Finite Group Databasebeta

← #14907121

Subgroups — #14907121

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622531C211yesmaximal, characteristic
2#13077491C211yesmaximal, characteristic
3#13077479C211yesmaximal, characteristic, complemented
4#13070487C211yesmaximal, characteristic, complemented
5#13070485C211yesmaximal, characteristic, complemented
6#13070479C211yesmaximal, characteristic, complemented
7#13070478C211yesmaximal, characteristic, complemented
8#13070472C211yesmaximal, characteristic, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070465C211yesmaximal, characteristic, complemented
11#13070401C211yesmaximal, characteristic, complemented
12#13070322C211yesmaximal, characteristic
13D11×#358C211yesmaximal, characteristic, complemented
14#13070211C211yesmaximal, characteristic, complemented
15C4×C11×Q32C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18#10623105—21no—
19#10623103—21no—
20C2×C11×Q32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×Q16C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25C2×#66893C2211yescharacteristic
26C2×#66892C2211yescharacteristic
27#10622643—21no—
28#10622639—21no—
29#10622531C418yescomplemented
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622430—21no—
38#10622416—21no—
39#10622415—21no—
40#10622402—21no—
41C4×Dic44C2211yescharacteristic
42C4×D88C2211yescharacteristic
43#10622302C2211yescharacteristic
44C11×#366C2211yescharacteristic
45C11×#358C2211yescharacteristic
46C11×#358C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622202C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59#10622099C2211yescharacteristic
60C2×#4343—21no—
61C2×Q8×D11—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68C2×#4326—21no—
69C2×#4325—21no—
70#66972—22no—
71#66972C2×C414yes—
72Q16×D11—22no—
73Q16×D11C2×C414yescomplemented
74C2×Dic44C2311yescharacteristic
75C2×D88C2311yescharacteristic
76C2×#4313D411yescharacteristic
77C2×C8×D11C2311yescharacteristic
78#66946—21no—
79#66946—41no—
80#66945—21no—
81#66945—41no—
82C4⋊C4×D11—21no—
83C4⋊C4×D11—41no—
84#66940—21no—
85#66940—41no—
86C4×D44—21no—
87C4×D44—41no—
88#66925—41no—
89#66925—41no—
90#66925D411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—41no—
93C11×Q32C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#103—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66899—21no—
103#66893C2×C414yescomplemented
104#66892C2×C414yescomplemented
105#66885—21no—
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66873—21no—
115#66872—21no—
116#66871—21no—
117#66867D411yescharacteristic
118#66864C2×C414yescomplemented
119#66862C2×C414yescomplemented
120C16×D11—22no—
121#33455—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124#4343—24no—
125#4343—42no—
126Q8×D11—24no—
127Q8×D11—42no—
128C2×D44—21no—
129C2×D44—41no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16C22×C412yes—
141C11×Q16C22×C412yes—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C42×C11—41no—
149C42×C11—41no—
150C42×C11C2×D411yescharacteristic
151#4326—24no—
152#4325—24no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4D811yescharacteristic
157(C2×D11)⋊C4D811yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4D811yescharacteristic
166Dic11⋊C4D811yescharacteristic
167C4×Dic11—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44C22×C412yes—
177D88—21no—
178D88C22×C412yes—
179#4313—22no—
180C8×D11C22×C412yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16C22×C412yes—
184C11⋊C16—21no—
185C11⋊C16C22×C412yes—
186C2×#510—111no—
187#2951—111no—
188#2950—111no—
189#2176—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193C4×Q32—111no—
194C4×Q32D1111yescharacteristic, complemented
195C4×SD32—111no—
196C4×SD32—111no—
197#2159—111no—
198#2138—111no—
199C2×#358—111no—
200#2108—111no—
201C22×D11—41no—
202C22×D11C2×D811yescharacteristic
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—22no—
221D44—44no—
222D44—41no—
223C4×D11—44no—
224C4×D11—44no—
225C4×D11—161no—
226C4×D11—161no—
227C4×D11—161no—
228C4×D11C4×D412yes—
229C4×D11#13512yes—
230Dic22—22no—
231Dic22—41no—
232Dic22—44no—
233C8×C11—21no—
234C8×C11C23×C411yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8C4×D412yes—
238C2×#135—111no—
239C22×Q16—111no—
240#520—221no—
241#519—221no—
242#510—118no—
243C2×Q32—111no—
244C2×Q32C2×D1111yescharacteristic
245C2×SD32—111no—
246C2×SD32—111no—
247C2×M32—111no—
248C22×C16—111no—
249#441—221no—
250#441—221no—
251#440—221no—
252#440—221no—
253C4×Q16—111no—
254C4×Q16—111no—
255C4×Q16—111no—
256C4×Q16—111no—
257C4×Q16C2×D1111yescharacteristic
258C4×Q16C2×D1111yescharacteristic
259C4×D8—111no—
260C4×D8—111no—
261#427—111no—
262C2×#107—111no—
263#419—221no—
264#417—221no—
265#405—111no—
266#367—111no—
267#367—111no—
268#366—111no—
269#366C2×D1111yescharacteristic
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358C2×D1111yescharacteristic
