Finite Group Databasebeta

← #14788724

Subgroups — #14788724

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13073978C211yesmaximal, characteristic, complemented
4#13069853C212yesmaximal, complemented
5#13069707C212yesmaximal, complemented
6#13069556C211yesmaximal, characteristic, complemented
7#13069440C211yesmaximal, characteristic
8#13068947C212yesmaximal, complemented
9#13068874C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#441C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2212yes—
16C22×#4325C2212yes—
17#10623116—24no—
18#10623116—24no—
19C2×#66947—22no—
20C2×#66946C2212yes—
21C2×#66928—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#441—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30#10622843C2212yes—
31C2×#66899C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34#10622640—24no—
35#10622599—21no—
36#10622592—21no—
37#10622586C2212yes—
38C2×#66873C2212yes—
39#10622549C2211yescharacteristic
40#10622546—22no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C22×C4×D11—22no—
51C22×Dic22D411yescharacteristic
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—22no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#67000—24no—
69#67000—24no—
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325—42no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4D412yes—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82#66947—216no—
83#66946—24no—
84#66946—24no—
85#66928—28no—
86#66927—22no—
87#66927D414yes—
88C4×D44—28no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×#106—22no—
92C11×#103—22no—
93C11×#103—22no—
94C11×#97—22no—
95#66899—42no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101#66885—24no—
102#66885—42no—
103#66873—24no—
104C4⋊(C11⋊C8)—22no—
105#24202—111nomaximal, Sylow
106C23×D11—22no—
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×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C2×D44—24no—
130C2×D44—24no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—44no—
137C2×D44—82no—
138C2×D44C2×D414yes—
139C2×C4×D11—28no—
140C2×C4×D11—84no—
141C2×Dic22—22no—
142C2×Dic22—42no—
143C11×Q16—28no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C2×D412yes—
156C42×C11—24no—
157C42×C11—42no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160#4325—48no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167Dic11⋊C4—24no—
168Dic11⋊C4—44no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×#559—111no—
175C2×#460—111no—
176C2×#441D1111yescharacteristic, complemented
177#2581—111no—
178#2042—112no—
179#2015—112no—
180#1985—111no—
181#1961—111no—
182#1877—112no—
183#1864—112no—
184#1805—111no—
185C23×C11C22×D411yescharacteristic
186C22×D11—24no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—44no—
190C22×D11—44no—
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—24no—
228D44—24no—
229D44—48no—
230D44—42no—
231D44—42no—
232D44—84no—
233C4×D11—88no—
234Dic22—44no—
235C8×C11—22no—
236C8×C11—41no—
237C11⋊C8—42no—
238C22×Q16C2×D1111yescharacteristic
239C22×SD16—112no—
240#559—224no—
241#559—224no—
242C2×#127—111no—
243C2×#124—112no—
244C2×#124—221no—
245C2×#123—222no—
246C2×C4×Q8—111no—
247C2×C4×Q8C2×D1111yescharacteristic
248C2×C4×Q8C2×D1111yescharacteristic
249C2×C4×D4—112no—
250C2×C4×D4—221no—
251#460—224no—
252#441—24no—
253C2×#106C2×D1111yescharacteristic
254C2×C4⋊C8—111no—
255C2×#103—112no—
256C2×#103C2×D1111yescharacteristic
257C2×#103C2×D1111yescharacteristic
258C2×#102—112no—
259C2×#102—112no—
260C2×#102—112no—
261C2×#97C2×D1111yescharacteristic
262#400—221no—
263#395—221no—
264#391—112no—
265#389—112no—
266#387—222no—
267#382—111no—
268#340—112no—
269#336—112no—
270#336—112no—
271C22×C11C2×#12011yescharacteristic
272C22×C11#54811yescharacteristic
273C22×C11#55011yescharacteristic
274C22×C11#57512yes—
275C22×C11#57712yes—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—84no—
280C2×D11—84no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11#52511yescharacteristic
