Finite Group Databasebeta

← #14656091

Subgroups — #14656091

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic, complemented
3#13073532C211yesmaximal, characteristic
4#13069576C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6C2×#10622121C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×#66948—21no—
10C2×#66948—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C2×#66885—21no—
18C2×#66882—21no—
19C2×#66880—21no—
20#10622604—22no—
21#10622600—21no—
22#10622600—21no—
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622459—22no—
25#10622459—22no—
26#10622454—22no—
27#10622454—22no—
28#10622167—22no—
29#10622121—22no—
30#10622121—22no—
31C22×D44—22no—
32C22×D44D411yescharacteristic
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C4×D11—21no—
36C22×Dic22—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C22×C11⋊C8—21no—
52C2×#4314—24no—
53C2×#4314—42no—
54C2×#4314—42no—
55#66948—42no—
56#66948—42no—
57#66948—42no—
58#66948—42no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44—21no—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922D412yescomplemented
71C11×C4⋊C8—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8D412yescomplemented
74C11×C4⋊C8D412yescomplemented
75C11⋊#95—22no—
76#66885—24no—
77#66882—24no—
78#66880—24no—
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81#10231—111nomaximal, Sylow
82C23×D11—21no—
83C23×D11—21no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—44no—
102C2×D44—44no—
103C2×D44—82no—
104C2×D44D812yes—
105C2×D44SD1612yescomplemented
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—41no—
121C2×Dic22—41no—
122C2×Dic22—41no—
123C2×Dic22—41no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156#4314—48no—
157C2×#474—111no—
158C2×#461—111no—
159#2537—111no—
160#1990—111no—
161C2×D4⋊C8—111no—
162C2×D4⋊C8—111no—
163#1296D1111yescharacteristic, complemented
164C23×C11#12011yescharacteristic
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×SD1611yescharacteristic
192C2×C4×C11#13511yescharacteristic
193C2×C4×C11#13511yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C11#13711yescharacteristic
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207D44—22no—
208D44—22no—
209D44—22no—
210D44—22no—
211D44—41no—
212D44—41no—
213D44—41no—
214D44—41no—
215D44—88no—
216C4×D11—81no—
217C4×D11—81no—
218C4×D11—81no—
219C4×D11—81no—
220C4×D11—81no—
221C4×D11—81no—
222C4×D11—81no—
223C4×D11—81no—
224Dic22—42no—
225Dic22—42no—
226Dic22—81no—
227Dic22—81no—
228C8×C11—42no—
229C8×C11—42no—
230C11⋊C8—42no—
231C22×SD16—221no—
232C2×C4⋊Q8—111no—
233C2×#121—221no—
234C2×#121—221no—
235C2×C4×D4—111no—
236C2×C4×D4—111no—
237#474—222no—
238#474—222no—
239#461—222no—
240#461—222no—
241C2×#107—221no—
242C2×C4⋊C8C2×D1111yescharacteristic
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#103—221no—
245C2×#102—221no—
246C2×C4×C8—111no—
247#394—222no—
248#384C2×D1111yescharacteristic
249#380—221no—
250#380—221no—
251#340—222no—
252D4⋊C8—222no—
253D4⋊C8—222no—
254C22×C11#39211yescharacteristic
255C22×C11#44711yescharacteristic
256C22×C11#44911yescharacteristic
257C22×C11#45011yescharacteristic
258C22×C11#45211yescharacteristic
259C22×C11#45511yescharacteristic
260C22×C11#45611yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—82no—
278C4×C11#44711yescharacteristic
279C4×C11#44811yescharacteristic
280C4×C11#44911yescharacteristic
281C4×C11#44911yescharacteristic
282C4×C11#46511yescharacteristic
283C4×C11#46611yescharacteristic
284C4×C11#46811yescharacteristic
285C4×C11#46911yescharacteristic
286Dic11—82no—
287Dic11—81no—
288Dic11—81no—
289C22×Q8—221no—
290C22×D4—111no—
291C22×D4—111no—
292C22×D4—222no—
293C23×C4—221no—
294C23×C4—221no—
295C2×SD16—224no—
296C2×SD16—442no—
297C2×SD16—442no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—221no—
301C4⋊Q8—112no—
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304C4⋊Q8—221no—
305#121—442no—
306#121—442no—
307#121—442no—
308#121—442no—