275#358C2×D1111yescharacteristic
276#357—111no—
277#357—111no—
278#346—111no—
279#346—111no—
280C4×C16—111no—
281C4×C16C2×D1111yescharacteristic
282C22×C11C22×D811yescharacteristic
283C2×D11—21no—
284C2×D11—21no—
285C2×D11—42no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11C4×D812yes—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11C2×C4×D411yescharacteristic
296C4×C11C2×#13511yescharacteristic
297Dic11—21no—
298Dic11—21no—
299Dic11—42no—
300Dic11—81no—
301Dic11—81no—
302Dic11C4×D812yes—
303C2×#41—221no—
304C22×Q8—221no—
305#135—114no—
306#135—222no—
307C2×Q16—114no—
308C2×Q16—111no—
309C2×Q16—222no—
310C2×Q16—221no—
311C2×Q16C22×D1111yescharacteristic
312C2×Q16C22×D1111yescharacteristic
313C2×SD16—221no—
314C2×D8—111no—
315C2×M16—111no—
316C22×C8—111no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—221no—
320C4×Q8—221no—
321C4×Q8—221no—
322C4×Q8—221no—
323C4×Q8—441no—
324C4×Q8—441no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—441no—
328C4×D4—441no—
329#117—111no—
330#117—221no—
331#117—441no—
332#117—441no—
333#117—441no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—441no—
336Q32—114no—
337Q32C4×D1114yescomplemented
338SD32—114no—
339SD32—114no—
340M32—114no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16—222no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—111no—
348#107—221no—
349#107C22×D1111yescharacteristic
350#107C22×D1111yescharacteristic
351#106—221no—
352#103—21no—
353#103—21no—
354#103—221no—
355#103—221no—
356#103—221no—
357#103—221no—
358#102—221no—
359#102—221no—
360#97—111no—
361#97—111no—
362C4×C8—111no—
363C4×C8C22×D1111yescharacteristic
364C2×C11C2×C4×D811yescharacteristic
365C2×C11#341611yescharacteristic
366C2×C11#341711yescharacteristic
367D11—22no—
368D11—82no—
369#41—224no—
370#41—442no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—224no—
374C2×Q8—221no—
375C2×Q8—441no—
376C2×Q8—442no—
377C2×D4—221no—
378C2×D4—441no—
379C22×C4—111no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385Q16—21no—
386Q16—21no—
387Q16—112no—
388Q16—224no—
389Q16—221no—
390Q16C2×C4×D1112yes—
391Q16C2×C4×D1112yes—
392SD16—224no—
393D8—112no—
394D8—221no—
395M16—222no—
396C2×C8—111no—
397C2×C8—112no—
398C2×C8—112no—
399C2×C8—111no—
400C2×C8D4×D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—111no—
407C4⋊C4—111no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C22⋊C4—111no—
416C22⋊C4—111no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C42—41no—
421C42—41no—
422C42—111no—
423C42—441no—
424C42—441no—
425C42—441no—
426C42—441no—
427C42—441no—
428C42D4×D1111yescharacteristic
429C16—21no—
430C16—112no—
431C16—221no—
432C16C2×C4×D1112yes—
433C11#3345511yescharacteristic, complemented, Sylow
434C23—111no—
435C23—441no—
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—222no—
441Q8—444no—
442Q8—441no—
443D4—222no—
444D4—444no—
445D4—441no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—111no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—111no—
454C2×C4—111no—
455C2×C4—444no—
456C2×C4—444no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—1761no—
461C2×C4—1761no—
462C2×C4—1761no—
463C2×C4D8×D1111yescharacteristic
464C2×C4D8×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C8—21no—
467C8—112no—
468C8—221no—
469C8C22×C4×D1111yescharacteristic
470C8#41×D1111yescharacteristic
471C22—112no—
472C22—221no—
473C22—221no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22C2×D8×D1111yescharacteristic
478C4—21no—
479C4—21no—
480C4—42no—
481C4—42no—
482C4—81no—
483C4—81no—
484C4—112no—
485C4—221no—
486C4—221no—
487C4—442no—
488C4—881no—
489C4—881no—
490C4C4×D4×D1111yescharacteristic
491C4D11×#13511yescharacteristic
492C2—222no—
493C2—882no—
494C2C4×D8×D1111yescharacteristic
495C2#1308175911yescharacteristic
496C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×Q32C2
socleC22×C11C22×D8
prime radicalC2×#66972C22
cosocleC2×C8×C11C24
hypercenterC4×Q32D11
hypocenterC11#33455
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
3. #13077479C2semidirect
4. #13070487C2semidirect
5. #13070485C2semidirect
6. #13070479C2semidirect
7. #13070478C2semidirect
8. #13070472C2semidirect
9. C4×#66864C2semidirect
10. #13070465C2semidirect
11. #13070401C2semidirect
13. D11×#358C2semidirect
14. #13070211C2semidirect
15. C4×C11×Q32C2semidirect
29. #10622531C4semidirect
73. Q16×D11C2×C4semidirect
93. C11×Q32C2×C4semidirect
103. #66893C2×C4semidirect
104. #66892C2×C4semidirect
118. #66864C2×C4semidirect
119. #66862C2×C4semidirect
194. C4×Q32D11semidirect
337. Q32C4×D11semidirect
433. C11#33455semidirect

Maximal subgroups

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

subgroupindex
C2×#106225312
#130774912
#130774792
#130704872
#130704852
#130704792
#130704782
#130704722
C4×#668642
#130704652
#130704012
#130703222
D11×#3582
#130702112
C4×C11×Q322
#3345511