C11×#390—21no—
27C11×#389—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4326—24no—
35#10622634—24no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2212yes—
38C2×#66871C2211yescharacteristic
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C23×Dic11—22no—
49C22×Dic22—21no—
50C22×Dic22C2311yescharacteristic
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—42no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70C2×#4326—22no—
71C2×#4326—22no—
72C2×#4326—22no—
73D4×Dic11—28no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2312yes—
80#66977—24no—
81#66977—24no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88#66943—28no—
89#66931—216no—
90#66922—22no—
91#66922D414yes—
92C4×Dic22—22no—
93C4×Dic22D414yes—
94C11×#95—22no—
95#66899—24no—
96#66899—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66874—22no—
100#66874—42no—
101#66871—24no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24122—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11#4112yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11Q1614yescomplemented
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—28no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—82no—
134C22×Dic11—82no—
135C2×Dic22—24no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—81no—
142C2×Dic22—81no—
143C2×Dic22C2×D412yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—82no—
156C42×C11—42no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C22⋊Dic11—28no—
160#4326—28no—
161C4⋊Dic11—28no—
162C4⋊Dic11—24no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11C2×D412yes—
166C4⋊Dic11C2×D414yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—24no—
169C4×Dic11—24no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8#4112yes—
179C2×#554—111no—
180C2×#477—111no—
181C2×C4×Q16—111no—
182#2538D1111yescharacteristic
183#2036—112no—
184#2001—112no—
185#1990—111no—
186#1954—111no—
187#1872—112no—
188#1852—112no—
189#1803—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11C2×Q1614yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—41no—
201Q8×C11—41no—
202D4×C11—28no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11C2×Q1612yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—88no—
241Dic22—22no—
242Dic22—22no—
243Dic22—41no—
244Dic22—41no—
245Dic22—84no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C11⋊C8—42no—
249C22×Q16—111no—
250#554—224no—
251#554—224no—
252C2×C4⋊Q8—111no—
253C2×#125—221no—
254C2×C22⋊Q8—112no—
255C2×C22⋊Q8—222no—
256C2×C22⋊Q8C2×D1112yes—
257C2×C4×Q8—111no—
258C2×C4×Q8C2×D1111yescharacteristic
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C4⋊C4—112no—
262#477—224no—
263C4×Q16—224no—
264C2×#107—112no—
265C2×#107—111no—
266C2×C4⋊C8—111no—
267C2×#103—112no—
268C2×#103—111no—
269C2×#103—111no—
270C2×#103—112no—
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273C2×C4×C8—111no—
274#396—22no—
275#390—21no—
276#389—21no—
277#384C2×D1111yescharacteristic
278#380C2×D1112yes—
279#340—112no—
280#340—112no—
281#340—112no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11C2×#12011yescharacteristic
290C22×C11#54611yescharacteristic
291C22×C11#54711yescharacteristic
292C22×C11C22×Q1611yescharacteristic
293C22×C11C2×#13711yescharacteristic
294C22×C11#57611yescharacteristic
295C22×C11#57711yescharacteristic
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—82no—
300C4×C11—81no—
301C4×C11#45114yes—
302C4×C11#52511yescharacteristic
303C4×C11#53711yescharacteristic
304C4×C11#54811yescharacteristic
305C4×C11#55011yescharacteristic
306Dic11—42no—
307Dic11—44no—
308Dic11—42no—
309C22×Q8—111no—
310C22×Q8—221no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4C22⋊D1111yescharacteristic
313C23×C4—222no—
314C23×C4C22×D1112yes—
315C2×Q16—222no—
316C2×Q16—222no—
317C2×Q16—222no—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8—112no—
321C4⋊Q8—114no—
322C4⋊Q8—222no—
323#125—228no—
324C22⋊Q8—24no—
325C22⋊Q8—42no—