309C4×D4—221no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4D4412yes—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C42C22×D1111yescharacteristic
329#107—224no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8D4412yescomplemented
333C4⋊C8D4412yescomplemented
334#103—224no—
335#102—224no—
336C4×C8—221no—
337C4×C8—221no—
338#95—222no—
339C2×C11#163911yescharacteristic
340C2×C11#164611yescharacteristic
341C2×C11#164711yescharacteristic
342C2×C11#165411yescharacteristic
343C2×C11#199911yescharacteristic
344C2×C11#200011yescharacteristic
345C2×C11#200711yescharacteristic
346D11—82no—
347D11—82no—
348C24—221no—
349C24—221no—
350C2×Q8—222no—
351C2×Q8—441no—
352C2×Q8—441no—
353C2×Q8—441no—
354C2×Q8—441no—
355C2×Q8—441no—
356C2×D4—112no—
357C2×D4—112no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—444no—
369C2×D4—444no—
370C2×D4—882no—
371C22×C4—22no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4C2×D4411yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390SD16—448no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—222no—
398C2×C8—441no—
399C2×C8—441no—
400C4⋊C4—42no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—222no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C22⋊C4—444no—
414C22⋊C4—444no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C42C2×D4411yescharacteristic
420C42C2×D4411yescharacteristic
421C42D4×D1111yescharacteristic
422C42#434311yescharacteristic
423C11#1023111yescharacteristic, complemented, Sylow
424C23—222no—
425C23—222no—
426C23—441no—
427C23—441no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23#6693511yescharacteristic
439Q8—442no—
440Q8—442no—
441Q8—881no—
442Q8—881no—
443D4—222no—
444D4—222no—
445D4—222no—
446D4—222no—
447D4—441no—
448D4—441no—
449D4—441no—
450D4—441no—
451D4—888no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—442no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—881no—
465C2×C4—881no—
466C2×C4—881no—
467C2×C4—881no—
468C2×C4—881no—
469C2×C4—881no—
470C2×C4—881no—
471C2×C4—881no—
472C2×C4—881no—
473C2×C4—881no—
474C2×C4#6692711yescharacteristic
475C2×C4#6693511yescharacteristic
476C2×C4#6693511yescharacteristic
477C2×C4#6694811yescharacteristic
478C2×C4#6694811yescharacteristic
479C2×C4#6694811yescharacteristic
480C2×C4D8×D1111yescharacteristic
481C2×C4#6696411yescharacteristic
482C2×C4SD16×D1111yescharacteristic
483C2×C4#6696711yescharacteristic
484C2×C4#6696711yescharacteristic
485C2×C4#6696911yescharacteristic
486C2×C4#6697111yescharacteristic
487C2×C4#6697211yescharacteristic
488C8—42no—
489C8—42no—
490C8—442no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22#1062228411yescharacteristic
506C22#1062235911yescharacteristic
507C22#1062236511yescharacteristic
508C22#1062238611yescharacteristic
509C22#1062238911yescharacteristic
510C22#1062242311yescharacteristic
511C22#1062242411yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—881no—
516C4—882no—
517C4—881no—
518C4#1062238611yescharacteristic
519C4#1062239411yescharacteristic
520C4#1062241911yescharacteristic
521C4#1062242411yescharacteristic
522C4#1062247711yescharacteristic
523C4#1062247811yescharacteristic
524C4#1062249611yescharacteristic
525C4#1062249911yescharacteristic
526C2—882no—
527C2—882no—
528C2#1306779611yescharacteristic
529C2#1306784511yescharacteristic
530C2#1306785211yescharacteristic
531C2#1306790111yescharacteristic
532C2#1306961511yescharacteristic
533C2#1306962211yescharacteristic
534C2#1306966511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
prime radical#13073532C2
hypercenter#1296D11
hypocenterC11#10231
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#10622459C2semidirect
2. C2×#10622454C2semidirect
4. #13069576C2semidirect
5. C2×#10622121C2semidirect
6. C2×#10622121C2semidirect
7. C11×#1296C2semidirect
70. #66922D4semidirect
73. C11×C4⋊C8D4semidirect
74. C11×C4⋊C8D4semidirect
105. C2×D44SD16semidirect
163. #1296D11semidirect
332. C4⋊C8D44semidirect
333. C4⋊C8D44semidirect
423. C11#10231semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106224542
#130735322
#130695762
C2×#106221212
C11×#12962
#1023111