288C4×C11#53711yescharacteristic
289C4×C11#54611yescharacteristic
290C4×C11#54711yescharacteristic
291Dic11—42no—
292Dic11—42no—
293Dic11—82no—
294C22×Q8—111no—
295C22×Q8C22×D1111yescharacteristic
296C22×Q8C22×D1111yescharacteristic
297C22×D4—112no—
298C22×D4—221no—
299C22×D4—221no—
300C23×C4—222no—
301C2×Q16—22no—
302C2×Q16—22no—
303C2×Q16—22no—
304C2×SD16—224no—
305C2×SD16—224no—
306C2×SD16—442no—
307C22×C8—112no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#127—114no—
311#127—222no—
312#124—228no—
313#124—224no—
314#124—224no—
315#123—2216no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—222no—
320C4×Q8—222no—
321C4×Q8C22⋊D1114yes—
322C4×D4—228no—
323C4×D4—224no—
324C4×D4—224no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4C22×D1111yescharacteristic
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—112no—
339C2×C42C22×D1111yescharacteristic
340#106—22no—
341C4⋊C8—222no—
342#103—22no—
343#103—22no—
344#103—442no—
345#102—224no—
346#102—224no—
347#102—442no—
348#97—22no—
349#95—222no—
350#95—222no—
351#95—222no—
352#95—221no—
353#95—221no—
354C2×C11#240711yescharacteristic
355C2×C11#300511yescharacteristic
356C2×C11#300911yescharacteristic
357C2×C11#337112yes—
358C2×C11#340112yes—
359D11—84no—
360C24—222no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—222no—
372C2×Q8—442no—
373C2×Q8#433912yes—
374C2×Q8C2×C22⋊D1112yes—
375C2×D4—114no—
376C2×D4—224no—
377C2×D4—224no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—444no—
384C2×D4—882no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—228no—
392C22×C4—222no—
393C22×C4—884no—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397Q16—28no—
398SD16—448no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8#433912yes—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C4⋊C4—222no—
414C4⋊C4—224no—
415C4⋊C4—222no—
416C4⋊C4—222no—
417C4⋊C4—444no—
418C4⋊C4C2×C22⋊D1112yes—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C22⋊C4—228no—
422C42—24no—
423C42—42no—
424C42—222no—
425C42—222no—
426C42D4×D1112yes—
427C42C2×C22⋊D1112yes—
428C11#2420211yescharacteristic, complemented, Sylow
429C23—224no—
430C23—444no—
431C23—444no—
432C23—442no—
433C23—442no—
434C23C2×D4×D1111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—22no—
438Q8—22no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—444no—
444D4—224no—
445D4—224no—
446D4—448no—
447D4—442no—
448D4—442no—
449D4—884no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—888no—
471C2×C4#6699012yes—
472C2×C4#6699012yes—
473C2×C4C2×#433911yescharacteristic
474C2×C4C2×#433911yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4#6704211yescharacteristic
477C2×C4#6704311yescharacteristic
478C2×C4C22×C22⋊D1111yescharacteristic
479C8—22no—
480C8—41no—
481C8—442no—
482C22—444no—
483C22—444no—
484C22—444no—
485C22—884no—
486C22—884no—
487C22#1062308311yescharacteristic
488C22#1062308411yescharacteristic
489C22#1062330812yes—
490C22#1062330912yes—
491C22C2×#6699011yescharacteristic
492C4—22no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—81no—
498C4—442no—
499C4—442no—
500C4—882no—
501C4#1062308111yescharacteristic
502C4#1062308211yescharacteristic
503C4#1062332211yescharacteristic
504C4#1062336411yescharacteristic
505C2—884no—
506C2#1307196111yescharacteristic
507C2#1307785711yescharacteristic
508C2#1307789211yescharacteristic
509C2#1308138512yes—
510C2#1308168312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#441D11
hypocenterC11#24202
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #13073978C2semidirect
4. #13069853C2semidirect
5. #13069707C2semidirect
6. #13069556C2semidirect
8. #13068947C2semidirect
9. #13068874C2semidirect
10. #13068631C2semidirect
11. C2×C11×#441C2semidirect
176. C2×#441D11semidirect
428. C11#24202semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106226402
#130739782
#130698532
#130697072
#130695562
#130694402
#130689472
#130688742
#130686312
C2×C11×#4412
#2420211