326C22⋊Q8—2216no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—114no—
332C4×Q8—222no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—228no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C22⋊D1111yescharacteristic
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C4⋊C4C22×D1112yes—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4C22⋊D1112yes—
355C2×C42—21no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358#107—222no—
359#107—224no—
360C4⋊C8—222no—
361#103—222no—
362#103—222no—
363#103—224no—
364#103—442no—
365C22⋊C8—224no—
366C22⋊C8—442no—
367C4×C8—222no—
368#95—22no—
369C2×C11—44no—
370C2×C11#240711yescharacteristic
371C2×C11C2×#45111yescharacteristic
372C2×C11#301211yescharacteristic
373C2×C11#329911yescharacteristic
374C2×C11#333311yescharacteristic
375C2×C11#333811yescharacteristic
376C2×C11#335611yescharacteristic
377C24C2×C22⋊D1112yes—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—112no—
384C2×Q8—224no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—221no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8—881no—
391C2×Q8—881no—
392C2×Q8#434112yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4#432614yescomplemented
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—228no—
409C22×C4—882no—
410C22×C4—882no—
411C22×C4C2×C22⋊D1112yes—
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C23×D1111yescharacteristic
415Q16—228no—
416C2×C8—112no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8—222no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—221no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—44no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—81no—
434C4⋊C4—112no—
435C4⋊C4—114no—
436C4⋊C4—228no—
437C4⋊C4—228no—
438C4⋊C4—224no—
439C4⋊C4—224no—
440C4⋊C4—221no—
441C4⋊C4—222no—
442C22⋊C4—24no—
443C22⋊C4—44no—
444C22⋊C4—82no—
445C22⋊C4—228no—
446C42—42no—
447C42—224no—
448C42D4×D1112yes—
449C42D4×D1112yes—
450C11#2412211yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23C2×#432614yes—
458C23C22×C22⋊D1111yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—41no—
462Q8—41no—
463Q8—222no—
464Q8—222no—
465Q8—441no—
466Q8—441no—
467Q8—884no—
468D4—28no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—224no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—442no—
494C2×C4—441no—
495C2×C4—442no—
496C2×C4—888no—
497C2×C4#6699012yes—
498C2×C4#6699012yes—
499C2×C4C2×#432612yes—
500C2×C4#6700412yes—
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4C2×#434111yescharacteristic
504C2×C4#6703711yescharacteristic
505C2×C4#41×D1111yescharacteristic
506C2×C4#6704311yescharacteristic
507C8—222no—
508C8—442no—
509C8—441no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22C2×#6699011yescharacteristic
518C22#1062333711yescharacteristic
519C22C22×#432611yescharacteristic
520C22C2×#6700411yescharacteristic
521C22#1062335511yescharacteristic
522C22#1062336611yescharacteristic
523C22#1062336811yescharacteristic
524C4—22no—
525C4—42no—
526C4—42no—
527C4—82no—
528C4—81no—
529C4—442no—
530C4—442no—
531C4—444no—
532C4#1062266314yes—
533C4#1062312911yescharacteristic
534C4#1062313011yescharacteristic
535C4#1062313711yescharacteristic
536C4#1062313911yescharacteristic
537C2—44no—
538C2#1307195711yescharacteristic
539C2C2×#1062266311yescharacteristic
540C2#1307791711yescharacteristic
541C2#1308049211yescharacteristic
542C2#1308095411yescharacteristic
543C2#1308100411yescharacteristic
544C2#1308122511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2538D11
hypocenterC11#24122
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
3. C2×C4×#4326C2semidirect
4. #13069819C2semidirect
5. #13069624C2semidirect
6. #13069576C2semidirect
8. #13068924C2semidirect
9. #13068803C2semidirect
10. #13068618C2semidirect
115. C2×D4×C11Q16semidirect
395. C2×D4#4326semidirect
450. C11#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226342
C2×C4×#43262
#130698192
#130696242
#130695762
#130694112
#130689242
#130688032
#130686182
C11×#25382
#2412211