Finite Group Databasebeta

← #14657287

Subgroups — #14657287

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073529C211yesmaximal, characteristic
2#13068772C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C11×#1802C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991—21no—
10C2×#66983—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×#102—21no—
14C11×#384C2211yescharacteristic
15#10622825—21no—
16#10622600—21no—
17C2×#66873—21no—
18C2×#66872—22no—
19#10622574—22no—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#340—21no—
24D4⋊(C11⋊C8)—22no—
25#10622167—21no—
26#10622121—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C22×C22⋊D11—22no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×C22⋊Dic11—22no—
44#66991—42no—
45#66991—42no—
46#66983—42no—
47#66983—42no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D412yes—
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#102—42no—
63C11⋊#95—22no—
64#66873—42no—
65#66872—44no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yescomplemented
70#10432—111nomaximal, Sylow
71C24×C11—21no—
72C23×D11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11SD1612yes—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—44no—
91C2×C22⋊D11—44no—
92C2×C22⋊D11—82no—
93C22×Dic11—21no—
94C22×Dic11—22no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44SD1612yes—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11#4111yescharacteristic
123C22⋊Dic11—44no—
124(C2×D11)⋊C4—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—42no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140#2537—111no—
141#1844—111no—
142#1802—111no—
143#1802D1111yescharacteristic, complemented
144C2×D4⋊C8—111no—
145C2×D4⋊C8—111no—
146#1296—111no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11#12011yescharacteristic
155C22×D11—22no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—41no—
165D4×C11—41no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C2×C4×C11#12411yescharacteristic
184C2×C4×C11C2×SD1611yescharacteristic
185C2×C4×C11C2×SD1611yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C22⋊D11—88no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199D44—22no—
200D44—22no—
201D44—41no—
202D44—41no—
203C4×D11—81no—
204C4×D11—81no—
205C4×D11—81no—
206C4×D11—81no—
207C8×C11—81no—
208C11⋊C8—24no—
209C11⋊C8—81no—
210C2×#121—221no—
211C2×#121—221no—
212C2×C4×D4—111no—
213C2×C4×D4C2×D1111yescharacteristic
214C2×#106—222no—
215C2×C4⋊C8—111no—
216C2×C4⋊C8C2×D1111yescharacteristic
217C2×#102—21no—
218C2×#102—221no—
219C2×C4×C8—111no—
220#394—222no—
221#384—111no—
222#384C2×D1111yescharacteristic
223#380—221no—
224#380—221no—
225#340—21no—
226#340—221no—
227D4⋊C8—222no—
228D4⋊C8—222no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11#39411yescharacteristic
237C22×C11#44911yescharacteristic
238C22×C11#44911yescharacteristic
239C22×C11#45011yescharacteristic
240C22×C11#45011yescharacteristic
241C22×C11#45311yescharacteristic
242C22×C11#45611yescharacteristic
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C2×D11—81no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—81no—
253C4×C11—161no—
254C4×C11#46511yescharacteristic
255C4×C11#46511yescharacteristic
256C4×C11#46911yescharacteristic
257C4×C11#46911yescharacteristic
258C4×C11#48111yescharacteristic
259C4×C11#48111yescharacteristic
260C4×C11#48211yescharacteristic
261C4×C11#48211yescharacteristic
262Dic11—82no—
263Dic11—81no—
264C22×D4—111no—
265C22×D4—222no—
266C22×D4C22⋊D1111yescharacteristic
267C23×C4—21no—
268C23×C4—221no—
269C22×C8—21no—
270C22×C8—221no—
271C22×C8—221no—
272#121—442no—
273#121—442no—
274#121—442no—
275#121—442no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—221no—
281C4×D4—221no—
282C4×D4—221no—
283C4×D4—221no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4C22⋊D1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—221no—
296C2×C42C22×D1111yescharacteristic
297#106—444no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302#102—42no—
303#102—442no—
304C4×C8—112no—
305C4×C8—221no—
306#95—222no—
307C2×C11—82no—
308C2×C11#162411yescharacteristic
309C2×C11#162911yescharacteristic
310C2×C11#165411yescharacteristic
311C2×C11#165411yescharacteristic
312C2×C11#203411yescharacteristic
313C2×C11#203411yescharacteristic
314C2×C11#203911yescharacteristic
315D11—82no—
316C24—21no—
317C24—221no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—112no—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—444no—
330C2×D4—444no—
331C2×D4—882no—
332C2×D4#432512yes—
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—441no—
359C2×C8—441no—
360C2×C8—441no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—442no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—444no—
378C22⋊C4—444no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C42#433911yescharacteristic
382C42#433911yescharacteristic
383C42D4×D1111yescharacteristic
384C42#434111yescharacteristic
385C11#1043211yescharacteristic, complemented, Sylow
386C23—22no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—222no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23#6699011yescharacteristic
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—222no—
406D4—222no—
407D4—441no—
408D4—441no—
409D4—888no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4#6693611yescharacteristic
433C2×C4#6693711yescharacteristic
434C2×C4#6693711yescharacteristic
435C2×C4#6693811yescharacteristic
436C2×C4#6696411yescharacteristic
437C2×C4#6696511yescharacteristic
438C2×C4SD16×D1111yescharacteristic
439C2×C4#6696711yescharacteristic
440C2×C4#6698211yescharacteristic
441C2×C4#6698511yescharacteristic
442C2×C4#6699211yescharacteristic
443C2×C4C2×#432511yescharacteristic
444C2×C4#6700211yescharacteristic
445C2×C4#6700311yescharacteristic
446C8—81no—
447C8—224no—
448C8—881no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22#1062257211yescharacteristic
464C22#1062265011yescharacteristic
465C22#1062265911yescharacteristic
466C22#1062277111yescharacteristic
467C22#1062278211yescharacteristic
468C22#1062281111yescharacteristic
469C22#1062281811yescharacteristic
470C4—21no—
471C4—21no—
472C4—81no—
473C4—161no—
474C4—882no—
475C4—881no—
476C4#1062239011yescharacteristic
477C4#1062239111yescharacteristic
478C4#1062239511yescharacteristic
479C4#1062239711yescharacteristic
480C4#1062258111yescharacteristic
481C4#1062261611yescharacteristic
482C4#1062265211yescharacteristic
483C4#1062266111yescharacteristic
484C2—82no—
485C2—882no—
486C2#1306769811yescharacteristic
487C2#1306773111yescharacteristic
488C2#1306789811yescharacteristic
489C2#1306789911yescharacteristic
490C2#1306980311yescharacteristic
491C2#1306980511yescharacteristic
492C2#1306983811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1802C2
socleC23×C11#120
prime radical#13073529C2
hypercenter#1802D11
hypocenterC11#10432
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #13068772C2semidirect
3. #13068613C2semidirect
4. C2×D4⋊(C11⋊C8)C2semidirect
5. C2×#10622121C2semidirect
6. #13066500C2semidirect
7. C11×#1802C2semidirect
69. C4×C11⋊C8D4semidirect
143. #1802D11semidirect
385. C11#10432semidirect

Maximal subgroups

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

subgroupindex
#130735292
#130687722
#130686132
C2×D4⋊(C11⋊C8)2
C2×#106221212
#130665002
C11×#18022
#1043211